Daily Papers

Recent advances in automatic rigging now deliver animation-ready 3D assets at scale, yet generating the motion to drive them remains a bottleneck. Existing learned animators are topology-constrained: they rely on category-specific templates or require per-skeleton fine-tuning and reference motions at inference. We present UniMate, a unified foundation model that synthesizes articulated motion for arbitrary skeletons from a rigged 3D asset and a text prompt, with no test-time optimization or per-skeleton retraining. UniMate introduces a topology-aware diffusion transformer, which integrates skeletal topology into attention via three mechanisms: (1) a graph-aware attention bias from pairwise joint relations and geodesic distances; (2) a spectral rotary position embedding generalizing RoPE to arbitrary kinematic trees via the graph Laplacian; and (3) a global topological conditioner attention-pooled from the rest-pose skeleton. We also curate UniML3D, 13,006 motion sequences spanning bipedal, quadrupedal, avian, marine, insectoid, serpentine, and articulated rigid objects with unified canonicalization and text pairing. Trained on this dataset, UniMate outperforms state-of-the-art baselines in quality, generalization, and efficiency, and supports zero-shot cross-topology transfer, in-betweening, expansion, and text-guided editing. Our project page is available at https://linzhanmou.com/unimate/.

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical studies have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in the ongoing diversity-stability debate. Within this context, however, there has been a severe lack of studies that consider spatial features explicitly, even though nearly all habitats are spatially embedded. To this end, we study here the linear stability of meta-ecosystems on networks that describe how discrete patches are connected by dispersal between them. By combining results from random-matrix theory and network theory, we are able to show that there are three distinct features that underlie stability: edge density, tendency to triadic closure, and isolation or fragmentation. Our results appear to further indicate that network sparsity does not necessarily reduce stability, and that connections between patches are just as, if not more, important to consider when studying the stability of large ecological systems.

Adversarially perturbed images of text can cause sophisticated OCR systems to produce misleading or incorrect transcriptions from seemingly invisible changes to humans. Some of these perturbations even survive physical capture, posing security risks to high-stakes applications such as document processing, license plate recognition, and automated compliance systems. Existing defenses, such as adversarial training, input preprocessing, or post-recognition correction, are often model-specific, computationally expensive, and affect performance on unperturbed inputs while remaining vulnerable to unseen or adaptive attacks. To address these challenges, TopoReformer is introduced, a model-agnostic reformation pipeline that mitigates adversarial perturbations while preserving the structural integrity of text images. Topology studies properties of shapes and spaces that remain unchanged under continuous deformations, focusing on global structures such as connectivity, holes, and loops rather than exact distance. Leveraging these topological features, TopoReformer employs a topological autoencoder to enforce manifold-level consistency in latent space and improve robustness without explicit gradient regularization. The proposed method is benchmarked on EMNIST, MNIST, against standard adversarial attacks (FGSM, PGD, Carlini-Wagner), adaptive attacks (EOT, BDPA), and an OCR-specific watermark attack (FAWA).

The capability of autonomous exploration in complex, unknown environments is important in many robotic applications. While recent research on autonomous exploration have achieved much progress, there are still limitations, e.g., existing methods relying on greedy heuristics or optimal path planning are often hindered by repetitive paths and high computational demands. To address such limitations, we propose a novel exploration framework that utilizes the global topology information of observed environment to improve exploration efficiency while reducing computational overhead. Specifically, global information is utilized based on a skeletal topological graph representation of the environment geometry. We first propose an incremental skeleton extraction method based on wavefront propagation, based on which we then design an approach to generate a lightweight topological graph that can effectively capture the environment's structural characteristics. Building upon this, we introduce a finite state machine that leverages the topological structure to efficiently plan coverage paths, which can substantially mitigate the back-and-forth maneuvers (BFMs) problem. Experimental results demonstrate the superiority of our method in comparison with state-of-the-art methods. The source code will be made publicly available at: https://github.com/Haochen-Niu/STGPlanner.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature has also led to a lack of unification in notation and language across Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL, and compare the recently published TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.

Generating visual layouts is an essential ingredient of graphic design. The ability to condition layout generation on a partial subset of component attributes is critical to real-world applications that involve user interaction. Recently, diffusion models have demonstrated high-quality generative performances in various domains. However, it is unclear how to apply diffusion models to the natural representation of layouts which consists of a mix of discrete (class) and continuous (location, size) attributes. To address the conditioning layout generation problem, we introduce DLT, a joint discrete-continuous diffusion model. DLT is a transformer-based model which has a flexible conditioning mechanism that allows for conditioning on any given subset of all the layout component classes, locations, and sizes. Our method outperforms state-of-the-art generative models on various layout generation datasets with respect to different metrics and conditioning settings. Additionally, we validate the effectiveness of our proposed conditioning mechanism and the joint continuous-diffusion process. This joint process can be incorporated into a wide range of mixed discrete-continuous generative tasks.

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse rendering of geometry rely on silhouette gradients for topology changes, such signals are sparse. In contrast, our theory derives topological derivatives that relate the introduction of vanishing holes and phases to changes in image intensity. As a result, we enable differentiable shape perturbations in the form of hole or phase nucleation. We validate the proposed theory with optimization of closed curves in 2D and surfaces in 3D to lend insights into limitations of current methods and enable improved applications such as image vectorization, vector-graphics generation from text prompts, single-image reconstruction of shape ambigrams and multi-view 3D reconstruction.

We introduce GlobalBuildingAtlas, a publicly available dataset providing global and complete coverage of building polygons, heights and Level of Detail 1 (LoD1) 3D building models. This is the first open dataset to offer high quality, consistent, and complete building data in 2D and 3D form at the individual building level on a global scale. Towards this dataset, we developed machine learning-based pipelines to derive building polygons and heights (called GBA.Height) from global PlanetScope satellite data, respectively. Also a quality-based fusion strategy was employed to generate higher-quality polygons (called GBA.Polygon) based on existing open building polygons, including our own derived one. With more than 2.75 billion buildings worldwide, GBA.Polygon surpasses the most comprehensive database to date by more than 1 billion buildings. GBA.Height offers the most detailed and accurate global 3D building height maps to date, achieving a spatial resolution of 3x3 meters-30 times finer than previous global products (90 m), enabling a high-resolution and reliable analysis of building volumes at both local and global scales. Finally, we generated a global LoD1 building model (called GBA.LoD1) from the resulting GBA.Polygon and GBA.Height. GBA.LoD1 represents the first complete global LoD1 building models, including 2.68 billion building instances with predicted heights, i.e., with a height completeness of more than 97%, achieving RMSEs ranging from 1.5 m to 8.9 m across different continents. With its height accuracy, comprehensive global coverage and rich spatial details, GlobalBuildingAltas offers novel insights on the status quo of global buildings, which unlocks unprecedented geospatial analysis possibilities, as showcased by a better illustration of where people live and a more comprehensive monitoring of the progress on the 11th Sustainable Development Goal of the United Nations.

Recent facial image synthesis methods have been mainly based on conditional generative models. Sketch-based conditions can effectively describe the geometry of faces, including the contours of facial components, hair structures, as well as salient edges (e.g., wrinkles) on face surfaces but lack effective control of appearance, which is influenced by color, material, lighting condition, etc. To have more control of generated results, one possible approach is to apply existing disentangling works to disentangle face images into geometry and appearance representations. However, existing disentangling methods are not optimized for human face editing, and cannot achieve fine control of facial details such as wrinkles. To address this issue, we propose DeepFaceEditing, a structured disentanglement framework specifically designed for face images to support face generation and editing with disentangled control of geometry and appearance. We adopt a local-to-global approach to incorporate the face domain knowledge: local component images are decomposed into geometry and appearance representations, which are fused consistently using a global fusion module to improve generation quality. We exploit sketches to assist in extracting a better geometry representation, which also supports intuitive geometry editing via sketching. The resulting method can either extract the geometry and appearance representations from face images, or directly extract the geometry representation from face sketches. Such representations allow users to easily edit and synthesize face images, with decoupled control of their geometry and appearance. Both qualitative and quantitative evaluations show the superior detail and appearance control abilities of our method compared to state-of-the-art methods.

We present GeoSynth, a model for synthesizing satellite images with global style and image-driven layout control. The global style control is via textual prompts or geographic location. These enable the specification of scene semantics or regional appearance respectively, and can be used together. We train our model on a large dataset of paired satellite imagery, with automatically generated captions, and OpenStreetMap data. We evaluate various combinations of control inputs, including different types of layout controls. Results demonstrate that our model can generate diverse, high-quality images and exhibits excellent zero-shot generalization. The code and model checkpoints are available at https://github.com/mvrl/GeoSynth.

Triangle meshes are fundamental to 3D applications, enabling efficient modification and rasterization while maintaining compatibility with standard rendering pipelines. However, current automatic mesh generation methods typically rely on intermediate representations that lack the continuous surface quality inherent to meshes. Converting these representations into meshes produces dense, suboptimal outputs. Although recent autoregressive approaches demonstrate promise in directly modeling mesh vertices and faces, they are constrained by the limitation in face count, scalability, and structural fidelity. To address these challenges, we propose Nautilus, a locality-aware autoencoder for artist-like mesh generation that leverages the local properties of manifold meshes to achieve structural fidelity and efficient representation. Our approach introduces a novel tokenization algorithm that preserves face proximity relationships and compresses sequence length through locally shared vertices and edges, enabling the generation of meshes with an unprecedented scale of up to 5,000 faces. Furthermore, we develop a Dual-stream Point Conditioner that provides multi-scale geometric guidance, ensuring global consistency and local structural fidelity by capturing fine-grained geometric features. Extensive experiments demonstrate that Nautilus significantly outperforms state-of-the-art methods in both fidelity and scalability. The project page is at https://nautilusmeshgen.github.io.

Diagram-to-graph topology extraction aims to extract a graph of entities and their connections from a structural diagram. This task remains challenging for current vision-language models because it requires both fine-grained perceptual grounding and topology-aware reasoning with global consistency. We present TopoBench-180, a human-verified benchmark for diagram-to-graph topology extraction, and TopoAgent, a structure-aware perception-to-reasoning framework for reliable topology extraction using large vision-language models. TopoBench-180 contains 180 structural diagrams spanning Web-style and Network-style categories, paired with canonical graph annotations. TopoAgent progressively extracts the target graph by combining grounded perception, global structural priors, canonical node inventory construction, node-centric local-to-global relation reasoning, and topological consistency enforcement. Experiments on TopoBench-180 show that TopoAgent outperforms strong vision-language model baselines and recent visual reasoning frameworks, especially on edge extraction. More broadly, this work fills an important gap in multimodal structured understanding by establishing a benchmark and framework for diagram-to-graph topology extraction. The benchmark and associated resources will be publicly released at https://huggingface.co/datasets/WayneGuo0011/TopoBench-180.

