Daily Papers

We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upper bound on the unknotting number. We have used this to determine the unknotting number of 57k knots. We took diagrams of connected sums of such knots with oppositely signed signatures, where the summands were overlaid. The agent has found examples where several of the crossing changes in an unknotting collection of crossings result in hyperbolic knots. Based on this, we have shown that, given knots K and K' that satisfy some mild assumptions, there is a diagram of their connected sum and u(K) + u(K') unknotting crossings such that changing any one of them results in a prime knot. As a by-product, we have obtained a dataset of 2.6 million distinct hard unknot diagrams; most of them under 35 crossings. Assuming the additivity of the unknotting number, we have determined the unknotting number of 43 at most 12-crossing knots for which the unknotting number is unknown.

When researchers ask whether two transformer layers are "equivalent" for compression, they often conflate distinct tests. Replacement asks whether one layer's map can substitute for another's in place; interchange asks whether two layers approximately commute when their positions are swapped. Both are output-grounded swap-KL probes, but they need not agree: on pretrained transformers the protocol gap can change which layers look safe to prune by several-fold under the same evaluator, especially when replacement distances are high. We measure both protocols across checkpoints and architectures. On a Pythia training trajectory (410M and 1.4B), the replacement-interchange gap grows from initialization to convergence. Under one matched WikiText-2 contract at 8B scale, Qwen3-8B enters a divergent regime: interchange-guided removal is several-fold safer than replacement-guided at the same layer budgets, while Llama-3.1-8B ties the two protocols for pruning cost even though interchange KL is lower, showing metric gaps need not map one-to-one to removal. Before layer removal or merging, score both swap-KLs on the target checkpoint; the diagnostic requires only unlabeled forward passes.

Coarse-mask local image editing asks a model to modify a user-indicated region while preserving the surrounding scene. In practice, however, rough masks often become unintended shape priors: instead of serving as flexible edit support, the mask can pull the generated object toward its accidental boundary. We study this failure as mask-shape bias and frame the task through a Two-Zone Constraint, where the background should remain stable while the editable region should follow the instruction without being forced to inherit the mask contour. BRIDGE addresses this setting by keeping masks outside the DiT backbone for support construction and blending, avoiding DiT-internal mask injection and copied control branches. It uses BridgePath generation, where a Main Path preserves background context and a Subject Path generates editable content from independent noise. Motivated by a diagnostic Qwen-Image experiment showing that positional embeddings and attention connectivity regulate which image context visual tokens reuse, BRIDGE introduces a learnable Discrete Geometric Gate for token-level positional-embedding routing. This gate lets subject tokens borrow background-anchored coordinates near fusion regions or keep subject-centric coordinates for geometric freedom. We evaluate BRIDGE on BRIDGE-Bench, MagicBrush, and ICE-Bench. On BRIDGE-Bench, BRIDGE improves Local SigLIP2-T from 0.262 with FLUX.1-Fill and 0.390 with ACE++ to 0.503, with parallel gains in local DINO and DreamSim. Zero-shot results on MagicBrush and ICE-Bench further indicate competitive alignment and source preservation beyond the curated benchmark, while the added routing module remains compact at 13.31M parameters compared with ControlNet-style copied branches.

Geometric data augmentation is widely used in segmentation workflows, but polygon annotations are often assumed to remain valid after transformation. This assumption can fail in structured domains such as architectural floorplan analysis, where a region may contain an interior void encoded as part of a single ordered polygon chain. Cropping or clipping can remove bridge vertices in this chain, causing one semantic region to split into disconnected components. We propose a lightweight topology-preserving augmentation strategy that repairs missing adjacency relations in index space while preserving the original vertex order. The method adds minimal overhead and can be integrated into existing preprocessing workflows. Experiments show that the proposed approach achieves near-perfect Cyclic Adjacency Preservation (CAP) across common geometric transformations and improves annotation consistency in polygon-based segmentation.

