Daily Papers

Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined perceptual scale. The perceptual scale can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the perceptual scale of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured perceptual scale corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the perceptual scale is mostly driven by the stimulus power spectrum. Finally, we propose that this measure of perceptual scale is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.

Image compression, restoration, and generation all require a way to measure how different two images look to a person. Pixel error ignores how people see, while the most accurate perceptual distances are typically fitted to human judgments, tying them to a fixed data and resolution. For example, when image resolution is doubled, the correlation of DISTS with human scores on TID2013 drops from 0.815 to 0.717. We introduce the Jacobian Lens Distance (JLD), which derives its perceptual geometry from a frozen vision encoder rather than from human labels. JLD combines the locality of early patch features with the perceptual sensitivity captured by later encoder representations. Specifically, we use the encoder Jacobian to identify directions in the early feature space that most strongly affect the encoder output, producing a fixed metric tensor, E[J^top J], which we call the Jacobian lens. The lens is fitted only once from 100 unlabeled images, taking about 35 seconds. Locally, this construction defines a pullback metric in pixel space, giving JLD a clear geometric interpretation that can be directly analyzed on real images. Across four standard perceptual databases, JLD achieves state-of-the-art performance and consistently outperforms LPIPS, DISTS, PieAPP, and DreamSim. JLD is also robust to changes in image resolution, on TID2013, its lens-term correlation remains nearly unchanged when the resolution is doubled, decreasing only from 0.850 to 0.845. We further introduce JLD-fast, which is 4times faster than LPIPS-VGG while achieving a mean correlation of 0.911. Finally, JLD naturally extends to video, reaching a correlation of 0.786 on Waterloo IVC 4K compared with 0.611 for VMAF.

Artificial intelligence systems are commonly evaluated through task performance and behavioral imitation, but such evaluations leave open whether an artificial agent can acquire, stabilize, and use new lexical meanings from grounded experience. This paper introduces Lexical Consensus, an experimental framework for studying grounded word learning over a structured perceptual substrate. Using frozen DINOv2 visual embeddings, Carroll-style nonce words, and interpretable lexical learners plus linear baselines, we test whether agents can acquire artificial labels for visual concepts, generalize them bidirectionally, and stabilize them across controlled settings. The main result is a robust perceptual-coherence gradient: native categories are easiest to learn, coherent overextensions remain learnable, mid-range disjunctive concepts degrade, and far-disjunctive concepts approach chance. A pre-registered CIFAR-100 dissociation experiment confirms that this gradient is governed by perceptual distance rather than semantic relatedness: perceptual distance predicts acquisition accuracy (partial R^2 = 0.245, p < 1e-7), while semantic distance adds no significant explanatory power (partial R^2 = 0.002, p = 0.660). Bidirectional evaluation shows that naming and retrieval are distinct: exemplar-based mechanisms outperform centroid prototypes in label-to-image retrieval, exposing a memory-fidelity dimension separate from naming accuracy. Falsification controls, homogeneous candidate-pool evaluations, and null results on representational restructuring indicate that frozen perceptual geometry both enables lexical grounding and limits what can be acquired without representational adaptation.

The success of image generative models has enabled us to build methods that can edit images based on text or other user input. However, these methods are bespoke, imprecise, require additional information, or are limited to only 2D image edits. We present GeoDiffuser, a zero-shot optimization-based method that unifies common 2D and 3D image-based object editing capabilities into a single method. Our key insight is to view image editing operations as geometric transformations. We show that these transformations can be directly incorporated into the attention layers in diffusion models to implicitly perform editing operations. Our training-free optimization method uses an objective function that seeks to preserve object style but generate plausible images, for instance with accurate lighting and shadows. It also inpaints disoccluded parts of the image where the object was originally located. Given a natural image and user input, we segment the foreground object using SAM and estimate a corresponding transform which is used by our optimization approach for editing. GeoDiffuser can perform common 2D and 3D edits like object translation, 3D rotation, and removal. We present quantitative results, including a perceptual study, that shows how our approach is better than existing methods. Visit https://ivl.cs.brown.edu/research/geodiffuser.html for more information.

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Understanding the physical world requires perceptual models grounded in physical laws rather than mere statistical correlations. However, existing multimodal learning frameworks, focused on vision and language, lack physical consistency and overlook the intrinsic causal relationships among an object's geometry, material, vibration modes, and the sounds it produces. We introduce VibraVerse, a large-scale geometry-acoustics alignment dataset that explicitly bridges the causal chain from 3D geometry -> physical attributes -> modal parameters -> acoustic signals. Each 3D model has explicit physical properties (density, Young's modulus, Poisson's ratio) and volumetric geometry, from which modal eigenfrequencies and eigenvectors are computed for impact sound synthesis under controlled excitations. To establish this coherence, we introduce CLASP, a contrastive learning framework for cross-modal alignment that preserves the causal correspondence between an object's physical structure and its acoustic response. This framework enforces physically consistent alignment across modalities, ensuring that every sample is coherent, traceable to the governing equations, and embedded within a unified representation space spanning shape, image, and sound. Built upon VibraVerse, we define a suite of benchmark tasks for geometry-to-sound prediction, sound-guided shape reconstruction, and cross-modal representation learning. Extensive validations on these tasks demonstrate that models trained on VibraVerse exhibit superior accuracy, interpretability, and generalization across modalities. These results establish VibraVerse as a benchmark for physically consistent and causally interpretable multimodal learning, providing a foundation for sound-guided embodied perception and a deeper understanding of the physical world. The dataset will be open-sourced.

Visual Language Models (VLMs) have increasingly become the main paradigm for understanding indoor scenes, but they still struggle with metric and spatial reasoning. Current approaches rely on end-to-end video understanding or large-scale spatial question answering fine-tuning, inherently coupling perception and reasoning. In this paper, we investigate whether decoupling perception and reasoning leads to improved spatial reasoning. We propose an agentic framework for static 3D indoor scene reasoning that grounds an LLM in an explicit 3D scene graph (3DSG). Rather than ingesting videos directly, each scene is represented as a persistent 3DSG constructed by a dedicated perception module. To isolate reasoning performance, we instantiate the 3DSG from ground-truth annotations. The agent interacts with the scene exclusively through structured geometric tools that expose fundamental properties such as object dimensions, distances, poses, and spatial relationships. The results we obtain on the static split of VSI-Bench provide an upper bound under ideal perceptual conditions on the spatial reasoning performance, and we find that it is significantly higher than previous works, by up to 16\%, without task specific fine-tuning. Compared to base VLMs, our agentic variant achieves significantly better performance, with average improvements between 33\% to 50\%. These findings indicate that explicit geometric grounding substantially improves spatial reasoning performance, and suggest that structured representations offer a compelling alternative to purely end-to-end visual reasoning.

It has been recently shown that the hidden variables of convolutional neural networks make for an efficient perceptual similarity metric that accurately predicts human judgment on relative image similarity assessment. First, we show that such learned perceptual similarity metrics (LPIPS) are susceptible to adversarial attacks that dramatically contradict human visual similarity judgment. While this is not surprising in light of neural networks' well-known weakness to adversarial perturbations, we proceed to show that self-ensembling with an infinite family of random transformations of the input --- a technique known not to render classification networks robust --- is enough to turn the metric robust against attack, while retaining predictive power on human judgments. Finally, we study the geometry imposed by our our novel self-ensembled metric (E-LPIPS) on the space of natural images. We find evidence of "perceptual convexity" by showing that convex combinations of similar-looking images retain appearance, and that discrete geodesics yield meaningful frame interpolation and texture morphing, all without explicit correspondences.

Reconstructing dynamic 3D scenes from sparse multi-view videos is highly ill-posed, often leading to geometric collapse, trajectory drift, and floating artifacts. Recent attempts introduce generative priors to hallucinate missing content, yet naive integration frequently causes structural drift and temporal inconsistency due to the mismatch between stochastic 2D generation and deterministic 3D geometry. In this paper, we propose GeoRect4D, a novel unified framework for sparse-view dynamic reconstruction that couples explicit 3D consistency with generative refinement via a closed-loop optimization process. Specifically, GeoRect4D introduces a degradation-aware feedback mechanism that incorporates a robust anchor-based dynamic 3DGS substrate with a single-step diffusion rectifier to hallucinate high-fidelity details. This rectifier utilizes a structural locking mechanism and spatiotemporal coordinated attention, effectively preserving physical plausibility while restoring missing content. Furthermore, we present a progressive optimization strategy that employs stochastic geometric purification to eliminate floaters and generative distillation to infuse texture details into the explicit representation. Extensive experiments demonstrate that GeoRect4D achieves state-of-the-art performance in reconstruction fidelity, perceptual quality, and spatiotemporal consistency across multiple datasets. Project Page: https://mediax-sjtu.github.io/GeoRect4D

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

We introduce StereoSpace, a diffusion-based framework for monocular-to-stereo synthesis that models geometry purely through viewpoint conditioning, without explicit depth or warping. A canonical rectified space and the conditioning guide the generator to infer correspondences and fill disocclusions end-to-end. To ensure fair and leakage-free evaluation, we introduce an end-to-end protocol that excludes any ground truth or proxy geometry estimates at test time. The protocol emphasizes metrics reflecting downstream relevance: iSQoE for perceptual comfort and MEt3R for geometric consistency. StereoSpace surpasses other methods from the warp & inpaint, latent-warping, and warped-conditioning categories, achieving sharp parallax and strong robustness on layered and non-Lambertian scenes. This establishes viewpoint-conditioned diffusion as a scalable, depth-free solution for stereo generation.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

Speaker verification (SV) models are commonly assumed to better capture nuances among speaker characteristics as verification accuracy improves, leading to their widespread use as automated proxies for human voice similarity in speech generation tasks. However, by establishing a human perceptual alignment metric and conducting systematic analysis, we demonstrate that perceptual alignment is governed far more by how a model is trained (its learning objective) than by how well it performs (EER). Notably, standard margin-based classification losses (e.g., AAM-Softmax) yield substantially lower perceptual alignment than prototypical metric losses, while EER itself fails to track human judgment, directly challenging the community's implicit assumption. We trace this divergence to embedding geometry, where a model's effective dimensionality (d_{eff}) tracks perceptual alignment with a -0.95 rank correlation, revealing that the dimensional spread favored by classification losses fundamentally clashes with the low-dimensional nature of human voice perception. Imposing a dimensionality bottleneck compresses d_{eff} and raises perceptual alignment (ρ_{align}) from 0.08 to 0.74, establishing a principled geometric criterion for evaluating voice similarity.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

Camera-controlled video generation has achieved remarkable progress in recent years. However, existing video-to-video re-rendering methods primarily rely on Supervised Fine-Tuning using synthetic datasets. At present, there is an extreme scarcity of synchronized, multi-view real-world video data. Consequently, the prevailing paradigm often exhibits limited generalization when processing out-of-distribution real-world videos, with models struggling to accurately adhere to physical scales and camera trajectories. To bridge this gap, we propose Geo-Align, the first Reinforcement Learning framework specifically designed for camera-controlled video re-rendering. Built upon a pretrained model, we optimize the model through a scale-aware perceptual reward mechanism. Specifically, we introduce a metric 3D estimator to extract precise camera trajectories from generated videos, explicitly penalizing deviations in rotation and translation. Furthermore, we meticulously designed a data pipeline strategy based on real-world conditioning videos and target camera trajectories derived from synthetic data, eliminating the reliance on paired data. Extensive experiments demonstrate that Geo-Align consistently outperforms existing supervised learning baselines in both precise camera controllability and visual fidelity, indicating the effectiveness of our method.

Large vision-language models (LVLMs) have demonstrated remarkable performance on multimodal reasoning benchmarks, yet their perceptual reliability under physically constrained imaging conditions remains poorly understood. Existing evaluations predominantly assume ideal visual inputs and therefore fail to characterize how camera distance, illumination, viewpoint, and pixel density fundamentally affect semantic recoverability. We introduce SynDORBench, the first physically grounded benchmark for evaluating LVLM perceptual robustness under DORI-calibrated conditions aligned with human visual capability standards. SynDORBench comprises over 54k question--answer pairs generated through a controllable synthetic pipeline that systematically varies viewing distance, lighting, camera geometry, and action pose according to physically interpretable pixel-density regimes. To support scalable low-visibility supervision, we further propose a discernibility annotation framework that propagates human perceptual labels using mask-conditioned statistical features and ensemble learning. We evaluate 16 open-source LVLMs, a commercial LVLM baseline, and YOLO11x across human-presence classification and action recognition tasks under progressively degraded visibility conditions. Our results reveal that perceptual failure in LVLMs is strongly governed by pixel density and physical imaging constraints rather than model scale alone. Surprisingly, several compact open-source LVLMs outperform larger commercial baselines and substantially exceed YOLO11x robustness under long-range and low-light conditions. SynDORBench establishes a new benchmark paradigm for physically grounded multimodal evaluation, enabling systematic analysis of LVLM reliability under real-world perceptual constraints and direct comparison against human visibility thresholds.

Modern robotic manipulation primarily relies on visual observations in a 2D color space for skill learning but suffers from poor generalization. In contrast, humans, living in a 3D world, depend more on physical properties-such as distance, size, and shape-than on texture when interacting with objects. Since such 3D geometric information can be acquired from widely available depth cameras, it appears feasible to endow robots with similar perceptual capabilities. Our pilot study found that using depth cameras for manipulation is challenging, primarily due to their limited accuracy and susceptibility to various types of noise. In this work, we propose Camera Depth Models (CDMs) as a simple plugin on daily-use depth cameras, which take RGB images and raw depth signals as input and output denoised, accurate metric depth. To achieve this, we develop a neural data engine that generates high-quality paired data from simulation by modeling a depth camera's noise pattern. Our results show that CDMs achieve nearly simulation-level accuracy in depth prediction, effectively bridging the sim-to-real gap for manipulation tasks. Notably, our experiments demonstrate, for the first time, that a policy trained on raw simulated depth, without the need for adding noise or real-world fine-tuning, generalizes seamlessly to real-world robots on two challenging long-horizon tasks involving articulated, reflective, and slender objects, with little to no performance degradation. We hope our findings will inspire future research in utilizing simulation data and 3D information in general robot policies.