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

We tackle the problem of generating a complete vector map representation from aerial imagery in a single run: producing polygons for all land-cover classes with shared boundaries and without gaps or overlaps. Existing polygonization methods are typically class-specific; extending them to multiple classes via per-class runs commonly leads to topological inconsistencies, such as duplicated edges, gaps, and overlaps. We formalize this new task as All-Class Polygonal Vectorization (ACPV) and release the first public benchmark, Deventer-512, with standardized metrics jointly evaluating semantic fidelity, geometric accuracy, vertex efficiency, per-class topological fidelity and global topological consistency. To realize ACPV, we propose ACPV-Net, a unified framework introducing a novel Semantically Supervised Conditioning (SSC) mechanism coupling semantic perception with geometric primitive generation, along with a topological reconstruction that enforces shared-edge consistency by design. While enforcing such strict topological constraints, ACPV-Net surpasses all class-specific baselines in polygon quality across classes on Deventer-512. It also applies to single-class polygonal vectorization without any architectural modification, achieving the best-reported results on WHU-Building. Data, code, and models will be released at: https://github.com/HeinzJiao/ACPV-Net.

We propose a system for rearranging objects in a scene to achieve a desired object-scene placing relationship, such as a book inserted in an open slot of a bookshelf. The pipeline generalizes to novel geometries, poses, and layouts of both scenes and objects, and is trained from demonstrations to operate directly on 3D point clouds. Our system overcomes challenges associated with the existence of many geometrically-similar rearrangement solutions for a given scene. By leveraging an iterative pose de-noising training procedure, we can fit multi-modal demonstration data and produce multi-modal outputs while remaining precise and accurate. We also show the advantages of conditioning on relevant local geometric features while ignoring irrelevant global structure that harms both generalization and precision. We demonstrate our approach on three distinct rearrangement tasks that require handling multi-modality and generalization over object shape and pose in both simulation and the real world. Project website, code, and videos: https://anthonysimeonov.github.io/rpdiff-multi-modal/

Solving topological grid puzzles requires reasoning over global spatial invariants such as connectivity, loop closure, and region symmetry and remains challenging for even the most powerful large language models (LLMs). To study these abilities under controlled settings, we introduce TopoBench, a benchmark of six puzzle families across three difficulty levels. We evaluate strong reasoning LLMs on TopoBench and find that even frontier models solve fewer than one quarter of hard instances, with two families nearly unsolved. To investigate whether these failures stem from reasoning limitations or from difficulty extracting and maintaining spatial constraints, we annotate 750 chain of thought traces with an error taxonomy that surfaces four candidate causal failure modes, then test them with targeted interventions simulating each error type. These interventions show that certain error patterns like premature commitment and constraint forgetting have a direct impact on the ability to solve the puzzle, while repeated reasoning is a benign effect of search. Finally we study mitigation strategies including prompt guidance, cell-aligned grid representations and tool-based constraint checking, finding that the bottleneck lies in extracting constraints from spatial representations and not in reasoning over them. Code and data are available at github.com/mayug/topobench-benchmark.

3D world generation is essential for applications such as immersive content creation or autonomous driving simulation. Recent advances in 3D world generation have shown promising results; however, these methods are constrained by grid layouts and suffer from inconsistencies in object scale throughout the entire world. In this work, we introduce a novel framework, Map2World, that first enables 3D world generation conditioned on user-defined segment maps of arbitrary shapes and scales, ensuring global-scale consistency and flexibility across expansive environments. To further enhance the quality, we propose a detail enhancer network that generates fine details of the world. The detail enhancer enables the addition of fine-grained details without compromising overall scene coherence by incorporating global structure information. We design the entire pipeline to leverage strong priors from asset generators, achieving robust generalization across diverse domains, even under limited training data for scene generation. Extensive experiments demonstrate that our method significantly outperforms existing approaches in user-controllability, scale consistency, and content coherence, enabling users to generate 3D worlds under more complex conditions.

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their latent representations are typically learned in Euclidean space, neglecting the underlying geometric and hierarchical structure among states, and (ii) they struggle with long-horizon prediction, which leads to rapid degradation across extended rollouts. To address these challenges, we introduce GeoWorld, a geometric world model that preserves geometric structure and hierarchical relations through a Hyperbolic JEPA, which maps latent representations from Euclidean space onto hyperbolic manifolds. We further introduce Geometric Reinforcement Learning for energy-based optimization, enabling stable multi-step planning in hyperbolic latent space. Extensive experiments on CrossTask and COIN demonstrate around 3% SR improvement in 3-step planning and 2% SR improvement in 4-step planning compared to the state-of-the-art V-JEPA 2. Project website: https://steve-zeyu-zhang.github.io/GeoWorld.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis (TDA) paradigm, of which real-world data exhibits multi-scale patterns, we construct several graphs using Persistent Homology Filtration -- a mathematical framework describing the multiscale structural properties of data points. Then, we use the constructed graphs as an input to create an ensemble of Graph Neural Networks. The ensemble aggregates the signals from the individual learners via an attention-based routing mechanism, thus systematically encoding the inherent multiscale structures of data. Four different real-world experiments on seismic activity prediction and traffic forecasting (PEMS-BAY, METR-LA) demonstrate that our approach consistently outperforms single-graph baselines while providing interpretable insights.

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 x 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

River systems operate as inherently interconnected continuous networks, meaning river hydrodynamic simulation ought to be a systemic process. However, widespread hydrology data scarcity often restricts data-driven forecasting to isolated predictions. To achieve systemic simulation and reduce reliance on river observations, we present GraphRiverCast (GRC), a topology-informed AI foundation model designed to simulate multivariate river hydrodynamics in global river systems. GRC is capable of operating in a "ColdStart" mode, generating predictions without relying on historical river states for initialization. In 7-day global pseudo-hindcasts, GRC-ColdStart functions as a robust standalone simulator, achieving a Nash-Sutcliffe Efficiency (NSE) of approximately 0.82 without exhibiting the significant error accumulation typical of autoregressive paradigms. Ablation studies reveal that topological encoding serves as indispensable structural information in the absence of historical states, explicitly guiding hydraulic connectivity and network-scale mass redistribution to reconstruct flow dynamics. Furthermore, when adapted locally via a pre-training and fine-tuning strategy, GRC consistently outperforms physics-based and locally-trained AI baselines. Crucially, this superiority extends from gauged reaches to full river networks, underscoring the necessity of topology encoding and physics-based pre-training. Built on a physics-aligned neural operator architecture, GRC enables rapid and cross-scale adaptive simulation, establishing a collaborative paradigm bridging global hydrodynamic knowledge with local hydrological reality.

We introduce TopoPrimer, a framework that makes the global topological structure of the series population an explicit input to any forecasting model. TopoPrimer improves accuracy across diverse domains, stabilizes forecasts under seasonal demand spikes, and closes the cold-start gap. Precomputed once per domain via persistent homology and spectral sheaf coordinates, TopoPrimer deploys per token for fully-trained models and as a lightweight adapter for pre-trained backbones. Of these two components, sheaf coordinates are the primary accuracy driver. Across four public benchmarks on Chronos and TimesFM, TopoPrimer consistently improves forecasting accuracy, with gains of up to 7.3% MSE on ECL. The topology advantage persists with near-identical magnitude across zero-shot and fine-tuned backbones, suggesting topology and per-series training capture complementary signals. The gains are most pronounced in difficult regimes. Under peak seasonal demand, classical and zero-shot models degrade by up to 50%, while TopoPrimer stays within 10%. At cold start with no item history, TopoPrimer reduces MAE by 27% over a topology-free baseline.

In this paper, we propose REASON, a novel framework that enables the automatic discovery of both intra-level (i.e., within-network) and inter-level (i.e., across-network) causal relationships for root cause localization. REASON consists of Topological Causal Discovery and Individual Causal Discovery. The Topological Causal Discovery component aims to model the fault propagation in order to trace back to the root causes. To achieve this, we propose novel hierarchical graph neural networks to construct interdependent causal networks by modeling both intra-level and inter-level non-linear causal relations. Based on the learned interdependent causal networks, we then leverage random walks with restarts to model the network propagation of a system fault. The Individual Causal Discovery component focuses on capturing abrupt change patterns of a single system entity. This component examines the temporal patterns of each entity's metric data (i.e., time series), and estimates its likelihood of being a root cause based on the Extreme Value theory. Combining the topological and individual causal scores, the top K system entities are identified as root causes. Extensive experiments on three real-world datasets with case studies demonstrate the effectiveness and superiority of the proposed framework.

Neural operators that accept arbitrary meshes are often treated as geometry-general, but unseen domain topology changes both the invariant and decaying subspaces of a PDE operator. We use Hodge heat flow as a controlled lens on this distinction and introduce TopoBox-3D, where tunnels and cavities vary Betti support while the exact Hodge decomposition separates the harmonic kernel from the positive spectrum. Across six architectures, models that infer topology implicitly suffer excess matched degradation in 37 of 45 model--task topology-OOD cells, yet cases that change harmonic dimension are not more strongly penalized on average. The dominant difficulty is instead spectral: the initial Rayleigh quotient is the most stable predictor of error, and spectral broadening adds information for edge and face cochains. Most strikingly, controlled probes show that explicit incidence and harmonic coordinates do not yield the best kernel-identity accuracy; nevertheless, TNO ranks first in mixed-input nonharmonic accuracy on all six tasks with nontrivial harmonic support. Together, these results establish topology as a distinct generalization axis beyond arbitrary-geometry compatibility and show that its influence extends across the Hodge spectrum rather than remaining confined to the harmonic kernel. More broadly, they suggest that global, low-frequency structural priors may help organize predictions in the faster-decaying complementary component, offering a new perspective on how neural operators may generalize across topology as well as geometry.

Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been shown to provide informative summaries of a shape's multiscale structure. In this paper we pose the question whether topological information can be derived from features produced by 3D encoders. To address this question, we first introduce DONUT, a synthetic benchmark with controlled topological complexity, and propose FILTR (Filtration Transformer), a learnable framework to predict persistence diagrams directly from frozen encoders. FILTR adapts a transformer decoder to treat diagram generation as a set prediction task. Our analysis on DONUT reveals that existing encoders retain only limited global topological signals, yet FILTR successfully leverages information produced by these encoders to approximate persistence diagrams. Our approach enables, for the first time, data-driven extraction of persistence diagrams from raw point clouds through an efficient learnable feed-forward mechanism.