In the literature, it has been shown that the evolution of the known explicit 3D surface to the target one can be learned from 2D images using the instantaneous flow field, where the known and target 3D surfaces may largely differ in topology. We are interested in capturing 4D shapes whose topology changes largely over time. We encounter that the straightforward extension of the existing 3D-based method to the desired 4D case performs poorly. In this work, we address the challenges in extending 3D neural evolution to 4D under large topological changes by proposing two novel modifications. More precisely, we introduce (i) a new architecture to discretize and encode the deformation and learn the SDF and (ii) a technique to impose the temporal consistency. (iii) Also, we propose a rendering scheme for color prediction based on Gaussian splatting. Furthermore, to facilitate learning directly from 2D images, we propose a learning framework that can disentangle the geometry and appearance from RGB images. This method of disentanglement, while also useful for the 4D evolution problem that we are concentrating on, is also novel and valid for static scenes. Our extensive experiments on various data provide awesome results and, most importantly, open a new approach toward reconstructing challenging scenes with significant topological changes and deformations. Our source code and the dataset are publicly available at https://github.com/insait-institute/N4DE.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

Extracting routable road networks from satellite imagery requires accurate topology recovery beyond pixel-level segmentation. Recent methods decompose the task into keypoint detection and connectivity prediction, but reliably inferring road connectivity under structural ambiguity remains challenging. Overpasses introduce non-planar crossings that can create false shortcuts, and occlusions break visual continuity, requiring long-range structural reasoning. We formulate road extraction as fully unobserved connectivity inference and construct a global but sparse Euclidean graph from detected keypoints to better leverage the long-term context. To improve link prediction, we transform this graph into its line graph and perform reasoning using a Graph Transformer. We propose an end-to-end pipeline that integrates vision-based segmentation, sparse graph construction, and structured inference. Our method explicitly models overpasses and uses topology-preserving vertex extraction to mitigate routing-critical errors. This approach achieves state-of-the-art performance on City-scale, SpaceNet, and Global-scale benchmarks in topology metrics including TOPO-F1 and APLS. In addition to quantitative gains, our method improves reconstruction of multi-level road structures crucial for real-world routing reliability. The code is available at: https://github.com/wzzzzzzy/LineGraph2Road.

Current alignment evaluation mostly measures whether models encode dangerous concepts and whether they refuse harmful requests. Both miss the layer where alignment often operates: routing from concept detection to behavioral policy. We study political censorship in Chinese-origin language models as a natural experiment, using probes, surgical ablations, and behavioral tests across nine open-weight models from five labs. Three findings follow. First, probe accuracy alone is non-diagnostic: political probes, null controls, and permutation baselines can all reach 100%, so held-out category generalization is the informative test. Second, surgical ablation reveals lab-specific routing. Removing the political-sensitivity direction eliminates censorship and restores accurate factual output in most models tested, while one model confabulates because its architecture entangles factual knowledge with the censorship mechanism. Cross-model transfer fails, indicating that routing geometry is model- and lab-specific. Third, refusal is no longer the dominant censorship mechanism. Within one model family, hard refusal falls to zero while narrative steering rises to the maximum, making censorship invisible to refusal-only benchmarks. These results support a three-stage descriptive framework: detect, route, generate. Models often retain the relevant knowledge; alignment changes how that knowledge is expressed. Evaluations that audit only detection or refusal therefore miss the routing mechanism that most directly determines behavior.

Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due to the data sparsity between slicing planes, while current bespoke methods struggle to reconstruct thin geometric structures and preserve topological continuity. This is important for medical applications where thin vessel structures are present in CT and MRI scans. This paper introduces CrossSDF, a novel approach for extracting a 3D signed distance field from 2D signed distances generated from planar contours. Our approach makes the training of neural SDFs contour-aware by using losses designed for the case where geometry is known within 2D slices. Our results demonstrate a significant improvement over existing methods, effectively reconstructing thin structures and producing accurate 3D models without the interpolation artifacts or over-smoothing of prior approaches.

This study investigates the dynamics of pedestrian crossing flows with varying crossing angles α to classify different scenarios and derive implications for crowd management. Probability density functions of four key features-velocity v, density ρ, avoidance number Av, and intrusion number In-were analyzed to characterize pedestrian behavior. Velocity-density fundamental diagrams were constructed for each α and fitted with functional forms from existing literature. Classification attempts using Av-In and v-ρ phase spaces revealed significant overlaps, highlighting the limitations of these metrics alone for scenario differentiation. To address this, machine learning models, including logistic regression and random forest, were employed using all four features. Results showed robust classification performance, with v and Av contributing most significantly. Insights from feature importance metrics and classification accuracy offer practical guidance for managing high-density crowds, optimizing pedestrian flow, and designing safer public spaces. These findings provide a data-driven framework for advancing pedestrian dynamics research.