Chain-of-Thought (CoT) reasoning excels in language models but struggles in vision-language models due to premature visual-to-text conversion that discards continuous information such as geometry and spatial layout. While recent methods enhance CoT through static enumeration or attention-based selection, they remain passive, i.e., processing pre-computed inputs rather than actively seeking task-relevant details. Inspired by human active perception, we introduce ViThinker, a framework that enables vision-language models to autonomously generate decision (query) tokens triggering the synthesis of expert-aligned visual features on demand. ViThinker internalizes vision-expert capabilities during training, performing generative mental simulation during inference without external tool calls. Through a two-stage curriculum: first distilling frozen experts into model parameters, then learning task-driven querying via sparsity penalties, i.e., ViThinker discovers minimal sufficient perception for each reasoning step. Evaluations across vision-centric benchmarks demonstrate consistent improvements, validating that active query generation outperforms passive approaches in both perceptual grounding and reasoning accuracy.

Recent Vision-Language-Action (VLA) models have made impressive progress toward general-purpose robotic manipulation by post-training large Vision-Language Models (VLMs) for action prediction. Yet most VLAs entangle perception and control in a monolithic pipeline optimized purely for action, which can erode language-conditioned grounding. In our real-world tabletop tests, policies over-grasp when the target is absent, are distracted by clutter, and overfit to background appearance. To address these issues, we propose OBEYED-VLA (OBject-centric and gEometrY groundED VLA), a framework that explicitly disentangles perceptual grounding from action reasoning. Instead of operating directly on raw RGB, OBEYED-VLA augments VLAs with a perception module that grounds multi-view inputs into task-conditioned, object-centric, and geometry-aware observations. This module includes a VLM-based object-centric grounding stage that selects task-relevant object regions across camera views, along with a complementary geometric grounding stage that emphasizes the 3D structure of these objects over their appearance. The resulting grounded views are then fed to a pretrained VLA policy, which we fine-tune exclusively on single-object demonstrations collected without environmental clutter or non-target objects. On a real-world UR10e tabletop setup, OBEYED-VLA substantially improves robustness over strong VLA baselines across four challenging regimes and multiple difficulty levels: distractor objects, absent-target rejection, background appearance changes, and cluttered manipulation of unseen objects. Ablation studies confirm that both semantic grounding and geometry-aware grounding are critical to these gains. Overall, the results indicate that making perception an explicit, object-centric component is an effective way to strengthen and generalize VLA-based robotic manipulation.

Face Video Restoration (FVR) aims to recover high-fidelity facial videos from degraded input while preserving identity and semantic consistency across frames. Existing methods often struggle to simultaneously address three key challenges: identity shift, viewpoint-entangled guidance, and perceptual realism. To tackle these issues, we propose TIGER, a structured tri-prior fusion framework that Tames Identity, Geometry, and gEnerative pRiors for high-quality FVR. Specifically, an Identity Prior is first established by injecting subject-discriminative embeddings into the latent space, effectively anchoring the subject's identity against severe degradations. Then, to provide temporally consistent structural guidance for dynamic videos, TIGER constructs a Geometry Prior by lifting 2D reference cues into a disentangled 3D parameter space, creating a geometric anchor through cross-source parameter fusion. Moreover, to achieve maximum efficiency without compromising realism, we harness the video generation model's Generative Prior through a one-step rectified flow. We further design a progressive three-stage training optimization strategy that refines structural fidelity, textural reconstruction, and distribution-level realism to ensure robust optimization. We also construct a large-scale FVR dataset to facilitate robust training and standardized evaluation. Extensive experiments demonstrate that TIGER achieves state-of-the-art performance in both identity fidelity and temporal stability, delivering a high-quality, efficient and identity-consistent FVR. Project page: https://yzhoulv.github.io/Tiger/.

Supervised synthetic CT (sCT) generation is commonly trained and evaluated as voxel-wise regression against registered reference CT images. In practice, MRI-CT and CBCT-CT pairs are aligned through registration procedures that leave residual misalignments. These residuals are not independent intensity noise but spatially coherent geometric discrepancies that act as structured label noise. We investigate how this registration-induced bias affects supervised MRI-to-CT and CBCT-to-CT synthesis on 1,784 paired patients covering five anatomical regions. Voxel-wise scores strongly depend on the consistency between the registration used to build the training targets and the one used for evaluation: models score best when both conventions match, showing that networks partly learn the geometric convention of the registration pipeline and that standard metrics reward it. Training on more anatomically consistent registrations reduces prediction variability and improves out-of-distribution robustness, and CT-only controls show that registration alone produces metric errors in the range of top challenge submissions. To mitigate the limits of voxel-wise supervision, we introduce a perceptual loss computed in the feature space of a pretrained Segment Anything encoder. Compared with MAE-only and VGG-based objectives, it improves downstream segmentation and yields sharper, more structurally coherent sCT. Perceptual and voxel-wise metrics disagree under imperfect alignment and agree when the evaluation geometry is reliable. These results identify registration-induced bias as a central confounder in supervised sCT generation and argue for complementing voxel-wise agreement with anatomy-oriented evaluation criteria.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

Generating audio that is acoustically consistent with a scene is essential for immersive virtual environments. Recent neural acoustic field methods enable spatially continuous sound rendering but remain scene-specific, requiring dense audio measurements and costly training for each environment. Few-shot approaches improve scalability across rooms but still rely on multiple recordings and, being deterministic, fail to capture the inherent uncertainty of scene acoustics under sparse context. We introduce flow-matching acoustic generation (FLAC), a probabilistic method for few-shot acoustic synthesis that models the distribution of plausible room impulse responses (RIRs) given minimal scene context. FLAC leverages a diffusion transformer trained with a flow-matching objective to generate RIRs at arbitrary positions in novel scenes, conditioned on spatial, geometric, and acoustic cues. FLAC outperforms state-of-the-art eight-shot baselines with one-shot on both the AcousticRooms and Hearing Anything Anywhere datasets. To complement standard perceptual metrics, we further introduce AGREE, a joint acoustic-geometry embedding, enabling geometry-consistent evaluation of generated RIRs through retrieval and distributional metrics. This work is the first to apply generative flow matching to explicit RIR synthesis, establishing a new direction for robust and data-efficient acoustic synthesis.

3D reconstruction and generation are commonly tackled by separate paradigms: pixel-based regression for reconstruction, and latent diffusion for generation. Recent works attempt to unify them in latent space, but with notable drawbacks: the diffusion objective is defined on latent features rather than the underlying 3D representation, and both branches suffer from information loss introduced by latent encoding, while requiring a pretrained Variational Autoencoder (VAE) or Representation Autoencoder (RAE). In this paper, we reformulate these two tasks under a unified pixel-space diffusion paradigm and introduce PixWorld, a single model that jointly addresses 3D reconstruction and generation. By supervising diffusion directly on rendered images, PixWorld removes the above limitations and aligns optimization with 3D scene fidelity. Beyond photometric and perceptual supervision that operates at the 2D image level and lacks 3D geometric awareness, we further introduce a geometry perception loss that aligns rendered views with their ground truth in the geometry-aware feature space of a pretrained 3D foundation model, providing 3D structural supervision. PixWorld consistently outperforms prior latent-space generation methods and matches state-of-the-art reconstruction methods, demonstrating the superiority of a unified pixel-space approach.

Estimating sewing patterns from images is a practical approach for creating high-quality 3D garments. Due to the lack of real-world pattern-image paired data, prior approaches fine-tune large vision language models (VLMs) on synthetic garment datasets generated by randomly sampling from a parametric garment model GarmentCode. However, these methods often struggle to generalize to in-the-wild images, fail to capture real-world correlations between garment parts, and are typically restricted to single-layer outfits. In contrast, we observe that VLMs are effective at describing garments in natural language, yet perform poorly when asked to directly regress GarmentCode parameters from images. To bridge this gap, we propose NGL (Natural Garment Language), a novel intermediate language that restructures GarmentCode into a representation more understandable to language models. Leveraging this language, we introduce NGL-Prompter, a training-free pipeline that queries large VLMs to extract structured garment parameters, which are then deterministically mapped to valid GarmentCode. We evaluate our method on the Dress4D, CloSe and a newly collected dataset of approximately 5,000 in-the-wild fashion images. Our approach achieves state-of-the-art performance on standard geometry metrics and is strongly preferred in both human and GPT-based perceptual evaluations compared to existing baselines. Furthermore, NGL-prompter can recover multi-layer outfits whereas competing methods focus mostly on single-layer garments, highlighting its strong generalization to real-world images even with occluded parts. These results demonstrate that accurate sewing pattern reconstruction is possible without costly model training. Our code and data will be released for research use.

Although recent 3D-native generators have made great progress in synthesizing reliable geometry, they still fall short in achieving realistic appearances. A key obstacle lies in the lack of diverse and high-quality real-world 3D assets with rich texture details, since capturing such data is intrinsically difficult due to the diverse scales of scenes, non-rigid motions of objects, and the limited precision of 3D scanners. We introduce Photo3D, a framework for advancing photorealistic 3D generation, which is driven by the image data generated by the GPT-4o-Image model. Considering that the generated images can distort 3D structures due to their lack of multi-view consistency, we design a structure-aligned multi-view synthesis pipeline and construct a detail-enhanced multi-view dataset paired with 3D geometry. Building on it, we present a realistic detail enhancement scheme that leverages perceptual feature adaptation and semantic structure matching to enforce appearance consistency with realistic details while preserving the structural consistency with the 3D-native geometry. Our scheme is general to different 3D-native generators, and we present dedicated training strategies to facilitate the optimization of geometry-texture coupled and decoupled 3D-native generation paradigms. Experiments demonstrate that Photo3D generalizes well across diverse 3D-native generation paradigms and achieves state-of-the-art photorealistic 3D generation performance.

Training a model to generate visual content can encourage it to learn rich perceptual capabilities related to geometry, spatial relationships, and objectness; yet, its benefits for visual understanding remain unclear. We ask: when and how does visual generation supervision improve visual understanding? We study controlled pairs of image-to-image (I2I) generation and image-to-text (I2T) understanding tasks that express the same underlying problem in different output modalities. We find that under the correct recipe, I2I training improves downstream I2T performance, with larger gains as the amount of I2I training data increases. We next ask which generation tasks benefit which understanding capabilities. To study transfer beyond paired tasks, we introduce OmniTaskonomy, a unified taxonomy spanning 19 I2I generation tasks and 25 I2T understanding capabilities. The resulting transfer map reveals selective, task-dependent benefits. Some follow intuitive correspondences, e.g., depth prediction improving metric 3D reasoning, object pointing improving counting, and jigsaw reconstruction improving 2D ordering. Interestingly, we also uncover surprising connections: 2.5D segmentation improving category recognition and Z-depth prediction improving localization. To probe these patterns, we analyze gradient alignment between generation and understanding tasks and find that stronger alignment is associated with larger downstream transfer gains. Together, our results highlight visual generation as a rich source of supervision for visual understanding and provide a roadmap for unlocking its benefits through the right training curriculum and task selection. Project page: https://omni-taskonomy.github.io/.

Monocular 3D object detection (Mono3D) aims to infer object locations and dimensions in 3D space from a single RGB image. Despite recent progress, existing methods remain highly sensitive to camera intrinsics and struggle to generalize across diverse settings, since intrinsics govern how 3D scenes are projected onto the image plane. We propose MonoIA, a unified intrinsic-aware framework that models and adapts to intrinsic variation through a language-grounded representation. The key insight is that intrinsic variation is not a numeric difference but a perceptual transformation that alters apparent scale, perspective, and spatial geometry. To capture this effect, MonoIA employs large language models and vision-language models to generate intrinsic embeddings that encode the visual and geometric implications of camera parameters. These embeddings are hierarchically integrated into the detection network via an Intrinsic Adaptation Module, allowing the model to modulate its feature representations according to camera-specific configurations and maintain consistent 3D detection across intrinsics. This shifts intrinsic modeling from numeric conditioning to semantic representation, enabling robust and unified perception across cameras. Extensive experiments show that MonoIA achieves new state-of-the-art results on standard benchmarks including KITTI, Waymo, and nuScenes (e.g., +1.18% on the KITTI leaderboard), and further improves performance under multi-dataset training (e.g., +4.46% on KITTI Val).

Generative video models are increasingly studied as implicit world models, yet evaluating whether they produce physically plausible 3D structure and motion remains challenging. Most existing video evaluation pipelines rely heavily on human judgment or learned graders, which can be subjective and weakly diagnostic for geometric failures. We introduce PDI-Bench (Perspective Distortion Index), a quantitative framework for auditing geometric coherence in generated videos. Given a generated clip, we obtain object-centric observations via segmentation and point tracking (e.g., SAM 2, MegaSaM, and CoTracker3), lift them to 3D world-space coordinates via monocular reconstruction, and compute a set of projective-geometry residuals capturing three failure dimensions: scale-depth alignment, 3D motion consistency, and 3D structural rigidity. To support systematic evaluation, we build PDI-Dataset, covering diverse scenarios designed to stress these geometric constraints. Across state-of-the-art video generators, PDI reveals consistent geometry-specific failure modes that are not captured by common perceptual metrics, and provides a diagnostic signal for progress toward physically grounded video generation and physical world model. Our code and dataset can be found at https://pdi-bench.github.io/.

