Daily Papers

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For n axis-aligned rectangles inside an axis-aligned bounding box B, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches B and the density k is minimized, where k is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box B. REP is NP-hard for k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 2-approximation algorithm for SEP with kgeq2 with time complexity O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for kgeq 3 is 3/2 which is tight. We also give a 8-approximation algorithm for REP with time complexity O(nlog n+nk) and give a MPC version of this algorithm for k=O(1) which is the first parallel algorithm for this problem.

Recently, the application of modern diffusion-based text-to-image generation models for creating artistic fonts, traditionally the domain of professional designers, has garnered significant interest. Diverging from the majority of existing studies that concentrate on generating artistic typography, our research aims to tackle a novel and more demanding challenge: the generation of text effects for multilingual fonts. This task essentially requires generating coherent and consistent visual content within the confines of a font-shaped canvas, as opposed to a traditional rectangular canvas. To address this task, we introduce a novel shape-adaptive diffusion model capable of interpreting the given shape and strategically planning pixel distributions within the irregular canvas. To achieve this, we curate a high-quality shape-adaptive image-text dataset and incorporate the segmentation mask as a visual condition to steer the image generation process within the irregular-canvas. This approach enables the traditionally rectangle canvas-based diffusion model to produce the desired concepts in accordance with the provided geometric shapes. Second, to maintain consistency across multiple letters, we also present a training-free, shape-adaptive effect transfer method for transferring textures from a generated reference letter to others. The key insights are building a font effect noise prior and propagating the font effect information in a concatenated latent space. The efficacy of our FontStudio system is confirmed through user preference studies, which show a marked preference (78% win-rates on aesthetics) for our system even when compared to the latest unrivaled commercial product, Adobe Firefly.

Understanding Rebus Puzzles (Rebus Puzzles use pictures, symbols, and letters to represent words or phrases creatively) requires a variety of skills such as image recognition, cognitive skills, commonsense reasoning, multi-step reasoning, image-based wordplay, etc., making this a challenging task for even current Vision-Language Models. In this paper, we present left|,circlearrowright,text{BUS},right|, a large and diverse benchmark of 1,333 English Rebus Puzzles containing different artistic styles and levels of difficulty, spread across 18 categories such as food, idioms, sports, finance, entertainment, etc. We also propose RebusDescProgICE, a model-agnostic framework which uses a combination of an unstructured description and code-based, structured reasoning, along with better, reasoning-based in-context example selection, improving the performance of Vision-Language Models on left|,circlearrowright,text{BUS},right| by 2.1-4.1% and 20-30% using closed-source and open-source models respectively compared to Chain-of-Thought Reasoning.

Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head. Muon groks modular addition faster, but its solutions do not hold. All nine configurations on (a+b) bmod 113 grok and later lose generalization. Across five seeds the selected AdamW reference falls below threshold on four, reaching 27.59%. Instability persists across two moduli, two widths, two training fractions, subtraction, and depth. The failure arises at the representation-readout interface, identified only jointly up to an invertible map unselected by the loss. After solving the training set, the gradient falls to order 10^{-6} and the optimizers respond differently: step-size elasticity is -0.03 for Muon versus +1.5 for AdamW, and the Muon group moves 8.0 times faster per parameter. From bit-identical states, freezing either group prevents failure. Freezing embeddings/readout removes it in five runs over 451,400 post-grokking steps and five paired seeds: unfrozen arms record 137-321 sub-threshold evaluations, frozen arms none. Removing Muon's normalization and orthogonalization is no substitute: it collapses representation from 326 effective conjugate pairs to 4, shows no recurrent collapse, and fails terminally. Fourier filtering separates circuit failure from masking. Across 43 checkpoints over five seeds and three regimes, the task-aligned family reaches exactly 100% alone. In circuit failure it no longer solves the task; in masking it remains perfect while the full model reaches 45.85%, giving a positive margin on every example, including errors, but being outvoted by a near-equal adversarial remainder. Rescaling it restores 99.9%; grokking is the same condition resolving upward. The task selects the family, swapping (k,k) for (k,-k) under subtraction. Across an abrupt collapse, standard Fourier support is unchanged and the power-distribution cosine remains 0.9899.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

