Daily Papers

We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder--decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .

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.

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.

Foundation segmentation models such as the Segment Anything Model (SAM) exhibit strong zero-shot generalization through large-scale pretraining, but adapting them to domain-specific semantic segmentation remains challenging, particularly for thin structures (e.g., retinal vessels) and noisy modalities (e.g., SAR imagery). Full fine-tuning is computationally expensive and risks catastrophic forgetting. We propose TopoLoRA-SAM, a topology-aware and parameter-efficient adaptation framework for binary semantic segmentation. TopoLoRA-SAM injects Low-Rank Adaptation (LoRA) into the frozen ViT encoder, augmented with a lightweight spatial convolutional adapter and optional topology-aware supervision via differentiable clDice. We evaluate our approach on five benchmarks spanning retinal vessel segmentation (DRIVE, STARE, CHASE\_DB1), polyp segmentation (Kvasir-SEG), and SAR sea/land segmentation (SL-SSDD), comparing against U-Net, DeepLabV3+, SegFormer, and Mask2Former. TopoLoRA-SAM achieves the best retina-average Dice and the best overall average Dice across datasets, while training only 5.2\% of model parameters (sim4.9M). On the challenging CHASE\_DB1 dataset, our method substantially improves segmentation accuracy and robustness, demonstrating that topology-aware parameter-efficient adaptation can match or exceed fully fine-tuned specialist models. Code is available at : https://github.com/salimkhazem/Seglab.git

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to 2.8times faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

Current repository agents encounter a reasoning disconnect due to fragmented representations, as existing methods rely on isolated API documentation or dependency graphs that lack semantic depth. We consider repository comprehension and generation to be inverse processes within a unified cycle: generation expands intent into implementation, while comprehension compresses implementation back into intent. To address this, we propose RPG-Encoder, a framework that generalizes the Repository Planning Graph (RPG) from a static generative blueprint into a unified, high-fidelity representation. RPG-Encoder closes the reasoning loop through three mechanisms: (1) Encoding raw code into the RPG that combines lifted semantic features with code dependencies; (2) Evolving the topology incrementally to decouple maintenance costs from repository scale, reducing overhead by 95.7%; and (3) Operating as a unified interface for structure-aware navigation. In evaluations, RPG-Encoder establishes state-of-the-art repository understanding on SWE-bench Verified with 93.7% Acc@5 and exceeds the best baseline by over 10% on SWE-bench Live Lite. These results highlight our superior fine-grained localization accuracy in complex codebases. Furthermore, it achieves 98.5% reconstruction coverage on RepoCraft, confirming RPG's high-fidelity capacity to mirror the original codebase and closing the loop between intent and implementation.

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.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

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.

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.

Generalizing motion representation across diverse characters remains challenging due to significant topological variations in skeletal structures across datasets and species, which hinder the development of scalable generative models. To bridge this gap, we propose a Semantic-Aware Topology-Agnostic framework that learns a unified latent manifold shared by disparate species. Unlike methods relying on fixed hierarchies or rigid padding strategies, our approach leverages a semantic modulation mechanism to align functional joint correspondences, thereby decoupling motion from topology. This design enables the construction of a continuous, generative-friendly motion space from large-scale, unaligned raw BVH data. Experiments on human and animal datasets demonstrate that our framework achieves high-fidelity reconstruction and supports downstream text-to-motion tasks. Notably, the model enables zero-shot cross-species retargeting without paired data. Code and demos are available at: https://github.com/zzysteve/SATA

Masked graph autoencoders have emerged as a powerful graph self-supervised learning method that has yet to be fully explored. In this paper, we unveil that the existing discrete edge masking and binary link reconstruction strategies are insufficient to learn topologically informative representations, from the perspective of message propagation on graph neural networks. These limitations include blocking message flows, vulnerability to over-smoothness, and suboptimal neighborhood discriminability. Inspired by these understandings, we explore non-discrete edge masks, which are sampled from a continuous and dispersive probability distribution instead of the discrete Bernoulli distribution. These masks restrict the amount of output messages for each edge, referred to as "bandwidths". We propose a novel, informative, and effective topological masked graph autoencoder using bandwidth masking and a layer-wise bandwidth prediction objective. We demonstrate its powerful graph topological learning ability both theoretically and empirically. Our proposed framework outperforms representative baselines in both self-supervised link prediction (improving the discrete edge reconstructors by at most 20%) and node classification on numerous datasets, solely with a structure-learning pretext. Our implementation is available at https://github.com/Newiz430/Bandana.

Approximate nearest neighbor (ANN) graph indices such as HNSW and Vamana construct their edge topology in full-precision or high-fidelity quantized metric spaces, relegating binary quantization (BQ) to a post-hoc distance estimator during search. This paper asks a different question: Can binary quantization define the graph topology itself -- and if so, under what conditions? We study this question through QuIVer (Quantized Index for Vector Retrieval), a training-free ANN graph index that performs Vamana edge selection, diversity pruning, and beam-search navigation entirely within a 2-bit Sign-Magnitude BQ metric space, accessing float32 vectors only for final reranking. Systematic evaluation on twelve million-scale datasets reveals a sharp applicability boundary: BQ-native topology is highly effective on cosine-native contrastive-learning embeddings (>=88% Recall@10 at ef=64 across five datasets, 384--3072 dimensions), moderately effective on multimodal CLIP data (71--78%), and empirically unsuitable for Euclidean-native or structureless distributions (<15%). Our results suggest an empirical "impossible triangle" between aggressive compression, high throughput, and universal data compatibility. The central contribution is not merely the system, but the boundary it reveals: falsifiable criteria for when industrial vector search systems can safely trade metric fidelity for compact BQ-native navigation. On compatible workloads, the system benefits are substantial: QuIVer's BQ-native hot path (<1.3 GB for 1M vectors) yields 2.5--5.5x higher multi-threaded throughput than DiskANN Rust and HNSW variants at matched recall, with 4.7x less hot memory and no codebook or rotation training (unlike PQ/OPQ/RaBitQ).

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

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).

Semantic maps are increasingly utilized in areas such as robotics, autonomous systems, and extended reality, motivating the investigation of efficient compression methods that preserve structured semantic information. This paper studies lossless compression of semantic maps through a novel chain-coding-based framework that explicitly exploits contour topology and shared boundaries between adjacent semantic regions. We propose an extended chain code (ECC) to represent long-range contour transitions more compactly, while retaining a legacy three-orthogonal chain code (3OT) as a fallback mode for further efficiency. To efficiently encode sequences of ECC symbols, a context-adaptive entropy coding scheme based on Markov modeling is employed. Furthermore, a skip-coding mechanism is introduced to eliminate redundant representations of shared contours between adjacent semantic regions, supporting both complete and partial skips via run-length signaling. Experimental results demonstrate that the proposed method achieves an average bitrate reduction of 18\% compared with a state-of-the-art benchmark on semantic map datasets. In addition, the proposed encoder and decoder achieve up to 98\% and 50\% runtime reduction, respectively, relative to a modern generic lossless codec. Extended evaluations on occupancy maps further confirm consistent compression gains across the majority of tested scenarios.