We present UniFuture, a simple yet effective driving world model that seamlessly integrates future scene generation and perception within a single framework. Unlike existing models focusing solely on pixel-level future prediction or geometric reasoning, our approach jointly models future appearance (i.e., RGB image) and geometry (i.e., depth), ensuring coherent predictions. Specifically, during the training, we first introduce a Dual-Latent Sharing scheme, which transfers image and depth sequence in a shared latent space, allowing both modalities to benefit from shared feature learning. Additionally, we propose a Multi-scale Latent Interaction mechanism, which facilitates bidirectional refinement between image and depth features at multiple spatial scales, effectively enhancing geometry consistency and perceptual alignment. During testing, our UniFuture can easily predict high-consistency future image-depth pairs by only using the current image as input. Extensive experiments on the nuScenes dataset demonstrate that UniFuture outperforms specialized models on future generation and perception tasks, highlighting the advantages of a unified, structurally-aware world model. The project page is at https://github.com/dk-liang/UniFuture.

We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud, and it is non-trivial to convert them to the more ready-to-use mesh model. Unlike the existing methods, our network represents 3D mesh in a graph-based convolutional neural network and produces correct geometry by progressively deforming an ellipsoid, leveraging perceptual features extracted from the input image. We adopt a coarse-to-fine strategy to make the whole deformation procedure stable, and define various of mesh related losses to capture properties of different levels to guarantee visually appealing and physically accurate 3D geometry. Extensive experiments show that our method not only qualitatively produces mesh model with better details, but also achieves higher 3D shape estimation accuracy compared to the state-of-the-art.

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.

What is the geometry of a visual percept? The most widely used protocols for decomposing neural network representations into interpretable parts treat concepts as isolated directions, yet recent work shows that concepts are often realized as geometric structures in low dimensional regions of activation space. We turn to the literature of Structured sparsity to close this gap, and show that block sparsity, which groups directions into blocks, is the prior matched to a generative model in which a representation is a sparse sum of low-dimensional manifolds: the modern, learned form of a classical idea in visual neuroscience, where a visual feature is carried by a coordinated group of neurons rather than a single tuned one. We implement three variants of block-sparse featurizers (BSFs) and, through a minimum-description-length analysis, show that all three describe activations more compactly than direction-based featurizers, with the recovered concepts typically two- to four-dimensional. We then use BSFs to (i) recontextualize prior work, showing that curve detectors in InceptionV1 actually read from a single continuous curve manifold, (ii) discover novel manifolds including shadows and lighting in DINOv3, and (iii) support interpretable control of image generation in diffusion models (SDXL) via manifold steering.

Geometric understanding - including depth and height perception - is fundamental to intelligence and crucial for navigating our environment. Despite the impressive capabilities of large Vision Language Models (VLMs), it remains unclear how well they possess the geometric understanding required for practical applications in visual perception. In this work, we focus on evaluating the geometric understanding of these models, specifically targeting their ability to perceive the depth and height of objects in an image. To address this, we introduce GeoMeter, a suite of benchmark datasets - encompassing 2D and 3D scenarios - to rigorously evaluate these aspects. By benchmarking 18 state-of-the-art VLMs, we found that although they excel in perceiving basic geometric properties like shape and size, they consistently struggle with depth and height perception. Our analysis reveal that these challenges stem from shortcomings in their depth and height reasoning capabilities and inherent biases. This study aims to pave the way for developing VLMs with enhanced geometric understanding by emphasizing depth and height perception as critical components necessary for real-world applications.

Vision-language models (VLMs) often struggle with geometric reasoning due to their limited perception of fundamental diagram elements. To tackle this challenge, we introduce GeoPerceive, a benchmark comprising diagram instances paired with domain-specific language (DSL) representations, along with an efficient automatic data generation pipeline. This design enables the isolated evaluation of geometric perception independently from reasoning. To exploit the data provided by GeoPerceive for enhancing the geometric perception capabilities of VLMs, we propose GeoDPO, a translator-guided reinforcement learning (RL) framework. GeoDPO employs an NL-to-DSL translator, which is trained on synthetic pairs generated by the data engine of GeoPerceive, to bridge natural language and DSL. This translator facilitates the computation of fine-grained, DSL-level scores, which serve as reward signals in reinforcement learning. We assess GeoDPO on both in-domain and out-of-domain datasets, spanning tasks in geometric perception as well as downstream reasoning. Experimental results demonstrate that, while supervised fine-tuning (SFT) offers only marginal improvements and may even impair performance in out-of-domain scenarios, GeoDPO achieves substantial gains: +26.5% on in-domain data, +8.0% on out-of-domain data, and +39.0% on downstream reasoning tasks. These findings underscore the superior performance and generalization ability of GeoDPO over SFT. All codes are released at https://github.com/Longin-Yu/GeoPerceive to ensure reproducibility.

Recent works augment Vision-Language Models with geometry features from pretrained 3D models, expecting that the geometric signal will boost spatial reasoning. However, we find that simply fusing geometry features and training on standard spatial QA yields only marginal improvements on high-level multi-hop tasks. We attribute this gap to a training-signal problem: standard spatial QA can be largely answered from visual features and language priors, so the geometry pathway receives weak gradients and fails to integrate with the visual features. To provide a training signal that requires geometry, we propose novel-view semantic rendering as an auxiliary training task that requires the model to predict the semantic layout of an unobserved viewpoint, inspired by humans' ability to mentally simulate novel viewpoints during spatial reasoning. This task encourages joint use of both pathways: geometry provides pose-dependent visibility, while vision provides semantic content. Our auxiliary task yields consistent improvements over the geometry-augmented baseline across all three benchmarks (up to +1.6 on VSI-Bench, +2.2 on ReVSI, +2.9 on our 3D-Point-QA dataset) and our full model surpasses prior open-source methods on VSI-Bench and on ReVSI. Project page: https://yuqunw.github.io/Render2Reason/.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

Understanding perspective is fundamental to human visual perception, yet the extent to which multimodal large language models (MLLMs) internalize perspective geometry remains unclear. We introduce MMPerspective, the first benchmark specifically designed to systematically evaluate MLLMs' understanding of perspective through 10 carefully crafted tasks across three complementary dimensions: Perspective Perception, Reasoning, and Robustness. Our benchmark comprises 2,711 real-world and synthetic image instances with 5,083 question-answer pairs that probe key capabilities, such as vanishing point perception and counting, perspective type reasoning, line relationship understanding in 3D space, invariance to perspective-preserving transformations, etc. Through a comprehensive evaluation of 43 state-of-the-art MLLMs, we uncover significant limitations: while models demonstrate competence on surface-level perceptual tasks, they struggle with compositional reasoning and maintaining spatial consistency under perturbations. Our analysis further reveals intriguing patterns between model architecture, scale, and perspective capabilities, highlighting both robustness bottlenecks and the benefits of chain-of-thought prompting. MMPerspective establishes a valuable testbed for diagnosing and advancing spatial understanding in vision-language systems. Resources available at: https://yunlong10.github.io/MMPerspective/

Recent advancements in reinforcement learning (RL) have enhanced the reasoning abilities of large language models (LLMs), yet the impact on multimodal LLMs (MLLMs) is limited. Particularly in vision-intensive tasks like geometric reasoning, MLLMs hallucinate frequently, leading to inaccurate reasoning. We attribute this to the perceptual bottleneck in MLLMs, which caps the benefits of reasoning training. To quantify this, we design a Geo-Perception Question-Answering (GeoPQA) benchmark, targeting basic geometric concepts and spatial relationships. Experiments on GeoPQA reveal significant shortcomings of MLLMs in visual perception, which constrain RL reward signals for effective training. To address this bottleneck, we propose a two-stage RL training framework by first enhancing the visual perception of geometric structures, then fostering reasoning capabilities. Applied to Qwen2.5-VL-3B-Instruct, our two-stage training improves geometric reasoning by 9.7% and geometric problem solving by 9.1%, compared to the direct reasoning training approach. Our method also generalizes to other vision-intensive domains like figure understanding, highlighting the importance of perceptual grounding in effective MLLM reasoning.

Current multimodal large language models (MLLMs) often underperform on mathematical problem-solving tasks that require fine-grained visual understanding. The limitation is largely attributable to inadequate perception of geometric primitives during image-level contrastive pre-training (e.g., CLIP). While recent efforts to improve math MLLMs have focused on scaling up mathematical visual instruction datasets and employing stronger LLM backbones, they often overlook persistent errors in visual recognition. In this paper, we systematically evaluate the visual grounding capabilities of state-of-the-art MLLMs and reveal a significant negative correlation between visual grounding accuracy and problem-solving performance, underscoring the critical role of fine-grained visual understanding. Notably, advanced models like GPT-4o exhibit a 70% error rate when identifying geometric entities, highlighting that this remains a key bottleneck in visual mathematical reasoning. To address this, we propose a novel approach, SVE-Math (Selective Vision-Enhanced Mathematical MLLM), featuring a geometric-grounded vision encoder and a feature router that dynamically adjusts the contribution of hierarchical visual feature maps. Our model recognizes accurate visual primitives and generates precise visual prompts tailored to the language model's reasoning needs. In experiments, SVE-Math-Qwen2.5-7B outperforms other 7B models by 15% on MathVerse and is compatible with GPT-4V on MathVista. Despite being trained on smaller datasets, SVE-Math-7B achieves competitive performance on GeoQA, rivaling models trained on significantly larger datasets. Our findings emphasize the importance of incorporating fine-grained visual understanding into MLLMs and provide a promising direction for future research.

Real-world phenomena do not generate arbitrary variability: their signals concentrate on compact, low-variability subsets of functional space, enabling rapid generalization from few examples. A small child can recognize a dog after extremely limited exposure because the perceptual manifold of "dog" is compact, structured, and low-dimensional. We formalize this principle through a deterministic functional-topological framework in which the set of valid realizations produced by a physical process forms a compact subset of a Banach space, endowed with stable invariants, a finite Hausdorff radius, and an induced continuous perceptual functional. This geometry provides explicit limits on knowledge, conditions for identifiability, and guarantees for generalization from sparse evidence -- properties fundamental to both natural and artificial intelligence. Across electromechanical, electrochemical, and physiological domains, we show that real-world processes consistently generate compact perceptual manifolds with the same geometric characteristics. Their boundaries can be discovered in a fully self-supervised manner as the empirical radius saturates with increasing sampling, even when the governing equations are unknown. These results demonstrate that deterministic functional topology offers a unified mathematical foundation for perception, representation, and world-model construction. It provides a geometric explanation for why biological learners and self-supervised AI systems can generalize from few observations, and establishes compact perceptual manifolds as a fundamental building block for future AI architectures. Finally, this work unifies biological perception and modern self-supervised models under a single geometric principle: both derive their generalization ability from the compactness and invariants of real-world perceptual manifolds.

Current perceptual similarity metrics operate at the level of pixels and patches. These metrics compare images in terms of their low-level colors and textures, but fail to capture mid-level similarities and differences in image layout, object pose, and semantic content. In this paper, we develop a perceptual metric that assesses images holistically. Our first step is to collect a new dataset of human similarity judgments over image pairs that are alike in diverse ways. Critical to this dataset is that judgments are nearly automatic and shared by all observers. To achieve this we use recent text-to-image models to create synthetic pairs that are perturbed along various dimensions. We observe that popular perceptual metrics fall short of explaining our new data, and we introduce a new metric, DreamSim, tuned to better align with human perception. We analyze how our metric is affected by different visual attributes, and find that it focuses heavily on foreground objects and semantic content while also being sensitive to color and layout. Notably, despite being trained on synthetic data, our metric generalizes to real images, giving strong results on retrieval and reconstruction tasks. Furthermore, our metric outperforms both prior learned metrics and recent large vision models on these tasks.

Despite the success of Large-Vision Language Models (LVLMs), general optimization objectives (e.g., standard MLE) fail to constrain visual trajectories, leading to language bias and hallucination. To mitigate this, current methods introduce geometric priors from visual experts as additional supervision. However, we observe that such supervision is typically suboptimal: it is biased toward geometric precision and offers limited reasoning utility. To bridge this gap, we propose Perceptual Flow Network (PFlowNet), which eschews rigid alignment with the expert priors and achieves interpretable yet more effective visual reasoning. Specifically, PFlowNet decouples perception from reasoning to establish a self-conditioned generation process. Based on this, it integrates multi-dimensional rewards with vicinal geometric shaping via variational reinforcement learning, thereby facilitating reasoning-oriented perceptual behaviors while preserving visual reliability. PFlowNet delivers a provable performance guarantee and competitive empirical results, particularly setting new SOTA records on V* Bench (90.6%) and MME-RealWorld-lite (67.0%).

We propose Perceptual Taxonomy, a structured process of scene understanding that first recognizes objects and their spatial configurations, then infers task-relevant properties such as material, affordance, function, and physical attributes to support goal-directed reasoning. While this form of reasoning is fundamental to human cognition, current vision-language benchmarks lack comprehensive evaluation of this ability and instead focus on surface-level recognition or image-text alignment. To address this gap, we introduce Perceptual Taxonomy, a benchmark for physically grounded visual reasoning. We annotate 3173 objects with four property families covering 84 fine-grained attributes. Using these annotations, we construct a multiple-choice question benchmark with 5802 images across both synthetic and real domains. The benchmark contains 28033 template-based questions spanning four types (object description, spatial reasoning, property matching, and taxonomy reasoning), along with 50 expert-crafted questions designed to evaluate models across the full spectrum of perceptual taxonomy reasoning. Experimental results show that leading vision-language models perform well on recognition tasks but degrade by 10 to 20 percent on property-driven questions, especially those requiring multi-step reasoning over structured attributes. These findings highlight a persistent gap in structured visual understanding and the limitations of current models that rely heavily on pattern matching. We also show that providing in-context reasoning examples from simulated scenes improves performance on real-world and expert-curated questions, demonstrating the effectiveness of perceptual-taxonomy-guided prompting.

Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on ImageNet classification has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new dataset of human perceptual similarity judgments. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by large margins on our dataset. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.

