Daily Papers

Large language models (LLMs) achieve remarkable performance through ever-increasing parameter counts, but scaling incurs steep computational costs. To better understand LLM scaling, we study representational differences between LLMs and their smaller counterparts, with the goal of replicating the representational qualities of larger models in the smaller models. We observe a geometric phenomenon which we term embedding condensation, where token embeddings collapse into a narrow cone-like subspace in some language models. Through systematic analyses across multiple Transformer families, we show that small models such as GPT2 and Qwen3-0.6B exhibit severe condensation, whereas the larger models such as GPT2-xl and Qwen3-32B are more resistant to this phenomenon. Additional observations show that embedding condensation is not reliably mitigated by knowledge distillation from larger models. To fight against it, we formulate a dispersion loss that explicitly encourages embedding dispersion during training. Experiments demonstrate that it mitigates condensation, recovers dispersion patterns seen in larger models, and yields performance gains across 10 benchmarks. We believe this work offers a principled path toward improving smaller Transformers without additional parameters.

The great success of machine learning with massive amounts of data comes at a price of huge computation costs and storage for training and tuning. Recent studies on dataset condensation attempt to reduce the dependence on such massive data by synthesizing a compact training dataset. However, the existing approaches have fundamental limitations in optimization due to the limited representability of synthetic datasets without considering any data regularity characteristics. To this end, we propose a novel condensation framework that generates multiple synthetic data with a limited storage budget via efficient parameterization considering data regularity. We further analyze the shortcomings of the existing gradient matching-based condensation methods and develop an effective optimization technique for improving the condensation of training data information. We propose a unified algorithm that drastically improves the quality of condensed data against the current state-of-the-art on CIFAR-10, ImageNet, and Speech Commands.

Diffusion models have achieved remarkable performance on a wide range of generative tasks, yet training them from scratch is notoriously resource-intensive, typically requiring millions of training images and many GPU days. Motivated by a data-centric view of this bottleneck, we adopt a condensation-based perspective: given a large training set, the goal is to construct a much smaller condensed dataset that still supports training strong diffusion models under minimal data and compute budgets. To operationalize this perspective, we introduce Diffusion Dataset Condensation (D2C), a two-phase framework comprising Select and Attach. In the Select phase, a diffusion difficulty score combined with interval sampling is used to identify a compact, informative training subset from the original data. Building on this subset, the Attach phase further strengthens the conditional signals by augmenting each selected image with rich semantic and visual representations. To our knowledge, D2C is the first framework that systematically investigates dataset condensation for diffusion models, whereas prior condensation methods have mainly targeted discriminative architectures. Extensive experiments across data budgets (0.8%-8% of ImageNet), model architectures, and image resolutions demonstrate that D2C dramatically accelerates diffusion model training while preserving high generative quality. On ImageNet 256x256 with SiT-XL/2, D2C attains an FID of 4.3 in just 40k steps using only 0.8% of the training images, corresponding to about 233x and 100x faster training than vanilla SiT-XL/2 and SiT-XL/2 + REPA, respectively.

Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset. As the size of datasets contemporary machine learning models rely on becomes increasingly large, condensation methods become a prominent direction for accelerating network training and reducing data storage. Despite numerous methods have been proposed in this rapidly growing field, evaluating and comparing different condensation methods is non-trivial and still remains an open issue. The quality of condensed dataset are often shadowed by many critical contributing factors to the end performance, such as data augmentation and model architectures. The lack of a systematic way to evaluate and compare condensation methods not only hinders our understanding of existing techniques, but also discourages practical usage of the synthesized datasets. This work provides the first large-scale standardized benchmark on Dataset Condensation. It consists of a suite of evaluations to comprehensively reflect the generability and effectiveness of condensation methods through the lens of their generated dataset. Leveraging this benchmark, we conduct a large-scale study of current condensation methods, and report many insightful findings that open up new possibilities for future development. The benchmark library, including evaluators, baseline methods, and generated datasets, is open-sourced to facilitate future research and application.

Embeddings have emerged as a standard representational interface linking foundation models with downstream systems. Most embedding benchmarks assess representations through discriminative tasks or geometric criteria centered on separability in embedding space. However, strong performance on such evaluations does not establish whether content compressed into an embedding remains accessible to a downstream generator. To address this gap, we introduce the Generative Embedding Benchmark (GEB), in which a decoder answers questions using only a frozen embedding and question text, without access to the original image or intermediate visual features. Answer quality under this readout measures generative information: the answer-relevant content recoverable from an embedding. GEB includes a curated visual-question-answering dataset with a 1,800-item development split and a held-out 900-item test split covering natural images, scene text, and visual documents. Using a common decoder and training recipe, we evaluate seven public embedding models in visual-only and vision-language joint modes. On the test set, visual-only scores range from 28.25 to 33.21; with image-question joint encoding, all five VLM-based embedding models score higher, and the best reaches 65.56. Matched embeddings also outperform text-only inputs, zero embeddings, and shuffled embeddings. Natural-image information is much easier to recover than scene text or visual-document information, while a Qwen3-VL-2B reference with access to the original image reaches 84.30. Together, these results show that generative readout exposes information bottlenecks that separability-based evaluation does not capture.

While dataset condensation effectively enhances training efficiency, its application in on-device scenarios brings unique challenges. 1) Due to the fluctuating computational resources of these devices, there's a demand for a flexible dataset size that diverges from a predefined size. 2) The limited computational power on devices often prevents additional condensation operations. These two challenges connect to the "subset degradation problem" in traditional dataset condensation: a subset from a larger condensed dataset is often unrepresentative compared to directly condensing the whole dataset to that smaller size. In this paper, we propose Multisize Dataset Condensation (MDC) by compressing N condensation processes into a single condensation process to obtain datasets with multiple sizes. Specifically, we introduce an "adaptive subset loss" on top of the basic condensation loss to mitigate the "subset degradation problem". Our MDC method offers several benefits: 1) No additional condensation process is required; 2) reduced storage requirement by reusing condensed images. Experiments validate our findings on networks including ConvNet, ResNet and DenseNet, and datasets including SVHN, CIFAR-10, CIFAR-100 and ImageNet. For example, we achieved 6.40% average accuracy gains on condensing CIFAR-10 to ten images per class. Code is available at: https://github.com/he-y/Multisize-Dataset-Condensation.

We introduce EmbeddingGemma, a new lightweight, open text embedding model based on the Gemma 3 language model family. Our innovative training recipe strategically captures knowledge from larger models via encoder-decoder initialization and geometric embedding distillation. We improve model robustness and expressiveness with a spread-out regularizer, and ensure generalizability by merging checkpoints from varied, optimized mixtures. Evaluated on the Massive Text Embedding Benchmark (MTEB) across multilingual, English, and code domains, EmbeddingGemma (300M) achieves state-of-the-art results. Notably, it outperforms prior top models, both proprietary and open, with fewer than 500M parameters, and provides performance comparable to models double its size, offering an exceptional performance-to-cost ratio. Remarkably, this lead persists when quantizing model weights or truncating embedding outputs. This makes EmbeddingGemma particularly well-suited for low-latency and high-throughput use cases such as on-device applications. We provide ablation studies exploring our key design choices. We release EmbeddingGemma to the community to promote further research.

Dataset Condensation (DC) aims to obtain a condensed dataset that allows models trained on the condensed dataset to achieve performance comparable to those trained on the full dataset. Recent DC approaches increasingly focus on encoding knowledge into realistic images with soft labeling, for their scalability to ImageNet-scale datasets and strong capability of cross-domain generalization. However, this strong performance comes at a substantial storage cost which could significantly exceed the storage cost of the original dataset. We argue that the three key properties to alleviate this performance-storage dilemma are informativeness, discriminativeness, and compressibility of the condensed data. Towards this end, this paper proposes a Soft label compression-centric dataset condensation framework using COding RatE (SCORE). SCORE formulates dataset condensation as a min-max optimization problem, which aims to balance the three key properties from an information-theoretic perspective. In particular, we theoretically demonstrate that our coding rate-inspired objective function is submodular, and its optimization naturally enforces low-rank structure in the soft label set corresponding to each condensed data. Extensive experiments on large-scale datasets, including ImageNet-1K and Tiny-ImageNet, demonstrate that SCORE outperforms existing methods in most cases. Even with 30times compression of soft labels, performance decreases by only 5.5\% and 2.7\% for ImageNet-1K with IPC 10 and 50, respectively. Code will be released upon paper acceptance.

High-fidelity 3D generation predominantly relies on scaling model capacity and data, which incurs prohibitive computational costs. This paradigm typically requires learning geometry from scratch and overlooks the rich semantic and structural priors already encapsulated in discriminative 3D foundation models. We contend that leveraging the profound understanding of the 3D world possessed by these discriminative models can significantly reduce generative cost. To this end, we propose ROAD, a framework that reduces the training cost of 3D generation by transferring these rich discriminative priors into diffusion transformers. To address the inherent semantic-structural heterogeneity between generative and discriminative latents, we introduce a reciprocal-objective alignment strategy. This method synergizes Holistic Semantic Condensing to enforce global semantic coherence and Structural Optimal Alignment, which is formulated as a bipartite matching problem to rigorously align microscopic geometric details between disparate latent spaces. The 3D foundation model is only used for training-time supervision of alignment and is not used at inference, incurring no additional inference cost. Compared with the industrial baseline Step1X-3D, the proposed ROAD achieves highly competitive generation performance with only 1.5% of the training data and significantly reduces training costs, effectively reducing the computational overhead of high-fidelity 3D generation. Code is available at https://github.com/H-EmbodVis/ROAD.

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-the-art performance when applied to data-efficient learning tasks. However, in this study, we prove that the existing DC methods can perform worse than the random selection method when task-irrelevant information forms a significant part of the training dataset. We attribute this to the lack of participation of the contrastive signals between the classes resulting from the class-wise gradient matching strategy. To address this problem, we propose Dataset Condensation with Contrastive signals (DCC) by modifying the loss function to enable the DC methods to effectively capture the differences between classes. In addition, we analyze the new loss function in terms of training dynamics by tracking the kernel velocity. Furthermore, we introduce a bi-level warm-up strategy to stabilize the optimization. Our experimental results indicate that while the existing methods are ineffective for fine-grained image classification tasks, the proposed method can successfully generate informative synthetic datasets for the same tasks. Moreover, we demonstrate that the proposed method outperforms the baselines even on benchmark datasets such as SVHN, CIFAR-10, and CIFAR-100. Finally, we demonstrate the high applicability of the proposed method by applying it to continual learning tasks.

Adapting decoder-only multimodal large language models (MLLMs) for unified multimodal retrieval faces two structural gaps. First, existing methods rely on implicit pooling, which overloads the hidden state of a standard vocabulary token (e.g., <EOS>) as the sequence-level representation, a mechanism never designed for information aggregation. Second, contrastive fine-tuning specifies what the embedding should match but provides no token-level guidance on how information should be compressed into it. We address both gaps with two complementary components. Architecturally, we introduce Bottleneck Tokens (BToks), a small set of learnable tokens that serve as a fixed-capacity explicit pooling mechanism. For training, we propose Generative Information Condensation: a next-token prediction objective coupled with a Condensation Mask that severs the direct attention path from target tokens to query tokens. All predictive signals are thereby forced through the BToks, converting the generative loss into dense, token-level supervision for semantic compression. At inference time, only the input and BToks are processed in a single forward pass with negligible overhead over conventional last-token pooling. On MMEB-V2 (78 datasets, 3 modalities, 9 meta-tasks), our approach achieves state-of-the-art among 2B-scale methods under comparable data conditions, attaining an Overall score of 59.0 (+3.6 over VLM2Vec-V2) with substantial gains on semantically demanding tasks (e.g., +12.6 on Video-QA).