Generative image editing models struggle with structured statistical charts when data modifications require geometric synchronization. We formalize this task as Visuo-Logical Cascading Editing (VLCE). However, existing methods remain confined to localized text substitutions and struggle with dependency-aware cascading updates. To systematically evaluate this capability, we introduce ChartSync, an expert-validated benchmark constructed via a programmatic rendering pipeline that guarantees deterministic visuo-logical coupling for the ground truth. ChartSync comprises 870 triplets across 9 chart categories and 4 task types, including 235 geometry-coupled VLCE instances that specifically test cascading text-to-geometry synchronization. We further evaluate these instances via a two-tier framework combining objective visual metrics with a vision-language model judge paradigm to assess low-level fidelity alongside multimodal comprehension and reasoning. Evaluating 14 image editing models and one code-mediated pipeline reveals a nuanced capability gap: most open-source models suffer severe drops in geometric synchronization, while only two frontier proprietary models show emerging VLCE capability, with their residual errors mainly involving semantic isolation and background corruption. Our detailed error analysis deconstructs these failure paradigms to identify core meta-abilities for guiding future multimodal architectures. The ChartSync dataset and code are publicly released at https://github.com/kaka-yjk/ChartSyncCodebase.

Detecting changes between images is a fundamental problem in computer vision with broad applications in situational awareness, infrastructure assessment, environment monitoring, and industrial automation. Existing supervised models are typically limited to detecting specific types of changes, necessitating retraining for new tasks. To address these limitations with a single approach, we propose a novel change detection method that is the first to utilize unaligned images and textual prompts to output a binary segmentation of changes relevant to user-provided text. Our architecture not only enables flexible detection across diverse change detection use cases, but also yields state-of-the art performance on established benchmarks. Additionally, we release an accompanying dataset comprising of 100,311 pairs of images with text prompts and the corresponding change detection labels. We demonstrate the effectiveness of our method both quantitatively and qualitatively on datasets with a wide variety of viewpoints in indoor, outdoor, street level, synthetic, and satellite images.

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. This morphing is obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto the target shape. In particular, our approach does not assume any knowledge of a boundary parametrization. Furthermore, we demonstrate how constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling scenarii involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The methodology is illustrated on the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.

While recent flow-based image editing models demonstrate general-purpose capabilities across diverse tasks, they often struggle to specialize in challenging scenarios -- particularly those involving large-scale shape transformations. When performing such structural edits, these methods either fail to achieve the intended shape change or inadvertently alter non-target regions, resulting in degraded background quality. We propose Follow-Your-Shape, a training-free and mask-free framework that supports precise and controllable editing of object shapes while strictly preserving non-target content. Motivated by the divergence between inversion and editing trajectories, we compute a Trajectory Divergence Map (TDM) by comparing token-wise velocity differences between the inversion and denoising paths. The TDM enables precise localization of editable regions and guides a Scheduled KV Injection mechanism that ensures stable and faithful editing. To facilitate a rigorous evaluation, we introduce ReShapeBench, a new benchmark comprising 120 new images and enriched prompt pairs specifically curated for shape-aware editing. Experiments demonstrate that our method achieves superior editability and visual fidelity, particularly in tasks requiring large-scale shape replacement.

Pairwise compatibility calculation is at the core of most fragments-reconstruction algorithms, in particular those designed to solve different types of the jigsaw puzzle problem. However, most existing approaches fail, or aren't designed to deal with fragments of realistic geometric properties one encounters in real-life puzzles. And in all other cases, compatibility methods rely strongly on the restricted shapes of the fragments. In this paper, we propose an efficient hybrid (geometric and pictorial) approach for computing the optimal alignment for pairs of fragments, without any assumptions about their shapes, dimensions, or pictorial content. We introduce a new image fragments dataset generated via a novel method for image fragmentation and a formal erosion model that mimics real-world archaeological erosion, along with evaluation metrics for the compatibility task. We then embed our proposed compatibility into an archaeological puzzle-solving framework and demonstrate state-of-the-art neighborhood-level precision and recall on the RePAIR 2D dataset, directly reflecting compatibility performance improvements.