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only manually define a single-value edge to describe the connectivity or strength of association between a pair of vertices, task-specific and crucial relationship cues may be disregarded by such manually defined topology and single-value edge features. In this paper, we propose the first general graph representation learning framework (called GRATIS) which can generate a strong graph representation with a task-specific topology and task-specific multi-dimensional edge features from any arbitrary input. To learn each edge's presence and multi-dimensional feature, our framework takes both of the corresponding vertices pair and their global contextual information into consideration, enabling the generated graph representation to have a globally optimal message passing mechanism for different down-stream tasks. The principled investigation results achieved for various graph analysis tasks on 11 graph and non-graph datasets show that our GRATIS can not only largely enhance pre-defined graphs but also learns a strong graph representation for non-graph data, with clear performance improvements on all tasks. In particular, the learned topology and multi-dimensional edge features provide complementary task-related cues for graph analysis tasks. Our framework is effective, robust and flexible, and is a plug-and-play module that can be combined with different backbones and Graph Neural Networks (GNNs) to generate a task-specific graph representation from various graph and non-graph data. Our code is made publicly available at https://github.com/SSYSteve/Learning-Graph-Representation-with-Task-specific-Topology-and-Multi-dimensional-Edge-Features.

We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yielding models that respect the geometric support of physical quantities and expose conservation and compatibility structure. We further propose Hierarchical TNOs (HTNOs), which incorporate learned coarse complexes to propagate long-range and topology-dependent information. Our framework subsumes existing NOs as a special case, providing a unified perspective on operator learning across discretizations. Across a range of PDE benchmarks, including irregular-geometry flow problems, TNOs and HTNOs improve accuracy; controlled studies further isolate the benefits of native higher-rank and topological structure. Project page: https://circle-group.github.io/research/TNO

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

This work introduces TopoBenchmarkX, a modular open-source library designed to standardize benchmarking and accelerate research in Topological Deep Learning (TDL). TopoBenchmarkX maps the TDL pipeline into a sequence of independent and modular components for data loading and processing, as well as model training, optimization, and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBenchmarkX is that it allows for the transformation and lifting between topological domains. This enables, for example, to obtain richer data representations and more fine-grained analyses by mapping the topology and features of a graph to higher-order topological domains such as simplicial and cell complexes. The range of applicability of TopoBenchmarkX is demonstrated by benchmarking several TDL architectures for various tasks and datasets.

Accurate reconstruction of both the geometric and topological details of a 3D object from a single 2D image embodies a fundamental challenge in computer vision. Existing explicit/implicit solutions to this problem struggle to recover self-occluded geometry and/or faithfully reconstruct topological shape structures. To resolve this dilemma, we introduce LIST, a novel neural architecture that leverages local and global image features to accurately reconstruct the geometric and topological structure of a 3D object from a single image. We utilize global 2D features to predict a coarse shape of the target object and then use it as a base for higher-resolution reconstruction. By leveraging both local 2D features from the image and 3D features from the coarse prediction, we can predict the signed distance between an arbitrary point and the target surface via an implicit predictor with great accuracy. Furthermore, our model does not require camera estimation or pixel alignment. It provides an uninfluenced reconstruction from the input-view direction. Through qualitative and quantitative analysis, we show the superiority of our model in reconstructing 3D objects from both synthetic and real-world images against the state of the art.

3D Gaussian Splatting (3DGS) has made significant strides in scene representation and neural rendering, with intense efforts focused on adapting it for dynamic scenes. Despite delivering remarkable rendering quality and speed, existing methods struggle with storage demands and representing complex real-world motions. To tackle these issues, we propose MoDecGS, a memory-efficient Gaussian splatting framework designed for reconstructing novel views in challenging scenarios with complex motions. We introduce GlobaltoLocal Motion Decomposition (GLMD) to effectively capture dynamic motions in a coarsetofine manner. This approach leverages Global Canonical Scaffolds (Global CS) and Local Canonical Scaffolds (Local CS), extending static Scaffold representation to dynamic video reconstruction. For Global CS, we propose Global Anchor Deformation (GAD) to efficiently represent global dynamics along complex motions, by directly deforming the implicit Scaffold attributes which are anchor position, offset, and local context features. Next, we finely adjust local motions via the Local Gaussian Deformation (LGD) of Local CS explicitly. Additionally, we introduce Temporal Interval Adjustment (TIA) to automatically control the temporal coverage of each Local CS during training, allowing MoDecGS to find optimal interval assignments based on the specified number of temporal segments. Extensive evaluations demonstrate that MoDecGS achieves an average 70% reduction in model size over stateoftheart methods for dynamic 3D Gaussians from realworld dynamic videos while maintaining or even improving rendering quality.

We present a new method for multimodal conditional 3D face geometry generation that allows user-friendly control over the output identity and expression via a number of different conditioning signals. Within a single model, we demonstrate 3D faces generated from artistic sketches, portrait photos, Canny edges, FLAME face model parameters, 2D face landmarks, or text prompts. Our approach is based on a diffusion process that generates 3D geometry in a 2D parameterized UV domain. Geometry generation passes each conditioning signal through a set of cross-attention layers (IP-Adapter), one set for each user-defined conditioning signal. The result is an easy-to-use 3D face generation tool that produces topology-consistent, high-quality geometry with fine-grain user control.

We present an algorithmic framework for incremental maintenance of first sheaf cohomology H^1(X; F) on dynamically evolving 1-dimensional cellular complexes equipped with finite-dimensional cellular sheaves. The classical computation of H^1 via factorization of the coboundary matrix requires O(n^3) time; when the complex evolves with a stream of m edits, full recomputation after each edit costs O(mn^3). Under a bounded local geometry assumption -- bounded cell size v_{max}, bounded stalk dimension d, and bounded nerve degree D -- each edit (vertex insertion, edge insertion, restriction map update) affects only a bounded set of local coboundary blocks. The algorithm therefore processes lazy streaming edits in O(1) time with respect to the total complex size n (with cost polynomial in the local geometry parameters v_{max}, d, and D, which are treated as constants independent of n), deferring local eigensolves and Mayer-Vietoris global assembly to synchronization points (Flush). At synchronization, the maintained state agrees with the corresponding batch assembly of the partitioned sheaf model; we observe zero measured drift in all batch-verified runs (through V = 10^6). We also give an amortized O(|E|) streaming construction for the cellular decomposition and discuss an adversarial algebraic-RAM barrier arguing that unpartitioned non-trivial sheaves (d geq 2, non-identity restriction maps) do not admit the same locality. Experiments on Barabasi-Albert graphs with up to 5 times 10^6 vertices and 1.7 times 10^7 streaming edits show 35 μs median lazy per-edit update latency (excluding flush); query time (global assembly at synchronization) is O(n) per flush in the implemented full-traversal path. Exact synchronization costs are reported separately.

We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they enable the application of differential geometry theory and are optimized for modern graphics pipelines. However, existing inverse rendering methods often fail catastrophically on high-genus surfaces, leading to the loss of key topological features, and tend to oversmooth low-genus surfaces, resulting in the loss of surface details. This failure stems from their overreliance on Adam-based optimizers, which can lead to vanishing and exploding gradients. To overcome these challenges, we introduce an adaptive V-cycle remeshing scheme in conjunction with a re-parametrized Adam optimizer to enhance topological and geometric awareness. By periodically coarsening and refining the deforming mesh, our method informs mesh vertices of their current topology and geometry before optimization, mitigating gradient issues while preserving essential topological features. Additionally, we enforce topological consistency by constructing topological primitives with genus numbers that match those of ground truth using Gauss-Bonnet theorem. Experimental results demonstrate that our inverse rendering approach outperforms the current state-of-the-art method, achieving significant improvements in Chamfer Distance and Volume IoU, particularly for high-genus surfaces, while also enhancing surface details for low-genus surfaces.

High-resolution 3D generation increasingly relies on voxel latents and multi-stage pipelines that first predict active structure and then synthesize local geometry. While effective, this design fragments continuous surfaces into many local tokens, inflates generation cost, and often weakens topological consistency for thin or highly connected shapes. We introduce SILSA, a topology-aware 3D generation framework that represents shapes with compact sliding-window slice latents. Instead of generating expensive voxel tokens, SILSA uses a fixed set of overlapping slices along the three canonical axes, where each token summarizes a local depth window to preserve cross-sectional continuity and support single-stage rectified-flow generation. A Slice VAE encodes oriented surface samples into multi-axis slice latents and reconstructs them with a sparse volumetric decoder, while a Volumetric Anchor Lattice coordinates directional slice streams through a shared 3D workspace. To preserve structural correctness, we introduce slice-level topology supervision that matches persistence diagrams and aligns Betti transitions across neighboring slices. Experiments show that SILSA improves structural fidelity while substantially reducing generation cost. SILSA improves PSNR by 8.7%, coverage by 5.96 absolute points, and Betti error by 9.2% over the strongest baseline, while using 70.0% fewer tokens than the next-most compact baseline and over 98% fewer tokens than sparse or hierarchical tokenizers, effectively reducing training memory by 40.4% and inference time by 58.5%. Qualitative results further show improved preservation of thin structures, repeated components, and long-range connectivity.

Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of existing TO approaches leverage numerical solvers for design evaluations during the optimization and hence have a nested nature and rely on discretizing the design variables. Contrary to these approaches, herein we develop a new class of TO methods based on the framework of Gaussian processes (GPs) whose mean functions are parameterized via deep neural networks. Specifically, we place GP priors on all design and state variables to represent them via parameterized continuous functions. These GPs share a deep neural network as their mean function but have as many independent kernels as there are state and design variables. We estimate all the parameters of our model in a single for loop that optimizes a penalized version of the performance metric where the penalty terms correspond to the state equations and design constraints. Attractive features of our approach include (1) having a built-in continuation nature since the performance metric is optimized at the same time that the state equations are solved, and (2) being discretization-invariant and accommodating complex domains and topologies. To test our method against conventional TO approaches implemented in commercial software, we evaluate it on four problems involving the minimization of dissipated power in Stokes flow. The results indicate that our approach does not need filtering techniques, has consistent computational costs, and is highly robust against random initializations and problem setup.

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, global utility, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present TabStruct, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

Structural pruning enhances hardware-agnostic inference efficiency for large language models (LLMs) yet often fails to maintain comparable performance. Local pruning performs efficient layer-by-layer compression but ignores global topology. Although global pruning aims to identify an optimal sparse model, intuitive methods typically adopt a two-stage paradigm that first evaluates substructure saliency and then applies global pruning, which ignores inter-structure dependencies and fails to achieve end-to-end optimization. To address these limitations, we propose T\'yr-the-Pruner, an efficient end-to-end search-based global structural pruning framework. This framework constructs a supernet by repeatedly applying local pruning across a range of sparsity ratios to each layer in an LLM, with the core goal of determining the optimal sparsity distribution under a target overall sparsity ratio. Concretely, we introduce an effective local pruning and an expectation error accumulation approach to improve supernet construction. Furthermore, we employ an iterative prune-and-search strategy with coarse-to-fine sparsity granularity to ensure efficient search convergence. Experimental results show that T\'yr-the-Pruner achieves state-of-the-art structural pruning, retaining 97% of the dense model's performance while removing a challenging 50% of Llama-3.1-70B's parameters. Code will be available at https://github.com/AMD-AGI/Tyr-the-Pruner.