Neuronal morphology encodes critical information about circuit function, development, and disease, yet current methods analyze topology or graph structure in isolation. We introduce GraPHFormer, a multimodal architecture that unifies these complementary views through CLIP-style contrastive learning. Our vision branch processes a novel three-channel persistence image encoding unweighted, persistence-weighted, and radius-weighted topological densities via DINOv2-ViT-S. In parallel, a TreeLSTM encoder captures geometric and radial attributes from skeleton graphs. Both project to a shared embedding space trained with symmetric InfoNCE loss, augmented by persistence-space transformations that preserve topological semantics. Evaluated on six benchmarks (BIL-6, ACT-4, JML-4, N7, M1-Cell, M1-REG) spanning self-supervised and supervised settings, GraPHFormer achieves state-of-the-art performance on five benchmarks, significantly outperforming topology-only, graph-only, and morphometrics baselines. We demonstrate practical utility by discriminating glial morphologies across cortical regions and species, and detecting signatures of developmental and degenerative processes. Code: https://github.com/Uzshah/GraPHFormer

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.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose two improvements to relative representations. First, we introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. The latter coincides with the symmetries in parameter space induced by common activation functions. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes. We provide an empirical investigation on a natural language task, where both the proposed variations yield improved performance on zero-shot model stitching.

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 introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

We propose SAM-Road, an adaptation of the Segment Anything Model (SAM) for extracting large-scale, vectorized road network graphs from satellite imagery. To predict graph geometry, we formulate it as a dense semantic segmentation task, leveraging the inherent strengths of SAM. The image encoder of SAM is fine-tuned to produce probability masks for roads and intersections, from which the graph vertices are extracted via simple non-maximum suppression. To predict graph topology, we designed a lightweight transformer-based graph neural network, which leverages the SAM image embeddings to estimate the edge existence probabilities between vertices. Our approach directly predicts the graph vertices and edges for large regions without expensive and complex post-processing heuristics, and is capable of building complete road network graphs spanning multiple square kilometers in a matter of seconds. With its simple, straightforward, and minimalist design, SAM-Road achieves comparable accuracy with the state-of-the-art method RNGDet++, while being 40 times faster on the City-scale dataset. We thus demonstrate the power of a foundational vision model when applied to a graph learning task. The code is available at https://github.com/htcr/sam_road.

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

Motion generation is fundamental to computer animation and widely used across entertainment, robotics, and virtual environments. While recent methods achieve impressive results, most rely on fixed skeletal templates, which prevent them from generalizing to skeletons with different or perturbed topologies. We address the core limitation of current motion generation methods - the combined lack of large-scale heterogeneous animal motion data and unified generative frameworks capable of jointly modeling arbitrary skeletal topologies and textual conditions. To this end, we introduce OmniZoo, a large-scale animal motion dataset spanning 140 species and 32,979 sequences, enriched with multimodal annotations. Building on OmniZoo, we propose a generalized autoregressive motion generation framework capable of producing text-driven motions for arbitrary skeletal topologies. Central to our model is a Topology-aware Skeleton Embedding Module that encodes geometric and structural properties of any skeleton into a shared token space, enabling seamless fusion with textual semantics. Given a text prompt and a target skeleton, our method generates temporally coherent, physically plausible, and semantically aligned motions, and further enables cross-species motion style transfer.

Long-horizon Flexible Job-Shop Scheduling~(FJSP) presents a formidable combinatorial challenge due to complex, interdependent decisions spanning extended time horizons. While learning-based Rolling Horizon Optimization~(RHO) has emerged as a promising paradigm to accelerate solving by identifying and fixing invariant operations, its effectiveness is hindered by the structural complexity of FJSP. Existing methods often fail to capture intricate graph-structured dependencies and ignore the asymmetric costs of prediction errors, in which misclassifying critical-path operations is significantly more detrimental than misclassifying non-critical ones. Furthermore, dynamic shifts in predictive confidence during the rolling process make static pruning thresholds inadequate. To address these limitations, we propose Graph-RHO, a novel critical-path-aware graph-based RHO framework. First, we introduce a topology-aware heterogeneous graph network that encodes subproblems as operation-machine graphs with multi-relational edges, leveraging edge-feature-aware message passing to predict operation stability. Second, we incorporate a critical-path-aware mechanism that injects inductive biases during training to distinguish highly sensitive bottleneck operations from robust ones. Third, we devise an adaptive thresholding strategy that dynamically calibrates decision boundaries based on online uncertainty estimation to align model predictions with the solver's search space. Extensive experiments on standard benchmarks demonstrate that Graph-RHO establishes a new state of the art in solution quality and computational efficiency. Remarkably, it exhibits exceptional zero-shot generalization, reducing solve time by over 30\% on large-scale instances (2000 operations) while achieving superior solution quality. Our code is available https://github.com/IntelliSensing/Graph-RHO{here}.

The dominant paradigm for high-fidelity 3D generation relies on a VAE-Diffusion pipeline, where the VAE's reconstruction capability sets a firm upper bound on generation quality. A fundamental challenge limiting existing VAEs is the representation mismatch between ground-truth meshes and network predictions: GT meshes have arbitrary, variable topology, while VAEs typically predict fixed-structure implicit fields (\eg, SDF on regular grids). This inherent misalignment prevents establishing explicit mesh-level correspondences, forcing prior work to rely on indirect supervision signals such as SDF or rendering losses. Consequently, fine geometric details, particularly sharp features, are poorly preserved during reconstruction. To address this, we introduce TopoMesh, a sparse voxel-based VAE that unifies both GT and predicted meshes under a shared Dual Marching Cubes (DMC) topological framework. Specifically, we convert arbitrary input meshes into DMC-compliant representations via a remeshing algorithm that preserves sharp edges using an Linfty distance metric. Our decoder outputs meshes in the same DMC format, ensuring that both predicted and target meshes share identical topological structures. This establishes explicit correspondences at the vertex and face level, allowing us to derive explicit mesh-level supervision signals for topology, vertex positions, and face orientations with clear gradients. Our sparse VAE architecture employs this unified framework and is trained with Teacher Forcing and progressive resolution training for stable and efficient convergence. Extensive experiments demonstrate that TopoMesh significantly outperforms existing VAEs in reconstruction fidelity, achieving superior preservation of sharp features and geometric details.