Recent feed-forward models have significantly advanced geometry perception for inferring dense 3D structure from sensor observations. However, its essential capabilities remain fragmented across multiple incompatible paradigms, including online perception, offline reconstruction, multi-modal integration, long-horizon scalability, and metric-scale estimation. We present UniT, a unified model built upon a novel Group Autoregressive Transformer, which reformulates these seemingly disparate capabilities within a single framework. The key idea is to treat groups of sensor observations as the basic autoregressive units and predict the corresponding point maps in an anchor-free and scale-adaptive manner. More specifically, diverse view configurations in both online and offline settings are naturally unified within a single group autoregression process. By varying the group size, online mode operates over multiple autoregressive steps with single-frame groups, whereas offline mode aggregates a multi-frame group in a single forward pass. Meanwhile, a queue-style KV caching mechanism ensures bounded autoregressive memory over long horizons. This is enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly. To improve metric-scale generalization across scenes, a scale-adaptive geometry loss is further introduced within this framework. It couples relative geometric constraints with a partial absolute scale term, implicitly regularizing global scale and inducing a progressive transition from scale-invariant geometry to metric-scale solutions. Together with a dedicated modal attention module for integrating auxiliary modalities, UniT achieves state-of-the-art performance in unified geometry perception, as validated on ten benchmarks spanning seven representative tasks.

We present a compact geometry-native latent space as a shared foundation for perception and generation. Visual generators can produce photorealistic frames without preserving a consistent 3D scene. We argue that this is not only a modeling problem but also a representation problem: generators typically evolve appearance-centric latents, while perception models recover geometry in a semantically rich space that encodes cross-view structure. Rather than adding geometry as another output, we reparameterize a geometry foundation model's features into a compact latent space for generation. We realize this shift with the geometry-native autoencoder (GAE), whose latent is jointly decodable to appearance, depth, cameras, and point maps. With this state, a standard conditional flow supports diverse generation tasks. In controlled comparisons that hold the generator and training protocol fixed, replacing the latent with GAE improves both visual quality and independently measured 3D coherence: FVD falls by 12.7% and 23.1% on RealEstate10K and DL3DV, and camera-trajectory error is halved on RealEstate10K. Together, these results show that the latent space is central to geometry-consistent generation and can serve as a shared interface between perception and generation.

Vision-Language Models (VLMs) have demonstrated remarkable performance across a variety of real-world tasks. However, existing VLMs typically process visual information by serializing images, a method that diverges significantly from the parallel nature of human vision. Moreover, their opaque internal mechanisms hinder both deeper understanding and architectural innovation. Inspired by the dual-stream hypothesis of human vision, which distinguishes the "what" and "where" pathways, we deconstruct the visual processing in VLMs into object recognition and spatial perception for separate study. For object recognition, we convert images into text token maps and find that the model's perception of image content unfolds as a two-stage process from shallow to deep layers, beginning with attribute recognition and culminating in semantic disambiguation. For spatial perception, we theoretically derive and empirically verify the geometric structure underlying the positional representation in VLMs. Based on these findings, we introduce an instruction-agnostic token compression algorithm based on a plug-and-play visual decoder to improve decoding efficiency, and a RoPE scaling technique to enhance spatial reasoning. Through rigorous experiments, our work validates these analyses, offering a deeper understanding of VLM internals and providing clear principles for designing more capable future architectures.

Vision-Language Models (VLMs) still lack robustness in spatial intelligence, demonstrating poor performance on spatial understanding and reasoning tasks. We attribute this gap to the absence of a visual geometry learning process capable of reconstructing 3D space from 2D images. We present G^2VLM, a geometry grounded vision-language model that bridges two fundamental aspects of spatial intelligence: spatial 3D reconstruction and spatial understanding. G^2VLM natively leverages learned 3D visual geometry features to directly predict 3D attributes and enhance spatial reasoning tasks via in-context learning and interleaved reasoning. Our unified design is highly scalable for spatial understanding: it trains on abundant multi-view image and video data, while simultaneously leveraging the benefits of 3D visual priors that are typically only derived from hard-to-collect annotations. Experimental results demonstrate G^2VLM is proficient in both tasks, achieving comparable results to state-of-the-art feed-forward 3D reconstruction models and achieving better or competitive results across spatial understanding and reasoning tasks. By unifying a semantically strong VLM with low-level 3D vision tasks, we hope G^2VLM can serve as a strong baseline for the community and unlock more future applications, such as 3D scene editing.

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at the pixel-level, and solved at inference-time, that can capture global and local image characteristics. The distance in embedding space is used to define a perceptual similarity metric which we call LASI: Linear Autoregressive Similarity Index. Experiments on full-reference image quality assessment datasets show LASI performs competitively with learned deep feature based methods like LPIPS (Zhang et al., 2018) and PIM (Bhardwaj et al., 2020), at a similar computational cost to hand-crafted methods such as MS-SSIM (Wang et al., 2003). We found that increasing the dimensionality of the embedding space consistently reduces the WLS loss while increasing performance on perceptual tasks, at the cost of increasing the computational complexity. LASI is fully differentiable, scales cubically with the number of embedding dimensions, and can be parallelized at the pixel-level. A Maximum Differentiation (MAD) competition (Wang & Simoncelli, 2008) between LASI and LPIPS shows that both methods are capable of finding failure points for the other, suggesting these metrics can be combined.

We investigate the ability of Vision Language Models (VLMs) to perform visual perspective taking using a novel set of visual tasks inspired by established human tests. Our approach leverages carefully controlled scenes, in which a single humanoid minifigure is paired with a single object. By systematically varying spatial configurations - such as object position relative to the humanoid minifigure and the humanoid minifigure's orientation - and using both bird's-eye and surface-level views, we created 144 unique visual tasks. Each visual task is paired with a series of 7 diagnostic questions designed to assess three levels of visual cognition: scene understanding, spatial reasoning, and visual perspective taking. Our evaluation of several state-of-the-art models, including GPT-4-Turbo, GPT-4o, Llama-3.2-11B-Vision-Instruct, and variants of Claude Sonnet, reveals that while they excel in scene understanding, the performance declines significantly on spatial reasoning and further deteriorates on perspective-taking. Our analysis suggests a gap between surface-level object recognition and the deeper spatial and perspective reasoning required for complex visual tasks, pointing to the need for integrating explicit geometric representations and tailored training protocols in future VLM development.

In Marius von Senden's Space and Sight, a newly sighted blind patient describes the experience of a corner as lemon-like, because corners "prick" sight like lemons prick the tongue. Prickliness, here, is a dimension in the feature space of sensory experience, an effect of the perceived on the perceiver that arises where the two interact. In the account of the newly sighted, an effect familiar from one interaction translates to a novel context. Perception serves as the vehicle for generalization, in that an effect shared across different experiences produces a concrete abstraction grounded in those experiences. Cezanne and the post-impressionists, fluent in the language of experience translation, realized that the way to paint a concrete form that best reflected reality was to paint not what they saw, but what it was like to see. We envision a future of creation using AI where what it is like to see is replicable, transferrable, manipulable - part of the artist's palette that is both grounded in a particular context, and generalizable beyond it. An active line of research maps human-interpretable features onto directions in GAN latent space. Supervised and self-supervised approaches that search for anticipated directions or use off-the-shelf classifiers to drive image manipulation in embedding space are limited in the variety of features they can uncover. Unsupervised approaches that discover useful new directions show that the space of perceptually meaningful directions is nowhere close to being fully mapped. As this space is broad and full of creative potential, we want tools for direction discovery that capture the richness and generalizability of human perception. Our approach puts creators in the discovery loop during real-time tool use, in order to identify directions that are perceptually meaningful to them, and generate interpretable image translations along those directions.

Significant advancements in Large Multimodal Models (LMMs) have enabled them to tackle complex problems involving visual-mathematical reasoning. However, their ability to identify geometric elements remains underexplored. To address this gap, we introduce Tangram, a novel benchmark designed to evaluate the performance of LMMs on geometric element recognition. Tangram comprises 1,080 diverse geometric diagrams sourced from primary and secondary school exams, competitions, and textbooks, ranging from simple geometric shapes to complex combinations. Each diagram is paired with four questions, resulting in 4,320 visual-question-answer pairs. Unlike existing benchmarks that emphasize higher-level cognition and reasoning, Tangram focuses on understanding geometric elements, requiring models to perform a ``simple yet challenging" counting task. Systematic evaluation of 13 prominent LMMs, such as GPT-4o and Claude 3.5 Sonnet, reveals that these models face significant challenges even in seemingly straightforward tasks. The top-performing model achieves an accuracy of only 53.0%, highlighting a substantial gap compared to human performance. These findings underscore the limitations of current multimodal AI systems in handling basic perception tasks and serve to inspire the development of the next generation of expert-level multimodal foundational models. The data and code will be released soon.

Recent advancements in Vision-Language Models (VLMs) have significantly pushed the boundaries of Visual Question Answering (VQA).However,high-resolution details can sometimes become noise that leads to hallucinations or reasoning errors. In this paper,we propose Degradation-Driven Prompting (DDP), a novel framework that improves VQA performance by strategically reducing image fidelity to force models to focus on essential structural information. We evaluate DDP across two distinct tasks. Physical attributes targets images prone to human misjudgment, where DDP employs a combination of 80p downsampling, structural visual aids (white background masks and orthometric lines), and In-Context Learning (ICL) to calibrate the model's focus. Perceptual phenomena addresses various machine-susceptible visual anomalies and illusions, including Visual Anomaly (VA), Color (CI), Motion(MI),Gestalt (GI), Geometric (GSI), and Visual Illusions (VI).For this task, DDP integrates a task-classification stage with specialized tools such as blur masks and contrast enhancement alongside downsampling. Our experimental results demonstrate that less is more: by intentionally degrading visual inputs and providing targeted structural prompts, DDP enables VLMs to bypass distracting textures and achieve superior reasoning accuracy on challenging visual benchmarks.

Many surface cues support three-dimensional shape perception, but people can sometimes still see shape when these features are missing -- in extreme cases, even when an object is completely occluded, as when covered with a draped cloth. We propose a framework for 3D shape perception that explains perception in both typical and atypical cases as analysis-by-synthesis, or inference in a generative model of image formation: the model integrates intuitive physics to explain how shape can be inferred from deformations it causes to other objects, as in cloth-draping. Behavioral and computational studies comparing this account with several alternatives show that it best matches human observers in both accuracy and response times, and is the only model that correlates significantly with human performance on difficult discriminations. Our results suggest that bottom-up deep neural network models are not fully adequate accounts of human shape perception, and point to how machine vision systems might achieve more human-like robustness.

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as images or point clouds acquired by 2D/3D sensors, one important goal is to understand the geometric structure and semantics of the 3D environment. Traditional approaches usually leverage hand-crafted features to estimate the shape and semantics of objects or scenes. However, they are difficult to generalize to novel objects and scenarios, and struggle to overcome critical issues caused by visual occlusions. By contrast, we aim to understand scenes and the objects within them by learning general and robust representations using deep neural networks, trained on large-scale real-world 3D data. To achieve these aims, this thesis makes three core contributions from object-level 3D shape estimation from single or multiple views to scene-level semantic understanding.

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

Every day, humans perceive objects and communicate these perceptions through various channels. In this paper, we present a computational model designed to track and simulate the perception of objects, as well as their representations as conveyed in communication. We delineate two fundamental components of our internal representation, termed "observed" and "seen", which we correlate with established concepts in computer vision, namely encoding and decoding. These components are integrated into semiotic networks, which simulate perceptual inference of object perception and human communication. Our model of object perception by a person allows us to define object perception by {\em a network}. We demonstrate this with an example of an image baseline classifier by constructing a new network that includes the baseline classifier and an additional layer. This layer produces the images "perceived" by the entire network, transforming it into a perceptualized image classifier. This facilitates visualization of the acquired network. Within our network, the image representations become more efficient for classification tasks when they are assembled and randomized. In our experiments, the perceptualized network outperformed the baseline classifier on MNIST training databases consisting of a restricted number of images. Our model is not limited to persons and can be applied to any system featuring a loop involving the processing from "internal" to "external" representations.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning ability in this task through accurate identification and adaptive application of geometric principles within visual contexts. However, existing benchmarks fail to jointly assess both dimensions of the human-like geometric reasoning mechanism in MLLMs, remaining a critical gap in assessing their ability to tackle GPS. To this end, we introduce GeoSense, the first comprehensive bilingual benchmark designed to systematically evaluate the geometric reasoning abilities of MLLMs through the lens of geometric principles. GeoSense features a five-level hierarchical framework of geometric principles spanning plane and solid geometry, an intricately annotated dataset of 1,789 problems, and an innovative evaluation strategy. Through extensive experiments on GeoSense with various open-source and closed-source MLLMs, we observe that Gemini-2.0-pro-flash performs best, achieving an overall score of 65.3. Our in-depth analysis reveals that the identification and application of geometric principles remain a bottleneck for leading MLLMs, jointly hindering their reasoning abilities. These findings underscore GeoSense's potential to guide future advancements in MLLMs' geometric reasoning capabilities, paving the way for more robust and human-like reasoning in artificial intelligence.

Spatial reasoning remains a persistent weakness of vision-language models (VLMs), because RGB inputs do not directly provide geometric evidence. Existing remedies either inject 3D into the model at inference, paying architecture and latency costs, or train with outcome rewards that supervise only the final answer. Spatial errors originate in perception: a misjudged depth or direction can be corrected only by the scene's true geometry, which the 3D-scanned sources of spatial training corpora already provide. We propose GPD (Geometry-Privileged Distillation), which makes geometric evidence the privilege in on-policy self-distillation (OPSD). For each question, depth, semantic, and bird's-eye-view (BEV) cues are rendered as compact text and routed to the teacher alongside the reference answer; a privileged KL, applied only to incorrect trajectories, augments GRPO, and the deployed model remains RGB-only. On the 4B backbone, GPD achieves 57.1 on VSI-Bench and 37.6 average across MindCube, SPARBench, MMSI-Bench, and ViewSpatial, outperforming both GRPO and answer-privileged OPSD across spatial reasoning benchmarks. Ablations confirm the complementarity of 3D and answer privilege, the advantage of question-conditioned routing over full-context injection, and the benefit of restricting distillation to incorrect trajectories.