Behavioral patterns captured in embeddings learned from interaction data are pivotal across various stages of production recommender systems. However, in the initial retrieval stage, practitioners face an inherent tradeoff between embedding expressiveness and the scalability and latency of serving components, resulting in the need for representations that are both compact and expressive. To address this challenge, we propose a training strategy for learning high-dimensional sparse embedding layers in place of conventional dense ones, balancing efficiency, representational expressiveness, and interpretability. To demonstrate our approach, we modified the production-grade collaborative filtering autoencoder ELSA, achieving up to 10x reduction in embedding size with no loss of recommendation accuracy, and up to 100x reduction with only a 2.5% loss. Moreover, the active embedding dimensions reveal an interpretable inverted-index structure that segments items in a way directly aligned with the model's latent space, thereby enabling integration of segment-level recommendation functionality (e.g., 2D homepage layouts) within the candidate retrieval model itself. Source codes, additional results, as well as a live demo are available at https://github.com/zombak79/compressed_elsa

Text embedding models are widely used for semantic similarity tasks, including information retrieval, clustering, and classification. General-purpose models are typically trained with single- or multi-stage processes using contrastive loss functions. We introduce a novel training regimen that combines model distillation techniques with task-specific contrastive loss to produce compact, high-performance embedding models. Our findings suggest that this approach is more effective for training small models than purely contrastive or distillation-based training paradigms alone. Benchmark scores for the resulting models, jina-embeddings-v5-text-small and jina-embeddings-v5-text-nano, exceed or match the state-of-the-art for models of similar size. jina-embeddings-v5-text models additionally support long texts (up to 32k tokens) in many languages, and generate embeddings that remain robust under truncation and binary quantization. Model weights are publicly available, hopefully inspiring further advances in embedding model development.

Joint-Embedding Predictive Architectures (JEPAs) provide a simpleframework for learning world models by predicting future latent representations.However, JEPA training is subject to a bias-variance tradeoff.Without sufficient structural constraints, excessive representationalvariance causes the model to collapse to trivial solutions.The recent LeWorldModel (LeWM) shows that this issue can be alleviated bysimply constraining latent embeddings with an isotropic Gaussian prior.However, latent representations inherently lie on low-dimensional manifoldswithin a high-dimensional ambient space, and enforcing an isotropic Gaussianprior directly in this ambient space introduces an overly strong bias.In this work, we propose ame, which seeks a favorable operatingpoint on the bias-variance frontier by applying Gaussian constraints inmultiple random subspaces rather than in the originalembedding space.This design relaxes the global constraint while preserving itsanti-collapse effect, leading to a better balance between trainingstability and representation flexibility.Extensive experiments across fourcontinuous-control environments demonstrate that consistentlyoutperforms LeWM with very clear margins.Our method is simple yet effective, and serves as a strong baseline for future JEPA-based world model research.fdefinedeeemodeThe code is available at https://github.com/intcomp/Sub-JEPA.

We consider the problem of predicting how the likelihood of an outcome of interest for a patient changes over time as we observe more of the patient data. To solve this problem, we propose a supervised contrastive learning framework that learns an embedding representation for each time step of a patient time series. Our framework learns the embedding space to have the following properties: (1) nearby points in the embedding space have similar predicted class probabilities, (2) adjacent time steps of the same time series map to nearby points in the embedding space, and (3) time steps with very different raw feature vectors map to far apart regions of the embedding space. To achieve property (3), we employ a nearest neighbor pairing mechanism in the raw feature space. This mechanism also serves as an alternative to data augmentation, a key ingredient of contrastive learning, which lacks a standard procedure that is adequately realistic for clinical tabular data, to our knowledge. We demonstrate that our approach outperforms state-of-the-art baselines in predicting mortality of septic patients (MIMIC-III dataset) and tracking progression of cognitive impairment (ADNI dataset). Our method also consistently recovers the correct synthetic dataset embedding structure across experiments, a feat not achieved by baselines. Our ablation experiments show the pivotal role of our nearest neighbor pairing.

A crucial component of many deep learning applications (such as FAQ and RAG) is dense retrieval, in which embedding models are used to convert raw text to numerical vectors and then get the most similar text by MIPS (Maximum Inner Product Search). Some text embedding benchmarks (e.g. MTEB, BEIR, and AIR-Bench) have been established to evaluate embedding models accurately. Thanks to these benchmarks, we can use SOTA models; however, the deployment and application of these models in industry were hampered by their large vector dimensions and numerous parameters. To alleviate this problem, 1) we present a distillation technique that can enable a smaller student model to achieve good performance. 2) Inspired by MRL we present a training approach of reducing the vector dimensions based on its own vectors or its teacher vectors. 3) We do simple yet effective alignment training between images and text to make our model a multimodal encoder. We trained Stella and Jasper models using the technologies above and achieved high scores on the MTEB leaderboard. We release the model and data at Hugging Face Hub (https://huggingface.co/infgrad/jasper_en_vision_language_v1) and the training logs are at https://api.wandb.ai/links/dunnzhang0/z8jqoqpb.

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated training data tailored to a given setting, one may instead wish to learn useful information from heterogeneous sources, or from real dynamical systems observations that are messy or incomplete. In this work, we learn general-purpose representations of PDEs from heterogeneous data by implementing joint embedding methods for self-supervised learning (SSL), a framework for unsupervised representation learning that has had notable success in computer vision. Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs.

Despite plentiful successes achieved by graph representation learning in various domains, the training of graph neural networks (GNNs) still remains tenaciously challenging due to the tremendous computational overhead needed for sizable graphs in practice. Recently, graph data distillation (GDD), which seeks to distill large graphs into compact and informative ones, has emerged as a promising technique to enable efficient GNN training. However, most existing GDD works rely on heuristics that align model gradients or representation distributions on condensed and original graphs, leading to compromised result quality, expensive training for distilling large graphs, or both. Motivated by this, this paper presents an efficient and effective GDD approach, ClustGDD. Under the hood, ClustGDD resorts to synthesizing the condensed graph and node attributes through fast and theoretically-grounded clustering that minimizes the within-cluster sum of squares and maximizes the homophily on the original graph. The fundamental idea is inspired by our empirical and theoretical findings unveiling the connection between clustering and empirical condensation quality using Fréchet Inception Distance, a well-known quality metric for synthetic images. Furthermore, to mitigate the adverse effects caused by the homophily-based clustering, ClustGDD refines the nodal attributes of the condensed graph with a small augmentation learned via class-aware graph sampling and consistency loss. Our extensive experiments exhibit that GNNs trained over condensed graphs output by ClustGDD consistently achieve superior or comparable performance to state-of-the-art GDD methods in terms of node classification on five benchmark datasets, while being orders of magnitude faster.

Transformer architectures rely on explicit position encodings in order to preserve a notion of word order. In this paper, we argue that existing work does not fully utilize position information. For example, the initial proposal of a sinusoid embedding is fixed and not learnable. In this paper, we first review absolute position embeddings and existing methods for relative position embeddings. We then propose new techniques that encourage increased interaction between query, key and relative position embeddings in the self-attention mechanism. Our most promising approach is a generalization of the absolute position embedding, improving results on SQuAD1.1 compared to previous position embeddings approaches. In addition, we address the inductive property of whether a position embedding can be robust enough to handle long sequences. We demonstrate empirically that our relative position embedding method is reasonably generalized and robust from the inductive perspective. Finally, we show that our proposed method can be adopted as a near drop-in replacement for improving the accuracy of large models with a small computational budget.

Algorithmic efficiency techniques such as distillation (hinton2015distillation) are useful in improving model quality without increasing serving costs, provided a larger teacher model is available for a smaller student model to learn from during training. Standard distillation methods are limited to only forcing the student to match the teacher's outputs. Given the costs associated with training a large model, we believe we should be extracting more useful information from a teacher model than by just making the student match the teacher's outputs. In this paper, we introduce \guide (Guided Initialization and Distillation of Embeddings). \guide can be considered a distillation technique that forces the student to match the teacher in the parameter space. Using \guide we show 25-26\% reduction in the teacher-student quality gap when using large student models (400M - 1B parameters) trained on approx 20B tokens. We also present a thorough analysis demonstrating that \guide can be combined with knowledge distillation with near additive improvements. Furthermore, we show that applying \guide alone leads to substantially better model quality than applying knowledge distillation by itself. Most importantly, \guide introduces no training or inference overhead and hence any model quality gains from our method are virtually free.

Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph structure so that it can be easily exploited by machine learning models. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about a graph (e.g., degree statistics or kernel functions). However, recent years have seen a surge in approaches that automatically learn to encode graph structure into low-dimensional embeddings, using techniques based on deep learning and nonlinear dimensionality reduction. Here we provide a conceptual review of key advancements in this area of representation learning on graphs, including matrix factorization-based methods, random-walk based algorithms, and graph neural networks. We review methods to embed individual nodes as well as approaches to embed entire (sub)graphs. In doing so, we develop a unified framework to describe these recent approaches, and we highlight a number of important applications and directions for future work.

Self-supervised visual representation learning aims to learn useful representations without relying on human annotations. Joint embedding approach bases on maximizing the agreement between embedding vectors from different views of the same image. Various methods have been proposed to solve the collapsing problem where all embedding vectors collapse to a trivial constant solution. Among these methods, contrastive learning prevents collapse via negative sample pairs. It has been shown that non-contrastive methods suffer from a lesser collapse problem of a different nature: dimensional collapse, whereby the embedding vectors end up spanning a lower-dimensional subspace instead of the entire available embedding space. Here, we show that dimensional collapse also happens in contrastive learning. In this paper, we shed light on the dynamics at play in contrastive learning that leads to dimensional collapse. Inspired by our theory, we propose a novel contrastive learning method, called DirectCLR, which directly optimizes the representation space without relying on an explicit trainable projector. Experiments show that DirectCLR outperforms SimCLR with a trainable linear projector on ImageNet.

Compact models often lose the structure of their embedding space. The issue shows up when the capacity is tight or the data spans several languages. Such collapse makes it difficult for downstream tasks to build on the resulting representation. Existing compression methods focus on aligning model outputs at a superficial level but fail to preserve the underlying manifold structure. This mismatch often leads to semantic drift in the compact model, causing both task behavior and linguistic properties to deviate from the reference model. To address those issues, we provide a new framework called Embedding Consistency Regulation (ECR). This framework first derives a set of semantic anchors from teacher embeddings (computed once offline). Then, the compact model learns to maintain consistent geometry around these anchors, without relying on matching logits or internal features. ECR adds only a small projection step at inference, without altering the decoding architecture or its runtime behavior. In experiments on a 100K multilingual corpus, ECR consistently stabilizes training and preserves semantic structure across tasks and languages. It also produces a more compact and task-aligned representation space, enabling low-capacity models to learn cleaner manifolds than conventional baselines. ECR works without teacher outputs and is compatible with, but independent of, distillation. Taken together, our results show that ECR helps compact models better follow task requirements and makes them easier to deploy under strict efficiency or privacy limits.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

Incorporating spatial information, particularly those influenced by climate, weather, and demographic factors, is crucial for improving underwriting precision and enhancing risk management in insurance. However, spatial data are often unstructured, high-dimensional, and difficult to integrate into predictive models. Embedding methods are needed to convert spatial data into meaningful representations for modelling tasks. We propose a novel multi-view contrastive learning framework for generating spatial embeddings that combine information from multiple spatial data sources. To train the model, we construct a spatial dataset that merges satellite imagery and OpenStreetMap features across Europe. The framework aligns these spatial views with coordinate-based encodings, producing low-dimensional embeddings that capture both spatial structure and contextual similarity. Once trained, the model generates embeddings directly from latitude-longitude pairs, enabling any dataset with coordinates to be enriched with meaningful spatial features without requiring access to the original spatial inputs. In a case study on French real estate prices, we compare models trained on raw coordinates against those using our spatial embeddings as inputs. The embeddings consistently improve predictive accuracy across generalised linear, additive, and boosting models, while providing interpretable spatial effects and demonstrating transferability to unseen regions.

The increasing frequency of extreme weather events due to global climate change urges accurate weather prediction. Recently, great advances have been made by the end-to-end methods, thanks to deep learning techniques, but they face limitations of representation inconsistency in multivariable integration and struggle to effectively capture the dependency between variables, which is required in complex weather systems. Treating different variables as distinct modalities and applying a two-stage training approach from multimodal models can partially alleviate this issue, but due to the inconformity in training tasks between the two stages, the results are often suboptimal. To address these challenges, we propose an implicit two-stage training method, configuring separate encoders and decoders for each variable. In detailed, in the first stage, the Translator is frozen while the Encoders and Decoders learn a shared latent space, in the second stage, the Encoders and Decoders are frozen, and the Translator captures inter-variable interactions for prediction. Besides, by introducing a self-attention mechanism for multivariable fusion in the latent space, the performance achieves further improvements. Empirically, extensive experiments show the state-of-the-art performance of our method. Specifically, it reduces the MSE for near-surface air temperature and relative humidity predictions by 28.82\% and 23.39\%, respectively. The source code is available at https://github.com/ShremG/Met2Net.