LLM coding agents issue Bash commands through interfaces that may serialize, wrap, and reparse model output. Matched execution scores alone cannot distinguish command-generation errors from failures introduced after generation. QuoteBench measures this boundary with exact final-state validation on 56 one-shot tasks from 14 incident-derived families, crossing the generation contract with the execution transport around one deliberately unescaped added parser. Escaping at the interpolation point reproduces each replayed reply's raw-path outcome, so any recovery under a disclosed boundary must come from the model changing its generation. Across eight same-window configurations, replaying the same reply through the added parser lowers success by 55.4 to 73.2 percentage points; disclosure recovers 30.4 to 60.7 points for six configurations, and zero or slightly negative for the other two. Raw generation is nearly saturated at the frontier; boundary adaptation is what still separates models. GPT-5.6-sol's matched gap of -3.6 points hides -64.3 points of damage and +60.7 points of compensation. The deployment configuration reorders models: one reversal among 26 comparable pairs is unambiguous and four more sit on single-task margins. Evaluations of command-issuing agents should report the model configuration, generation contract, execution path, operating point, and final-state validator rather than treat a matched score as an intrinsic model property.

Text-to-image models encounter safety issues, including concerns related to copyright and Not-Safe-For-Work (NSFW) content. Despite several methods have been proposed for erasing inappropriate concepts from diffusion models, they often exhibit incomplete erasure, consume a lot of computing resources, and inadvertently damage generation ability. In this work, we introduce Reliable and Efficient Concept Erasure (RECE), a novel approach that modifies the model in 3 seconds without necessitating additional fine-tuning. Specifically, RECE efficiently leverages a closed-form solution to derive new target embeddings, which are capable of regenerating erased concepts within the unlearned model. To mitigate inappropriate content potentially represented by derived embeddings, RECE further aligns them with harmless concepts in cross-attention layers. The derivation and erasure of new representation embeddings are conducted iteratively to achieve a thorough erasure of inappropriate concepts. Besides, to preserve the model's generation ability, RECE introduces an additional regularization term during the derivation process, resulting in minimizing the impact on unrelated concepts during the erasure process. All the processes above are in closed-form, guaranteeing extremely efficient erasure in only 3 seconds. Benchmarking against previous approaches, our method achieves more efficient and thorough erasure with minor damage to original generation ability and demonstrates enhanced robustness against red-teaming tools. Code is available at https://github.com/CharlesGong12/RECE.

Image stitching from different captures often results in non-rectangular boundaries, which is often considered unappealing. To solve non-rectangular boundaries, current solutions involve cropping, which discards image content, inpainting, which can introduce unrelated content, or warping, which can distort non-linear features and introduce artifacts. To overcome these issues, we introduce a novel diffusion-based learning framework, RecDiffusion, for image stitching rectangling. This framework combines Motion Diffusion Models (MDM) to generate motion fields, effectively transitioning from the stitched image's irregular borders to a geometrically corrected intermediary. Followed by Content Diffusion Models (CDM) for image detail refinement. Notably, our sampling process utilizes a weighted map to identify regions needing correction during each iteration of CDM. Our RecDiffusion ensures geometric accuracy and overall visual appeal, surpassing all previous methods in both quantitative and qualitative measures when evaluated on public benchmarks. Code is released at https://github.com/lhaippp/RecDiffusion.

We analyze the general version of the classic guessing game Mastermind with n positions and k colors. Since the case k le n^{1-varepsilon}, varepsilon>0 a constant, is well understood, we concentrate on larger numbers of colors. For the most prominent case k = n, our results imply that Codebreaker can find the secret code with O(n log log n) guesses. This bound is valid also when only black answer-pegs are used. It improves the O(n log n) bound first proven by Chvátal (Combinatorica 3 (1983), 325--329). We also show that if both black and white answer-pegs are used, then the O(n loglog n) bound holds for up to n^2 loglog n colors. These bounds are almost tight as the known lower bound of Ω(n) shows. Unlike for k le n^{1-varepsilon}, simply guessing at random until the secret code is determined is not sufficient. In fact, we show that an optimal non-adaptive strategy (deterministic or randomized) needs Θ(n log n) guesses.