Encoder-free architectures have been preliminarily explored in the 2D visual domain, yet it remains an open question whether they can be effectively applied to 3D understanding scenarios. In this paper, we present the first comprehensive investigation into the potential of encoder-free architectures to overcome the challenges of encoder-based 3D Large Multimodal Models (LMMs). These challenges include the failure to adapt to varying point cloud resolutions and the point features from the encoder not meeting the semantic needs of Large Language Models (LLMs). We identify key aspects for 3D LMMs to remove the encoder and enable the LLM to assume the role of the 3D encoder: 1) We propose the LLM-embedded Semantic Encoding strategy in the pre-training stage, exploring the effects of various point cloud self-supervised losses. And we present the Hybrid Semantic Loss to extract high-level semantics. 2) We introduce the Hierarchical Geometry Aggregation strategy in the instruction tuning stage. This incorporates inductive bias into the LLM early layers to focus on the local details of the point clouds. To the end, we present the first Encoder-free 3D LMM, ENEL. Our 7B model rivals the current state-of-the-art model, ShapeLLM-13B, achieving 55.0%, 50.92%, and 42.7% on the classification, captioning, and VQA tasks, respectively. Our results demonstrate that the encoder-free architecture is highly promising for replacing encoder-based architectures in the field of 3D understanding. The code is released at https://github.com/Ivan-Tang-3D/ENEL

Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS.

The automated extraction of complete and precise road network graphs from remote sensing imagery remains a critical challenge in geospatial computer vision. Segmentation-based approaches, while effective in pixel-level recognition, struggle to maintain topology fidelity after vectorization postprocessing. Graph-growing methods build more topologically faithful graphs but suffer from computationally prohibitive iterative ROI cropping. Graph-generating methods first predict global static candidate road network vertices, and then infer possible edges between vertices. They achieve fast topology-aware inference, but limits the dynamic insertion of vertices. To address these challenges, we propose DeH4R, a novel hybrid model that combines graph-generating efficiency and graph-growing dynamics. This is achieved by decoupling the task into candidate vertex detection, adjacent vertex prediction, initial graph contruction, and graph expansion. This architectural innovation enables dynamic vertex (edge) insertions while retaining fast inference speed and enhancing both topology fidelity and spatial consistency. Comprehensive evaluations on CityScale and SpaceNet benchmarks demonstrate state-of-the-art (SOTA) performance. DeH4R outperforms the prior SOTA graph-growing method RNGDet++ by 4.62 APLS and 10.18 IoU on CityScale, while being approximately 10 times faster. The code will be made publicly available at https://github.com/7777777FAN/DeH4R.

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.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

LiDAR point clouds are fundamental to various applications, yet the extreme sparsity of high-precision geometric details hinders efficient context modeling, thereby limiting the compression speed and performance of existing methods. To address this challenge, we propose a compact representation for efficient predictive lossless coding. Our framework comprises two lightweight modules. First, the Geometry Re-Densification Module iteratively densifies encoded sparse geometry, extracts features at a dense scale, and then sparsifies the features for predictive coding. This module avoids costly computation on highly sparse details while maintaining a lightweight prediction head. Second, the Cross-scale Feature Propagation Module leverages occupancy cues from multiple resolution levels to guide hierarchical feature propagation, enabling information sharing across scales and reducing redundant feature extraction. Additionally, we introduce an integer-only inference pipeline to enable bit-exact cross-platform consistency, which avoids the entropy-coding collapse observed in existing neural compression methods and further accelerates coding. Experiments demonstrate competitive compression performance at real-time speed. Code will be released upon acceptance. Code is available at https://github.com/pengpeng-yu/FastPCC.

Flow matching over carefully designed latent representations has recently emerged as a powerful paradigm for topology-aware mesh generation. Existing approaches, however, model vertices and connectivity jointly in a joint latent space, entangling continuous vertex geometry with discrete combinatorial structure; this complicates flow learning and manifests as drifting vertices and broken surfaces. We present LATO.2, a factorized flow matching framework that decomposes mesh generation into a vertex flow followed by a connectivity flow conditioned on the realized vertices, with both stages anchored to a shared coarse voxel scaffold. Dedicated VAEs underpin the two stages, recovering vertices at sub-voxel precision and embedding discrete connectivity into a continuous latent space. We demonstrate two advantages unique to this factorization: (i) part-wise generation, in which the scaffold is partitioned and each part synthesized at full latent capacity, yielding substantially higher-resolution meshes than a monolithic latent permits; and (ii) topology-adaptive editing, in which manipulating first-stage vertices induces the corresponding connectivity without re-optimization. Experiments show that LATO.2 surpasses state-of-the-art topology-aware mesh generators in geometric fidelity and connectivity quality.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

Modern interactive applications increasingly demand dynamic 3D content, yet the transformation of static 3D models into animated assets constitutes a significant bottleneck in content creation pipelines. While recent advances in generative AI have revolutionized static 3D model creation, rigging and animation continue to depend heavily on expert intervention. We present Puppeteer, a comprehensive framework that addresses both automatic rigging and animation for diverse 3D objects. Our system first predicts plausible skeletal structures via an auto-regressive transformer that introduces a joint-based tokenization strategy for compact representation and a hierarchical ordering methodology with stochastic perturbation that enhances bidirectional learning capabilities. It then infers skinning weights via an attention-based architecture incorporating topology-aware joint attention that explicitly encodes inter-joint relationships based on skeletal graph distances. Finally, we complement these rigging advances with a differentiable optimization-based animation pipeline that generates stable, high-fidelity animations while being computationally more efficient than existing approaches. Extensive evaluations across multiple benchmarks demonstrate that our method significantly outperforms state-of-the-art techniques in both skeletal prediction accuracy and skinning quality. The system robustly processes diverse 3D content, ranging from professionally designed game assets to AI-generated shapes, producing temporally coherent animations that eliminate the jittering issues common in existing methods.

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.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

Autoregressive Transformers dominate high-quality mesh generation by producing artist-worthy topologies, yet their inherent sequential decoding induces substantial computational overhead, falling orders of magnitude slower than parallel generative models. On the other hand, while continuous diffusion and flow-matching methods support efficient parallel synthesis across a variety of domains, they cannot be directly applied to meshes: mesh connectivity is inherently discrete and incompatible with standard continuous noise injection and denoising operations. To resolve this fundamental incompatibility, we introduce a compact topology embedder that projects discrete mesh vertex positions and normals into continuous per-vertex embeddings, where the original discrete adjacency information can be faithfully recovered via spacetime distance thresholding. After pretraining and freezing this embedder, any raw mesh can be fully converted into a continuous per-vertex state space unifying position, normal, and implicit topological attributes. Built upon this novel continuous mesh representation, we present PolyFlow, a Transformer-based flow-matching framework that achieves fully parallel vertex state denoising conditioned on extracted point-cloud features. During inference, our model completes generation rapidly via an ODE solver, and supports explicit, precise control over output mesh resolution by directly specifying the target vertex count. Extensive evaluations on the Toys4K benchmark demonstrate that PolyFlow surpasses state-of-the-art autoregressive baselines in both Chamfer Distance and Hausdorff Distance.