Dataset distillation or condensation aims to condense a large-scale training dataset into a much smaller synthetic one such that the training performance of distilled and original sets on neural networks are similar. Although the number of training samples can be reduced substantially, current state-of-the-art methods heavily rely on enormous soft labels to achieve satisfactory performance. As a result, the required storage can be comparable even to original datasets, especially for large-scale ones. To solve this problem, instead of storing these heavy labels, we propose a novel label-lightening framework termed HeLlO aiming at effective image-to-label projectors, with which synthetic labels can be directly generated online from synthetic images. Specifically, to construct such projectors, we leverage prior knowledge in open-source foundation models, e.g., CLIP, and introduce a LoRA-like fine-tuning strategy to mitigate the gap between pre-trained and target distributions, so that original models for soft-label generation can be distilled into a group of low-rank matrices. Moreover, an effective image optimization method is proposed to further mitigate the potential error between the original and distilled label generators. Extensive experiments demonstrate that with only about 0.003% of the original storage required for a complete set of soft labels, we achieve comparable performance to current state-of-the-art dataset distillation methods on large-scale datasets. Our code will be available.

The rapid advancement of Multimodal Large Language Models (MLLMs) has extended CLIP-based frameworks to produce powerful, universal embeddings for retrieval tasks. However, existing methods primarily focus on natural images, offering limited support for other crucial visual modalities such as videos and visual documents. To bridge this gap, we introduce RzenEmbed, a unified framework to learn embeddings across a diverse set of modalities, including text, images, videos, and visual documents. We employ a novel two-stage training strategy to learn discriminative representations. The first stage focuses on foundational text and multimodal retrieval. In the second stage, we introduce an improved InfoNCE loss, incorporating two key enhancements. Firstly, a hardness-weighted mechanism guides the model to prioritize challenging samples by assigning them higher weights within each batch. Secondly, we implement an approach to mitigate the impact of false negatives and alleviate data noise. This strategy not only enhances the model's discriminative power but also improves its instruction-following capabilities. We further boost performance with learnable temperature parameter and model souping. RzenEmbed sets a new state-of-the-art on the MMEB benchmark. It not only achieves the best overall score but also outperforms all prior work on the challenging video and visual document retrieval tasks. Our models are available in https://huggingface.co/qihoo360/RzenEmbed.

Effective approaches that can scale embedding model depth (i.e. layers) and embedding size allow for the creation of models that are highly scalable across different computational resources and task requirements. While the recently proposed 2D Matryoshka training approach can efficiently produce a single embedding model such that its sub-layers and sub-dimensions can measure text similarity, its effectiveness is significantly worse than if smaller models were trained separately. To address this issue, we propose Starbucks, a new training strategy for Matryoshka-like embedding models, which encompasses both the fine-tuning and pre-training phases. For the fine-tuning phase, we discover that, rather than sampling a random sub-layer and sub-dimensions for each training steps, providing a fixed list of layer-dimension pairs, from small size to large sizes, and computing the loss across all pairs significantly improves the effectiveness of 2D Matryoshka embedding models, bringing them on par with their separately trained counterparts. To further enhance performance, we introduce a new pre-training strategy, which applies masked autoencoder language modelling to sub-layers and sub-dimensions during pre-training, resulting in a stronger backbone for subsequent fine-tuning of the embedding model. Experimental results on both semantic text similarity and retrieval benchmarks demonstrate that the proposed pre-training and fine-tuning strategies significantly improved the effectiveness over 2D Matryoshka models, enabling Starbucks models to perform more efficiently and effectively than separately trained models.

Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for producing new realizations from a limited set of available runs by transferring structure learned across an ensemble. Using monthly near-surface temperature time series from ten independent reanalysis realizations (ERA5), we find that a vanilla conditional variational autoencoder (CVAE) trained jointly across realizations yields a fragmented latent space that fails to generalize to unseen ensemble members. To address this, we introduce a latent-constrained CVAE (LC-CVAE) that enforces cross-realization homogeneity of latent embeddings at a small set of shared geographic 'anchor' locations. We then use multi-output Gaussian process regression in the latent space to predict latent coordinates at unsampled locations in a new realization, followed by decoding to generate full time series fields. Experiments and ablations demonstrate (i) instability when training on a single realization, (ii) diminishing returns after incorporating roughly five realizations, and (iii) a trade-off between spatial coverage and reconstruction quality that is closely linked to the average neighbor distance in latent space.

Recent research demonstrates the effectiveness of using fine-tuned language models~(LM) for dense retrieval. However, dense retrievers are hard to train, typically requiring heavily engineered fine-tuning pipelines to realize their full potential. In this paper, we identify and address two underlying problems of dense retrievers: i)~fragility to training data noise and ii)~requiring large batches to robustly learn the embedding space. We use the recently proposed Condenser pre-training architecture, which learns to condense information into the dense vector through LM pre-training. On top of it, we propose coCondenser, which adds an unsupervised corpus-level contrastive loss to warm up the passage embedding space. Retrieval experiments on MS-MARCO, Natural Question, and Trivia QA datasets show that coCondenser removes the need for heavy data engineering such as augmentation, synthesis, or filtering, as well as the need for large batch training. It shows comparable performance to RocketQA, a state-of-the-art, heavily engineered system, using simple small batch fine-tuning.

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

We introduce the Granite Embedding models, a family of encoder-based embedding models designed for retrieval tasks, spanning dense-retrieval and sparse retrieval architectures, with both English and Multilingual capabilities. This report provides the technical details of training these highly effective 12 layer embedding models, along with their efficient 6 layer distilled counterparts. Extensive evaluations show that the models, developed with techniques like retrieval oriented pretraining, contrastive finetuning, knowledge distillation, and model merging significantly outperform publicly available models of similar sizes on both internal IBM retrieval and search tasks, and have equivalent performance on widely used information retrieval benchmarks, while being trained on high-quality data suitable for enterprise use. We publicly release all our Granite Embedding models under the Apache 2.0 license, allowing both research and commercial use at https://huggingface.co/collections/ibm-granite.

With hundreds of thousands of language models available on Huggingface today, efficiently evaluating and utilizing these models across various downstream, tasks has become increasingly critical. Many existing methods repeatedly learn task-specific representations of Large Language Models (LLMs), which leads to inefficiencies in both time and computational resources. To address this, we propose EmbedLLM, a framework designed to learn compact vector representations, of LLMs that facilitate downstream applications involving many models, such as model routing. We introduce an encoder-decoder approach for learning such embeddings, along with a systematic framework to evaluate their effectiveness. Empirical results show that EmbedLLM outperforms prior methods in model routing both in accuracy and latency. Additionally, we demonstrate that our method can forecast a model's performance on multiple benchmarks, without incurring additional inference cost. Extensive probing experiments validate that the learned embeddings capture key model characteristics, e.g. whether the model is specialized for coding tasks, even without being explicitly trained on them. We open source our dataset, code and embedder to facilitate further research and application.

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method, which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIME-FACE dataset (2.80 vs. 2.26 in Inception score). The code is available at https://github.com/HaozheLiu-ST/MEE

Large Lanugage Models (LLMs) are gaining increasing popularity in a variety of use cases, from language understanding and writing to assistance in application development. One of the most important aspects for optimal funcionality of LLMs is embedding layers. Word embeddings are distributed representations of words in a continuous vector space. In the context of LLMs, words or tokens from the input text are transformed into high-dimensional vectors using unique algorithms specific to the model. Our research examines the embedding algorithms from leading companies in the industry, such as OpenAI, Google's PaLM, and BERT. Using medical data, we have analyzed similarity scores of each embedding layer, observing differences in performance among each algorithm. To enhance each model and provide an additional encoding layer, we also implemented Siamese Neural Networks. After observing changes in performance with the addition of the model, we measured the carbon footage per epoch of training. The carbon footprint associated with large language models (LLMs) is a significant concern, and should be taken into consideration when selecting algorithms for a variety of use cases. Overall, our research compared the accuracy different, leading embedding algorithms and their carbon footage, allowing for a holistic review of each embedding algorithm.

Dataset distillation or condensation aims to generate a smaller but representative subset from a large dataset, which allows a model to be trained more efficiently, meanwhile evaluating on the original testing data distribution to achieve decent performance. Previous decoupled methods like SRe^2L simply use a unified gradient update scheme for synthesizing data from Gaussian noise, while, we notice that the initial several update iterations will determine the final outline of synthesis, thus an improper gradient update strategy may dramatically affect the final generation quality. To address this, we introduce a simple yet effective global-to-local gradient refinement approach enabled by curriculum data augmentation (CDA) during data synthesis. The proposed framework achieves the current published highest accuracy on both large-scale ImageNet-1K and 21K with 63.2% under IPC (Images Per Class) 50 and 36.1% under IPC 20, using a regular input resolution of 224times224 with faster convergence speed and less synthetic time. The proposed model outperforms the current state-of-the-art methods like SRe^2L, TESLA, and MTT by more than 4% Top-1 accuracy on ImageNet-1K/21K and for the first time, reduces the gap to its full-data training counterparts to less than absolute 15%. Moreover, this work represents the inaugural success in dataset distillation on the larger-scale ImageNet-21K dataset under the standard 224times224 resolution. Our code and distilled ImageNet-21K dataset of 20 IPC, 2K recovery budget are available at https://github.com/VILA-Lab/SRe2L/tree/main/CDA.

In this work, we introduce frozen-encoder model composition, a novel approach to multimodal embedding models. We build on the VLM-style architecture, in which non-text encoders are adapted to produce input for a language model, which in turn generates embeddings for all varieties of input. We present the result: the jina-embeddings-v5-omni suite, a pair of models that encode text, image, audio, and video input into a single semantic embedding space. Our method is to extend the two Jina Embeddings v5 Text models to support additional media by adding encoders for images and audio. The backbone text embedding models and the added non-text media encoders remain frozen. We only trained the connecting components, representing 0.35% of the total weights of the joint model. Training is therefore much more efficient than full-parameter retraining. Additionally, the language model remains effectively unaltered, producing exactly the same embeddings for text inputs as the Jina Embeddings v5 Text models. Our evaluations show that this approach produces results that are competitive with the state-of-the-art, yielding nearly equal performance to larger multimodal embedding models.

Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream tasks make use of these compressed representations, meaningful interpretation usually requires visualization using dimensionality reduction or specialized machine learning interpretability methods. This paper addresses the challenge of making such embeddings more interpretable and broadly useful, by employing Large Language Models (LLMs) to directly interact with embeddings -- transforming abstract vectors into understandable narratives. By injecting embeddings into LLMs, we enable querying and exploration of complex embedding data. We demonstrate our approach on a variety of diverse tasks, including: enhancing concept activation vectors (CAVs), communicating novel embedded entities, and decoding user preferences in recommender systems. Our work couples the immense information potential of embeddings with the interpretative power of LLMs.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

While Mixture-of-Experts (MoE) architectures have become the standard for sparsity scaling in large language models, they increasingly face diminishing returns and system-level bottlenecks. In this work, we explore embedding scaling as a potent, orthogonal dimension for scaling sparsity. Through a comprehensive analysis and experiments, we identify specific regimes where embedding scaling achieves a superior Pareto frontier compared to expert scaling. We systematically characterize the critical architectural factors governing this efficacy -- ranging from parameter budgeting to the interplay with model width and depth. Moreover, by integrating tailored system optimizations and speculative decoding, we effectively convert this sparsity into tangible inference speedups. Guided by these insights, we introduce LongCat-Flash-Lite, a 68.5B parameter model with ~3B activated trained from scratch. Despite allocating over 30B parameters to embeddings, LongCat-Flash-Lite not only surpasses parameter-equivalent MoE baselines but also exhibits exceptional competitiveness against existing models of comparable scale, particularly in agentic and coding domains.