Despite strong performance on vision-language tasks, Multimodal Large Language Models (MLLMs) struggle with mathematical problem-solving, with both open-source and state-of-the-art models falling short of human performance on visual-math benchmarks. To systematically examine visual-mathematical reasoning in MLLMs, we (1) evaluate their understanding of geometric primitives, (2) test multi-step reasoning, and (3) explore a potential solution to improve visual reasoning capabilities. Our findings reveal fundamental shortcomings in shape recognition, with top models achieving under 50% accuracy in identifying regular polygons. We analyze these failures through the lens of dual-process theory and show that MLLMs rely on System 1 (intuitive, memorized associations) rather than System 2 (deliberate reasoning). Consequently, MLLMs fail to count the sides of both familiar and novel shapes, suggesting they have neither learned the concept of sides nor effectively process visual inputs. Finally, we propose Visually Cued Chain-of-Thought (VC-CoT) prompting, which enhances multi-step mathematical reasoning by explicitly referencing visual annotations in diagrams, boosting GPT-4o's accuracy on an irregular polygon side-counting task from 7% to 93%. Our findings suggest that System 2 reasoning in MLLMs remains an open problem, and visually-guided prompting is essential for successfully engaging visual reasoning. Code available at: https://github.com/rsinghlab/Shape-Blind.

Perceptual constancy is the ability to maintain stable perceptions of objects despite changes in sensory input, such as variations in distance, angle, or lighting. This ability is crucial for recognizing visual information in a dynamic world, making it essential for Vision-Language Models (VLMs). However, whether VLMs are currently and theoretically capable of mastering this ability remains underexplored. In this study, we evaluated 33 VLMs using 253 experiments across three domains: color, size, and shape constancy. The experiments included single-image and video adaptations of classic cognitive tasks, along with novel tasks in in-the-wild conditions, to evaluate the models' recognition of object properties under varying conditions. We found significant variability in VLM performance, with models performance in shape constancy clearly dissociated from that of color and size constancy.

Perceiving and remembering the visual world is fundamental to navigating and interacting with our environment. Current 4D foundation models, such as camera-controllable video models or 4D reconstruction models, can perceive and reconstruct dynamic environments, but how well they remember what they have perceived remains an open question. Existing benchmarks largely rely on pixel-level metrics and lack ground truth for objects once they leave the field of view, making them unable to evaluate visual memory in an object-centric manner against references. To fill this gap, we introduce PersistBench, a dataset and metric suite that leverages 360° videos as omniscient ground truth and proposes three evaluation aspects: object permanence, motion continuity, and appearance preservation. Evaluating various models across diverse categories reveals that current models can only maintain short-term consistency that degrades significantly once objects leave the field of view. Our findings highlight the gap between current model capabilities and robust visual memory ("seeing is not remembering"), providing guidance for future development of 4D foundation models. Dataset and code are available on the project page: https://guangzhaohe.com/persistbench.

Vision-language models (VLMs) have achieved strong image and video understanding, yet their visual-spatial representations remain geometrically fragile, leading to failures in spatial reasoning needed for embodied AI, robotics, and autonomous driving. Prior approaches to geometry grounding either fine-tune VLMs on spatial question answering, which can perpetuate spurious visual representations, or fuse features from large geometry-grounded vision models, which substantially increases model size at inference. Knowledge distillation from geometry-grounded vision models offers an alternative, but directly matching multi-view teacher features can disrupt the pretrained alignment between visual and textual representations, degrading object- and language-semantic capabilities. We propose multi-view relational distillation (MVRD), which distills patch-wise cosine similarities across views instead of the teacher features themselves. These relations encode geometric correspondences adequate for spatial understanding, while leaving the student representation underdetermined, allowing it to remain close to its pretrained vision- language space. Across representative VLMs, MVRD improves visual-spatial reasoning, outperforming supervised fine-tuning and feature distillation while approaching feature fusion methods with considerably fewer added parameters and lower latency. We show that MVRD makes visual representations more geometric while retaining language alignment, and generalizes to 3D scene understanding tasks such as object grounding, dense captioning, and question answering. Code is available at https://github.com/kietngt00/MVRD

Spatial understanding of the physical world from 2D visual inputs hinges on two complementary forms of geometric knowledge: holistic 3D structural perception and fine-grained metric scale estimation. Existing multimodal large language models (MLLMs) typically address only one facet, ingesting either depth maps or point clouds as additional model inputs, which incurs substantial computational overhead and inherits the generalization limitations of upstream prediction models. We propose GAMSI, a dual-pathway Geometry-Aware MLLM for Spatial Intelligence that takes only RGB images as input while internalizing both forms of geometric prior within a unified autoregressive backbone. Specifically, we introduce Metric-Structure Decoupled Queries (MSDQ) which employ two groups of learnable queries to respectively extract dense metric signals and sparse structural cues from the shared visual context, with a task-decoupled attention mask further preventing the two pathways from contaminating each other. Building on this, an Expert-Guided Visual Grounding (EVG) module projects the aggregated cues back to frame-level visual features and aligns them with vision foundation models, which serve purely as training-time supervision, rather than as model inputs. We further build a multi-task spatial instruction-tuning dataset (MTS) comprising 152{,}776 samples spanning 13 task types and three visual modalities, consolidated from six public datasets. Trained with a two-stage curriculum, GAMSI achieves state-of-the-art performance on seven spatial intelligence benchmarks.

The advent of Unified Multimodal Models (UMMs) signals a paradigm shift in artificial intelligence, moving from passive perception to active, cross-modal generation. Despite their unprecedented ability to synthesize information, a critical gap persists in evaluation: existing benchmarks primarily assess discriminative understanding or unconstrained image generation separately, failing to measure the integrated cognitive process of generative reasoning. To bridge this gap, we propose that geometric construction provides an ideal testbed as it inherently demands a fusion of language comprehension and precise visual generation. We introduce GGBench, a benchmark designed specifically to evaluate geometric generative reasoning. It provides a comprehensive framework for systematically diagnosing a model's ability to not only understand and reason but to actively construct a solution, thereby setting a more rigorous standard for the next generation of intelligent systems. Project website: https://opendatalab-raiser.github.io/GGBench/.

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold M_h to representations and a behavior manifold M_y to output probability distributions. We then test the link M_h leftrightarrow M_y via interventions: we find that steering along M_h, which we term manifold steering, yields behavioral trajectories that follow M_y, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

Large Vision Language Models (LVLMs) excel at semantic understanding but struggle with fine grained spatial grounding, as the model must implicitly infer complex geometry without ever producing a spatial interpretation. We present Perceptio, a perception enhanced LVLM with 2D and 3D spatial reasoning abilities, enabled via explicit semantic segmentation tokens and depth tokens generated directly within the autoregressive sequence. Concretely, we (i) distill a VQVAE depth codebook from a strong monocular teacher to tokenize dense depth into compact sequences, and (ii) integrate SAM2 based semantic segmentation tokens and VQ-VAE depth tokens inside the LLM so the model first emits spatial tokens and then answers. To stabilize depth token generation, we introduce novel composite depth-token objectives (marker, token, and count losses) and a soft-merging technique for differentiable reconstruction. We adopt a multi-task co-training strategy across diverse datasets, letting the model learn perception tokens to tackle multiple downstream tasks. Building on InternVL, Perceptio achieves state-of-the-art performance across benchmarks: improving referring expression segmentation by +0.8/+1.4/+1.1 cIoU on RefCOCO/+/g HardBLINK spatial understanding accuracy by 10.3%, and MMBench accuracy by 1.0%, demonstrating that explicit spatial chain-of-thought materially strengthens spatial grounding in LVLMs.

Vision-Language Models (VLMs) have shown remarkable performance on diverse visual and linguistic tasks, yet they remain fundamentally limited in their understanding of 3D spatial structures. We propose Geometric Distillation, a lightweight, annotation-free fine-tuning framework that injects human-inspired geometric cues into pretrained VLMs without modifying their architecture. By distilling (1) sparse correspondences, (2) relative depth relations, and (3) dense cost volumes from off-the-shelf 3D foundation models (e.g., MASt3R, VGGT), our method shapes representations to be geometry-aware while remaining compatible with natural image-text inputs. Through extensive evaluations on 3D vision-language reasoning and 3D perception benchmarks, our method consistently outperforms prior approaches, achieving improved 3D spatial reasoning with significantly lower computational cost. Our work demonstrates a scalable and efficient path to bridge 2D-trained VLMs with 3D understanding, opening up wider use in spatially grounded multimodal tasks.

This work investigates the fundamental fragility of state-of-the-art Vision-Language Models (VLMs) under basic geometric transformations. While modern VLMs excel at semantic tasks such as recognizing objects in canonical orientations and describing complex scenes, they exhibit systematic failures at a more fundamental level: lack of robust spatial invariance and equivariance required to reliably determine object identity under simple rotations, scaling, and identity transformations. We demonstrate this limitation through a systematic evaluation across diverse visual domains, including symbolic sketches, natural photographs, and abstract art. Performance drops sharply as semantic content becomes sparse, and this behavior is observed across architectures, model capacities, and prompting strategies. Overall, our results reveal a systematic gap between semantic understanding and spatial reasoning in current VLMs, highlighting the need for stronger geometric grounding in future multimodal systems.

Perceiving and reconstructing 3D scene geometry from visual inputs is crucial for autonomous driving. However, there still lacks a driving-targeted dense geometry perception model that can adapt to different scenarios and camera configurations. To bridge this gap, we propose a Driving Visual Geometry Transformer (DVGT), which reconstructs a global dense 3D point map from a sequence of unposed multi-view visual inputs. We first extract visual features for each image using a DINO backbone, and employ alternating intra-view local attention, cross-view spatial attention, and cross-frame temporal attention to infer geometric relations across images. We then use multiple heads to decode a global point map in the ego coordinate of the first frame and the ego poses for each frame. Unlike conventional methods that rely on precise camera parameters, DVGT is free of explicit 3D geometric priors, enabling flexible processing of arbitrary camera configurations. DVGT directly predicts metric-scaled geometry from image sequences, eliminating the need for post-alignment with external sensors. Trained on a large mixture of driving datasets including nuScenes, OpenScene, Waymo, KITTI, and DDAD, DVGT significantly outperforms existing models on various scenarios. Code is available at https://github.com/wzzheng/DVGT.

We present PVSeRF, a learning framework that reconstructs neural radiance fields from single-view RGB images, for novel view synthesis. Previous solutions, such as pixelNeRF, rely only on pixel-aligned features and suffer from feature ambiguity issues. As a result, they struggle with the disentanglement of geometry and appearance, leading to implausible geometries and blurry results. To address this challenge, we propose to incorporate explicit geometry reasoning and combine it with pixel-aligned features for radiance field prediction. Specifically, in addition to pixel-aligned features, we further constrain the radiance field learning to be conditioned on i) voxel-aligned features learned from a coarse volumetric grid and ii) fine surface-aligned features extracted from a regressed point cloud. We show that the introduction of such geometry-aware features helps to achieve a better disentanglement between appearance and geometry, i.e. recovering more accurate geometries and synthesizing higher quality images of novel views. Extensive experiments against state-of-the-art methods on ShapeNet benchmarks demonstrate the superiority of our approach for single-image novel view synthesis.

Many colour maps provided by vendors have highly uneven perceptual contrast over their range. It is not uncommon for colour maps to have perceptual flat spots that can hide a feature as large as one tenth of the total data range. Colour maps may also have perceptual discontinuities that induce the appearance of false features. Previous work in the design of perceptually uniform colour maps has mostly failed to recognise that CIELAB space is only designed to be perceptually uniform at very low spatial frequencies. The most important factor in designing a colour map is to ensure that the magnitude of the incremental change in perceptual lightness of the colours is uniform. The specific requirements for linear, diverging, rainbow and cyclic colour maps are developed in detail. To support this work two test images for evaluating colour maps are presented. The use of colour maps in combination with relief shading is considered and the conditions under which colour can enhance or disrupt relief shading are identified. Finally, a set of new basis colours for the construction of ternary images are presented. Unlike the RGB primaries these basis colours produce images whereby the salience of structures are consistent irrespective of the assignment of basis colours to data channels.

Vision-Language Models (VLMs) have recently witnessed significant progress in visual comprehension. As the permitting length of image context grows, VLMs can now comprehend a broader range of views and spaces. Current benchmarks provide insightful analysis of VLMs in tasks involving complex visual instructions following, multi-image understanding and spatial reasoning. However, they usually focus on spatially irrelevant images or discrete images captured from varied viewpoints. The compositional characteristic of images captured from a static viewpoint remains underestimated. We term this characteristic as Continuous Space Perception. When observing a scene from a static viewpoint while shifting orientations, it produces a series of spatially continuous images, enabling the reconstruction of the entire space. In this paper, we present CoSpace, a multi-image visual understanding benchmark designed to assess the Continuous Space perception ability for VLMs. CoSpace contains 2,918 images and 1,626 question-answer pairs, covering seven types of tasks. We conduct evaluation across 19 proprietary and open-source VLMs. Results reveal that there exist pitfalls on the continuous space perception ability for most of the evaluated models, including proprietary ones. Interestingly, we find that the main discrepancy between open-source and proprietary models lies not in accuracy but in the consistency of responses. We believe that enhancing the ability of continuous space perception is essential for VLMs to perform effectively in real-world tasks and encourage further research to advance this capability.