Existing routers rely on semantic query features or handcrafted features, which often fail to capture model-specific failures or intrinsic task difficulty. We instead route using internal LLM activations, specifically the residual stream. Our key idea, Encoder-Target Decoupling, separates the model that produces the predictive signal (the Encoder) from the model whose correctness is being estimated (the Target), allowing open-weight encoders to predict the performance of closed-source target models. We evaluate layerwise geometric probes, finding that Fisher Separability (J) effectively identifies informative layers, supported by Effective Dimensionality (d_{eff}) diagnostics. We then utilize a SharedTrunkNet, a joint multi-output MLP that predicts simultaneous correctness probabilities across candidate models using concatenated prefill features. In our experiments, SharedTrunkNet consistently outperforms semantic baselines. At its best, SharedTrunkNet closes 45.58% of the gap between the strongest standalone model and the oracle while achieving 74.31% cost savings relative to the most expensive model. These results demonstrate that prefill activations provide a robust routing signal, establishing activation-based routing as a high-performance alternative to purely semantic selection.

Spatial-temporal forecasting and imputation are important for real-world intelligent systems. Most existing methods are tailored for individual forecasting or imputation tasks but are not designed for both. Additionally, they are less effective for zero-shot and few-shot learning. While pre-trained language model (PLM) have exhibited strong pattern recognition and reasoning abilities across various tasks, including few-shot and zero-shot learning, their applications in spatial-temporal data understanding has been constrained by insufficient modeling of complex correlations such as the temporal correlations, spatial connectivity, non-pairwise and high-order spatial-temporal correlations within data. In this paper, we propose STD-PLM for understanding both spatial and temporal properties of Spatial-Temporal Data with PLM, which is capable of implementing both spatial-temporal forecasting and imputation tasks. STD-PLM understands spatial-temporal correlations via explicitly designed spatial and temporal tokenizers. Topology-aware node embeddings are designed for PLM to comprehend and exploit the topology structure of data in inductive manner. Furthermore, to mitigate the efficiency issues introduced by the PLM, we design a sandglass attention module (SGA) combined with a specific constrained loss function, which significantly improves the model's efficiency while ensuring performance. Extensive experiments demonstrate that STD-PLM exhibits competitive performance and generalization capabilities across the forecasting and imputation tasks on various datasets. Moreover, STD-PLM achieves promising results on both few-shot and zero-shot tasks.The code is made available at https://anonymous.4open.science/r/STD-PLM-F3BA{https://anonymous.4open.science/r/STD-PLM-F3BA}

Existing skeleton-based action recognition methods typically follow a centralized learning paradigm, which can pose privacy concerns when exposing human-related videos. Federated Learning (FL) has attracted much attention due to its outstanding advantages in privacy-preserving. However, directly applying FL approaches to skeleton videos suffers from unstable training. In this paper, we investigate and discover that the heterogeneous human topology graph structure is the crucial factor hindering training stability. To address this limitation, we pioneer a novel Federated Skeleton-based Action Recognition (FSAR) paradigm, which enables the construction of a globally generalized model without accessing local sensitive data. Specifically, we introduce an Adaptive Topology Structure (ATS), separating generalization and personalization by learning a domain-invariant topology shared across clients and a domain-specific topology decoupled from global model aggregation.Furthermore, we explore Multi-grain Knowledge Distillation (MKD) to mitigate the discrepancy between clients and server caused by distinct updating patterns through aligning shallow block-wise motion features. Extensive experiments on multiple datasets demonstrate that FSAR outperforms state-of-the-art FL-based methods while inherently protecting privacy.

There is a growing body of work that leverages features extracted via topological data analysis to train machine learning models. While this field, sometimes known as topological machine learning (TML), has seen some notable successes, an understanding of how the process of learning from topological features differs from the process of learning from raw data is still limited. In this work, we begin to address one component of this larger issue by asking whether a model trained with topological features learns internal representations of data that are fundamentally different than those learned by a model trained with the original raw data. To quantify ``different'', we exploit two popular metrics that can be used to measure the similarity of the hidden representations of data within neural networks, neural stitching and centered kernel alignment. From these we draw a range of conclusions about how training with topological features does and does not change the representations that a model learns. Perhaps unsurprisingly, we find that structurally, the hidden representations of models trained and evaluated on topological features differ substantially compared to those trained and evaluated on the corresponding raw data. On the other hand, our experiments show that in some cases, these representations can be reconciled (at least to the degree required to solve the corresponding task) using a simple affine transformation. We conjecture that this means that neural networks trained on raw data may extract some limited topological features in the process of making predictions.

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

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.

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 foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Previous representation and generation approaches for the B-rep relied on graph-based representations that disentangle geometric and topological features through decoupled computational pipelines, thereby precluding the application of sequence-based generative frameworks, such as transformer architectures that have demonstrated remarkable performance. In this paper, we propose BrepARG, the first attempt to encode B-rep's geometry and topology into a holistic token sequence representation, enabling sequence-based B-rep generation with an autoregressive architecture. Specifically, BrepARG encodes B-rep into 3 types of tokens: geometry and position tokens representing geometric features, and face index tokens representing topology. Then the holistic token sequence is constructed hierarchically, starting with constructing the geometry blocks (i.e., faces and edges) using the above tokens, followed by geometry block sequencing. Finally, we assemble the holistic sequence representation for the entire B-rep. We also construct a transformer-based autoregressive model that learns the distribution over holistic token sequences via next-token prediction, using a multi-layer decoder-only architecture with causal masking. Experiments demonstrate that BrepARG achieves state-of-the-art (SOTA) performance. BrepARG validates the feasibility of representing B-rep as holistic token sequences, opening new directions for B-rep generation.

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space. However, this paradigm suffers from two critical challenges: Structural Degeneration, where hierarchical and semantic representations are entangled, and Optimization Instability, which arises from oscillatory dynamics of minimax adversarial training. To tackle these issues, we propose DisRFM, a geometry-aware GDA framework that unifies Riemannian embedding and flow-based transport. First, to overcome structural degeneration, we embed graphs into a Riemannian manifold. By adopting polar coordinates, we explicitly disentangle structure (radius) from semantics (angle). Then, we enforce topology preservation through radial Wasserstein alignment and semantic discrimination via angular clustering, thereby preventing feature entanglement and collapse. Second, we address the instability of adversarial alignment by using Riemannian flow matching. This method learns a smooth vector field to guide source features toward the target along geodesic paths, guaranteeing stable convergence. The geometric constraints further guide the flow to maintain the disentangled structure during transport. Theoretically, we prove the asymptotic stability of the flow matching and derive a tighter bound for the target risk. Extensive experiments demonstrate that DisRFM consistently outperforms state-of-the-art methods.

Generative recommendation (GR) aligns with advances in generative AI by casting next-item prediction as token-level generation rather than score-based ranking. Most GR methods adopt a two-stage pipeline: (i) item tokenization, which maps each item to a sequence of discrete, hierarchically organized tokens; and (ii) autoregressive generation, which predicts the next item's tokens conditioned on the tokens of user's interaction history. Although hierarchical tokenization induces a prefix tree (trie) over items, standard autoregressive modeling with conventional Transformers often flattens item tokens into a linear stream and overlooks the underlying topology. To address this, we propose TrieRec, a trie-aware generative recommendation method that augments Transformers with structural inductive biases via two positional encodings. First, a trie-aware absolute positional encoding aggregates a token's (node's) local structural context (\eg depth, ancestors, and descendants) into the token representation. Second, a topology-aware relative positional encoding injects pairwise structural relations into self-attention to capture topology-induced semantic relatedness. TrieRec is also model-agnostic, efficient, and hyperparameter-free. In our experiments, we implement TrieRec within three representative GR backbones, achieving notably improvements of 8.83\% on average across four real-world datasets.