The significant advancements of Large Language Models (LLMs) in generative tasks have led to a growing body of work exploring LLM-based embedding models. While these models, employing different pooling and attention strategies, have achieved state-of-the-art performance on public embedding benchmarks, questions still arise about what constitutes an effective design for LLM-based embedding models. However, these models are often trained on different datasets, using different LLM base models or training settings. Moreover, evaluations on public embedding benchmarks often fail to report statistical significance, making it difficult to determine which designs truly contribute to final performance. This complicates the process for practitioners seeking optimal training recipes for LLM-based embedding models. In this study, we conduct a large-scale experiment by training a series of LLM-based embedding models using the same training data and base model but differing in their pooling and attention strategies. The results show that there is no one-size-fits-all solution: while bidirectional attention and an additional trainable pooling layer outperform in text similarity and information retrieval tasks, they do not significantly surpass simpler designs like EOS-last token pooling and default causal attention in clustering and classification tasks. Furthermore, we propose a new pooling strategy, Multi-Layers Trainable Pooling, which transforms the outputs of all hidden layers, rather than just the last layer, using a cross-attention network. This method proves to be statistically superior in text similarity and retrieval tasks compared to existing pooling methods. Overall, this paper sheds light on effective training strategies for LLM-based embedding models.

Large pre-trained transformers are on top of contemporary semantic segmentation benchmarks, but come with high computational cost and a lengthy training. To lift this constraint, we look at efficient semantic segmentation from a perspective of comprehensive knowledge distillation and consider to bridge the gap between multi-source knowledge extractions and transformer-specific patch embeddings. We put forward the Transformer-based Knowledge Distillation (TransKD) framework which learns compact student transformers by distilling both feature maps and patch embeddings of large teacher transformers, bypassing the long pre-training process and reducing the FLOPs by >85.0%. Specifically, we propose two fundamental and two optimization modules: (1) Cross Selective Fusion (CSF) enables knowledge transfer between cross-stage features via channel attention and feature map distillation within hierarchical transformers; (2) Patch Embedding Alignment (PEA) performs dimensional transformation within the patchifying process to facilitate the patch embedding distillation; (3) Global-Local Context Mixer (GL-Mixer) extracts both global and local information of a representative embedding; (4) Embedding Assistant (EA) acts as an embedding method to seamlessly bridge teacher and student models with the teacher's number of channels. Experiments on Cityscapes, ACDC, and NYUv2 datasets show that TransKD outperforms state-of-the-art distillation frameworks and rivals the time-consuming pre-training method. Code is available at https://github.com/RuipingL/TransKD.

Similarity between training examples is used to curate pretraining datasets for language models by many methods -- for diversification and to select examples similar to high-quality data. However, similarity is typically measured with off-the-shelf embedding models that are generic or trained for tasks such as retrieval. This paper introduces a framework to analyze the suitability of embedding models specifically for data curation in the language model pretraining setting. We quantify the correlation between similarity in the embedding space to similarity in pretraining loss between different training examples, and how diversifying in the embedding space affects pretraining quality. We analyze a variety of embedding models in our framework, with experiments using the Pile dataset for pretraining a 1.7B parameter decoder-only language model. We find that the embedding models we consider are all useful for pretraining data curation. Moreover, a simple approach of averaging per-token embeddings proves to be surprisingly competitive with more sophisticated embedding models -- likely because the latter are not designed specifically for pretraining data curation. Indeed, we believe our analysis and evaluation framework can serve as a foundation for the design of embedding models that specifically reason about similarity in pretraining datasets.

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as features, especially for neural-network-based models. Directly feeding raw Gaussian parameters into learning frameworks fails to address the non-unique and heterogeneous nature of the Gaussian parameterization, yielding highly data-dependent models. This challenge motivates us to explore a more principled approach to represent 3D Gaussian Splatting in neural networks that preserves the underlying color and geometric structure while enforcing unique mapping and channel homogeneity. In this paper, we propose an embedding representation of 3DGS based on continuous submanifold fields that encapsulate the intrinsic information of Gaussian primitives, thereby benefiting the learning of 3DGS.

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

Recent advances in distilling expensive diffusion models into efficient few-step generators show significant promise. However, these methods typically demand substantial computational resources and extended training periods, limiting accessibility for resource-constrained researchers, and existing supplementary loss functions have notable limitations. Regression loss requires pre-generating large datasets before training and limits the student model to the teacher's performance, while GAN-based losses suffer from training instability and require careful tuning. In this paper, we propose Embedding Loss (EL), a novel supplementary loss function that complements existing diffusion distillation methods to enhance generation quality and accelerate training with smaller batch sizes. Leveraging feature embeddings from a diverse set of randomly initialized networks, EL effectively aligns the feature distributions between the distilled few-step generator and the original data. By computing Maximum Mean Discrepancy (MMD) in the embedded feature space, EL ensures robust distribution matching, thereby preserving sample fidelity and diversity during distillation. Within distribution matching distillation frameworks, EL demonstrates strong empirical performance for one-step generators. On the CIFAR-10 dataset, our approach achieves state-of-the-art FID values of 1.475 for unconditional generation and 1.380 for conditional generation. Beyond CIFAR-10, we further validate EL across multiple benchmarks and distillation methods, including ImageNet, AFHQ-v2, and FFHQ datasets, using DMD, DI, and CM distillation frameworks, demonstrating consistent improvements over existing one-step distillation methods. Our method also reduces training iterations by up to 80%, offering a more practical and scalable solution for deploying diffusion-based generative models in resource-constrained environments.

Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies and analyze the challenges between the continuous data space and the embedding space which have not been carefully explored. Firstly, the data distribution is learnable for embeddings, which may lead to the collapse of the loss function. Secondly, as the norm of embeddings varies between popular and rare words, adding the same noise scale will lead to sub-optimal results. In addition, we find the normal level of noise causes insufficient training of the model. To address the above challenges, we propose Difformer, an embedding diffusion model based on Transformer, which consists of three essential modules including an additional anchor loss function, a layer normalization module for embeddings, and a noise factor to the Gaussian noise. Experiments on two seminal text generation tasks including machine translation and text summarization show the superiority of Difformer over compared embedding diffusion baselines.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

While LLMs are powerful embedding backbones, their application in training-free settings faces two structural challenges: causal attention restricts early tokens from accessing subsequent context, and the next-token prediction objective biases representations toward generation rather than semantic compression. To address these limitations, we propose KV-Embedding, a framework that activates the latent representation power of frozen LLMs. Our method leverages the observation that the key-value (KV) states of the final token at each layer encode a compressed view of the sequence. By re-routing these states as a prepended prefix, we enable all tokens to access sequence-level context within a single forward pass. To ensure model-agnostic applicability, we introduce an automated layer selection strategy based on intrinsic dimensionality. Evaluations on MTEB across Qwen, Mistral, and Llama backbones show that KV-Embedding outperforms existing training-free baselines by up to 10%, while maintaining robust performance on sequences up to 4,096 tokens. These results demonstrate that internal state manipulation offers an efficient alternative to input modification, and we hope this work encourages further exploration of LLM internals for representation learning.

Large language models exhibit impressive zero-shot capabilities across a wide range of downstream tasks. However, they struggle to function as off-the-shelf embedding models, leading to suboptimal performance on massive text embedding benchmarks. In this paper, we identify a potential cause underlying this deficiency. Our motivation stems from an unexpected observation: text embeddings tend to align with frequent but uninformative tokens when projected onto the vocabulary space. We argue that this excessive expression of high-frequency tokens suppresses the model's ability to capture nuanced semantics. To address this, we introduce EmbedFilter, a simple linear transformation designed to refine text embeddings derived from LLMs directly. Specifically, we uncover that the unembedding matrix within LLMs encodes a latent space that is actively writing these frequent tokens into embedding space. By filtering out this subspace, EmbedFilter suppress the influence of high-frequency tokens, thereby enhancing semantic representations. As a compelling byproduct, this enables an inherent dimensionality reduction, lowering index storage and speedup retrieval while fully preserving the refined embedding quality. Our experiments across multiple LLM backbones demonstrate that LLMs equipped with EmbedFilter achieve superior zero-shot downstream performance even with significantly reduced embedding dimensions. We hope our findings provide deeper insights into the mechanisms of LLM-based representations and inspire more principled designs to improve text embeddings training. Our code is available at https://github.com/CentreChen/EmbFilter.

A single embedding space that covers text, images, video, and audio lets one index serve every query a user can pose. Embedding models built on vision-language backbones now lead text/image/video retrieval benchmarks but lack audio entirely, while audio-text retrieval is led by specialist systems that serve no other modality. We present the Fusion Embedding family, which adds audio to a frozen vision-language embedding base whose parameters are never updated: generation 1 (fusion-embedding-1) trains only a 16.4M-parameter connector between a frozen audio tower and the frozen base, and generation 2 (fusion-embedding-2) adds modality-gated deep adapters (44.2M parameters) whose branch never executes on text, image, or video inputs: their outputs are bit-for-bit those of the released base, verified after every training run. Because the base already binds text, images, and video, aligning audio to text alone makes audio-image retrieval emerge, with zero paired audio-visual training data. Alongside the recipe we map its design space with controlled negative results (rewriting training captions with an LLM, substituting a leaderboard-stronger audio tower, and widening the connector each reduce retrieval) and with training-protocol findings that we expect to transfer to any frozen decoder-LM embedding backbone. Both generations train in hours on a single GPU. Weights, code, and the evaluation harness are openly released.

The latest advancements in unsupervised learning of sentence embeddings predominantly involve employing contrastive learning-based (CL-based) fine-tuning over pre-trained language models. In this study, we analyze the latest sentence embedding methods by adopting representation rank as the primary tool of analysis. We first define Phase 1 and Phase 2 of fine-tuning based on when representation rank peaks. Utilizing these phases, we conduct a thorough analysis and obtain essential findings across key aspects, including alignment and uniformity, linguistic abilities, and correlation between performance and rank. For instance, we find that the dynamics of the key aspects can undergo significant changes as fine-tuning transitions from Phase 1 to Phase 2. Based on these findings, we experiment with a rank reduction (RR) strategy that facilitates rapid and stable fine-tuning of the latest CL-based methods. Through empirical investigations, we showcase the efficacy of RR in enhancing the performance and stability of five state-of-the-art sentence embedding methods.

LLM-based text embedders typically encode the semantic content of their input. However, embedding tasks require mapping diverse inputs to similar outputs. Typically, this input-output is addressed by training embedding models with paired data using contrastive learning. In this work, we propose a novel self-supervised approach, LLM2Vec-Gen, which adopts a different paradigm: rather than encoding the input, we learn to represent the model's potential response. Specifically, we add trainable special tokens to the LLM's vocabulary, append them to input, and optimize them to represent the LLM's response in a fixed-length sequence. Training is guided by the LLM's own completion for the query, along with an unsupervised embedding teacher that provides distillation targets. This formulation helps to bridge the input-output gap and transfers LLM capabilities such as safety alignment and reasoning to embedding tasks. Crucially, the LLM backbone remains frozen and training requires only unlabeled queries. LLM2Vec-Gen achieves state-of-the-art self-supervised performance on the Massive Text Embedding Benchmark (MTEB), improving by 9.3% over the best unsupervised embedding teacher. We also observe up to 43.2% reduction in harmful content retrieval and 29.3% improvement in reasoning capabilities for embedding tasks. Finally, the learned embeddings are interpretable and can be decoded into text to reveal their semantic content.

We present LEAF ("Lightweight Embedding Alignment Framework"), a knowledge distillation framework for text embedding models. A key distinguishing feature is that our distilled leaf models are aligned to their teacher. In the context of information retrieval, this allows for flexible asymmetric architectures where documents are encoded with the larger teacher model, while queries can be served with the smaller leaf models. We also show that leaf models automatically inherit MRL and robustness to output quantization whenever these properties are present in the teacher model, without explicitly training for them. To demonstrate the capability of our framework we publish leaf-ir, a 23M parameters information retrieval oriented text embedding model trained using LEAF, which sets a new state-of-the-art (SOTA) on BEIR, ranking #1 on the public leaderboard for this benchmark and for models of its size. When run in asymmetric mode, its retrieval performance is further increased. Our scheme is however not restricted to the information retrieval setting, and we demonstrate its wider applicability by synthesizing the multi-task leaf-mt model. This also sets a new SOTA, ranking #1 on the public MTEB v2 (English) leaderboard for its size. LEAF is applicable to black-box models and in contrast to other embedding model training frameworks, it does not require judgments nor hard negatives, and training can be conducted using small batch sizes. Thus, dataset and training infrastructure requirements for our framework are modest. We make our models publicly available under a permissive Apache 2.0 license.