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

We introduce PerceptionComp, a manually annotated benchmark for complex, long-horizon, perception-centric video reasoning. PerceptionComp is designed so that no single moment is sufficient: answering each question requires multiple temporally separated pieces of visual evidence and compositional constraints under conjunctive and sequential logic, spanning perceptual subtasks such as objects, attributes, relations, locations, actions, and events, and requiring skills including semantic recognition, visual correspondence, temporal reasoning, and spatial reasoning. The benchmark contains 1,114 highly complex questions on 279 videos from diverse domains including city walk tours, indoor villa tours, video games, and extreme outdoor sports, with 100% manual annotation. Human studies show that PerceptionComp requires substantial test-time thinking and repeated perception steps: participants take much longer than on prior benchmarks, and accuracy drops to near chance (18.97%) when rewatching is disallowed. State-of-the-art MLLMs also perform substantially worse on PerceptionComp than on existing benchmarks: the best model in our evaluation, Gemini-3-Flash, reaches only 45.96% accuracy in the five-choice setting, while open-source models remain below 40%. These results suggest that perception-centric long-horizon video reasoning remains a major bottleneck, and we hope PerceptionComp will help drive progress in perceptual reasoning.

Human perception of 3D shapes goes beyond reconstructing them as a set of points or a composition of geometric primitives: we also effortlessly understand higher-level shape structure such as the repetition and reflective symmetry of object parts. In contrast, recent advances in 3D shape sensing focus more on low-level geometry but less on these higher-level relationships. In this paper, we propose 3D shape programs, integrating bottom-up recognition systems with top-down, symbolic program structure to capture both low-level geometry and high-level structural priors for 3D shapes. Because there are no annotations of shape programs for real shapes, we develop neural modules that not only learn to infer 3D shape programs from raw, unannotated shapes, but also to execute these programs for shape reconstruction. After initial bootstrapping, our end-to-end differentiable model learns 3D shape programs by reconstructing shapes in a self-supervised manner. Experiments demonstrate that our model accurately infers and executes 3D shape programs for highly complex shapes from various categories. It can also be integrated with an image-to-shape module to infer 3D shape programs directly from an RGB image, leading to 3D shape reconstructions that are both more accurate and more physically plausible.

Attention sinks, representation collapse, and norm stratification are treated as transformer-specific pathologies. We show they are not specific to attention: they are what content-based routing does under a fixed similarity metric. We give a reframing identity: softmax attention is Boltzmann-weighted aggregation over Euclidean distances with constant key norms, so its score omits a -|k|^2 term and is blind to key magnitude. This predicts that any router whose metric is ill-matched to its representations should compensate, by concentrating its routing and collapsing the routed representations. We test it on routers that score and aggregate over different axes: softmax attention over tokens (nine pretrained transformers), graph attention over nodes, a selective state-space model and a recurrent mixer over time, and learned residuals over depth. All develop the same signature, and two within-model ablations show it is caused by the routing mechanism rather than by incidental dynamics. The form is contingent, set by the strength of the positional brake each router carries alongside its content score; we sweep that brake and move the onset across its whole range. The mechanism is not contingent, and it does not require norm stratification: a router with norm-normalized keys concentrates just the same. We do not claim these models implement Riemannian geometry; the geometric view is a diagnostic that names the inadequacy of the flat, norm-blind metric.

Robust 3D representation learning forms the perceptual foundation of spatial intelligence, enabling downstream tasks in scene understanding and embodied AI. However, learning such representations directly from unposed multi-view images remains challenging. Recent self-supervised methods attempt to unify geometry, appearance, and semantics in a feed-forward manner, but they often suffer from weak geometry induction, limited appearance detail, and inconsistencies between geometry and semantics. We introduce UniSplat, a feed-forward framework designed to address these limitations through three complementary components. First, we propose a dual-masking strategy that strengthens geometry induction in the encoder. By masking both encoder and decoder tokens, and targeting decoder masks toward geometry-rich regions, the model is forced to infer structural information from incomplete visual cues, yielding geometry-aware representations even under unposed inputs. Second, we develop a coarse-to-fine Gaussian splatting strategy that reduces appearance-semantics inconsistencies by progressively refining the radiance field. Finally, to enforce geometric-semantic consistency, we introduce a pose-conditioned recalibration mechanism that interrelates the outputs of multiple heads by re-projecting predicted 3D point and semantic maps into the image plane using estimated camera parameters, and aligning them with corresponding RGB and semantic predictions to ensure cross-task consistency, thereby resolving geometry-semantic mismatches. Together, these components yield unified 3D representations that are robust to unposed, sparse-view inputs and generalize across diverse tasks, laying a perceptual foundation for spatial intelligence.

As reasoning models scale rapidly, the essential role of multimodality in human cognition has come into sharp relief, driving a growing need to probe vision-centric cognitive behaviors. Yet, existing multimodal benchmarks either overemphasize textual reasoning or fall short of systematically capturing vision-centric cognitive behaviors, leaving the cognitive capacity of MLLMs insufficiently assessed. To address this limitation, we introduce MME-CC (Multi-Modal Evaluation benchmark of Cognitive Capacity), a vision-grounded benchmark that organizes 11 representative reasoning tasks into three fundamental categories of visual information: spatial, geometric, and knowledge-based reasoning, and provides fine-grained analyses of MLLMs' cognitive capacity across these dimensions. Based on MME-CC, we conduct extensive experiments over 16 representative MLLMs. Our study reveals that closed-source models currently lead overall (e.g., 42.66 for Gemini-2.5-Pro vs. 30.45 for GLM-4.5V), while spatial and geometric reasoning remain broadly weak (less than or equal to 30%). We further identify common error patterns, including orientation mistakes, fragile cross-view identity persistence, and poor adherence to counterfactual instructions, and observe that Chain-of-Thought typically follows a three-stage process (extract -> reason -> verify) with heavy reliance on visual extraction. We hope this work catalyzes a shift toward treating the cognitive capacity of MLLMs as central to both evaluation and model design.

Object detection under image degradation can benefit from clean-image supervision, but aggregate gains do not imply that transferred representation changes are uniformly useful. We study how clean task knowledge affects degraded-image representations and whether local responses to structured representation directions can be characterized geometrically. Using paired clean and Gaussian-degraded BDD100K images, we show that clean-teacher distillation improves observed detection accuracy while producing heterogeneous object-level transfer. We isolate a representation component complementary to direct clean-teacher alignment and map it into the distilled student space through an orthogonal bridge. Controlled interventions rescue 13.22% of objects lost under the distilled representation, versus 4.30% under norm-matched random perturbations, with very low harm on preserved objects. We introduce task-sensitive geometry, a gradient-derived channel-space geometry constructed from normalized detection-loss gradients. On a reserved cohort, mapped-complement orientation within this frozen geometry is positively associated with local intervention-response magnitude after controlling for intervention magnitude (partial Spearman ρ = 0.242, 95% CI [0.108, 0.359]). The relationship eplicates on independent data (ρ = 0.180) and with RT-DETR-L (ρ = 0.227), but not for the direct clean-teacher residual family, and it weakens for large interventions. Routing rules and specialized distillation objectives based on these signals do not yield statistically reliable gains over CLEANKD. These results support a local, direction-family-dependent task-sensitive geometry while showing that converting such structure into improved global training remains an open problem.

Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges in effectively using image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://github.com/Lanyu0303/GeoGPT4V_Project

Large vision-language models (LVLMs) struggle to reliably detect visual primitives in charts and align them with semantic representations, which severely limits their performance on complex visual reasoning. This lack of perceptual grounding constitutes a major bottleneck for chart-based reasoning. We propose VisDoT, a framework that enhances visual reasoning through human-like interpretation grounding. We formalize four perceptual tasks based on the theory of graphical perception, including position and length. Building on this foundation, we introduce Decomposition-of-Thought (DoT) prompting, which sequentially separates questions into visual perception sub-questions and logic sub-questions. Fine-tuning InternVL with VisDoT achieves a +11.2% improvement on ChartQA and surpasses GPT-4o on the more challenging ChartQAPro benchmark. On the newly introduced VisDoTQA benchmark, the model improves by +33.2%. Furthermore, consistent zero-shot gains on diverse open-domain VQA benchmarks confirm the generalizability of the perception-logic separation strategy for visual question answering. VisDoT leverages human-like perception to enhance visual grounding, achieving state-of-the-art chart understanding and interpretable visual reasoning.

How do we know that a kitchen is a kitchen by looking? Relatively little is known about how we conceptualize and categorize different visual environments. Traditional models of visual perception posit that scene categorization is achieved through the recognition of a scene's objects, yet these models cannot account for the mounting evidence that human observers are relatively insensitive to the local details in an image. Psychologists have long theorized that the affordances, or actionable possibilities of a stimulus are pivotal to its perception. To what extent are scene categories created from similar affordances? Using a large-scale experiment using hundreds of scene categories, we show that the activities afforded by a visual scene provide a fundamental categorization principle. Affordance-based similarity explained the majority of the structure in the human scene categorization patterns, outperforming alternative similarities based on objects or visual features. We all models were combined, affordances provided the majority of the predictive power in the combined model, and nearly half of the total explained variance is captured only by affordances. These results challenge many existing models of high-level visual perception, and provide immediately testable hypotheses for the functional organization of the human perceptual system.

Panoramic images capture the full visual sphere in a frame, offering context unavailable to conventional cameras. Yet this completeness has an unavoidable geometric cost: the 2-sphere cannot be faithfully mapped to the plane, and every projection introduces distortions that challenge standard vision architectures. This survey traces panoramic scene understanding from projection-based adaptation and distortion-aware engineering to sphere-native modeling, reflecting increasing commitment to spherical geometry. Foundation models form a fourth family, geometry-aware tokenization, which adapts the input interface while reusing perspective-pretrained weights. We review these approaches across five task families: dense prediction, unified multi-task understanding, open-world perception, vision-language reasoning, and dynamic video analysis. Across tasks, the same shift toward spherical geometry recurs. In practice, however, the field has converged not on the strongest sphere-native operators, which are exactly rotation-equivariant but cannot reuse perspective-pretrained backbones and thus have not scaled, but on a compatibility-preserving middle ground combining moderate geometric awareness with large pretrained models. This commitment is uneven: deepest in dense prediction and shallowest in dynamic perception, where methods are spatially sphere-aware yet temporally planar. Foundation-model adaptation has advanced panoramic depth fastest, while layout, surface-normal, and video-level understanding remain largely unexplored. No panoramic foundation model has yet been pretrained on spherical data. We identify five evaluation gaps: spherical-area-weighted metrics, seam-consistency tests, polar-robustness stratification, cross-projection generalization, and standardized open-world protocols. We conclude with a six-point roadmap toward general-purpose panoramic intelligence.

Current vision-language models may incorporate single-dimensional spatial cues, such as depth, object boundary, and basic spatial directions (e.g. left, right, front, back), yet often lack the multi-dimensional spatial reasoning necessary for human-like understanding and real-world applications. To address this gap, we develop SPHERE (Spatial Perception and Hierarchical Evaluation of REasoning), a hierarchical evaluation framework with a new human-annotated dataset to pinpoint model strengths and weaknesses, advancing from single-skill tasks to multi-skill tasks, and ultimately to complex reasoning tasks that require the integration of multiple spatial and visual cues with logical reasoning. Benchmark evaluation of state-of-the-art open-source models reveal significant shortcomings, especially in the abilities to understand distance and proximity, to reason from both allocentric and egocentric viewpoints, and to perform complex reasoning in a physical context. This work underscores the need for more advanced approaches to spatial understanding and reasoning, paving the way for improvements in vision-language models and their alignment with human-like spatial capabilities. The dataset will be open-sourced upon publication.

While multimodal reasoning has advanced rapidly, solving complex geometry problems critically hinges on active visual assistance, such as constructing auxiliary lines, spurring the rise of Visual Chain-of-Thought (VCoT). However, existing evaluations typically assess visual generation quality and final answer accuracy in isolation, failing to examine whether intermediate visual aids are geometrically valid, effectively utilized in subsequent reasoning, or causally responsible for task success. To bridge this gap, we introduce GeoVAD-Bench, a diagnostic benchmark that pairs a fine-grained five-dimensional trajectory diagnosis covering perception, auxiliary quality, utilization, deductive reasoning, and final correctness with controlled No-Aux, Auto-Aux, and GT-Aux intervention settings to systematically isolate intermediate error modes, the causal gains of visual aids, and the resulting autonomy gap. Our findings reveal that while high-quality auxiliary aids offer substantial theoretical gains for geometric problem solving, autonomous generation is frequently hampered by compounding errors across geometric perception, faithful visual manipulation, visual-state grounding, and deductive reasoning. Guided by these diagnostic insights, we establish a specialized data construction pipeline encompassing geometric perception, diagram editing, and interleaved visual-textual reasoning trajectories, and develop a progressive SFT and multimodal RL training framework. The resulting model, GeoWeave-8B, outperforms the base model by +25.3% in final geometric accuracy and achieves a +30.4% gain in process average across the four intermediate diagnostic dimensions.