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in this field, much of the focus has been on single polygons, overlooking the intricate inner- and inter-polygonal relationships inherent in multipolygons. To address this gap, our study introduces a comprehensive framework specifically designed for learning representations of polygonal geometries, particularly multipolygons. Central to our approach is the incorporation of a heterogeneous visibility graph, which seamlessly integrates both inner- and inter-polygonal relationships. To enhance computational efficiency and minimize graph redundancy, we implement a heterogeneous spanning tree sampling method. Additionally, we devise a rotation-translation invariant geometric representation, ensuring broader applicability across diverse scenarios. Finally, we introduce Multipolygon-GNN, a novel model tailored to leverage the spatial and semantic heterogeneity inherent in the visibility graph. Experiments on five real-world and synthetic datasets demonstrate its ability to capture informative representations for polygonal geometries. Code and data are available at https://github.com/dyu62/PolyGNN{github.com/dyu62/PolyGNN}.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Kolmogorov-Arnold Networks (KANs) face a fundamental memory wall: their learned basis functions create parameter counts that impose extreme bandwidth demands, hindering deployment in memory-constrained environments. We show that Vision KANs exhibit a holographic topology, where information is distributed across the interference of splines rather than localized to specific edges. Consequently, traditional pruning fails (10% sparsity degrades mAP from 85.23% to 45%, a sim40-point drop). To address this, we present SHARe-KAN, a framework utilizing Gain-Shape-Bias Vector Quantization to exploit functional redundancy while preserving the dense topology. Coupled with LUTHAM, a hardware-aware compiler with static memory planning, we achieve 88times runtime memory reduction (1.13 GB to 12.91 MB) and match uncompressed baseline accuracy on PASCAL VOC. Profiling on NVIDIA Ampere architecture confirms >90% L2 cache residency, demonstrating that the workload is decoupled from DRAM bandwidth constraints inherent to spline-based architectures.

The inference of topological principles is a key problem in structured reconstruction. We observe that wrongly predicted topological relationships are often incurred by the lack of holistic geometry clues in low-level features. Inspired by the fact that massive signals can be compactly described with frequency analysis, we experimentally explore the efficiency and tendency of learning structure geometry in the frequency domain. Accordingly, we propose a frequency-domain feature learning strategy (F-Learn) to fuse scattered geometric fragments holistically for topology-intact structure reasoning. Benefiting from the parsimonious design, the F-Learn strategy can be easily deployed into a deep reconstructor with a lightweight model modification. Experiments demonstrate that the F-Learn strategy can effectively introduce structure awareness into geometric primitive detection and topology inference, bringing significant performance improvement to final structured reconstruction. Code and pre-trained models are available at https://github.com/Geo-Tell/F-Learn.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are publicly available.

Hierarchical LiDAR geometry compression encodes voxel occupancies from low to high bit-depths, yet prior methods treat each depth independently and re-estimate local context from coordinates at every level, limiting compression efficiency. We present ELiC, a real-time framework that combines cross-bit-depth feature propagation, a Bag-of-Encoders (BoE) selection scheme, and a Morton-order-preserving hierarchy. Cross-bit-depth propagation reuses features extracted at denser, lower depths to support prediction at sparser, higher depths. BoE selects, per depth, the most suitable coding network from a small pool, adapting capacity to observed occupancy statistics without training a separate model for each level. The Morton hierarchy maintains global Z-order across depth transitions, eliminating per-level sorting and reducing latency. Together these components improve entropy modeling and computation efficiency, yielding state-of-the-art compression at real-time throughput on Ford and SemanticKITTI. Code and models will be released upon publication.

Recent large vision-language models (LVLMs) have demonstrated strong potential for device control. However, existing research has primarily focused on point-and-click (PnC) interaction, while remote-control (RC) interaction commonly encountered in everyday TV usage remains largely underexplored. To fill this gap, we introduce TVWorld, an offline graph-based abstraction of real-world TV navigation that enables reproducible and deployment-free evaluation. On this basis, we derive two complementary benchmarks that comprehensively assess TV-use capabilities: TVWorld-N for topology-aware navigation and TVWorld-G for focus-aware grounding. These benchmarks expose a key limitation of existing agents: insufficient topology awareness for focus-based, long-horizon TV navigation. Motivated by this finding, we propose a Topology-Aware Training framework that injects topology awareness into LVLMs. Using this framework, we develop TVTheseus, a foundation model specialized for TV navigation. TVTheseus achieves a success rate of 68.3% on TVWorld-N, surpassing strong closed-source baselines such as Gemini 3 Flash and establishing state-of-the-art (SOTA) performance. Additional analyses further provide valuable insights into the development of effective TV-use agents.

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.

We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder that maps natural images uniformly onto a spherical latent space, and a decoder that maps random latent vectors back to the image space. Trained solely through image reconstruction losses, the model generates an image by simply decoding a random point on the sphere. Our architecture naturally supports conditional generation, and looping the encoder/decoder a few times can further enhance image quality. Across several datasets, the sphere encoder approach yields performance competitive with state of the art diffusions, but with a small fraction of the inference cost. Project page is available at https://sphere-encoder.github.io .

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.

The explosion of generative 3D assets has created a massive demand for animation, yet current motion capture methods remain brittle, restricted to species-specific templates (e.g., SMPL) or requiring labor-intensive manual rigging. We introduce TopoCap, the first unified framework capable of extracting motion from monocular video and retargeting it onto characters with arbitrary, unseen skeletal topologies, i.e., from bipeds to hexapods and inanimate objects, without test-time optimization. Our key insight is that while skeletal structures are combinatorial and discrete, the underlying physics of motion occupy a continuous, low-dimensional manifold. We materialize this insight via a two-stage generative pipeline. First, we learn a Universal Motion Manifold using a Graph CVAE that compresses heterogeneous kinematic chains into a shared, fixed-length latent code. By explicitly conditioning the decoder on a structural embedding of the target rig, we disentangle motion dynamics from skeletal topology. Second, we treat video-to-animation as a conditional flow matching problem, predicting these topology-agnostic codes from visual features. To learn this generalized prior, we introduce Mobjaverse, a massive-scale dataset curated from Objaverse-XL. Comprising over 5,000 unique skeletal topologies and 2 million frames, it exceeds the structural diversity of existing datasets by two orders of magnitude. Extensive experiments demonstrate that \MethodMotion outperforms specialist models on human and quadruped benchmarks while enabling zero-shot retargeting for the long tail of 3D creatures. Dataset is publicly available at https://huggingface.co/datasets/duckduckplz/Mobjaverse.

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.