Joint Embedding Predictive Architectures (JEPA) have emerged as a powerful framework for learning general-purpose representations. However, these models often lack interpretability and suffer from inefficiencies due to dense embedding representations. We propose SparseJEPA, an extension that integrates sparse representation learning into the JEPA framework to enhance the quality of learned representations. SparseJEPA employs a penalty method that encourages latent space variables to be shared among data features with strong semantic relationships, while maintaining predictive performance. We demonstrate the effectiveness of SparseJEPA by training on the CIFAR-100 dataset and pre-training a lightweight Vision Transformer. The improved embeddings are utilized in linear-probe transfer learning for both image classification and low-level tasks, showcasing the architecture's versatility across different transfer tasks. Furthermore, we provide a theoretical proof that demonstrates that the grouping mechanism enhances representation quality. This was done by displaying that grouping reduces Multiinformation among latent-variables, including proofing the Data Processing Inequality for Multiinformation. Our results indicate that incorporating sparsity not only refines the latent space but also facilitates the learning of more meaningful and interpretable representations. In further work, hope to further extend this method by finding new ways to leverage the grouping mechanism through object-centric representation learning.

Text autoencoders are often used for unsupervised conditional text generation by applying mappings in the latent space to change attributes to the desired values. Recently, Mai et al. (2020) proposed Emb2Emb, a method to learn these mappings in the embedding space of an autoencoder. However, their method is restricted to autoencoders with a single-vector embedding, which limits how much information can be retained. We address this issue by extending their method to Bag-of-Vectors Autoencoders (BoV-AEs), which encode the text into a variable-size bag of vectors that grows with the size of the text, as in attention-based models. This allows to encode and reconstruct much longer texts than standard autoencoders. Analogous to conventional autoencoders, we propose regularization techniques that facilitate learning meaningful operations in the latent space. Finally, we adapt Emb2Emb for a training scheme that learns to map an input bag to an output bag, including a novel loss function and neural architecture. Our empirical evaluations on unsupervised sentiment transfer show that our method performs substantially better than a standard autoencoder.

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which uses a single pre-training stage to address both families of tasks simultaneously. We identify diffusion models as a prime candidate. Diffusion models have risen to prominence as a state-of-the-art method for image generation, denoising, inpainting, super-resolution, manipulation, etc. Such models involve training a U-Net to iteratively predict and remove noise, and the resulting model can synthesize high fidelity, diverse, novel images. The U-Net architecture, as a convolution-based architecture, generates a diverse set of feature representations in the form of intermediate feature maps. We present our findings that these embeddings are useful beyond the noise prediction task, as they contain discriminative information and can also be leveraged for classification. We explore optimal methods for extracting and using these embeddings for classification tasks, demonstrating promising results on the ImageNet classification task. We find that with careful feature selection and pooling, diffusion models outperform comparable generative-discriminative methods such as BigBiGAN for classification tasks. We investigate diffusion models in the transfer learning regime, examining their performance on several fine-grained visual classification datasets. We compare these embeddings to those generated by competing architectures and pre-trainings for classification tasks.

We present Gecko, a compact and versatile text embedding model. Gecko achieves strong retrieval performance by leveraging a key idea: distilling knowledge from large language models (LLMs) into a retriever. Our two-step distillation process begins with generating diverse, synthetic paired data using an LLM. Next, we further refine the data quality by retrieving a set of candidate passages for each query, and relabeling the positive and hard negative passages using the same LLM. The effectiveness of our approach is demonstrated by the compactness of the Gecko. On the Massive Text Embedding Benchmark (MTEB), Gecko with 256 embedding dimensions outperforms all existing entries with 768 embedding size. Gecko with 768 embedding dimensions achieves an average score of 66.31, competing with 7x larger models and 5x higher dimensional embeddings.

In recent years supervised representation learning has provided state of the art or close to the state of the art results in semantic analysis tasks including ranking and information retrieval. The core idea is to learn how to embed items into a latent space such that they optimize a supervised objective in that latent space. The dimensions of the latent space have no clear semantics, and this reduces the interpretability of the system. For example, in personalization models, it is hard to explain why a particular item is ranked high for a given user profile. We propose a novel model of representation learning called Supervised Explicit Semantic Analysis (SESA) that is trained in a supervised fashion to embed items to a set of dimensions with explicit semantics. The model learns to compare two objects by representing them in this explicit space, where each dimension corresponds to a concept from a knowledge base. This work extends Explicit Semantic Analysis (ESA) with a supervised model for ranking problems. We apply this model to the task of Job-Profile relevance in LinkedIn in which a set of skills defines our explicit dimensions of the space. Every profile and job are encoded to this set of skills their similarity is calculated in this space. We use RNNs to embed text input into this space. In addition to interpretability, our model makes use of the web-scale collaborative skills data that is provided by users for each LinkedIn profile. Our model provides state of the art result while it remains interpretable.

Learning representations that transfer well to diverse downstream tasks remains a central challenge in representation learning. Existing paradigms -- contrastive learning, self-supervised masking, and denoising auto-encoders -- balance this challenge with different trade-offs. We introduce the {contrastive Mutual Information Machine} (cMIM), a probabilistic framework that extends the Mutual Information Machine (MIM) with a contrastive objective. While MIM maximizes mutual information between inputs and latents and promotes clustering of codes, it falls short on discriminative tasks. cMIM addresses this gap by imposing global discriminative structure while retaining MIM's generative fidelity. Our contributions are threefold. First, we propose cMIM, a contrastive extension of MIM that removes the need for positive data augmentation and is substantially less sensitive to batch size than InfoNCE. Second, we introduce {informative embeddings}, a general technique for extracting enriched features from encoder-decoder models that boosts discriminative performance without additional training and applies broadly beyond MIM. Third, we provide empirical evidence across vision and molecular benchmarks showing that cMIM outperforms MIM and InfoNCE on classification and regression tasks while preserving competitive reconstruction quality. These results position cMIM as a unified framework for representation learning, advancing the goal of models that serve both discriminative and generative applications effectively.

Latent representations learned by neural networks often exhibit semantic structure, where concept similarity is reflected by geometric proximity in embedding space. However, comparing such spaces across models remains difficult: changes in architecture, pretraining data, objective, or random seed can yield embeddings with similar content but incompatible geometry. This latent space alignment problem is central to interpretability, transfer and multimodal learning, federated systems, and semantic communication; however, progress remains limited by the lack of large-scale, model-diverse, and metadata-rich benchmarks. To address this gap, we introduce SEMASIA, a large-scale collection of latent representations extracted from approximately 1,700 pretrained vision models across eight standard image-classification benchmarks. SEMASIA pairs embeddings with structured metadata describing architectures, training regimes, pretraining sources, and model scale. We demonstrate three applications of the resource. First, we analyze the conceptual organization of individual latent spaces, showing consistent prototype-like clustering and hierarchical semantic neighborhoods across models and datasets. Second, we benchmark supervised alignment mappings between latent spaces using reconstruction error and downstream task performance. Third, we perform a large-scale regression analysis of how pretraining-data complexity, specialization, transfer learning, augmentation, and model scale relate to geometric and probing properties of embeddings. By coupling representational scale with standardized metadata, SEMASIA provides a reproducible foundation for studying latent geometry, evaluating alignment methods, and developing next-generation heterogeneous and interoperable AI systems.

In this paper, we present a new embedding model, called M3-Embedding, which is distinguished for its versatility in Multi-Linguality, Multi-Functionality, and Multi-Granularity. It can support more than 100 working languages, leading to new state-of-the-art performances on multi-lingual and cross-lingual retrieval tasks. It can simultaneously perform the three common retrieval functionalities of embedding model: dense retrieval, multi-vector retrieval, and sparse retrieval, which provides a unified model foundation for real-world IR applications. It is able to process inputs of different granularities, spanning from short sentences to long documents of up to 8192 tokens. The effective training of M3-Embedding involves the following technical contributions. We propose a novel self-knowledge distillation approach, where the relevance scores from different retrieval functionalities can be integrated as the teacher signal to enhance the training quality. We also optimize the batching strategy, enabling a large batch size and high training throughput to ensure the discriminativeness of embeddings. To the best of our knowledge, M3-Embedding is the first embedding model which realizes such a strong versatility. The model and code will be publicly available at https://github.com/FlagOpen/FlagEmbedding.

In this paper, we show that the performance of a learnt generative model is closely related to the model's ability to accurately represent the inferred latent data distribution, i.e. its topology and structural properties. We propose LaDDer to achieve accurate modelling of the latent data distribution in a variational autoencoder framework and to facilitate better representation learning. The central idea of LaDDer is a meta-embedding concept, which uses multiple VAE models to learn an embedding of the embeddings, forming a ladder of encodings. We use a non-parametric mixture as the hyper prior for the innermost VAE and learn all the parameters in a unified variational framework. From extensive experiments, we show that our LaDDer model is able to accurately estimate complex latent distribution and results in improvement in the representation quality. We also propose a novel latent space interpolation method that utilises the derived data distribution.

This technical report presents the training methodology and evaluation results of the open-source Jasper-Token-Compression-600M model, released in November 2025. Building on previous distillation-based recipes from the English Stella and Jasper models, we successfully extend this approach to a bilingual (English and Chinese) domain, further enhancing model performance through the incorporation of contrastive learning. A key innovation of our model is the introduction of a one-dimensional convolution-based token compression module. We dynamically adjust the compression rate during training, enabling the model to learn more robust and efficient compressed text representations. By combining knowledge distillation with token compression techniques, we achieve significant improvements in both embedding quality and inference efficiency. Our model performs with higher efficiency than a traditional 0.6B model while achieving performance comparable to that of an 8B model. For more information on the model release, visit: https://huggingface.co/infgrad/Jasper-Token-Compression-600M.

Pre-trained language models have been found to capture a surprisingly rich amount of lexical knowledge, ranging from commonsense properties of everyday concepts to detailed factual knowledge about named entities. Among others, this makes it possible to distill high-quality word vectors from pre-trained language models. However, it is currently unclear to what extent it is possible to distill relation embeddings, i.e. vectors that characterize the relationship between two words. Such relation embeddings are appealing because they can, in principle, encode relational knowledge in a more fine-grained way than is possible with knowledge graphs. To obtain relation embeddings from a pre-trained language model, we encode word pairs using a (manually or automatically generated) prompt, and we fine-tune the language model such that relationally similar word pairs yield similar output vectors. We find that the resulting relation embeddings are highly competitive on analogy (unsupervised) and relation classification (supervised) benchmarks, even without any task-specific fine-tuning. Source code to reproduce our experimental results and the model checkpoints are available in the following repository: https://github.com/asahi417/relbert

Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph embedding methods, such as Canonical decomposition/Parallel factorization (CP), DistMult, and ComplEx, have been proposed to address this issue. These methods represent entities and relations as embedding vectors in semantic space and predict the links between them. The embedding vectors themselves contain rich semantic information and can be used in other applications such as data analysis. However, mechanisms in these models and the embedding vectors themselves vary greatly, making it difficult to understand and compare them. Given this lack of understanding, we risk using them ineffectively or incorrectly, particularly for complicated models, such as CP, with two role-based embedding vectors, or the state-of-the-art ComplEx model, with complex-valued embedding vectors. In this paper, we propose a multi-embedding interaction mechanism as a new approach to uniting and generalizing these models. We derive them theoretically via this mechanism and provide empirical analyses and comparisons between them. We also propose a new multi-embedding model based on quaternion algebra and show that it achieves promising results using popular benchmarks. Source code is available on GitHub at https://github.com/tranhungnghiep/AnalyzeKGE.