Humans have the ability to reason about geometric patterns in images and scenes from a young age. However, developing large multimodal models (LMMs) capable of similar reasoning remains a challenge, highlighting the need for robust evaluation methods to assess these capabilities. We introduce \Turtle, a benchmark designed to evaluate LMMs' capacity to interpret geometric patterns -- given visual examples, textual instructions, or both -- and generate precise code outputs. Inspired by turtle geometry, a notion used to teach children foundational coding and geometric concepts, TurtleBench features tasks with patterned shapes that have underlying algorithmic logic. Our evaluation reveals that leading LMMs struggle significantly with these tasks, with GPT-4o achieving only 19\% accuracy on the simplest tasks and few-shot prompting only marginally improves their performance (<2%). \Turtle highlights the gap between human and AI performance in intuitive and visual geometrical understanding, setting the stage for future research in this area. \Turtle stands as one of the few benchmarks to evaluate the integration of visual understanding and code generation capabilities in LMMs, setting the stage for future research. Code and Dataset for this paper is provided here: https://github.com/sinaris76/TurtleBench{https://github.com/sinaris76/TurtleBench}

Perceptual similarity metrics have progressively become more correlated with human judgments on perceptual similarity; however, despite recent advances, the addition of an imperceptible distortion can still compromise these metrics. In our study, we systematically examine the robustness of these metrics to imperceptible adversarial perturbations. Following the two-alternative forced-choice experimental design with two distorted images and one reference image, we perturb the distorted image closer to the reference via an adversarial attack until the metric flips its judgment. We first show that all metrics in our study are susceptible to perturbations generated via common adversarial attacks such as FGSM, PGD, and the One-pixel attack. Next, we attack the widely adopted LPIPS metric using spatial-transformation-based adversarial perturbations (stAdv) in a white-box setting to craft adversarial examples that can effectively transfer to other similarity metrics in a black-box setting. We also combine the spatial attack stAdv with PGD (ell_infty-bounded) attack to increase transferability and use these adversarial examples to benchmark the robustness of both traditional and recently developed metrics. Our benchmark provides a good starting point for discussion and further research on the robustness of metrics to imperceptible adversarial perturbations.

Humans possess the remarkable skill of Visual Perception, the ability to see and understand the seen, helping them make sense of the visual world and, in turn, reason. Multimodal Large Language Models (MLLM) have recently achieved impressive performance on vision-language tasks ranging from visual question-answering and image captioning to visual reasoning and image generation. However, when prompted to identify or count (perceive) the entities in a given image, existing MLLM systems fail. Working towards developing an accurate MLLM system for perception and reasoning, we propose using Versatile vision enCoders (VCoder) as perception eyes for Multimodal LLMs. We feed the VCoder with perception modalities such as segmentation or depth maps, improving the MLLM's perception abilities. Secondly, we leverage the images from COCO and outputs from off-the-shelf vision perception models to create our COCO Segmentation Text (COST) dataset for training and evaluating MLLMs on the object perception task. Thirdly, we introduce metrics to assess the object perception abilities in MLLMs on our COST dataset. Lastly, we provide extensive experimental evidence proving the VCoder's improved object-level perception skills over existing Multimodal LLMs, including GPT-4V. We open-source our dataset, code, and models to promote research. We open-source our code at https://github.com/SHI-Labs/VCoder

Human perception of similarity across uni- and multimodal inputs is highly complex, making it challenging to develop automated metrics that accurately mimic it. General purpose vision-language models, such as CLIP and large multi-modal models (LMMs), can be applied as zero-shot perceptual metrics, and several recent works have developed models specialized in narrow perceptual tasks. However, the extent to which existing perceptual metrics align with human perception remains unclear. To investigate this question, we introduce UniSim-Bench, a benchmark encompassing 7 multi-modal perceptual similarity tasks, with a total of 25 datasets. Our evaluation reveals that while general-purpose models perform reasonably well on average, they often lag behind specialized models on individual tasks. Conversely, metrics fine-tuned for specific tasks fail to generalize well to unseen, though related, tasks. As a first step towards a unified multi-task perceptual similarity metric, we fine-tune both encoder-based and generative vision-language models on a subset of the UniSim-Bench tasks. This approach yields the highest average performance, and in some cases, even surpasses taskspecific models. Nevertheless, these models still struggle with generalization to unseen tasks, highlighting the ongoing challenge of learning a robust, unified perceptual similarity metric capable of capturing the human notion of similarity. The code and models are available at https://github.com/SaraGhazanfari/UniSim.

Recent advances in vision-language models (VLMs) emphasize long chain-of-thought reasoning; yet, we find that their performance on visual tasks is primarily limited by a lack of visual perception as opposed to reasoning itself. In this work, we systematically study the interplay between perception and reasoning in VLM post-training by decomposing their capabilities into three separate training stages: visual perception, visual reasoning, and textual reasoning, incorporating specialized training data. We demonstrate that visual perception (a) requires targeted optimization with specialized data; (b) serves as a fundamental scaffold that should be solidified through staged training before refining visual reasoning; and (c) is more effectively learned via RL than caption-based SFT. Our experiments across multiple VLMs demonstrate that staged training consistently improves both visual perception and reasoning performance over merged training. Notably, models trained with our approach achieve 1.5% higher reasoning accuracy with 20.8% shorter reasoning traces, suggesting that superior perception reduces the need for excessive reasoning. Furthermore, we show that this capability-based staging represents a new curriculum dimension orthogonal to traditional difficulty-based curricula, and combining both yields further additive gains. Our staged-training models achieve superior performance among open-weight VLMs, establishing advanced results on several visual math and perception (e.g., +5.2% on WeMath and +3.7% on RealWorldQA) tasks compared with the base counterpart.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

Reasoning about the 3D world from multi-view images remains a fundamental challenge for Multimodal Large Language Models (MLLMs). While modern MLLMs handle single-image inputs effectively, they struggle to integrate evidence across viewpoints into a coherent 3D understanding. A growing body of work attempts to close this gap by injecting 3D awareness into MLLMs, either by boosting fine-grained pixel-level cross-view correspondence or by fusing features from 3D geometry foundation models, yet a substantial gap to human reasoning persists. In this work, we revisit human spatial reasoning, which suggests that rather than relying on fine-grained geometry cues, humans roughly identify common objects across views, infer the relative geometry between viewpoints, and assemble a coarse 3D layout of the scene. Inspired by this process, we introduce Imagine3D-LLM, an MLLM that learns to assemble a similar compact 3D representation of the scene and conditions its answer on this representation. Concretely, we append a small set of learnable summary tokens after the image tokens, decode them into a compact 3D Gaussian Splatting representation supervised by a photometric reconstruction loss, and train jointly with the standard next-token prediction objective. Notably, although only the summary tokens receive direct reconstruction supervision, this objective also induces stronger cross-frame correspondence within the LLM's underlying image features, suggesting that learning to reconstruct propagates 3D-aware signals throughout the model. As a result, Imagine3D-LLM consistently outperforms prior approaches across multiple spatial reasoning and 3D understanding benchmarks, suggesting that imagining the scene can be more effective than being told its pixel-wise geometry.

We present a central-peripheral vision-inspired framework (CVP), a simple yet effective multimodal model for spatial reasoning that draws inspiration from the two types of human visual fields -- central vision and peripheral vision. Existing approaches primarily rely on unstructured representations, such as point clouds, voxels, or patch features, and inject scene context implicitly via coordinate embeddings. However, this often results in limited spatial reasoning capabilities due to the lack of explicit, high-level structural understanding. To address this limitation, we introduce two complementary components into a Large Multimodal Model-based architecture: target-affinity token, analogous to central vision, that guides the model's attention toward query-relevant objects; and allocentric grid, akin to peripheral vision, that captures global scene context and spatial arrangements. These components work in tandem to enable structured, context-aware understanding of complex 3D environments. Experiments show that CVP achieves state-of-the-art performance across a range of 3D scene understanding benchmarks.

Across scientific domains, empirical data often give rise to positive semidefinite matrices that encode similarities, couplings or interactions and induce natural geometries. We investigate whether changing the geometry used to compare the same empirical representations preserves subject-level performance and the local structures from which explanations are derived, a question we term the prediction explanation invariance problem. We address this problem across morphometric MRI, fMRI and EEG data by comparing Frobenius and trace geometries applied to the same empirical matrices. Predictive performance was broadly preserved across geometries, but comparable performance did not imply agreement in subject-level decision scores or predicted labels. Predictive similarity also masked geometry-dependent differences in local neighbourhoods, perturbation sensitivities and explanatory rankings. Dimensionality reduction made the two subject-space geometries progressively more concordant, while classification performance and decision-level agreement declined. These results identify data geometry as a hidden degree of freedom in explainability: similar performance does not guarantee invariant decisions or explanations.

A core aspect of human perception is situated awareness, the ability to relate ourselves to the surrounding physical environment and reason over possible actions in context. However, most existing benchmarks for multimodal foundation models (MFMs) emphasize environment-centric spatial relations (relations among objects in a scene), while largely overlooking observer-centric relationships that require reasoning relative to agent's viewpoint, pose, and motion. To bridge this gap, we introduce SAW-Bench (Situated Awareness in the Real World), a novel benchmark for evaluating egocentric situated awareness using real-world videos. SAW-Bench comprises 786 self-recorded videos captured with Ray-Ban Meta (Gen 2) smart glasses spanning diverse indoor and outdoor environments, and over 2,071 human-annotated question-answer pairs. It probes a model's observer-centric understanding with six different awareness tasks. Our comprehensive evaluation reveals a human-model performance gap of 37.66%, even with the best-performing MFM, Gemini 3 Flash. Beyond this gap, our in-depth analysis uncovers several notable findings; for example, while models can exploit partial geometric cues in egocentric videos, they often fail to infer a coherent camera geometry, leading to systematic spatial reasoning errors. We position SAW-Bench as a benchmark for situated spatial intelligence, moving beyond passive observation to understanding physically grounded, observer-centric dynamics.

Hyperbolic vision-language models are designed to encode abstraction geometrically: general concepts near the origin, specific ones farther out, and entailment cones representing directed order. We ask whether trained MERU, HyCoCLIP, and PHyCLIP models actually use these mechanisms. We audit seven released checkpoints and matched from-scratch interventions, using diagnostics that distinguish active hyperbolic geometry from angular structure and supervision effects. All audited converged checkpoints remain near-Euclidean in the dimensionless radius u=cρ, which measures how strongly embeddings experience hyperbolic geometry: the largest observed image-side value is 0.37 -- well below uapprox0.84, where local metric distortion reaches 10%. Releasing the curvature floor changes curvature and norms but not this regime, with mixed, generally modest downstream shifts. Trained entailment cones are saturated or nearly saturated, so low violation rates can arise from trivially wide cones rather than learned order. Preregistered semantic traversal detects weak within-branch order but no operative full-hierarchy readout. Shuffle-controlled tests detect no pair-specific radial ordering in released checkpoints, and no positive result is consistent across all three matched ViT-B seeds. We trace this to a low-curvature shortcut: lowering curvature widens entailment cones and suppresses violations without learning order. In the probed trajectories, gradient decomposition identifies entailment as the dominant curvature-lowering pressure during collapse. Yet curvature contracts even when entailment is removed, so the shortcut is not the sole cause. Under our diagnostics, the audited formulations do not demonstrate an operative radial or cone-based hierarchy. We distill the audit into a five-number geometry report for evaluating future hierarchy claims.

Feedforward 3D reconstruction has largely followed an {appearance-driven paradigm}: multi-view images are encoded into visual representations, cross-view correspondence is implicitly inferred from learned features, and 3D primitives are subsequently predicted from these representations. However, calibrated cameras and sparse metric measurements already provide explicit constraints on where the same physical point should appear across views. We propose a novel paradigm, Geometry-Conditioned Feedforward Reconstruction, in which metric geometry establishes cross-view correspondence before the 3D representation is formed, while learned visual features refine rather than discover this correspondence. Based on this paradigm, we introduce GeoForward. Sparse LiDAR points are unprojected into 3D and analytically projected across calibrated cameras to provide metric correspondence anchors. A bounded continuous local search then refines these anchors using visual features, and the resulting geometry-conditioned representation is fused with global multi-view context from VGGT. The shared representation drives separate metric-depth and Gaussian-attribute prediction, establishing a direct path from explicit geometry to both Gaussian centers and spatial attributes. A sparse 3D refinement module subsequently improves local attribute compatibility while preserving the geometrically determined centers. For temporal reconstruction, endpoint Gaussians are composed using vehicle masks and motion priors. On nuScenes, GeoForward achieves the lowest cross-camera depth-consistency error and Chamfer distance among the compared methods while maintaining competitive reconstruction quality. These results demonstrate that explicitly conditioning correspondence formation on metric geometry provides an effective alternative to purely appearance-driven feedforward 3D reconstruction.

Spatial reasoning is a fundamental capability for vision-language models (VLMs) deployed in real-world environments. However, visual observations are inherently limited representations of a 3D world: occlusion can render objects invisible, and perspective can make geometric properties misleading. Despite this, existing spatial reasoning benchmarks typically assume that observations are sufficient and reliable, focusing on whether models produce correct answers rather than whether they recognize when a question cannot be answered and what additional observations would be needed. In this work, we challenge this assumption by constructing a controlled evaluation framework, SpatialUncertain, and introducing two types of observation challenges: (1) occlusion, which hides target information, and (2) perspective ambiguity, which produces misleading visual cues. For each configuration, we design spatial questions that are answerable under clean observations but require abstention under the introduced challenges. We further evaluate whether models can identify which additional viewpoints would resolve perspective ambiguity. Our results across a diverse set of frontier open- and closed-source VLMs reveal two consistent failure modes. First, models are prone to overconfident answering, attempting to solve spatial reasoning tasks even when visual evidence is incomplete or misleading, with average accuracy around 30\% under occlusion and below 10\% under perspective ambiguity. Second, even when additional views are available, some models perform near random chance in identifying which would provide reliable evidence. Together, our findings call for moving beyond answer correctness toward evaluating whether models know when to abstain and how to seek reliable evidence.

Multimodal large language models (MLLMs) often struggle to ground reasoning in perceptual evidence. We present a systematic study of perception strategies-explicit, implicit, visual, and textual-across four multimodal benchmarks and two MLLMs. Our findings show that explicit perception, especially when paired with textual cues, consistently yields the best improvements, particularly for smaller models. Based on this insight, we propose VTPerception-R1, a unified two-stage framework that decouples perception from reasoning. Stage 1 introduces perception-augmented fine-tuning, and Stage 2 applies perception-aware reinforcement learning with novel visual, textual, and consistency rewards. Experiments demonstrate that VTPerception-R1 significantly improves reasoning accuracy and robustness across diverse tasks, offering a scalable and auditable solution for perception-grounded multimodal reasoning. Our code is available at: https://github.com/yizhuoDi/VTPerceprion-R1.