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

Vectorized high-definition map online construction has garnered considerable attention in the field of autonomous driving research. Most existing approaches model changeable map elements using a fixed number of points, or predict local maps in a two-stage autoregressive manner, which may miss essential details and lead to error accumulation. Towards precise map element learning, we propose a simple yet effective architecture named PivotNet, which adopts unified pivot-based map representations and is formulated as a direct set prediction paradigm. Concretely, we first propose a novel point-to-line mask module to encode both the subordinate and geometrical point-line priors in the network. Then, a well-designed pivot dynamic matching module is proposed to model the topology in dynamic point sequences by introducing the concept of sequence matching. Furthermore, to supervise the position and topology of the vectorized point predictions, we propose a dynamic vectorized sequence loss. Extensive experiments and ablations show that PivotNet is remarkably superior to other SOTAs by 5.9 mAP at least. The code will be available soon.

Text-attributed graphs integrate semantic information of node texts with topological structure, offering significant value in various applications such as document classification and information extraction. Existing approaches typically encode textual content using language models (LMs), followed by graph neural networks (GNNs) to process structural information. However, during the LM-based text encoding phase, most methods not only perform semantic interaction solely at the word-token granularity, but also neglect the structural dependencies among texts from different nodes. In this work, we propose DuConTE, a dual-granularity text encoder with topology-constrained attention. The model employs a cascaded architecture of two pretrained LMs, encoding semantics first at the word-token granularity and then at the node granularity. During the self-attention computation in each LM, we dynamically adjust the attention mask matrix based on node connectivity, guiding the model to learn semantic correlations informed by the graph structure. Furthermore, when composing node representations from word-token embeddings, we separately evaluate the importance of tokens under the center-node context and the neighborhood context, enabling the capture of more contextually relevant semantic information. Extensive experiments on multiple benchmark datasets demonstrate that DuConTE achieves state-of-the-art performance on the majority of them.

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.

Object detection in point clouds is an important aspect of many robotics applications such as autonomous driving. In this paper we consider the problem of encoding a point cloud into a format appropriate for a downstream detection pipeline. Recent literature suggests two types of encoders; fixed encoders tend to be fast but sacrifice accuracy, while encoders that are learned from data are more accurate, but slower. In this work we propose PointPillars, a novel encoder which utilizes PointNets to learn a representation of point clouds organized in vertical columns (pillars). While the encoded features can be used with any standard 2D convolutional detection architecture, we further propose a lean downstream network. Extensive experimentation shows that PointPillars outperforms previous encoders with respect to both speed and accuracy by a large margin. Despite only using lidar, our full detection pipeline significantly outperforms the state of the art, even among fusion methods, with respect to both the 3D and bird's eye view KITTI benchmarks. This detection performance is achieved while running at 62 Hz: a 2 - 4 fold runtime improvement. A faster version of our method matches the state of the art at 105 Hz. These benchmarks suggest that PointPillars is an appropriate encoding for object detection in point clouds.

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

Graph learning has become indispensable for interpreting and harnessing relational data in diverse fields, ranging from recommendation systems to social network analysis. In this context, a variety of GNNs have emerged as promising methodologies for encoding the structural information of graphs. By effectively capturing the graph's underlying structure, these GNNs have shown great potential in enhancing performance in graph learning tasks, such as link prediction and node classification. However, despite their successes, a significant challenge persists: these advanced methods often face difficulties in generalizing to unseen graph data that significantly differs from the training instances. In this work, our aim is to advance the graph learning paradigm by developing a general graph foundation model. This model is designed to understand the complex topological patterns present in diverse graph data, enabling it to excel in zero-shot graph learning tasks across different downstream datasets. To achieve this goal, we address several key technical challenges in our OpenGraph model. Firstly, we propose a unified graph tokenizer to adapt our graph model to generalize well on unseen graph data, even when the underlying graph properties differ significantly from those encountered during training. Secondly, we develop a scalable graph transformer as the foundational encoder, which effectively captures node-wise dependencies within the global topological context. Thirdly, we introduce a data augmentation mechanism enhanced by a LLM to alleviate the limitations of data scarcity in real-world scenarios. Extensive experiments validate the effectiveness of our framework. By adapting our OpenGraph to new graph characteristics and comprehending the nuances of diverse graphs, our approach achieves remarkable zero-shot graph learning performance across various settings and domains.

Representation learning on text-attributed graphs (TAGs) integrates structural connectivity with rich textual semantics, enabling applications in diverse domains. Current methods largely rely on contrastive learning to maximize cross-modal similarity, assuming tighter coupling between graph and text representations improves transfer performance. However, our empirical analysis reveals that both natural gap expansion and forced gap reduction result in performance degradation by disrupting pre-trained knowledge structures and impairing generalization. This arises from the geometric incompatibility between encoders, where graph encoders capture topological patterns, while text encoders capture semantic structures. Over-alignment compresses these distinct spaces into shared subspaces, causing structure collapse that diminishes both topological reasoning and semantic understanding. We propose LLM4GTA, a gap-aware alignment framework that preserves representation gaps as geometric necessities for maintaining modality-specific knowledge and improving transfer performance. LLM4GTA includes an adaptive gap preservation module to prevent over-alignment by monitoring similarity evolution and an intra-modal compensation mechanism that boosts discriminative power using auxiliary classifiers in graph space. Extensive experiments show significant improvements over existing methods in zero-shot and few-shot scenarios.

Contrastive Vision-Language Models (VLMs) have demonstrated strong zero-shot capabilities. However, their cross-modal alignment remains biased toward English due to limited multilingual multimodal data. Recent multilingual extensions have alleviated this gap but enforce instance-level alignment while neglecting the global geometry of the shared embedding space. We address this problem by introducing ToMCLIP (Topological Alignment for Multilingual CLIP), a topology-aware framework aligning embedding spaces with topology-preserving constraints. The proposed method applies persistent homology to define a topological alignment loss and approximates persistence diagram with theoretical error bounds using graph sparsification strategy. This work validates the proposed approach, showing enhanced structural coherence of multilingual representations, higher zero-shot accuracy on the CIFAR-100, and stronger multilingual retrieval performance on the xFlickr&CO. Beyond VLMs, the proposed approach provides a general method for incorporating topological alignment into representation learning. Code is available at https://github.com/junwon0/ToMCLIP.git.

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on volumetric overlap, often at the expense of preserving structural connectivity or topology. This can lead to segmentation errors that adversely affect downstream tasks, including flow calculation, navigation, and structural inspection. Although current topology-focused losses mark an improvement, they introduce significant computational and memory overheads. This is particularly relevant for 3D data, rendering these losses infeasible for larger volumes as well as increasingly important multi-class segmentation problems. To mitigate this, we propose a novel Skeleton Recall Loss, which effectively addresses these challenges by circumventing intensive GPU-based calculations with inexpensive CPU operations. It demonstrates overall superior performance to current state-of-the-art approaches on five public datasets for topology-preserving segmentation, while substantially reducing computational overheads by more than 90%. In doing so, we introduce the first multi-class capable loss function for thin structure segmentation, excelling in both efficiency and efficacy for topology-preservation.