Unsupervised fine-grained class clustering is a practical yet challenging task due to the difficulty of feature representations learning of subtle object details. We introduce C3-GAN, a method that leverages the categorical inference power of InfoGAN with contrastive learning. We aim to learn feature representations that encourage a dataset to form distinct cluster boundaries in the embedding space, while also maximizing the mutual information between the latent code and its image observation. Our approach is to train a discriminator, which is also used for inferring clusters, to optimize the contrastive loss, where image-latent pairs that maximize the mutual information are considered as positive pairs and the rest as negative pairs. Specifically, we map the input of a generator, which was sampled from the categorical distribution, to the embedding space of the discriminator and let them act as a cluster centroid. In this way, C3-GAN succeeded in learning a clustering-friendly embedding space where each cluster is distinctively separable. Experimental results show that C3-GAN achieved the state-of-the-art clustering performance on four fine-grained image datasets, while also alleviating the mode collapse phenomenon. Code is available at https://github.com/naver-ai/c3-gan.

Recent advances in text-to-image synthesis largely benefit from sophisticated sampling strategies and classifier-free guidance (CFG) to ensure high-quality generation. However, CFG's reliance on two forward passes, especially when combined with intricate sampling algorithms, results in prohibitively high inference costs. To address this, we introduce TeEFusion (Text Embeddings Fusion), a novel and efficient distillation method that directly incorporates the guidance magnitude into the text embeddings and distills the teacher model's complex sampling strategy. By simply fusing conditional and unconditional text embeddings using linear operations, TeEFusion reconstructs the desired guidance without adding extra parameters, simultaneously enabling the student model to learn from the teacher's output produced via its sophisticated sampling approach. Extensive experiments on state-of-the-art models such as SD3 demonstrate that our method allows the student to closely mimic the teacher's performance with a far simpler and more efficient sampling strategy. Consequently, the student model achieves inference speeds up to 6times faster than the teacher model, while maintaining image quality at levels comparable to those obtained through the teacher's complex sampling approach. The code is publicly available at https://github.com/AIDC-AI/TeEFusion{github.com/AIDC-AI/TeEFusion}.

Transformer-based embedding models rely on pooling to map variable-length text into a single vector, enabling efficient similarity search but also inducing well-known geometric pathologies such as anisotropy and length-induced embedding collapse. Existing accounts largely describe what these pathologies look like, yet provide limited insight into when and why they harm downstream retrieval. In this work, we argue that the missing causal factor is semantic shift: the intrinsic, structured evolution and dispersion of semantics within a text. We first present a theoretical analysis of semantic smoothing in Transformer embeddings: as the semantic diversity among constituent sentences increases, the pooled representation necessarily shifts away from every individual sentence embedding, yielding a smoothed and less discriminative vector. Building on this foundation, we formalize semantic shift as a computable measure integrating local semantic evolution and global semantic dispersion. Through controlled experiments across corpora and multiple embedding models, we show that semantic shift aligns closely with the severity of embedding concentration and predicts retrieval degradation, whereas text length alone does not. Overall, semantic shift offers a unified and actionable lens for understanding embedding collapse and for diagnosing when anisotropy becomes harmful.

We present StarSpace, a general-purpose neural embedding model that can solve a wide variety of problems: labeling tasks such as text classification, ranking tasks such as information retrieval/web search, collaborative filtering-based or content-based recommendation, embedding of multi-relational graphs, and learning word, sentence or document level embeddings. In each case the model works by embedding those entities comprised of discrete features and comparing them against each other -- learning similarities dependent on the task. Empirical results on a number of tasks show that StarSpace is highly competitive with existing methods, whilst also being generally applicable to new cases where those methods are not.

Pre-trained Transformer language models (LM) have become go-to text representation encoders. Prior research fine-tunes deep LMs to encode text sequences such as sentences and passages into single dense vector representations for efficient text comparison and retrieval. However, dense encoders require a lot of data and sophisticated techniques to effectively train and suffer in low data situations. This paper finds a key reason is that standard LMs' internal attention structure is not ready-to-use for dense encoders, which needs to aggregate text information into the dense representation. We propose to pre-train towards dense encoder with a novel Transformer architecture, Condenser, where LM prediction CONditions on DENSE Representation. Our experiments show Condenser improves over standard LM by large margins on various text retrieval and similarity tasks.

Knowledge Distillation (KD) has emerged as a promising approach for transferring knowledge from a larger, more complex teacher model to a smaller student model. Traditionally, KD involves training the student to mimic the teacher's output probabilities, while more advanced techniques have explored guiding the student to adopt the teacher's internal representations. Despite its widespread success, the performance of KD in binary classification and few-class problems has been less satisfactory. This is because the information about the teacher model's generalization patterns scales directly with the number of classes. Moreover, several sophisticated distillation methods may not be universally applicable or effective for data types beyond Computer Vision. Consequently, effective distillation techniques remain elusive for a range of key real-world applications, such as sentiment analysis, search query understanding, and advertisement-query relevance assessment. Taking these observations into account, we introduce a novel method for distilling knowledge from the teacher's model representations, which we term Learning Embedding Linear Projections (LELP). Inspired by recent findings about the structure of final-layer representations, LELP works by identifying informative linear subspaces in the teacher's embedding space, and splitting them into pseudo-subclasses. The student model is then trained to replicate these pseudo-classes. Our experimental evaluation on large-scale NLP benchmarks like Amazon Reviews and Sentiment140 demonstrate the LELP is consistently competitive with, and typically superior to, existing state-of-the-art distillation algorithms for binary and few-class problems, where most KD methods suffer.

A number of recent self-supervised learning methods have shown impressive performance on image classification and other tasks. A somewhat bewildering variety of techniques have been used, not always with a clear understanding of the reasons for their benefits, especially when used in combination. Here we treat the embeddings of images as point particles and consider model optimization as a dynamic process on this system of particles. Our dynamic model combines an attractive force for similar images, a locally dispersive force to avoid local collapse, and a global dispersive force to achieve a globally-homogeneous distribution of particles. The dynamic perspective highlights the advantage of using a delayed-parameter image embedding (a la BYOL) together with multiple views of the same image. It also uses a purely-dynamic local dispersive force (Brownian motion) that shows improved performance over other methods and does not require knowledge of other particle coordinates. The method is called MSBReg which stands for (i) a Multiview centroid loss, which applies an attractive force to pull different image view embeddings toward their centroid, (ii) a Singular value loss, which pushes the particle system toward spatially homogeneous density, (iii) a Brownian diffusive loss. We evaluate downstream classification performance of MSBReg on ImageNet as well as transfer learning tasks including fine-grained classification, multi-class object classification, object detection, and instance segmentation. In addition, we also show that applying our regularization term to other methods further improves their performance and stabilize the training by preventing a mode collapse.

Large-scale contrastive learning models can learn very informative sentence embeddings, but are hard to serve online due to the huge model size. Therefore, they often play the role of "teacher", transferring abilities to small "student" models through knowledge distillation. However, knowledge distillation inevitably brings some drop in embedding effect. To tackle that, we propose an effective knowledge distillation framework for contrastive sentence embeddings, termed DistilCSE. It first applies knowledge distillation on a large amount of unlabeled data, and then fine-tunes student models through contrastive learning on limited labeled data. To achieve better distillation results, we further propose Contrastive Knowledge Distillation (CKD). CKD uses InfoNCE as the loss function in knowledge distillation, enhancing the objective consistency among teacher model training, knowledge distillation, and student model fine-tuning. Extensive experiments show that student models trained with the proposed DistilCSE and CKD suffer from little or even no performance decrease and consistently outperform the corresponding counterparts of the same parameter size. Impressively, our 110M student model outperforms the latest state-of-the-art model, i.e., Sentence-T5 (11B), with only 1% parameters and 0.25% unlabeled data.

Decoder-only large language model (LLM)-based embedding models are beginning to outperform BERT or T5-based embedding models in general-purpose text embedding tasks, including dense vector-based retrieval. In this work, we introduce the NV-Embed model with a variety of architectural designs and training procedures to significantly enhance the performance of LLM as a versatile embedding model, while maintaining its simplicity and reproducibility. For model architecture, we propose a latent attention layer to obtain pooled embeddings, which consistently improves retrieval and downstream task accuracy compared to mean pooling or using the last <EOS> token embedding from LLMs. To enhance representation learning, we remove the causal attention mask of LLMs during contrastive training. For model training, we introduce a two-stage contrastive instruction-tuning method. It first applies contrastive training with instructions on retrieval datasets, utilizing in-batch negatives and curated hard negative examples. At stage-2, it blends various non-retrieval datasets into instruction tuning, which not only enhances non-retrieval task accuracy but also improves retrieval performance. Combining these techniques, our NV-Embed model, using only publicly available data, has achieved a record-high score of 69.32, ranking No. 1 on the Massive Text Embedding Benchmark (MTEB) (as of May 24, 2024), with 56 tasks, encompassing retrieval, reranking, classification, clustering, and semantic textual similarity tasks. Notably, our model also attains the highest score of 59.36 on 15 retrieval tasks in the MTEB benchmark (also known as BEIR). We will open-source the model at: https://huggingface.co/nvidia/NV-Embed-v1.

We present a new dataset condensation framework termed Squeeze, Recover and Relabel (SRe^2L) that decouples the bilevel optimization of model and synthetic data during training, to handle varying scales of datasets, model architectures and image resolutions for efficient dataset condensation. The proposed method demonstrates flexibility across diverse dataset scales and exhibits multiple advantages in terms of arbitrary resolutions of synthesized images, low training cost and memory consumption with high-resolution synthesis, and the ability to scale up to arbitrary evaluation network architectures. Extensive experiments are conducted on Tiny-ImageNet and full ImageNet-1K datasets. Under 50 IPC, our approach achieves the highest 42.5% and 60.8% validation accuracy on Tiny-ImageNet and ImageNet-1K, outperforming all previous state-of-the-art methods by margins of 14.5% and 32.9%, respectively. Our approach also surpasses MTT in terms of speed by approximately 52times (ConvNet-4) and 16times (ResNet-18) faster with less memory consumption of 11.6times and 6.4times during data synthesis. Our code and condensed datasets of 50, 200 IPC with 4K recovery budget are available at https://github.com/VILA-Lab/SRe2L.

Video Joint Embedding Predictive Architectures (V-JEPA) learn generalizable off-the-shelf video representation by predicting masked regions in latent space with an exponential moving average (EMA)-updated teacher. While EMA prevents representation collapse, it complicates scalable model selection and couples teacher and student architectures. We revisit masked-latent prediction and show that a frozen teacher suffices. Concretely, we (i) train a target encoder with a simple pixel-reconstruction objective under V-JEPA masking, then (ii) freeze it and train a student to predict the teacher's latents on masked regions. This leads to a two-stage, unregularized scheme that we refer to as SALT (Static-teacher Asymmetric Latent Training). SALT decouples optimization into pixel reconstruction (teacher) and masked latent prediction (student), increasing transparency, efficiency, and scalability while preserving the ability of representation to generalize under frozen evaluation. Empirically, our student models outperform recently proposed V-JEPA 2 encoders under frozen backbone evaluation across diverse benchmarks. They are also more compute-optimal: at matched pretraining FLOPs, our method achieves higher probing accuracy, and its scaling curves dominate V-JEPA's accuracy-FLOPs Pareto frontier. Finally, we find that student quality is remarkably robust to teacher quality: high-performing students emerge even with small, sub-optimal teachers. This points to a compute budget allocation that should overwhelmingly favor the student. These results position SALT as a simple, scalable, and compute-efficient alternative to EMA-based self-distillation for video representation learning.

For convolutional neural network models that optimize an image embedding, we propose a method to highlight the regions of images that contribute most to pairwise similarity. This work is a corollary to the visualization tools developed for classification networks, but applicable to the problem domains better suited to similarity learning. The visualization shows how similarity networks that are fine-tuned learn to focus on different features. We also generalize our approach to embedding networks that use different pooling strategies and provide a simple mechanism to support image similarity searches on objects or sub-regions in the query image.

The paper presents an O(N log N)-implementation of t-SNE -- an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots and that normally runs in O(N^2). The new implementation uses vantage-point trees to compute sparse pairwise similarities between the input data objects, and it uses a variant of the Barnes-Hut algorithm - an algorithm used by astronomers to perform N-body simulations - to approximate the forces between the corresponding points in the embedding. Our experiments show that the new algorithm, called Barnes-Hut-SNE, leads to substantial computational advantages over standard t-SNE, and that it makes it possible to learn embeddings of data sets with millions of objects.