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

Leaf-lesion segmentation is topology-sensitive: small merges, splits, or false holes can be biologically meaningful descriptors of biochemical pathways, yet they are weakly penalized by standard pixel-wise losses in Euclidean latents. I explore HyperTopo-Adapters, a lightweight, parameter-efficient head trained on top of a frozen vision encoder, which embeds features on a product manifold -- hyperbolic + Euclidean + spherical (H + E + S) -- to encourage hierarchical separation (H), local linear detail (E), and global closure (S). A topology prior complements Dice/BCE in two forms: (i) persistent-homology (PH) distance for evaluation and selection, and (ii) a differentiable surrogate that combines a soft Euler-characteristic match with total variation regularization for stable training. I introduce warm-ups for both the hyperbolic contrastive term and the topology prior, per-sample evaluation of structure-aware metrics (Boundary-F1, Betti errors, PD distance), and a min-PD within top-K Dice rule for checkpoint selection. On a Kaggle leaf-lesion dataset (N=2,940), early results show consistent gains in boundary and topology metrics (reducing Delta beta_1 hole error by 9%) while Dice/IoU remain competitive. The study is diagnostic by design: I report controlled ablations (curvature learning, latent dimensions, contrastive temperature, surrogate settings), and ongoing tests varying encoder strength (ResNet-50, DeepLabV3, DINOv2/v3), input resolution, PH weight, and partial unfreezing of late blocks. The contribution is an open, reproducible train/eval suite (available at https://github.com/ChimdiWalter/HyperTopo-Adapters) that isolates geometric/topological priors and surfaces failure modes to guide stronger, topology-preserving architectures.

Accurate agricultural field boundary delineation at large scale is a foundational task for food security, supply chain transparency, and carbon accounting. While vision foundation models like SAM show remarkable zero-shot capabilities, they frequently fail in geospatial domains due to topological complexity, cropland texturing patterns, and a lack of physical scale awareness. In this work, we introduce Delineate Anything v2, a globally scalable foundation model designed specifically for wide-area field boundary mapping. We construct FBIS-73M, a 73-million-instance multi-resolution dataset spanning 61 countries. To address the pervasive issue of multi-field administrative parcel merging, we introduce a resolution-specific data curation pipeline that leverages topological image-space adaptation to homogenize merged parcels and strengthen weak physical boundaries. Furthermore, we establish a novel, manually curated evaluation benchmark covering 100 countries to assess independent zero-shot generalization. Our results show that Delineate Anything v2 surpasses the current state-of-the-art, including the Delineate Anything framework, by 0.284 mAP@0.5 (+103.3% relative gain), while maintaining execution speeds suitable for rapid national- and global-scale deployment, as demonstrated by nationwide mapping of Ukraine (603,000 km^2) in 5.4 hours on a consumer-grade workstation. Code, pre-trained weights, the FBIS-73M dataset, and ready-to-use national-scale vector boundary products are publicly available at https://github.com/Lavreniuk/Delineate-Anything.

Diffusion-based world models have shown strong potential for unified world simulation, but the iterative denoising remains too costly for interactive use and long-horizon rollouts. While feature caching can accelerate inference without training, we find that policies designed for single-modal diffusion transfer poorly to world models due to two world-model-specific obstacles: token heterogeneity from multi-modal coupling and spatial variation, and non-uniform temporal dynamics where a small set of hard tokens drives error growth, making uniform skipping either unstable or overly conservative. We propose WorldCache, a caching framework tailored to diffusion world models. We introduce Curvature-guided Heterogeneous Token Prediction, which uses a physics-grounded curvature score to estimate token predictability and applies a Hermite-guided damped predictor for chaotic tokens with abrupt direction changes. We also design Chaotic-prioritized Adaptive Skipping, which accumulates a curvature-normalized, dimensionless drift signal and recomputes only when bottleneck tokens begin to drift. Experiments on diffusion world models show that WorldCache delivers up to 3.7times end-to-end speedups while maintaining 98\% rollout quality, demonstrating the vast advantages and practicality of WorldCache in resource-constrained scenarios. Our code is released in https://github.com/FofGofx/WorldCache.

Climate-vulnerable road networks require a paradigm shift from reactive, fix-on-failure repairs to predictive, decision-ready maintenance. This paper introduces ST-ResGAT, a novel Spatio-Temporal Residual Graph Attention Network that fuses residual graph-attention encoding with GRU temporal aggregation to forecast pavement deterioration. Engineered for resource-constrained deployment, the framework translates continuous Pavement Condition Index (PCI) forecasts directly into the American Society for Testing and Materials (ASTM)-compliant maintenance priorities. Using a real-world inspection dataset of 750 segments in Sylhet, Bangladesh (2021-2024), ST-ResGAT significantly outperforms traditional non-spatial machine learning baselines, achieving exceptional predictive fidelity (R2 = 0.93, RMSE = 2.72). Crucially, ablation testing confirmed the mathematical necessity of modeling topological neighbor effects, proving that structural decay acts as a spatial contagion. Uniquely, we integrate GNNExplainer to unbox the model, demonstrating that its learned priorities align perfectly with established physical engineering theory. Furthermore, we quantify classification safety: achieving 85.5% exact ASTM class agreement and 100% adjacent-class containment, ensuring bounded, engineer-safe predictions. To connect model outputs to policy, we generate localized longitudinal maintenance profiles, perform climate stress-testing, and derive Pareto sustainability frontiers. ST-ResGAT therefore offers a practical, explainable, and sustainable blueprint for intelligent infrastructure management in high-risk, low-resource geological settings.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between model pre-training and domain adaptation. In this paper, we propose a fresh Riemannian geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then "glues" the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue's geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold. Codes are available at https://github.com/RiemannGraph/GraphGlue.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Geometry-conditioned 3D scene generation enables the creation of 3D environments from user-provided geometry, offering direct control over scene structure and object layout. To generate such 3D scenes, current methods commonly adopt a three-stage design that first defines a view schedule, then synthesizes multi-view observations along the scheduled views, and finally reconstructs a 3D representation from the generated images. However, defining the view schedule becomes a major bottleneck for outdoor scenes, where large, unstructured, and unbounded geometry makes it difficult to obtain views that provide sufficient coverage while supporting stable generation. To address this bottleneck, we present SceneFrom3D, a framework that automatically schedules views from outdoor input geometries. SceneFrom3D constructs a directed generation graph whose nodes represent anchor views and whose edges represent interpolation trajectories, defining which views to synthesize, which view pairs to interpolate, and in which order generation should proceed. Beyond automatic view scheduling, SceneFrom3D further improves controllability through object-level conditioning, assigning each object an identity image for appearance guidance and a geometry-adherence parameter for region-wise control over the input geometry. Experiments demonstrate that SceneFrom3D achieves state-of-the-art geometry-conditioned outdoor 3D scene generation, producing high-quality scenes with controllable object appearance and geometry adherence.

Global placement is a critical step with high computational complexity in VLSI physical design. Modern analytical placers formulate the placement problem as a nonlinear optimization, where initialization strongly affects both convergence behavior and final placement quality. However, existing initialization methods exhibit a trade-off: area-aware initializers account for cell areas but are computationally expensive and can dominate total runtime, while fast point-based initializers ignore cell area, leading to a modeling gap that impairs convergence and solution quality. We propose a lightweight co-optimization framework that bridges this initialization gap through two strategies. First, an area-hint refinement initializer incorporates heuristic cell area information into a signed graph signal by augmenting the netlist graph with virtual nodes and negative-weight edges, yielding an area-aware and spectrally smooth placement initialization. Second, a macro-schedule placement procedure progressively restores area constraints, enabling a smooth transition from the refined initializer to the full area-aware objective and producing high-quality placement results. We evaluate the framework on macro-heavy ISPD2005 academic benchmarks and two real-world industrial designs across two technology nodes (12 cases in total). Experimental results show that our method consistently improves half-perimeter wirelength (HPWL) over point-based initializers in 11 out of 12 cases, achieving up to 2.2% HPWL reduction, while running approximately 100 times faster than the state-of-the-art area-aware initializer.

Large language models place structured concepts on geometrically faithful manifolds: weekdays lie on a circle, months on another, usually taken to be a fixed world-model the network stores and looks up. We show that context is king: the structure a model actually uses is set by the in-context specification. A declarative rule fixes not only which relations the geometry encodes but its topology type: the same tokens form a cycle or a branching tree on command, built even on arbitrary, meaning-free tokens with no prior to inherit, which a relabeled stored shape cannot do. When the specification conflicts with a strong pretrained prior, the context-set geometry dominates it in capable models, read from the same activations (representational similarity 0.6--0.9 to the imposed structure versus near-zero to the prior), across the priors we test and both families we study (Gemma, Qwen). Activation patching shows the map is causally used, not a probe correlate: swapping one entity's activation for another's makes the model answer with the other entity's successor under the imposed order. A rough map forms readily, present even in small and base models; what scale gates is using it cleanly: clean dominance and the causal crossover emerge only in the larger models (up to Gemma-31B and Qwen-27B) and weaken or reverse below, so a mechanism present in a large model can be absent in a smaller one of the same family. Whether the model builds this geometry anew or reconfigures a stored one we leave open; operationally, the geometry it uses is the one the context specifies.

Data quality is crucial for the successful training, generalization and performance of artificial intelligence models. Furthermore, it is known that the leading approaches in artificial intelligence are notoriously data-hungry. In this paper, we propose the use of small training datasets towards faster training. Specifically, we provide a novel topological method based on morphisms between persistence modules to measure the training data quality with respect to the complete dataset. This way, we can provide an explanation of why the chosen training dataset will lead to poor performance.

Global operations, such as global average pooling, are widely used in top-performance image restorers. They aggregate global information from input features along entire spatial dimensions but behave differently during training and inference in image restoration tasks: they are based on different regions, namely the cropped patches (from images) and the full-resolution images. This paper revisits global information aggregation and finds that the image-based features during inference have a different distribution than the patch-based features during training. This train-test inconsistency negatively impacts the performance of models, which is severely overlooked by previous works. To reduce the inconsistency and improve test-time performance, we propose a simple method called Test-time Local Converter (TLC). Our TLC converts global operations to local ones only during inference so that they aggregate features within local spatial regions rather than the entire large images. The proposed method can be applied to various global modules (e.g., normalization, channel and spatial attention) with negligible costs. Without the need for any fine-tuning, TLC improves state-of-the-art results on several image restoration tasks, including single-image motion deblurring, video deblurring, defocus deblurring, and image denoising. In particular, with TLC, our Restormer-Local improves the state-of-the-art result in single image deblurring from 32.92 dB to 33.57 dB on GoPro dataset. The code is available at https://github.com/megvii-research/tlc.