Hypergraphs are marked by complex topology, expressing higher-order interactions among multiple nodes with hyperedges, and better capturing the topology is essential for effective representation learning. Recent advances in generative self-supervised learning (SSL) suggest that hypergraph neural networks learned from generative self supervision have the potential to effectively encode the complex hypergraph topology. Designing a generative SSL strategy for hypergraphs, however, is not straightforward. Questions remain with regard to its generative SSL task, connection to downstream tasks, and empirical properties of learned representations. In light of the promises and challenges, we propose a novel generative SSL strategy for hypergraphs. We first formulate a generative SSL task on hypergraphs, hyperedge filling, and highlight its theoretical connection to node classification. Based on the generative SSL task, we propose a hypergraph SSL method, HypeBoy. HypeBoy learns effective general-purpose hypergraph representations, outperforming 16 baseline methods across 11 benchmark datasets.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

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.

Recent techniques such as retrieval-augmented generation or chain-of-thought reasoning have led to longer contexts and increased inference costs. Context compression techniques can reduce these costs, but the most effective approaches require fine-tuning the target model or even modifying its architecture. This can degrade its general abilities when not used for this specific purpose. Here we explore an alternative approach: an encoder that compresses the context into continuous representations which replace token embeddings in decoder LLMs. First, we perform a systematic study of training strategies and architecture choices for the encoder. Our findings led to the design of an Adaptable text Representations Compressor, named ARC-Encoder, which outputs x-times fewer continuous representations (typically x!in!{4,8}) than text tokens. We evaluate ARC-Encoder across a variety of LLM usage scenarios, ranging from in-context learning to context window extension, on both instruct and base decoders. Results show that ARC-Encoder achieves state-of-the-art performance on several benchmarks while improving computational efficiency at inference. Finally, we demonstrate that our models can be adapted to multiple decoders simultaneously, allowing a single encoder to generalize across different decoder LLMs. This makes ARC-Encoder a flexible and efficient solution for portable encoders that work seamlessly with multiple LLMs. We release a training code at https://github.com/kyutai-labs/ARC-Encoder , fine-tuning dataset and pretrained models are available at https://huggingface.co/collections/kyutai/arc-encoders-68ee18787301407d60a57047 .

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks.

Volumetric video is emerging as a key medium for digitizing the dynamic physical world, creating the virtual environments with six degrees of freedom to deliver immersive user experiences. However, robustly modeling general dynamic scenes, especially those involving topological changes while maintaining long-term tracking remains a fundamental challenge. In this paper, we present TaoGS, a novel topology-aware dynamic Gaussian representation that disentangles motion and appearance to support, both, long-range tracking and topological adaptation. We represent scene motion with a sparse set of motion Gaussians, which are continuously updated by a spatio-temporal tracker and photometric cues that detect structural variations across frames. To capture fine-grained texture, each motion Gaussian anchors and dynamically activates a set of local appearance Gaussians, which are non-rigidly warped to the current frame to provide strong initialization and significantly reduce training time. This activation mechanism enables efficient modeling of detailed textures and maintains temporal coherence, allowing high-fidelity rendering even under challenging scenarios such as changing clothes. To enable seamless integration into codec-based volumetric formats, we introduce a global Gaussian Lookup Table that records the lifespan of each Gaussian and organizes attributes into a lifespan-aware 2D layout. This structure aligns naturally with standard video codecs and supports up to 40 compression. TaoGS provides a unified, adaptive solution for scalable volumetric video under topological variation, capturing moments where "elegance in motion" and "Power in Stillness", delivering immersive experiences that harmonize with the physical world.

In this paper, we introduce LATO, a novel topology-preserving latent representation that enables scalable, flow matching-based synthesis of explicit 3D meshes. LATO represents a mesh as a Vertex Displacement Field (VDF) anchored on surface, incorporating a sparse voxel Variational Autoencoder (VAE) to compress this explicit signal into a structured, topology-aware voxel latent. To decapsulate the mesh, the VAE decoder progressively subdivides and prunes latent voxels to instantiate precise vertex locations. In the end, a dedicated connection head queries the voxel latent to predict edge connectivity between vertex pairs directly, allowing mesh topology to be recovered without isosurface extraction or heuristic meshing. For generative modeling, LATO adopts a two-stage flow matching process, first synthesizing the structure voxels and subsequently refining the voxel-wise topology features. Compared to prior isosurface/triangle-based diffusion models and autoregressive generation approaches, LATO generates meshes with complex geometry, well-formed topology while being highly efficient in inference.

We introduce Thinking with Spatial Code, a framework that transforms RGB video into explicit, temporally coherent 3D representations for physical-world visual question answering. We highlight the empirical finding that our proposed spatial encoder can parse videos into structured spatial code with explicit 3D oriented bounding boxes and semantic labels, enabling large language models (LLMs) to reason directly over explicit spatial variables. Specifically, we propose the spatial encoder that encodes image and geometric features by unifying 6D object parsing and tracking backbones with geometric prediction, and we further finetuning LLMs with reinforcement learning using a spatial rubric reward that encourages perspective-aware, geometrically grounded inference. As a result, our model outperforms proprietary vision-language models on VSI-Bench, setting a new state-of-the-art. Code is available at https://github.com/Beckschen/spatialcode.

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

Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This overhead can only be partially eliminated with elaborate schemes such as bits-back coding, often resulting in poor single-sample compression rates. To overcome such problems, we establish a new class of tractable lossless compression models that permit efficient encoding and decoding: Probabilistic Circuits (PCs). These are a class of neural networks involving |p| computational units that support efficient marginalization over arbitrary subsets of the D feature dimensions, enabling efficient arithmetic coding. We derive efficient encoding and decoding schemes that both have time complexity O (log(D) cdot |p|), where a naive scheme would have linear costs in D and |p|, making the approach highly scalable. Empirically, our PC-based (de)compression algorithm runs 5-40 times faster than neural compression algorithms that achieve similar bitrates. By scaling up the traditional PC structure learning pipeline, we achieve state-of-the-art results on image datasets such as MNIST. Furthermore, PCs can be naturally integrated with existing neural compression algorithms to improve the performance of these base models on natural image datasets. Our results highlight the potential impact that non-standard learning architectures may have on neural data compression.

Recent advancements in discrete image generation showed that scaling the VQ codebook size significantly improves reconstruction fidelity. However, training generative models with a large VQ codebook remains challenging, typically requiring larger model size and a longer training schedule. In this work, we propose Stochastic Neighbor Cross Entropy Minimization (SNCE), a novel training objective designed to address the optimization challenges of large-codebook discrete image generators. Instead of supervising the model with a hard one-hot target, SNCE constructs a soft categorical distribution over a set of neighboring tokens. The probability assigned to each token is proportional to the proximity between its code embedding and the ground-truth image embedding, encouraging the model to capture semantically meaningful geometric structure in the quantized embedding space. We conduct extensive experiments across class-conditional ImageNet-256 generation, large-scale text-to-image synthesis, and image editing tasks. Results show that SNCE significantly improves convergence speed and overall generation quality compared to standard cross-entropy objectives.