Style representations aim to embed texts with similar writing styles closely and texts with different styles far apart, regardless of content. However, the contrastive triplets often used for training these representations may vary in both style and content, leading to potential content leakage in the representations. We introduce StyleDistance, a novel approach to training stronger content-independent style embeddings. We use a large language model to create a synthetic dataset of near-exact paraphrases with controlled style variations, and produce positive and negative examples across 40 distinct style features for precise contrastive learning. We assess the quality of our synthetic data and embeddings through human and automatic evaluations. StyleDistance enhances the content-independence of style embeddings, which generalize to real-world benchmarks and outperform leading style representations in downstream applications. Our model can be found at https://huggingface.co/StyleDistance/styledistance .

Joint Embedding Predictive Architectures (JEPAs) offer a compelling framework for learning world models in compact latent spaces, yet existing methods remain fragile, relying on complex multi-term losses, exponential moving averages, pre-trained encoders, or auxiliary supervision to avoid representation collapse. In this work, we introduce LeWorldModel (LeWM), the first JEPA that trains stably end-to-end from raw pixels using only two loss terms: a next-embedding prediction loss and a regularizer enforcing Gaussian-distributed latent embeddings. This reduces tunable loss hyperparameters from six to one compared to the only existing end-to-end alternative. With ~15M parameters trainable on a single GPU in a few hours, LeWM plans up to 48x faster than foundation-model-based world models while remaining competitive across diverse 2D and 3D control tasks. Beyond control, we show that LeWM's latent space encodes meaningful physical structure through probing of physical quantities. Surprise evaluation confirms that the model reliably detects physically implausible events.

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

Models for image representation learning are typically designed for either recognition or generation. Various forms of contrastive learning help models learn to convert images to embeddings that are useful for classification, detection, and segmentation. On the other hand, models can be trained to reconstruct images with pixel-wise, perceptual, and adversarial losses in order to learn a latent space that is useful for image generation. We seek to unify these two directions with a first-of-its-kind model that learns representations which are simultaneously useful for recognition and generation. We train our model as a hyper-network for implicit neural representation, which learns to map images to model weights for fast, accurate reconstruction. We further integrate our INR hyper-network with knowledge distillation to improve its generalization and performance. Beyond the novel training design, the model also learns an unprecedented compressed embedding space with outstanding performance for various visual tasks. The complete model competes with state-of-the-art results for image representation learning, while also enabling generative capabilities with its high-quality tiny embeddings. The code is available at https://github.com/tiktok/huvr.

Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Early works performed this task via simple models developed over KG triples. Recent attempts focused on either designing more complicated triple scoring models, or incorporating extra information beyond triples. This paper, by contrast, investigates the potential of using very simple constraints to improve KG embedding. We examine non-negativity constraints on entity representations and approximate entailment constraints on relation representations. The former help to learn compact and interpretable representations for entities. The latter further encode regularities of logical entailment between relations into their distributed representations. These constraints impose prior beliefs upon the structure of the embedding space, without negative impacts on efficiency or scalability. Evaluation on WordNet, Freebase, and DBpedia shows that our approach is simple yet surprisingly effective, significantly and consistently outperforming competitive baselines. The constraints imposed indeed improve model interpretability, leading to a substantially increased structuring of the embedding space. Code and data are available at https://github.com/iieir-km/ComplEx-NNE_AER.

Domain-specific embedding models have shown promise for applications that require specialized semantic understanding, such as coding agents and financial retrieval systems, often achieving higher performance gains than general models. However, state-of-the-art embedding models are typically based on LLMs, which contain billions of parameters, making deployment challenging in resource-constrained environments. Model compression through pruning offers a promising solution, but existing pruning methods treat all parameters uniformly, failing to distinguish between general semantic representations and domain-specific patterns, leading to suboptimal pruning decisions. Thus, we propose GAPrune, a pruning framework that addresses this challenge by considering both domain importance and preserving general linguistic foundation. Our method uses Fisher Information to measure importance and general-domain gradient alignment to assess parameter behavior, then combines these signals using our Domain Alignment Importance (DAI) scoring. Lower DAI scores indicate that the parameter is either less important for the domain task or creates conflicts between domain and general objectives. Experiments on two domain benchmarks, FinMTEB and ChemTEB, show that GAPrune maintains performance within 2.5% of dense models in one-shot pruning at 50% sparsity, while outperforming all baselines. With retraining in 100 steps, GAPrune achieves +4.51% improvement on FinMTEB and +1.73% on ChemTEB, demonstrating that our pruning strategy not only preserves but enhances domain-specific capabilities. Our findings demonstrate that principled pruning strategies can achieve model compression and enhanced domain specialization, providing the research community with a new approach for development.

Generative models and vision encoders have largely advanced on separate tracks, optimized for different goals and grounded in different mathematical principles. Yet, they share a fundamental property: latent space Gaussianity. Generative models map Gaussian noise to images, while encoders map images to semantic embeddings whose coordinates empirically behave as Gaussian. We hypothesize that both are views of a shared latent source, the Universal Normal Embedding (UNE): an approximately Gaussian latent space from which encoder embeddings and DDIM-inverted noise arise as noisy linear projections. To test our hypothesis, we introduce NoiseZoo, a dataset of per-image latents comprising DDIM-inverted diffusion noise and matching encoder representations (CLIP, DINO). On CelebA, linear probes in both spaces yield strong, aligned attribute predictions, indicating that generative noise encodes meaningful semantics along linear directions. These directions further enable faithful, controllable edits (e.g., smile, gender, age) without architectural changes, where simple orthogonalization mitigates spurious entanglements. Taken together, our results provide empirical support for the UNE hypothesis and reveal a shared Gaussian-like latent geometry that concretely links encoding and generation. Code and data are available https://rbetser.github.io/UNE/

This article focuses on the development and evaluation of Small-sized Czech sentence embedding models. Small models are important components for real-time industry applications in resource-constrained environments. Given the limited availability of labeled Czech data, alternative approaches, including pre-training, knowledge distillation, and unsupervised contrastive fine-tuning, are investigated. Comprehensive intrinsic and extrinsic analyses are conducted, showcasing the competitive performance of our models compared to significantly larger counterparts, with approximately 8 times smaller size and 5 times faster speed than conventional Base-sized models. To promote cooperation and reproducibility, both the models and the evaluation pipeline are made publicly accessible. Ultimately, this article presents practical applications of the developed sentence embedding models in Seznam.cz, the Czech search engine. These models have effectively replaced previous counterparts, enhancing the overall search experience for instance, in organic search, featured snippets, and image search. This transition has yielded improved performance.

Building predictive models for companies often relies on inference using historical data of companies in the same industry sector. However, companies are similar across a variety of dimensions that should be leveraged in relevant prediction problems. This is particularly true for large, complex organizations which may not be well defined by a single industry and have no clear peers. To enable prediction using company information across a variety of dimensions, we create an embedding of company stocks, Stock2Vec, which can be easily added to any prediction model that applies to companies with associated stock prices. We describe the process of creating this rich vector representation from stock price fluctuations, and characterize what the dimensions represent. We then conduct comprehensive experiments to evaluate this embedding in applied machine learning problems in various business contexts. Our experiment results demonstrate that the four features in the Stock2Vec embedding can readily augment existing cross-company models and enhance cross-company predictions.

A primary challenge when deploying speaker recognition systems in real-world applications is performance degradation caused by environmental mismatch. We propose a diffusion-based method that takes speaker embeddings extracted from a pre-trained speaker recognition model and generates refined embeddings. For training, our approach progressively adds Gaussian noise to both clean and noisy speaker embeddings extracted from clean and noisy speech, respectively, via forward process of a diffusion model, and then reconstructs them to clean embeddings in the reverse process. While inferencing, all embeddings are regenerated via diffusion process. Our method needs neither speaker label nor any modification to the existing speaker recognition pipeline. Experiments on evaluation sets simulating environment mismatch scenarios show that our method can improve recognition accuracy by up to 19.6% over baseline models while retaining performance on conventional scenarios. We publish our code here https://github.com/kaistmm/seed-pytorch

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.

Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of cellular sheaves: a knowledge graph embedding can be described as an approximate global section of an appropriate knowledge sheaf over the graph, with consistency constraints induced by the knowledge graph's schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.

Joint representation learning over multi-sourced knowledge graphs (KGs) yields transferable and expressive embeddings that improve downstream tasks. Entity alignment (EA) is a critical step in this process. Despite recent considerable research progress in embedding-based EA, how it works remains to be explored. In this paper, we provide a similarity flooding perspective to explain existing translation-based and aggregation-based EA models. We prove that the embedding learning process of these models actually seeks a fixpoint of pairwise similarities between entities. We also provide experimental evidence to support our theoretical analysis. We propose two simple but effective methods inspired by the fixpoint computation in similarity flooding, and demonstrate their effectiveness on benchmark datasets. Our work bridges the gap between recent embedding-based models and the conventional similarity flooding algorithm. It would improve our understanding of and increase our faith in embedding-based EA.

Contrastive learning (CL) is a prevalent technique for training embedding models, which pulls semantically similar examples (positives) closer in the representation space while pushing dissimilar ones (negatives) further apart. A key source of negatives are 'in-batch' examples, i.e., positives from other examples in the batch. Effectiveness of such models is hence strongly influenced by the size and quality of training batches. In this work, we propose 'Breaking the Batch Barrier' (B3), a novel batch construction strategy designed to curate high-quality batches for CL. Our approach begins by using a pretrained teacher embedding model to rank all examples in the dataset, from which a sparse similarity graph is constructed. A community detection algorithm is then applied to this graph to identify clusters of examples that serve as strong negatives for one another. The clusters are then used to construct batches that are rich in in-batch negatives. Empirical results on the MMEB multimodal embedding benchmark (36 tasks) demonstrate that our method sets a new state of the art, outperforming previous best methods by +1.3 and +2.9 points at the 7B and 2B model scales, respectively. Notably, models trained with B3 surpass existing state-of-the-art results even with a batch size as small as 64, which is 4-16x smaller than that required by other methods.

Large-scale vision-language models (VLMs) like CLIP successfully find correspondences between images and text. Through the standard deterministic mapping process, an image or a text sample is mapped to a single vector in the embedding space. This is problematic: as multiple samples (images or text) can abstract the same concept in the physical world, deterministic embeddings do not reflect the inherent ambiguity in the embedding space. We propose ProbVLM, a probabilistic adapter that estimates probability distributions for the embeddings of pre-trained VLMs via inter/intra-modal alignment in a post-hoc manner without needing large-scale datasets or computing. On four challenging datasets, i.e., COCO, Flickr, CUB, and Oxford-flowers, we estimate the multi-modal embedding uncertainties for two VLMs, i.e., CLIP and BLIP, quantify the calibration of embedding uncertainties in retrieval tasks and show that ProbVLM outperforms other methods. Furthermore, we propose active learning and model selection as two real-world downstream tasks for VLMs and show that the estimated uncertainty aids both tasks. Lastly, we present a novel technique for visualizing the embedding distributions using a large-scale pre-trained latent diffusion model.

In ImageNet-condensation, the storage for auxiliary soft labels exceeds that of the condensed dataset by over 30 times. However, are large-scale soft labels necessary for large-scale dataset distillation? In this paper, we first discover that the high within-class similarity in condensed datasets necessitates the use of large-scale soft labels. This high within-class similarity can be attributed to the fact that previous methods use samples from different classes to construct a single batch for batch normalization (BN) matching. To reduce the within-class similarity, we introduce class-wise supervision during the image synthesizing process by batching the samples within classes, instead of across classes. As a result, we can increase within-class diversity and reduce the size of required soft labels. A key benefit of improved image diversity is that soft label compression can be achieved through simple random pruning, eliminating the need for complex rule-based strategies. Experiments validate our discoveries. For example, when condensing ImageNet-1K to 200 images per class, our approach compresses the required soft labels from 113 GB to 2.8 GB (40x compression) with a 2.6% performance gain. Code is available at: https://github.com/he-y/soft-label-pruning-for-dataset-distillation

Two competing paradigms exist for self-supervised learning of data representations. Joint Embedding Predictive Architecture (JEPA) is a class of architectures in which semantically similar inputs are encoded into representations that are predictive of each other. A recent successful approach that falls under the JEPA framework is self-distillation, where an online encoder is trained to predict the output of the target encoder, sometimes using a lightweight predictor network. This is contrasted with the Masked AutoEncoder (MAE) paradigm, where an encoder and decoder are trained to reconstruct missing parts of the input in the data space rather, than its latent representation. A common motivation for using the JEPA approach over MAE is that the JEPA objective prioritizes abstract features over fine-grained pixel information (which can be unpredictable and uninformative). In this work, we seek to understand the mechanism behind this empirical observation by analyzing the training dynamics of deep linear models. We uncover a surprising mechanism: in a simplified linear setting where both approaches learn similar representations, JEPAs are biased to learn high-influence features, i.e., features characterized by having high regression coefficients. Our results point to a distinct implicit bias of predicting in latent space that may shed light on its success in practice.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora.

Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned embeddings controls predictive performance for a fixed trained model. We show that population risk can be bounded by two factors: (i) the intrinsic dimension of the embedding distribution, which determines the convergence rate of empirical embedding distribution to the population distribution in Wasserstein distance, and (ii) the sensitivity of the downstream mapping from embeddings to predictions, characterized by Lipschitz constants. Together, these yield an embedding-dependent error bound that does not rely on parameter counts or hypothesis class complexity. At the final embedding layer, architectural sensitivity vanishes and the bound is dominated by embedding dimension, explaining its strong empirical correlation with generalization performance. Experiments across architectures and datasets validate the theory and demonstrate the utility of embedding-based diagnostics.

Vision-language models advance multimodal representation learning by acquiring transferable semantic embeddings, thereby substantially enhancing performance across a range of vision-language tasks, including cross-modal retrieval, clustering, and classification. An effective embedding is expected to comprehensively preserve the semantic content of the input while simultaneously emphasizing features that are discriminative for downstream tasks. Recent approaches demonstrate that VLMs can be adapted into competitive embedding models via large-scale contrastive learning, enabling the simultaneous optimization of two complementary objectives. We argue that the two aforementioned objectives can be decoupled: a comprehensive understanding of the input facilitates the embedding model in achieving superior performance in downstream tasks via contrastive learning. In this paper, we propose CoMa, a compressed pre-training phase, which serves as a warm-up stage for contrastive learning. Experiments demonstrate that with only a small amount of pre-training data, we can transform a VLM into a competitive embedding model. CoMa achieves new state-of-the-art results among VLMs of comparable size on the MMEB, realizing optimization in both efficiency and effectiveness.

Large neural models (such as Transformers) achieve state-of-the-art performance for information retrieval (IR). In this paper, we aim to improve distillation methods that pave the way for the resource-efficient deployment of such models in practice. Inspired by our theoretical analysis of the teacher-student generalization gap for IR models, we propose a novel distillation approach that leverages the relative geometry among queries and documents learned by the large teacher model. Unlike existing teacher score-based distillation methods, our proposed approach employs embedding matching tasks to provide a stronger signal to align the representations of the teacher and student models. In addition, it utilizes query generation to explore the data manifold to reduce the discrepancies between the student and the teacher where training data is sparse. Furthermore, our analysis also motivates novel asymmetric architectures for student models which realizes better embedding alignment without increasing online inference cost. On standard benchmarks like MSMARCO, we show that our approach successfully distills from both dual-encoder (DE) and cross-encoder (CE) teacher models to 1/10th size asymmetric students that can retain 95-97% of the teacher performance.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

The inductive bias of a graph neural network (GNN) is largely encoded in its specified graph. Latent graph inference relies on latent geometric representations to dynamically rewire or infer a GNN's graph to maximize the GNN's predictive downstream performance, but it lacks solid theoretical foundations in terms of embedding-based representation guarantees. This paper addresses this issue by introducing a trainable deep learning architecture, coined neural snowflake, that can adaptively implement fractal-like metrics on R^d. We prove that any given finite weights graph can be isometrically embedded by a standard MLP encoder. Furthermore, when the latent graph can be represented in the feature space of a sufficiently regular kernel, we show that the combined neural snowflake and MLP encoder do not succumb to the curse of dimensionality by using only a low-degree polynomial number of parameters in the number of nodes. This implementation enables a low-dimensional isometric embedding of the latent graph. We conduct synthetic experiments to demonstrate the superior metric learning capabilities of neural snowflakes when compared to more familiar spaces like Euclidean space. Additionally, we carry out latent graph inference experiments on graph benchmarks. Consistently, the neural snowflake model achieves predictive performance that either matches or surpasses that of the state-of-the-art latent graph inference models. Importantly, this performance improvement is achieved without requiring random search for optimal latent geometry. Instead, the neural snowflake model achieves this enhancement in a differentiable manner.

Embedding projections are popular for visualizing large datasets and models. However, people often encounter "friction" when using embedding visualization tools: (1) barriers to adoption, e.g., tedious data wrangling and loading, scalability limits, no integration of results into existing workflows, and (2) limitations in possible analyses, without integration with external tools to additionally show coordinated views of metadata. In this paper, we present Embedding Atlas, a scalable, interactive visualization tool designed to make interacting with large embeddings as easy as possible. Embedding Atlas uses modern web technologies and advanced algorithms -- including density-based clustering, and automated labeling -- to provide a fast and rich data analysis experience at scale. We evaluate Embedding Atlas with a competitive analysis against other popular embedding tools, showing that Embedding Atlas's feature set specifically helps reduce friction, and report a benchmark on its real-time rendering performance with millions of points. Embedding Atlas is available as open source to support future work in embedding-based analysis.

Term clustering is important in biomedical knowledge graph construction. Using similarities between terms embedding is helpful for term clustering. State-of-the-art term embeddings leverage pretrained language models to encode terms, and use synonyms and relation knowledge from knowledge graphs to guide contrastive learning. These embeddings provide close embeddings for terms belonging to the same concept. However, from our probing experiments, these embeddings are not sensitive to minor textual differences which leads to failure for biomedical term clustering. To alleviate this problem, we adjust the sampling strategy in pretraining term embeddings by providing dynamic hard positive and negative samples during contrastive learning to learn fine-grained representations which result in better biomedical term clustering. We name our proposed method as CODER++, and it has been applied in clustering biomedical concepts in the newly released Biomedical Knowledge Graph named BIOS.

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at https://github.com/zknus/Hamiltonian-GNN.

LLM-based text embedders have substantially improved retrieval and semantic representation quality, but their deployment remains costly: large backbone models slow down embedding inference, while high-dimensional full-precision embeddings impose substantial storage and bandwidth overhead on large-scale indexes. In this paper, we present BITEMBED, an extreme low-bit framework for LLM-based text embedding that jointly targets encoding efficiency and vector storage. BITEMBED converts pretrained LLM backbones into BitNet-style embedding encoders with ternary weights, quantized activations, and lightweight normalization refinement. The converted model is adapted to representation learning through continual contrastive pre-training, followed by supervised contrastive fine-tuning with both similarity-distribution distillation and attention-relation distillation from a full-precision teacher. Beyond quantizing the backbone, BITEMBED further trains output embeddings to support multiple storage precisions meeting different storage needs in various scenarios. Experiments on MMTEB (eng, v2) with Qwen3-0.6B and Gemma3-270M show that BITEMBED is largely comparable to full precision teacher embedders. Moreover, BITEMBED flexibly obtains text embeddings of various precisions, achieving a trade-off between performance and storage cost.

Modern deep neural networks remain challenging to interpret due to the opacity of their latent representations, impeding model understanding, debugging, and debiasing. Concept Embedding Models (CEMs) address this by mapping inputs to human-interpretable concept representations from which tasks can be predicted. Yet, CEMs fail to represent inter-concept relationships and require concept annotations at different granularities during training, limiting their applicability. In this paper, we introduce Hierarchical Concept Embedding Models (HiCEMs), a new family of CEMs that explicitly model concept relationships through hierarchical structures. To enable HiCEMs in real-world settings, we propose Concept Splitting, a method for automatically discovering finer-grained sub-concepts from a pretrained CEM's embedding space without requiring additional annotations. This allows HiCEMs to generate fine-grained explanations from limited concept labels, reducing annotation burdens. Our evaluation across multiple datasets, including a user study and experiments on PseudoKitchens, a newly proposed concept-based dataset of 3D kitchen renders, demonstrates that (1) Concept Splitting discovers human-interpretable sub-concepts absent during training that can be used to train highly accurate HiCEMs, and (2) HiCEMs enable powerful test-time concept interventions at different granularities, leading to improved task accuracy.

Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various problem settings, the discussion of initialization strategies in the learning process is often missed. In this work, we address this important issue of initialization for network embedding that could dramatically improve the performance of the algorithms on both effectiveness and efficiency. Specifically, we first exploit the graph partition technique that divides the graph into several disjoint subsets, and then construct an abstract graph based on the partitions. We obtain the initialization of the embedding for each node in the graph by computing the network embedding on the abstract graph, which is much smaller than the input graph, and then propagating the embedding among the nodes in the input graph. With extensive experiments on various datasets, we demonstrate that our initialization technique significantly improves the performance of the state-of-the-art algorithms on the evaluations of link prediction and node classification by up to 7.76% and 8.74% respectively. Besides, we show that the technique of initialization reduces the running time of the state-of-the-arts by at least 20%.

Pre-trained language models (PLMs) are widely used to derive semantic representations from item metadata in recommendation and search. In sequential recommendation, PLMs enhance ID-based embeddings through textual metadata, while in product search, they align item characteristics with user intent. Recent studies suggest task and domain-specific fine-tuning are needed to improve representational power. This paper challenges this assumption, showing that Generalist Text Embedding Models (GTEs), pre-trained on large-scale corpora, can guarantee strong zero-shot performance without specialized adaptation. Our experiments demonstrate that GTEs outperform traditional and fine-tuned models in both sequential recommendation and product search. We attribute this to a superior representational power, as they distribute features more evenly across the embedding space. Finally, we show that compressing embedding dimensions by focusing on the most informative directions (e.g., via PCA) effectively reduces noise and improves the performance of specialized models. To ensure reproducibility, we provide our repository at https://split.to/gte4ps.

Deep learning on climatic data holds potential for macroecological applications. However, its adoption remains limited among scientists outside the deep learning community due to storage, compute, and technical expertise barriers. To address this, we introduce Climplicit, a spatio-temporal geolocation encoder pretrained to generate implicit climatic representations anywhere on Earth. By bypassing the need to download raw climatic rasters and train feature extractors, our model uses x3500 less disk space and significantly reduces computational needs for downstream tasks. We evaluate our Climplicit embeddings on biomes classification, species distribution modeling, and plant trait regression. We find that single-layer probing our Climplicit embeddings consistently performs better or on par with training a model from scratch on downstream tasks and overall better than alternative geolocation encoding models.

Pretrained language models like BERT have achieved good results on NLP tasks, but are impractical on resource-limited devices due to memory footprint. A large fraction of this footprint comes from the input embeddings with large input vocabulary and embedding dimensions. Existing knowledge distillation methods used for model compression cannot be directly applied to train student models with reduced vocabulary sizes. To this end, we propose a distillation method to align the teacher and student embeddings via mixed-vocabulary training. Our method compresses BERT-LARGE to a task-agnostic model with smaller vocabulary and hidden dimensions, which is an order of magnitude smaller than other distilled BERT models and offers a better size-accuracy trade-off on language understanding benchmarks as well as a practical dialogue task.

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical contributions that are tailored to the numerical properties of time-series data and allow the model to scale to large datasets, e.g., millions of temporal sequences. We adopt the Transformer architecture by first partitioning the input into non-overlapping windows. Each window is then characterized by its normalized shape and two scalar values denoting the mean and standard deviation within each window. To embed scalar values that may possess arbitrary numerical scales to high-dimensional vectors, we propose a numerically multi-scaled embedding module enumerating all possible scales for the scalar values. The model undergoes pretraining using the proposed numerically multi-scaled embedding with a simple contrastive objective on a large-scale dataset containing over a million sequences. We study its transfer performance on a number of univariate and multivariate classification benchmarks. Our method exhibits remarkable improvement against previous representation learning approaches and establishes the new state of the art, even compared with domain-specific non-learning-based methods.