The boundary representation (B-Rep) is the standard data structure used in Computer-Aided Design (CAD) for defining solid models. Despite recent progress, directly generating B-Reps end-to-end with precise geometry and watertight topology remains a challenge. This paper presents AutoBrep, a novel Transformer model that autoregressively generates B-Reps with high quality and validity. AutoBrep employs a unified tokenization scheme that encodes both geometric and topological characteristics of a B-Rep model as a sequence of discrete tokens. Geometric primitives (i.e., surfaces and curves) are encoded as latent geometry tokens, and their structural relationships are defined as special topological reference tokens. Sequence order in AutoBrep naturally follows a breadth first traversal of the B-Rep face adjacency graph. At inference time, neighboring faces and edges along with their topological structure are progressively generated. Extensive experiments demonstrate the advantages of our unified representation when coupled with next-token prediction for B-Rep generation. AutoBrep outperforms baselines with better quality and watertightness. It is also highly scalable to complex solids with good fidelity and inference speed. We further show that autocompleting B-Reps is natively supported through our unified tokenization, enabling user-controllable CAD generation with minimal changes. Code is available at https://github.com/AutodeskAILab/AutoBrep.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

Controllable layout generation refers to the process of creating a plausible visual arrangement of elements within a graphic design (e.g., document and web designs) with constraints representing design intentions. Although recent diffusion-based models have achieved state-of-the-art FID scores, they tend to exhibit more pronounced misalignment compared to earlier transformer-based models. In this work, we propose the LAyout Constraint diffusion modEl (LACE), a unified model to handle a broad range of layout generation tasks, such as arranging elements with specified attributes and refining or completing a coarse layout design. The model is based on continuous diffusion models. Compared with existing methods that use discrete diffusion models, continuous state-space design can enable the incorporation of differentiable aesthetic constraint functions in training. For conditional generation, we introduce conditions via masked input. Extensive experiment results show that LACE produces high-quality layouts and outperforms existing state-of-the-art baselines.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

We present a data-driven approach for forecasting global weather using graph neural networks. The system learns to step forward the current 3D atmospheric state by six hours, and multiple steps are chained together to produce skillful forecasts going out several days into the future. The underlying model is trained on reanalysis data from ERA5 or forecast data from GFS. Test performance on metrics such as Z500 (geopotential height) and T850 (temperature) improves upon previous data-driven approaches and is comparable to operational, full-resolution, physical models from GFS and ECMWF, at least when evaluated on 1-degree scales and when using reanalysis initial conditions. We also show results from connecting this data-driven model to live, operational forecasts from GFS.

Interactive 3D assets used in games and simulation are typically decomposed into specific semantic parts to support animation, physics, and scripted behaviors, yet most generative 3D models produce either monolithic meshes or arbitrary part decompositions that cannot be aligned with application-specific requirements. We present CubePart, a generative framework for open-vocabulary, part-controllable 3D mesh generation that exposes part structure as an explicit inference-time control signal. Given a global text prompt and a user-defined parts schema expressed as an open-ended list of part names, our method generates a set of meshes - one per schema element - that assemble into a coherent object while respecting the specified semantic structure. To enable this capability, we introduce a scalable data pipeline to construct a large open-vocabulary, part-labeled 3D dataset, along with a two-stage generative architecture that separates global shape synthesis from part-level decoding. We demonstrate that the resulting assets can be directly integrated into game engines and driven by animation and behavior scripts without manual post-processing. Project Page: https://cubepart.github.io/

In this work, we seek new insights into the underlying challenges of the Scene Graph Generation (SGG) task. Quantitative and qualitative analysis of the Visual Genome dataset implies -- 1) Ambiguity: even if inter-object relationship contains the same object (or predicate), they may not be visually or semantically similar, 2) Asymmetry: despite the nature of the relationship that embodied the direction, it was not well addressed in previous studies, and 3) Higher-order contexts: leveraging the identities of certain graph elements can help to generate accurate scene graphs. Motivated by the analysis, we design a novel SGG framework, Local-to-Global Interaction Networks (LOGIN). Locally, interactions extract the essence between three instances of subject, object, and background, while baking direction awareness into the network by explicitly constraining the input order of subject and object. Globally, interactions encode the contexts between every graph component (i.e., nodes and edges). Finally, Attract & Repel loss is utilized to fine-tune the distribution of predicate embeddings. By design, our framework enables predicting the scene graph in a bottom-up manner, leveraging the possible complementariness. To quantify how much LOGIN is aware of relational direction, a new diagnostic task called Bidirectional Relationship Classification (BRC) is also proposed. Experimental results demonstrate that LOGIN can successfully distinguish relational direction than existing methods (in BRC task), while showing state-of-the-art results on the Visual Genome benchmark (in SGG task).

We address the problem of detecting human-object interactions in images using graphical neural networks. Unlike conventional methods, where nodes send scaled but otherwise identical messages to each of their neighbours, we propose to condition messages between pairs of nodes on their spatial relationships, resulting in different messages going to neighbours of the same node. To this end, we explore various ways of applying spatial conditioning under a multi-branch structure. Through extensive experimentation we demonstrate the advantages of spatial conditioning for the computation of the adjacency structure, messages and the refined graph features. In particular, we empirically show that as the quality of the bounding boxes increases, their coarse appearance features contribute relatively less to the disambiguation of interactions compared to the spatial information. Our method achieves an mAP of 31.33% on HICO-DET and 54.2% on V-COCO, significantly outperforming state-of-the-art on fine-tuned detections.

Point cloud completion aims to recover accurate global geometry and preserve fine-grained local details from partial point clouds. Conventional methods typically predict unseen points directly from 3D point cloud coordinates or use self-projected multi-view depth maps to ease this task. However, these gray-scale depth maps cannot reach multi-view consistency, consequently restricting the performance. In this paper, we introduce a GeoFormer that simultaneously enhances the global geometric structure of the points and improves the local details. Specifically, we design a CCM Feature Enhanced Point Generator to integrate image features from multi-view consistent canonical coordinate maps (CCMs) and align them with pure point features, thereby enhancing the global geometry feature. Additionally, we employ the Multi-scale Geometry-aware Upsampler module to progressively enhance local details. This is achieved through cross attention between the multi-scale features extracted from the partial input and the features derived from previously estimated points. Extensive experiments on the PCN, ShapeNet-55/34, and KITTI benchmarks demonstrate that our GeoFormer outperforms recent methods, achieving the state-of-the-art performance. Our code is available at https://github.com/Jinpeng-Yu/GeoFormer{https://github.com/Jinpeng-Yu/GeoFormer}.

Accurate weather forecasts are important for disaster prevention, agricultural planning, etc. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneForecast) based on graph neural networks. By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that OneForecast performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions. Codes link https://github.com/YuanGao-YG/OneForecast.

Deep learning models are known to exhibit a strong texture bias, while human tends to rely heavily on global shape structure for object recognition. The current benchmark for evaluating a model's global shape bias is a set of style-transferred images with the assumption that resistance to the attack of style transfer is related to the development of global structure sensitivity in the model. In this work, we show that networks trained with style-transfer images indeed learn to ignore style, but its shape bias arises primarily from local detail. We provide a Disrupted Structure Testbench (DiST) as a direct measurement of global structure sensitivity. Our test includes 2400 original images from ImageNet-1K, each of which is accompanied by two images with the global shapes of the original image disrupted while preserving its texture via the texture synthesis program. We found that black{(1) models that performed well on the previous cue-conflict dataset do not fare well in the proposed DiST; (2) the supervised trained Vision Transformer (ViT) lose its global spatial information from positional embedding, leading to no significant advantages over Convolutional Neural Networks (CNNs) on DiST. While self-supervised learning methods, especially mask autoencoder significantly improves the global structure sensitivity of ViT. (3) Improving the global structure sensitivity is orthogonal to resistance to style-transfer, indicating that the relationship between global shape structure and local texture detail is not an either/or relationship. Training with DiST images and style-transferred images are complementary, and can be combined to train network together to enhance the global shape sensitivity and robustness of local features.} Our code will be hosted in github: https://github.com/leelabcnbc/DiST

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered using methods that involve symmetry-based analysis of the quantum wavefunction. Here we use machine learning to develop a simple-to-use heuristic chemical rule that diagnoses with a high accuracy whether a material is topological using only its chemical formula. This heuristic rule is based on a notion that we term topogivity, a machine-learned numerical value for each element that loosely captures its tendency to form topological materials. We next implement a high-throughput procedure for discovering topological materials based on the heuristic topogivity-rule prediction followed by ab initio validation. This way, we discover new topological materials that are not diagnosable using symmetry indicators, including several that may be promising for experimental observation.

Generating high-quality triangle meshes is essential for film, gaming, and interactive 3D applications. Mainstream methods rely on mesh serialization and autoregressive processes, which stuggles in effective inference and is sensitive to error accumulation. In this paper, we present Nexus, a diffusion method that achieves holistic mesh generation via decoupled vertex and topology generation. First, we view mesh vertices as sparse voxels organized as an octree and adopt a diffusion model to generate the vertices in a coarse-to-fine manner. Second, for topology modeling, we propose Spacetime Interval, as an extension of Spacetime Distance to encode arbitrary edge and face topology into continuous per-vertex embeddings. It allows for a global and efficient recovery of complex topology. We then employ a diffusion model to generate the continuous embeddings on the generated vertices. Extensive experiments on the Objaverse and Toys4K datasets and in-the-wild images demonstrate that our method outperforms state-of-the-art autoregressive and two-stage baselines, effectively circumventing the inherent limitations of sequential mesh modeling. A blind user study from 3D practitioners confirms strong perceptual preference for our results.

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.