The wide-angle lens shows appealing applications in VR technologies, but it introduces severe radial distortion into its captured image. To recover the realistic scene, previous works devote to rectifying the content of the wide-angle image. However, such a rectification solution inevitably distorts the image boundary, which potentially changes related geometric distributions and misleads the current vision perception models. In this work, we explore constructing a win-win representation on both content and boundary by contributing a new learning model, i.e., Rectangling Rectification Network (RecRecNet). In particular, we propose a thin-plate spline (TPS) module to formulate the non-linear and non-rigid transformation for rectangling images. By learning the control points on the rectified image, our model can flexibly warp the source structure to the target domain and achieves an end-to-end unsupervised deformation. To relieve the complexity of structure approximation, we then inspire our RecRecNet to learn the gradual deformation rules with a DoF (Degree of Freedom)-based curriculum learning. By increasing the DoF in each curriculum stage, namely, from similarity transformation (4-DoF) to homography transformation (8-DoF), the network is capable of investigating more detailed deformations, offering fast convergence on the final rectangling task. Experiments show the superiority of our solution over the compared methods on both quantitative and qualitative evaluations. The code and dataset will be made available.

GUI agents are rapidly shifting from multi-module pipelines to end-to-end, native vision-language models (VLMs) that perceive raw screenshots and directly interact with digital devices. Despite rapid progress on general GUI tasks, CAPTCHA solving remains a major challenge. On the other hand, although specialized CAPTCHA solving pipelines exist, they cannot handle general GUI tasks. To address this gap, we introduce ReCAP: a CAPTCHA-capable native GUI agent that solves modern, interactive CAPTCHA challenges while retaining general GUI-agent performance. We first develop a dynamic CAPTCHA system spanning seven representative CAPTCHA types, designed to stress primitive and complementary capabilities for CAPTCHA solving. Then, we develop an automated data collection and curation pipeline that generates large-scale CAPTCHA interaction trajectories paired with reasoning traces. As CAPTCHA solving often requires multi-step interaction and recovery from intermediate mistakes, we further leverage failed trajectories to construct self-correction data, training agents to reflect on errors and correct their actions online. Across synthetic and real-world test sets, ReCAP substantially improves CAPTCHA-solving success over its base agents, while maintaining strong performance on general GUI-agent benchmarks.

Current open-source prompt-injection detectors converge on two architectural choices: regular-expression pattern matching and fine-tuned transformer classifiers. Both share failure modes that recent work has made concrete. Regular expressions miss paraphrased attacks. Fine-tuned classifiers are vulnerable to adaptive adversaries: a 2025 NAACL Findings study reported that eight published indirect-injection defenses were bypassed with greater than fifty percent attack success rates under adaptive attacks. This work proposes seven detection techniques that each port a specific mechanism from a discipline outside large-language-model security: forensic linguistics, materials-science fatigue analysis, deception technology from network security, local-sequence alignment from bioinformatics, mechanism design from economics, spectral signal analysis from epidemiology, and taint tracking from compiler theory. Three of the seven techniques are implemented in the prompt-shield v0.4.1 release (Apache 2.0) and evaluated in a four-configuration ablation across six datasets including deepset/prompt-injections, NotInject, LLMail-Inject, AgentHarm, and AgentDojo. The local-alignment detector lifts F1 on deepset from 0.033 to 0.378 with zero additional false positives. The stylometric detector adds 11.1 percentage points of F1 on an indirect-injection benchmark. The fatigue tracker is validated via a probing-campaign integration test. All code, data, and reproduction scripts are released under Apache 2.0.