Unsupervised learning for geometric perception (depth, optical flow, etc.) is of great interest to autonomous systems. Recent works on unsupervised learning have made considerable progress on perceiving geometry; however, they usually ignore the coherence of objects and perform poorly under scenarios with dark and noisy environments. In contrast, supervised learning algorithms, which are robust, require large labeled geometric dataset. This paper introduces SIGNet, a novel framework that provides robust geometry perception without requiring geometrically informative labels. Specifically, SIGNet integrates semantic information to make depth and flow predictions consistent with objects and robust to low lighting conditions. SIGNet is shown to improve upon the state-of-the-art unsupervised learning for depth prediction by 30% (in squared relative error). In particular, SIGNet improves the dynamic object class performance by 39% in depth prediction and 29% in flow prediction. Our code will be made available at https://github.com/mengyuest/SIGNet

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

Recent advances in inference-time scaling, particularly those leveraging reinforcement learning with verifiable rewards, have substantially enhanced the reasoning capabilities of Large Vision-Language Models (LVLMs). Inspired by this success, similar strategies have been applied to multimodal reasoning, yet their impact on visual perception remains unclear. To investigate this gap, we introduce DisTANCE, a perception-centric benchmark for visual estimation tasks. Evaluation results show that LVLMs exhibit limited estimation precision, and inference-time scaling offers only marginal gains. We attribute this to the fast perception paradigm of current LVLMs, where visual understanding is treated as a one-shot output without modeling the underlying perceptual process. To address this, we propose Perception-Time Scaling (PTS), a novel paradigm that encourages token-rich perception and decomposes complex perception problems into intermediate tractable sub-problems, thereby enabling perception to align with and benefit from inference-time scaling. Combined with reinforcement learning techniques, PTS significantly improves perception accuracy, raising high-precision performance on DisTANCE from 8.0% to 64.7%, and generalizes well to out-of-domain tasks. Surprisingly, even though PTS data are purely synthetic, combining them with math reasoning data yields consistent gains in both reasoning and real-world perception benchmarks. Further analysis reveals that PTS introduces more perception-related tokens and increases the model's attention to image tokens. Our code and data will be publicly released.

Recent advances in multimodal large language models (MLLMs) have yielded increasingly powerful models, yet their perceptual capacities remain poorly characterized. In practice, most model families scale language component while reusing nearly identical vision encoders (e.g., Qwen2.5-VL 3B/7B/72B), which raises pivotal concerns about whether progress reflects genuine visual grounding or reliance on internet-scale textual world knowledge. Existing evaluation methods emphasize end-task accuracy, overlooking robustness, attribution fidelity, and reasoning under controlled perturbations. We present The Perceptual Observatory, a framework that characterizes MLLMs across verticals like: (i) simple vision tasks, such as face matching and text-in-vision comprehension capabilities; (ii) local-to-global understanding, encompassing image matching, grid pointing game, and attribute localization, which tests general visual grounding. Each vertical is instantiated with ground-truth datasets of faces and words, systematically perturbed through pixel-based augmentations and diffusion-based stylized illusions. The Perceptual Observatory moves beyond leaderboard accuracy to yield insights into how MLLMs preserve perceptual grounding and relational structure under perturbations, providing a principled foundation for analyzing strengths and weaknesses of current and future models.

Vision-language models (VLM) excel at general understanding yet remain weak at dynamic spatial reasoning (DSR), i.e., reasoning about the evolvement of object geometry and relationship in 3D space over time, largely due to the scarcity of scalable 4D-aware training resources. To bridge this gap across aspects of dataset, benchmark and model, we introduce DSR Suite. First, we propose an automated pipeline that generates multiple-choice question-answer pairs from in-the-wild videos for DSR. By leveraging modern vision foundation models, the pipeline extracts rich geometric and motion information, including camera poses, local point clouds, object masks, orientations, and 3D trajectories. These geometric cues enable the construction of DSR-Train for learning and further human-refined DSR-Bench for evaluation. Compared with previous works, our data emphasize (i) in-the-wild video sources, (ii) object- and scene-level 3D requirements, (iii) viewpoint transformations, (iv) multi-object interactions, and (v) fine-grained, procedural answers. Beyond data, we propose a lightweight Geometry Selection Module (GSM) to seamlessly integrate geometric priors into VLMs, which condenses question semantics and extracts question-relevant knowledge from pretrained 4D reconstruction priors into a compact set of geometry tokens. This targeted extraction avoids overwhelming the model with irrelevant knowledge. Experiments show that integrating DSR-Train and GSM into Qwen2.5-VL-7B significantly enhances its dynamic spatial reasoning capability, while maintaining accuracy on general video understanding benchmarks.

Human perception is structured around objects which form the basis for our higher-level cognition and impressive systematic generalization abilities. Yet most work on representation learning focuses on feature learning without even considering multiple objects, or treats segmentation as an (often supervised) preprocessing step. Instead, we argue for the importance of learning to segment and represent objects jointly. We demonstrate that, starting from the simple assumption that a scene is composed of multiple entities, it is possible to learn to segment images into interpretable objects with disentangled representations. Our method learns -- without supervision -- to inpaint occluded parts, and extrapolates to scenes with more objects and to unseen objects with novel feature combinations. We also show that, due to the use of iterative variational inference, our system is able to learn multi-modal posteriors for ambiguous inputs and extends naturally to sequences.

Recently, polar-based representation has shown promising properties in perceptual tasks. In addition to Cartesian-based approaches, which separate point clouds unevenly, representing point clouds as polar grids has been recognized as an alternative due to (1) its advantage in robust performance under different resolutions and (2) its superiority in streaming-based approaches. However, state-of-the-art polar-based detection methods inevitably suffer from the feature distortion problem because of the non-uniform division of polar representation, resulting in a non-negligible performance gap compared to Cartesian-based approaches. To tackle this issue, we present PARTNER, a novel 3D object detector in the polar coordinate. PARTNER alleviates the dilemma of feature distortion with global representation re-alignment and facilitates the regression by introducing instance-level geometric information into the detection head. Extensive experiments show overwhelming advantages in streaming-based detection and different resolutions. Furthermore, our method outperforms the previous polar-based works with remarkable margins of 3.68% and 9.15% on Waymo and ONCE validation set, thus achieving competitive results over the state-of-the-art methods.

Visual perceptual tasks aim to predict human judgment of images (e.g., emotions invoked by images, image quality assessment). Unlike objective tasks such as object/scene recognition, perceptual tasks rely on subjective human assessments, making its data-labeling difficult. The scarcity of such human-annotated data results in small datasets leading to poor generalization. Typically, specialized models were designed for each perceptual task, tailored to its unique characteristics and its own training dataset. We propose a unified architectural framework for solving multiple different perceptual tasks leveraging CLIP as a prior. Our approach is based on recent cognitive findings which indicate that CLIP correlates well with human judgment. While CLIP was explicitly trained to align images and text, it implicitly also learned human inclinations. We attribute this to the inclusion of human-written image captions in CLIP's training data, which contain not only factual image descriptions, but inevitably also human sentiments and emotions. This makes CLIP a particularly strong prior for perceptual tasks. Accordingly, we suggest that minimal adaptation of CLIP suffices for solving a variety of perceptual tasks. Our simple unified framework employs a lightweight adaptation to fine-tune CLIP to each task, without requiring any task-specific architectural changes. We evaluate our approach on three tasks: (i) Image Memorability Prediction, (ii) No-reference Image Quality Assessment, and (iii) Visual Emotion Analysis. Our model achieves state-of-the-art results on all three tasks, while demonstrating improved generalization across different datasets.

Despite their success, modern convolutional neural networks (CNNs) exhibit fundamental limitations, including data inefficiency, poor out-of-distribution generalization, and vulnerability to adversarial perturbations. These shortcomings can be traced to a lack of inductive biases that reflect the inherent geometric structure of the visual world. The primate visual system, in contrast, demonstrates superior efficiency and robustness, suggesting that its architectural and computational principles,which evolved to internalize these structures,may offer a blueprint for more capable artificial vision. This paper introduces Visual Cortex Network (VCNet), a novel neural network architecture whose design is informed by the macro-scale organization of the primate visual cortex. VCNet is framed as a geometric framework that emulates key biological mechanisms, including hierarchical processing across distinct cortical areas, dual-stream information segregation for learning disentangled representations, and top-down predictive feedback for representation refinement. We interpret these mechanisms through the lens of geometry and dynamical systems, positing that they guide the learning of structured, low-dimensional neural manifolds. We evaluate VCNet on two specialized benchmarks: the Spots-10 animal pattern dataset, which probes sensitivity to natural textures, and a light field image classification task, which requires processing higher-dimensional visual data. Our results show that VCNet achieves state-of-the-art accuracy of 92.1\% on Spots-10 and 74.4\% on the light field dataset, surpassing contemporary models of comparable size. This work demonstrates that integrating high-level neuroscientific principles, viewed through a geometric lens, can lead to more efficient and robust models, providing a promising direction for addressing long-standing challenges in machine learning.

Vision-language models (VLMs) can benefit from geometric priors for multi-view spatial reasoning, yet answer-only training does not directly supervise the intermediate geometric estimates and their use in deriving quantitative spatial answers. We hypothesize that spatial chain-of-thought (CoT) supervision becomes more effective when the VLM first jointly learns complementary local geometry and global scene context through multi-view reconstruction. We introduce SpatialSpeak, a two-stage framework that connects QA-native reconstruction pretraining with spatial CoT learning. In Stage I, QA-Native Reconstruction Pretraining (QA-RP) combines marked-point 3D queries for fine-grained local geometry with object-center queries for global scene context across views. Both tasks are formulated as text-based question answering, allowing geometric estimation and subsequent reasoning to share the same autoregressive output interface. In Stage II, spatial CoT with Visual Compensation (CoT-VC) trains the model to express question-relevant geometric estimates and use them to derive answers, with reliability assessment and visual compensation supporting answer refinement when needed. On ReVSI, QA-RP increases the gain from CoT-VC from 2.6 to 6.9 points, and ablations show that both local and global reconstruction supervision are beneficial. SpatialSpeak achieves state-of-the-art results on ReVSI, VSI-Bench, and SPAR-Bench, with a ReVSI score of 62.8 that exceeds the strongest compared baseline by 8.7 points.

Visual world models increasingly support spatial reasoning by generating RGB views of unobserved states. However, RGB has become the default interface largely because it is well suited for visual generation, rather than necessarily being the most effective representation for downstream reasoning. Different spatial questions may benefit from different representations of the same imagined state: top-down geometry can facilitate global distance comparisons, while panoramic views provide broader context for reasoning about open space. To isolate the role of representation in spatial imagination, we introduce ImagiRep, a simulator-grounded benchmark of 922 questions spanning seven question types across two settings, Viewpoint Imagination and Cross-view Integration, providing oracle RGB and six alternative representations (e.g., depth, panoramic views, and top-down geometry) of the same unobserved state. This controlled comparison reveals that even accurate imagined RGB does not guarantee accurate spatial reasoning, and different questions benefit from different representations. Similar trends hold for representations derived from world-model-estimated states. Notably, estimated RGB alone can mislead spatial reasoning, while alternative representations retain complementary benefits. Building on these findings, we introduce GEARS, a lightweight test-time strategy for adaptive representation selection, outperforming existing spatial imagination methods and showing that reasoning about unseen states requires more than generating RGB views.

Video spatial reasoning requires accumulating viewpoint-dependent evidence over time while retaining information useful to the question being asked. Existing spatial video-language models improve geometric perception and long-range context modeling, but often treat memory as a generic temporal cache, which can introduce redundant or irrelevant geometry and weaken long-horizon reasoning. We propose \ours, a question-guided geometric memory framework for video spatial reasoning. \ours injects camera-conditioned geometry into visual tokens and maintains two complementary memories: a Fine-Grained Context Bank for recent dense features and camera states, and a Semantic-Geometric Evidence Bank for compact long-range evidence. Each candidate frame is scored by the product of Q-Former-based question relevance and novelty with respect to the retained bank; this score is stored and reused during reading, while a capacity-based replacement rule keeps the bank compact. During reasoning, both memories are read before update and adaptively fused with the current frame representation. Experiments on VSI-Bench and VSTI-Bench show that \ours achieves state-of-the-art performance among evaluated spatial reasoning models, validating the effectiveness of question-guided geometric memory. Ablations further verify the contribution of the proposed evidence scoring mechanism.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks. Our data and code are available at Geoparsing.

The primal sketch is a fundamental representation in Marr's vision theory, which allows for parsimonious image-level processing from 2D to 2.5D perception. This paper takes a further step by computing 3D primal sketch of wireframes from a set of images with known camera poses, in which we take the 2D wireframes in multi-view images as the basis to compute 3D wireframes in a volumetric rendering formulation. In our method, we first propose a NEural Attraction (NEAT) Fields that parameterizes the 3D line segments with coordinate Multi-Layer Perceptrons (MLPs), enabling us to learn the 3D line segments from 2D observation without incurring any explicit feature correspondences across views. We then present a novel Global Junction Perceiving (GJP) module to perceive meaningful 3D junctions from the NEAT Fields of 3D line segments by optimizing a randomly initialized high-dimensional latent array and a lightweight decoding MLP. Benefitting from our explicit modeling of 3D junctions, we finally compute the primal sketch of 3D wireframes by attracting the queried 3D line segments to the 3D junctions, significantly simplifying the computation paradigm of 3D wireframe parsing. In experiments, we evaluate our approach on the DTU and BlendedMVS datasets with promising performance obtained. As far as we know, our method is the first approach to achieve high-fidelity 3D wireframe parsing without requiring explicit matching.