In this paper, we propose a simple and general framework for self-supervised point cloud representation learning. Human beings understand the 3D world by extracting two levels of information and establishing the relationship between them. One is the global shape of an object, and the other is the local structures of it. However, few existing studies in point cloud representation learning explored how to learn both global shapes and local-to-global relationships without a specified network architecture. Inspired by how human beings understand the world, we utilize knowledge distillation to learn both global shape information and the relationship between global shape and local structures. At the same time, we combine contrastive learning with knowledge distillation to make the teacher network be better updated. Our method achieves the state-of-the-art performance on linear classification and multiple other downstream tasks. Especially, we develop a variant of ViT for 3D point cloud feature extraction, which also achieves comparable results with existing backbones when combined with our framework, and visualization of the attention maps show that our model does understand the point cloud by combining the global shape information and multiple local structural information, which is consistent with the inspiration of our representation learning method. Our code will be released soon.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Spatial reasoning depends not only on metric properties such as distance, angle, and shape, but also on topological relations that remain invariant under continuous deformation. Cognitive science identifies these relations as foundational to spatial understanding, yet foundation-model evaluations largely focus on metric or viewpoint-dependent relations. We introduce MindTopo, a benchmark of topological intuition across five properties grounded in cognitive science and formal topology: continuity, separation, order, enclosure, and knots. MindTopo evaluates each property at two cognitive levels. Reasoning asks a model to identify topological relations or infer how they change. Planning instantiates a foundation model as a closed-loop agent whose policy selects environment actions. MindTopo contains 11,030 instances across 13 procedurally generated task types with controllable difficulty. We benchmark 14 MLLMs and study agent configurations augmented with image and video generation, including 3 video generative models in planning settings. Every MLLM performs better on reasoning than on planning, and the best-performing model remains far below observed human performance. On Qwen3-VL-2B-Instruct, supervised fine-tuning and reinforcement learning improve reasoning more than planning. Generated observations retain local cues and reach plausible endpoints, but audited rollouts do not reliably follow environment dynamics or preserve topology across transitions. Our website is at https://mind-topo.github.io/

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

This paper introduces a novel method for merging open-domain terminological knowledge. It takes advantage of the Region Connection Calculus (RCC5), a formalism used to represent regions in a topological space and to reason about their set-theoretic relationships. To this end, we first propose a faithful translation of terminological knowledge provided by several and potentially conflicting sources into region spaces. The merging is then performed on these spaces, and the result is translated back into the underlying language of the input sources. Our approach allows us to benefit from the expressivity and the flexibility of RCC5 while dealing with conflicting knowledge in a principled way.

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering.

The structure of topology underpins much of the research on performance and robustness, yet available topology data are typically scarce, necessitating the generation of synthetic graphs with desired properties for testing or release. Prior diffusion-based approaches either embed conditions into the diffusion model, requiring retraining for each attribute and hindering real-time applicability, or use classifier-based guidance post-training, which does not account for topology scale and practical constraints. In this paper, we show from a discrete perspective that gradients from a pre-trained graph-level classifier can be incorporated into the discrete reverse diffusion posterior to steer generation toward specified structural properties. Based on this insight, we propose Classifier-guided Conditional Topology Generation with Persistent Homology (CoPHo), which builds a persistent homology filtration over intermediate graphs and interprets features as guidance signals that steer generation toward the desired properties at each denoising step. Experiments on four generic/network datasets demonstrate that CoPHo outperforms existing methods at matching target metrics, and we further validate its transferability on the QM9 molecular dataset.

Boundary representation (B-Rep) generation is a fundamental task in computer-aided design, yet the direct synthesis of high-fidelity and structurally valid B-Reps remains a major challenge. Existing deep generative methods suffer from two forms of brittleness: representation brittleness, caused by padding noise and feature contamination in the latent space, and generation brittleness, stemming from sequential error propagation and a train-inference mismatch due to non-differentiable validity enforcement. We propose HiFi-BRep, a novel framework that addresses these limitations through two synergistic contributions. First, a topology-aware encoder constructs a high-fidelity latent representation by eliminating padding via learnable queries and preventing feature contamination with topology-guided attention. Second, a single-stage decoder jointly predicts geometry and topology in parallel, embedding core manifold constraints as a differentiable learning objective. This design ensures mutual guidance between geometry and topology while avoiding cascaded errors. Extensive experiments show that HiFi-BRep significantly outperforms state-of-the-art methods in both structural validity and geometric fidelity, providing a robust solution for high-quality B-Rep synthesis. Code and models are publicly available at https://github.com/1nnoh/HiFi-BRep.

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

Global climate models typically operate at a grid resolution of hundreds of kilometers and fail to resolve atmospheric mesoscale processes, e.g., clouds, precipitation, and gravity waves (GWs). Model representation of these processes and their sources is essential to the global circulation and planetary energy budget, but subgrid scale contributions from these processes are often only approximately represented in models using parameterizations. These parameterizations are subject to approximations and idealizations, which limit their capability and accuracy. The most drastic of these approximations is the "single-column approximation" which completely neglects the horizontal evolution of these processes, resulting in key biases in current climate models. With a focus on atmospheric GWs, we present the first-ever global simulation of atmospheric GW fluxes using machine learning (ML) models trained on the WINDSET dataset to emulate global GW emulation in the atmosphere, as an alternative to traditional single-column parameterizations. Using an Attention U-Net-based architecture trained on globally resolved GW momentum fluxes, we illustrate the importance and effectiveness of global nonlocality, when simulating GWs using data-driven schemes.

End-to-end human animation with rich multi-modal conditions, e.g., text, image and audio has achieved remarkable advancements in recent years. However, most existing methods could only animate a single subject and inject conditions in a global manner, ignoring scenarios that multiple concepts could appears in the same video with rich human-human interactions and human-object interactions. Such global assumption prevents precise and per-identity control of multiple concepts including humans and objects, therefore hinders applications. In this work, we discard the single-entity assumption and introduce a novel framework that enforces strong, region-specific binding of conditions from modalities to each identity's spatiotemporal footprint. Given reference images of multiple concepts, our method could automatically infer layout information by leveraging a mask predictor to match appearance cues between the denoised video and each reference appearance. Furthermore, we inject local audio condition into its corresponding region to ensure layout-aligned modality matching in a iterative manner. This design enables the high-quality generation of controllable multi-concept human-centric videos. Empirical results and ablation studies validate the effectiveness of our explicit layout control for multi-modal conditions compared to implicit counterparts and other existing methods.

The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method, the Differentiable Euler Characteristic Transform (DECT), is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly simple statistic provides the same topological expressivity as more complex topological deep learning layers.

Realistic 3D city generation is fundamental to a wide range of applications, including virtual reality and digital twins. However, most existing methods rely on training a single diffusion model, which limits their ability to generate personalized and boundless city-scale scenes. In this paper, we present Yo'City, a novel agentic framework that enables user-customized and infinitely expandable 3D city generation by leveraging the reasoning and compositional capabilities of off-the-shelf large models. Specifically, Yo'City first conceptualize the city through a top-down planning strategy that defines a hierarchical "City-District-Grid" structure. The Global Planner determines the overall layout and potential functional districts, while the Local Designer further refines each district with detailed grid-level descriptions. Subsequently, the grid-level 3D generation is achieved through a "produce-refine-evaluate" isometric image synthesis loop, followed by image-to-3D generation. To simulate continuous city evolution, Yo'City further introduces a user-interactive, relationship-guided expansion mechanism, which performs scene graph-based distance- and semantics-aware layout optimization, ensuring spatially coherent city growth. To comprehensively evaluate our method, we construct a diverse benchmark dataset and design six multi-dimensional metrics that assess generation quality from the perspectives of semantics, geometry, texture, and layout. Extensive experiments demonstrate that Yo'City consistently outperforms existing state-of-the-art methods across all evaluation aspects.

Graph Foundation Models (GFMs) have achieved remarkable success in generalizing across diverse domains. However, they mainly focus on Text-Attributed Graphs (TAGs), leaving Multimodal-Attributed Graphs (MAGs) largely untapped. Developing Multimodal Graph Foundation Models (MGFMs) allows for leveraging the rich multimodal information in MAGs, and extends applicability to broader types of downstream tasks. While recent MGFMs integrate diverse modality information, our empirical investigation reveals two fundamental limitations of existing MGFMs: (1)they fail to explicitly model modality interaction, essential for capturing intricate cross-modal semantics beyond simple aggregation, and (2)they exhibit sub-optimal modality alignment, which is critical for bridging the significant semantic disparity between distinct modal spaces. To address these challenges, we propose PLANET (graPh topoLogy-aware modAlity iNteraction and alignmEnT), a novel framework employing a Divide-and-Conquer strategy to decouple modality interaction and alignment across distinct granularities. At the embedding granularity, (1)Embedding-wise Domain Gating (EDG) performs local semantic enrichment by adaptively infusing topology-aware cross-modal context, achieving modality interaction. At the node granularity, (2)Node-wise Discretization Retrieval (NDR) ensures global modality alignment by constructing a Discretized Semantic Representation Space (DSRS) to bridge modality gaps. Extensive experiments demonstrate that PLANET significantly outperforms state-of-the-art baselines across diverse graph-centric and multimodal generative tasks.

Foundation models for Earth systems have so far been trained primarily on physical climate and weather data, with limited representation of the human systems that both drive and respond to environmental change. The lack of a unified global training resource that combines climate, land, ocean, cryosphere, infrastructure, hazards, and socioeconomic data on a common grid hinders progress toward truly multimodal Earth system foundation models. We present WorldTensor, a harmonised global dataset that aligns hundreds of environmental and socioeconomic variables to a standardised 0.25^circ spatial grid and annual temporal framework. WorldTensor integrates reanalysis products, remote sensing, emissions inventories, land use reconstructions, hydrological observations, infrastructure and hazard datasets, and socioeconomic indicators within a single representation designed for machine learning workflows. To build the dataset, we regridded inputs across heterogeneous native resolutions and projections, rasterised point and vector datasets into spatially meaningful gridded fields, and reconciled temporal coverages ranging from daily observations to sparse multiyear socioeconomic snapshots. All outputs are distributed as NetCDF files with standardised coordinates, variable metadata, and a common CF metadata convention. WorldTensor provides a reproducible resource for training and evaluating foundation models that learn coupled dynamics across environmental and human systems at planetary scale.

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {Haldane bundle dataset}, which consists of synthetically generated complex line bundles on the 2-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

Visual navigation in robotics traditionally relies on globally-consistent 3D maps or learned controllers, which can be computationally expensive and difficult to generalize across diverse environments. In this work, we present a novel RGB-only, object-level topometric navigation pipeline that enables zero-shot, long-horizon robot navigation without requiring 3D maps or pre-trained controllers. Our approach integrates global topological path planning with local metric trajectory control, allowing the robot to navigate towards object-level sub-goals while avoiding obstacles. We address key limitations of previous methods by continuously predicting local trajectory using monocular depth and traversability estimation, and incorporating an auto-switching mechanism that falls back to a baseline controller when necessary. The system operates using foundational models, ensuring open-set applicability without the need for domain-specific fine-tuning. We demonstrate the effectiveness of our method in both simulated environments and real-world tests, highlighting its robustness and deployability. Our approach outperforms existing state-of-the-art methods, offering a more adaptable and effective solution for visual navigation in open-set environments. The source code is made publicly available: https://github.com/podgorki/TANGO.

With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These changes reveal semantic coherence, logical redundancy, and identify logical breaks and gaps. By calculating homology groups, we assess connectivity and redundancy at various scales, using barcode and persistence diagrams to quantify stability and consistency. Our results show that the topological structural complexity of reasoning chains correlates positively with accuracy. More complex chains identify correct answers sooner, while successful reasoning exhibits simpler topologies, reducing redundancy and cycles, enhancing efficiency and interpretability. This work provides a new perspective on reasoning chain quality assessment and offers guidance for future optimization.

Regular screening and early discovery of uterine fibroid are crucial for preventing potential malignant transformations and ensuring timely, life-saving interventions. To this end, we collect and annotate the first ultrasound video dataset with 100 videos for uterine fibroid segmentation (UFUV). We also present Local-Global Reciprocal Network (LGRNet) to efficiently and effectively propagate the long-term temporal context which is crucial to help distinguish between uninformative noisy surrounding tissues and target lesion regions. Specifically, the Cyclic Neighborhood Propagation (CNP) is introduced to propagate the inter-frame local temporal context in a cyclic manner. Moreover, to aggregate global temporal context, we first condense each frame into a set of frame bottleneck queries and devise Hilbert Selective Scan (HilbertSS) to both efficiently path connect each frame and preserve the locality bias. A distribute layer is then utilized to disseminate back the global context for reciprocal refinement. Extensive experiments on UFUV and three public Video Polyp Segmentation (VPS) datasets demonstrate consistent improvements compared to state-of-the-art segmentation methods, indicating the effectiveness and versatility of LGRNet. Code, checkpoints, and dataset are available at https://github.com/bio-mlhui/LGRNet

We present UniTEX, a novel two-stage 3D texture generation framework to create high-quality, consistent textures for 3D assets. Existing approaches predominantly rely on UV-based inpainting to refine textures after reprojecting the generated multi-view images onto the 3D shapes, which introduces challenges related to topological ambiguity. To address this, we propose to bypass the limitations of UV mapping by operating directly in a unified 3D functional space. Specifically, we first propose that lifts texture generation into 3D space via Texture Functions (TFs)--a continuous, volumetric representation that maps any 3D point to a texture value based solely on surface proximity, independent of mesh topology. Then, we propose to predict these TFs directly from images and geometry inputs using a transformer-based Large Texturing Model (LTM). To further enhance texture quality and leverage powerful 2D priors, we develop an advanced LoRA-based strategy for efficiently adapting large-scale Diffusion Transformers (DiTs) for high-quality multi-view texture synthesis as our first stage. Extensive experiments demonstrate that UniTEX achieves superior visual quality and texture integrity compared to existing approaches, offering a generalizable and scalable solution for automated 3D texture generation. Code will available in: https://github.com/YixunLiang/UniTEX.

We present LooseControl to allow generalized depth conditioning for diffusion-based image generation. ControlNet, the SOTA for depth-conditioned image generation, produces remarkable results but relies on having access to detailed depth maps for guidance. Creating such exact depth maps, in many scenarios, is challenging. This paper introduces a generalized version of depth conditioning that enables many new content-creation workflows. Specifically, we allow (C1) scene boundary control for loosely specifying scenes with only boundary conditions, and (C2) 3D box control for specifying layout locations of the target objects rather than the exact shape and appearance of the objects. Using LooseControl, along with text guidance, users can create complex environments (e.g., rooms, street views, etc.) by specifying only scene boundaries and locations of primary objects. Further, we provide two editing mechanisms to refine the results: (E1) 3D box editing enables the user to refine images by changing, adding, or removing boxes while freezing the style of the image. This yields minimal changes apart from changes induced by the edited boxes. (E2) Attribute editing proposes possible editing directions to change one particular aspect of the scene, such as the overall object density or a particular object. Extensive tests and comparisons with baselines demonstrate the generality of our method. We believe that LooseControl can become an important design tool for easily creating complex environments and be extended to other forms of guidance channels. Code and more information are available at https://shariqfarooq123.github.io/loose-control/ .

Generative models are a promising tool to produce cosmological simulations but face significant challenges in scalability, physical consistency, and adherence to domain symmetries, limiting their utility as alternatives to N-body simulations. To address these limitations, we introduce a score-based generative model with an equivariant graph neural network that simulates gravitational clustering of galaxies across cosmologies starting from an informed prior, respects periodic boundaries, and scales to full galaxy counts in simulations. A novel topology-aware noise schedule, crucial for large geometric graphs, is introduced. The proposed equivariant score-based model successfully generates full-scale cosmological point clouds of up to 600,000 halos, respects periodicity and a uniform prior, and outperforms existing diffusion models in capturing clustering statistics while offering significant computational advantages. This work advances cosmology by introducing a generative model designed to closely resemble the underlying gravitational clustering of structure formation, moving closer to physically realistic and efficient simulators for the evolution of large-scale structures in the universe.

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into pictures representing a topological view. The result is a map of the predictions that enables inspection. The methods scale up to large datasets across different domains and enable us to detect labeling errors in training data, understand generalization in image classification, and inspect predictions of likely pathogenic mutations in the BRCA1 gene.

World models that forecast scene evolution by generating future video frames devote the bulk of their capacity to photometric details, yet the resulting predictions often remain geometrically inconsistent. We present VGGT-World, a geometry world model that side-steps video generation entirely and instead forecasts the temporal evolution of frozen geometry-foundation-model (GFM) features. Concretely, we repurpose the latent tokens of a frozen VGGT as the world state and train a lightweight temporal flow transformer to autoregressively predict their future trajectory. Two technical challenges arise in this high-dimensional (d=1024) feature space: (i) standard velocity-prediction flow matching collapses, and (ii) autoregressive rollout suffers from compounding exposure bias. We address the first with a clean-target (z-prediction) parameterization that yields a substantially higher signal-to-noise ratio, and the second with a two-stage latent flow-forcing curriculum that progressively conditions the model on its own partially denoised rollouts. Experiments on KITTI, Cityscapes, and TartanAir demonstrate that VGGT-World significantly outperforms the strongest baselines in depth forecasting while running 3.6-5 times faster with only 0.43B trainable parameters, establishing frozen GFM features as an effective and efficient predictive state for 3D world modeling.

Visual navigation ability is strongly tied to its underlying representation of the world. Unlike classical 3D maps that require globally-consistent geometry, image- or object-relative topological graphs almost entirely do away with geometric understanding. But, this comes at the cost of navigation capability, often limiting it to merely teach-and-repeat. In this work, we propose a novel map representation in the form of pixel-relative connectivity, which is geometrically accurate but does not require global geometric consistency. Inspired by recent progress in 3D grounded image matching, we construct a map from an image sequence through inter-image connectivity based on pixel correspondences in the relative 3D coordinate systems of individual image pairs. We then use this pixel-level graph to perform global path planning by approximating and sparsifying intra-image pixel connectivity. Through this, we derive a ''WayPixel Costmap'' representation and train a controller conditioned on it to predict a trajectory rollout. We show that this dense pixel-level costmap based on relative geometry is a more accurate conditioning variable for control prediction than its image- and object-level counterparts. This enables a highly capable navigation system, as validated on four types of navigation tasks in the simulator and through real world demonstrations.

Different research lines use the term world model in different ways, yet they share a common aim: to capture how the world evolves under action in a form that supports perception, simulation, and planning. Two prominent realizations are neural predictors that learn dynamics in continuous vector spaces, and hand-built physics engines that expose explicit state and physical laws. Neural predictors scale from data but leave the form of the dynamics implicit; physics engines are inspectable and editable but difficult to construct at scale. We introduce VisualPatchWorld (VPW), which represents world dynamics as code. VPW first selects a qualitative dynamical form with short active probes, then fits that form's free parameters from recorded state-action traces by minimizing multi-step prediction error. The resulting programs can be rolled forward like a simulator, inspected in source form, and used inside model-predictive control; image-derived scene graphs can supply the live state at replan time. Across comparisons with prior code-based world models, VPW attains 69.0% mean planning success and exceeds the strongest code baseline by 23.5 points. The largest gains arise when choosing the correct qualitative dynamics is essential. Under the same planner, the induced models approach ground-truth engine success on navigation and grasp-rich control; a residual gap remains for contact-rich pushing, and checking a shortlist of promising plans in the engine closes most of that gap. These results establish a practical route toward automatically constructed code world models that are useful for planning. Code is available at https://github.com/HKBU-KnowComp/VisualPatchWorld/.

The field of face recognition (FR) has undergone significant advancements with the rise of deep learning. Recently, the success of unsupervised learning and graph neural networks has demonstrated the effectiveness of data structure information. Considering that the FR task can leverage large-scale training data, which intrinsically contains significant structure information, we aim to investigate how to encode such critical structure information into the latent space. As revealed from our observations, directly aligning the structure information between the input and latent spaces inevitably suffers from an overfitting problem, leading to a structure collapse phenomenon in the latent space. To address this problem, we propose TopoFR, a novel FR model that leverages a topological structure alignment strategy called PTSA and a hard sample mining strategy named SDE. Concretely, PTSA uses persistent homology to align the topological structures of the input and latent spaces, effectively preserving the structure information and improving the generalization performance of FR model. To mitigate the impact of hard samples on the latent space structure, SDE accurately identifies hard samples by automatically computing structure damage score (SDS) for each sample, and directs the model to prioritize optimizing these samples. Experimental results on popular face benchmarks demonstrate the superiority of our TopoFR over the state-of-the-art methods. Code and models are available at: https://github.com/modelscope/facechain/tree/main/face_module/TopoFR.

Amazing progress has been made in controllable generative modeling, especially over the last few years. However, some challenges remain. One of them is precise and iterative object editing. In many of the current methods, trying to edit the generated image (for example, changing the color of a particular object in the scene or changing the background while keeping other elements unchanged) by changing the conditioning signals often leads to unintended global changes in the scene. In this work, we take the first steps to address the above challenges. Taking inspiration from the Universal Scene Descriptor (USD) standard developed in the computer graphics community, we introduce the "Neural Universal Scene Descriptor" or Neural USD. In this framework, we represent scenes and objects in a structured, hierarchical manner. This accommodates diverse signals, minimizes model-specific constraints, and enables per-object control over appearance, geometry, and pose. We further apply a fine-tuning approach which ensures that the above control signals are disentangled from one another. We evaluate several design considerations for our framework, demonstrating how Neural USD enables iterative and incremental workflows. More information at: https://escontrela.me/neural_usd .

Pruning neural networks has become popular in the last decade when it was shown that a large number of weights can be safely removed from modern neural networks without compromising accuracy. Numerous pruning methods have been proposed since then, each claiming to be better than the previous. Many state-of-the-art (SOTA) techniques today rely on complex pruning methodologies utilizing importance scores, getting feedback through back-propagation or having heuristics-based pruning rules amongst others. In this work, we question whether this pattern of introducing complexity is really necessary to achieve better pruning results. We benchmark these SOTA techniques against a naive pruning baseline, namely, Global Magnitude Pruning (Global MP). Global MP ranks weights in order of their magnitudes and prunes the smallest ones. Hence, in its vanilla form, it is one of the simplest pruning techniques. Surprisingly, we find that vanilla Global MP outperforms all the other SOTA techniques and achieves a new SOTA result. It also achieves promising performance on FLOPs sparsification, which we find is enhanced, when pruning is conducted in a gradual fashion. We also find that Global MP is generalizable across tasks, datasets, and models with superior performance. Moreover, a common issue that many pruning algorithms run into at high sparsity rates, namely, layer-collapse, can be easily fixed in Global MP by setting a minimum threshold of weights to be retained in each layer. Lastly, unlike many other SOTA techniques, Global MP does not require any additional algorithm specific hyper-parameters and is very straightforward to tune and implement. We showcase our findings on various models (WRN-28-8, ResNet-32, ResNet-50, MobileNet-V1 and FastGRNN) and multiple datasets (CIFAR-10, ImageNet and HAR-2). Code is available at https://github.com/manasgupta-1/GlobalMP.

Large vision-language models have significantly advanced GUI agents, enabling executable interaction across web, mobile, and desktop interfaces. Yet these gains largely rely on a forgiving region-tolerant paradigm, where many nearby pixels inside the same component remain valid. Precise geometric construction breaks this assumption: actions must land on points in continuous canvas space rather than tolerant regions. Because geometric primitives carry ontological dependencies, a local coordinate error can induce cascading topological failures that distort downstream objects and invalidate the final construction. We identify this regime as precision-sensitive GUI tasks, requiring point-level accuracy, geometry-aware verification, and robustness to dependency-driven error propagation. To benchmark it, we introduce PAGE Bench, with 4,906 problems and over 224K process-supervised, pixel-level GUI actions. We further propose PAGER, a topology-aware agent that decomposes construction into dependency-structured planning and pixel-level execution. Pixel-grounded supervised tuning establishes executable action grammar, while precision-aligned reinforcement learning mitigates rollout-induced exposure bias through state-conditioned geometric feedback. Experiments reveal a pronounced Semantic-Execution Gap: general multimodal models can exceed 88% action type accuracy yet remain below 6% task success. PAGER closes this gap, delivering 4.1x higher task success than the strongest evaluated general baseline and raising step success rate from below 9% for GUI-specialized agents to over 62%, establishing a new state of the art for point-precise GUI control.

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically. We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

Graphic design plays a vital role in visual communication across advertising, marketing, and multimedia entertainment. Prior work has explored automated graphic design generation using diffusion models, aiming to streamline creative workflows and democratize design capabilities. However, complex graphic design scenarios require accurately adhering to design intent specified by multiple heterogeneous user-provided elements (\eg images, layouts, and texts), which pose multi-condition control challenges for existing methods. Specifically, previous single-condition control models demonstrate effectiveness only within their specialized domains but fail to generalize to other conditions, while existing multi-condition methods often lack fine-grained control over each sub-condition and compromise overall compositional harmony. To address these limitations, we introduce CreatiDesign, a systematic solution for automated graphic design covering both model architecture and dataset construction. First, we design a unified multi-condition driven architecture that enables flexible and precise integration of heterogeneous design elements with minimal architectural modifications to the base diffusion model. Furthermore, to ensure that each condition precisely controls its designated image region and to avoid interference between conditions, we propose a multimodal attention mask mechanism. Additionally, we develop a fully automated pipeline for constructing graphic design datasets, and introduce a new dataset with 400K samples featuring multi-condition annotations, along with a comprehensive benchmark. Experimental results show that CreatiDesign outperforms existing models by a clear margin in faithfully adhering to user intent.

Combinatorial complexes have unified set-based (e.g., graphs, hypergraphs) and part-whole (e.g., simplicial, cellular complexes) structures into a common topological framework. Existing topological neural networks and Weisfeiler-Lehman variants remain fragmented, lacking a unified theoretical foundation for topological deep learning. In this work, we introduce the Combinatorial Complex Weisfeiler-Lehman (CCWL) test, an axiomatic-style extension of the WL test to combinatorial complexes. CCWL formalizes topological message passing through four types of neighborhood relation and provides a unified perspective on the expressive power of higher-order variants. We further prove that upper and lower neighborhoods are sufficient among the four adjacent WL tests to reach the expressivity of the full CCWL framework across topological structures of combinatorial complexes. Building on this framework, we also propose the Combinatorial Complex Isomorphism Network (CCIN) and evaluate it on synthetic and real-world benchmarks. Experimental results indicate CCIN outperforms baseline methods and offers a generalized expressive framework for topological deep learning.

The Non-Local Network (NLNet) presents a pioneering approach for capturing long-range dependencies, via aggregating query-specific global context to each query position. However, through a rigorous empirical analysis, we have found that the global contexts modeled by non-local network are almost the same for different query positions within an image. In this paper, we take advantage of this finding to create a simplified network based on a query-independent formulation, which maintains the accuracy of NLNet but with significantly less computation. We further observe that this simplified design shares similar structure with Squeeze-Excitation Network (SENet). Hence we unify them into a three-step general framework for global context modeling. Within the general framework, we design a better instantiation, called the global context (GC) block, which is lightweight and can effectively model the global context. The lightweight property allows us to apply it for multiple layers in a backbone network to construct a global context network (GCNet), which generally outperforms both simplified NLNet and SENet on major benchmarks for various recognition tasks. The code and configurations are released at https://github.com/xvjiarui/GCNet.

Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains computationally intensive in most cases. To address this, we revisit the superposition theorem, which has served as the foundation for the decomposition of numerous power system problems over the past decades, particularly those involving changes in generation and loads. However, its application has traditionally been restricted to fixed grid topologies, breaking down as soon as a topology change occurs. In this paper, we extend the superposition theorem to accommodate varying grid topologies by leveraging well-known distribution factors. This unified framework applies to all types of topological changes, including line disconnection and reconnection, as well as bus splitting and merging. We provide numerical experiments to validate our approach and highlight its advantages in terms of speed-up and interpretability. Finally, we demonstrate its application in two key use cases: remedial action search and updated security analysis following a topological change. Our results show that the proposed approach achieves more than an order-of-magnitude speed-up for real-sized grids compared to the fastest power flow solvers.

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss function that enforces a segmentation to have the same topology as the ground truth, i.e., having the same Betti number. The proposed topology-preserving loss function is differentiable and we incorporate it into end-to-end training of a deep neural network. Our method achieves much better performance on the Betti number error, which directly accounts for the topological correctness. It also performs superiorly on other topology-relevant metrics, e.g., the Adjusted Rand Index and the Variation of Information. We illustrate the effectiveness of the proposed method on a broad spectrum of natural and biomedical datasets.

This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.

We present TopoMortar, a brick wall dataset that is the first dataset specifically designed to evaluate topology-focused image segmentation methods, such as topology loss functions. TopoMortar enables to investigate in two ways whether methods incorporate prior topological knowledge. First, by eliminating challenges seen in real-world data, such as small training set, noisy labels, and out-of-distribution test-set images, that, as we show, impact the effectiveness of topology losses. Second, by allowing to assess in the same dataset topology accuracy across dataset challenges, isolating dataset-related effects from the effect of incorporating prior topological knowledge. In these two experiments, it is deliberately difficult to improve topology accuracy without actually using topology information, thus, permitting to attribute an improvement in topology accuracy to the incorporation of prior topological knowledge. To this end, TopoMortar includes three types of labels (accurate, noisy, pseudo-labels), two fixed training sets (large and small), and in-distribution and out-of-distribution test-set images. We compared eight loss functions on TopoMortar, and we found that clDice achieved the most topologically accurate segmentations, Skeleton Recall loss performed best particularly with noisy labels, and the relative advantageousness of the other loss functions depended on the experimental setting. Additionally, we show that simple methods, such as data augmentation and self-distillation, can elevate Cross entropy Dice loss to surpass most topology loss functions, and that those simple methods can enhance topology loss functions as well. clDice and Skeleton Recall loss, both skeletonization-based loss functions, were also the fastest to train, making this type of loss function a promising research direction. TopoMortar and our code can be found at https://github.com/jmlipman/TopoMortar

Parts manufactured with Fused Deposition Modeling (FDM) often require Design for Additive Manufacturing (DFAM) modifications to ensure printability, structural integrity, and reduced post-processing. Current slicers identify defects such as steep overhangs but are unable to modify the underlying geometry. This work presents AgentsCAD, a multi-agent system that bridges raw boundary-representation (B-Rep) geometry and Large Language Model (LLM) reasoning to automate targeted DFM. The workflow begins by parsing a STEP file. The agentic system detects overhangs above a 45°threshold, constructs a face-adjacency topology graph, and optionally injects semantic feature labels from a GraphSAGE model trained on MFCAD++ (59,665 parts), before dispatching a Claude Sonnet design-reasoning agent that recommends reorientations, fillets, chamfers, and similar modifications. A GPT-4o vision-language verifier inspects rendered views to confirm geometric integrity. Outputs include a modified STEP file and a human-readable report. A test case on a birdhouse model demonstrates that the system correctly diagnoses overhangs, selects appropriate defect mitigation strategies, and proposes physically valid corrections, partially solving the geometry-to-language translation problem central to LLM-driven CAD modification.

Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long chains is often insufficient for a coherent global structure to emerge. Recent works tackle this limitation through intrinsic search, which explores multiple paths during the denoising process. While intrinsic search improves global coherence, it comes at the cost of repeated evaluations of an already compute-heavy model. In this work, we argue that extrinsic search, performed outside the denoising process, offers a more effective mode of exploration for long-horizon planning while naturally enabling the use of classical algorithms to solve unseen combinatorial tasks at test time. Our eXtrinsic search-guided Diffuser (XDiffuser) first computes a plan over a state-space graph -- serving as a lightweight local connectivity oracle for the diffusion model. The plan is then used to guide denoising for a single trajectory, effectively offloading the burden of exploration. XDiffuser outperforms diffusion-based baselines on long-horizon tasks, with particularly large gains in the low-quality data regime and on unseen tasks beyond goal-reaching, including multi-agent coordination and TSP-style reasoning. Project website: https://yanivhass.github.io/XDiffuser-site/