Implicit Neural Representations (INRs) offer exceptional fidelity for video compression by learning per-video optimized functions, but their adoption is crippled by impractically slow encoding times. Existing attempts to accelerate INR encoding often sacrifice reconstruction quality or crucial coordinate-level control essential for adaptive streaming and transcoding. We introduce SIEDD (Shared-Implicit Encoder with Discrete Decoders), a novel architecture that fundamentally accelerates INR encoding without these compromises. SIEDD first rapidly trains a shared, coordinate-based encoder on sparse anchor frames to efficiently capture global, low-frequency video features. This encoder is then frozen, enabling massively parallel training of lightweight, discrete decoders for individual frame groups, further expedited by aggressive coordinate-space sampling. This synergistic design delivers a remarkable 20-30X encoding speed-up over state-of-the-art INR codecs on HD and 4K benchmarks, while maintaining competitive reconstruction quality and compression ratios. Critically, SIEDD retains full coordinate-based control, enabling continuous resolution decoding and eliminating costly transcoding. Our approach significantly advances the practicality of high-fidelity neural video compression, demonstrating a scalable and efficient path towards real-world deployment. Our codebase is available at https://github.com/VikramRangarajan/SIEDD .

Recent advances in dense 3D reconstruction have led to significant progress, yet achieving accurate unified geometric prediction remains a major challenge. Most existing methods are limited to predicting a single geometry quantity from input images. However, geometric quantities such as depth, surface normals, and point maps are inherently correlated, and estimating them in isolation often fails to ensure consistency, thereby limiting both accuracy and practical applicability. This motivates us to explore a unified framework that explicitly models the structural coupling among different geometric properties to enable joint regression. In this paper, we present Dens3R, a 3D foundation model designed for joint geometric dense prediction and adaptable to a wide range of downstream tasks. Dens3R adopts a two-stage training framework to progressively build a pointmap representation that is both generalizable and intrinsically invariant. Specifically, we design a lightweight shared encoder-decoder backbone and introduce position-interpolated rotary positional encoding to maintain expressive power while enhancing robustness to high-resolution inputs. By integrating image-pair matching features with intrinsic invariance modeling, Dens3R accurately regresses multiple geometric quantities such as surface normals and depth, achieving consistent geometry perception from single-view to multi-view inputs. Additionally, we propose a post-processing pipeline that supports geometrically consistent multi-view inference. Extensive experiments demonstrate the superior performance of Dens3R across various dense 3D prediction tasks and highlight its potential for broader applications.

Can we model non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The non-Euclidean property have posed a long term challenge in graph modeling. Despite recent GNN and Graphformer efforts encoding graphs as Euclidean vectors, recovering original graph from the vectors remains a challenge. We introduce GraphsGPT, featuring a Graph2Seq encoder that transforms non-Euclidean graphs into learnable graph words in a Euclidean space, along with a GraphGPT decoder that reconstructs the original graph from graph words to ensure information equivalence. We pretrain GraphsGPT on 100M molecules and yield some interesting findings: (1) Pretrained Graph2Seq excels in graph representation learning, achieving state-of-the-art results on 8/9 graph classification and regression tasks. (2) Pretrained GraphGPT serves as a strong graph generator, demonstrated by its ability to perform both unconditional and conditional graph generation. (3) Graph2Seq+GraphGPT enables effective graph mixup in the Euclidean space, overcoming previously known non-Euclidean challenge. (4) Our proposed novel edge-centric GPT pretraining task is effective in graph fields, underscoring its success in both representation and generation.

Recent advances in scene understanding benefit a lot from depth maps because of the 3D geometry information, especially in complex conditions (e.g., low light and overexposed). Existing approaches encode depth maps along with RGB images and perform feature fusion between them to enable more robust predictions. Taking into account that depth can be regarded as a geometry supplement for RGB images, a straightforward question arises: Do we really need to explicitly encode depth information with neural networks as done for RGB images? Based on this insight, in this paper, we investigate a new way to learn RGBD feature representations and present DFormerv2, a strong RGBD encoder that explicitly uses depth maps as geometry priors rather than encoding depth information with neural networks. Our goal is to extract the geometry clues from the depth and spatial distances among all the image patch tokens, which will then be used as geometry priors to allocate attention weights in self-attention. Extensive experiments demonstrate that DFormerv2 exhibits exceptional performance in various RGBD semantic segmentation benchmarks. Code is available at: https://github.com/VCIP-RGBD/DFormer.

Recent advancements in self-supervised learning in the point cloud domain have demonstrated significant potential. However, these methods often suffer from drawbacks, including lengthy pre-training time, the necessity of reconstruction in the input space, or the necessity of additional modalities. In order to address these issues, we introduce Point-JEPA, a joint embedding predictive architecture designed specifically for point cloud data. To this end, we introduce a sequencer that orders point cloud patch embeddings to efficiently compute and utilize their proximity based on the indices during target and context selection. The sequencer also allows shared computations of the patch embeddings' proximity between context and target selection, further improving the efficiency. Experimentally, our method achieves competitive results with state-of-the-art methods while avoiding the reconstruction in the input space or additional modality.

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.

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.

We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being local, global or relative. The prior GTs are constrained to small graphs with a few hundred nodes, here we propose the first architecture with a complexity linear in the number of nodes and edges O(N+E) by decoupling the local real-edge aggregation from the fully-connected Transformer. We argue that this decoupling does not negatively affect the expressivity, with our architecture being a universal function approximator on graphs. Our GPS recipe consists of choosing 3 main ingredients: (i) positional/structural encoding, (ii) local message-passing mechanism, and (iii) global attention mechanism. We provide a modular framework GraphGPS that supports multiple types of encodings and that provides efficiency and scalability both in small and large graphs. We test our architecture on 16 benchmarks and show highly competitive results in all of them, show-casing the empirical benefits gained by the modularity and the combination of different strategies.

Recent advances in Graph Neural Networks (GNNs) and Graph Transformers (GTs) have been driven by innovations in architectures and Positional Encodings (PEs), which are critical for augmenting node features and capturing graph topology. PEs are essential for GTs, where topological information would otherwise be lost without message-passing. However, PEs are often tested alongside novel architectures, making it difficult to isolate their effect on established models. To address this, we present a comprehensive benchmark of PEs in a unified framework that includes both message-passing GNNs and GTs. We also establish theoretical connections between MPNNs and GTs and introduce a sparsified GRIT attention mechanism to examine the influence of global connectivity. Our findings demonstrate that previously untested combinations of GNN architectures and PEs can outperform existing methods and offer a more comprehensive picture of the state-of-the-art. To support future research and experimentation in our framework, we make the code publicly available.

Reconstructing 3D objects into editable programs is pivotal for applications like reverse engineering and shape editing. However, existing methods often rely on limited domain-specific languages (DSLs) and small-scale datasets, restricting their ability to model complex geometries and structures. To address these challenges, we introduce MeshCoder, a novel framework that reconstructs complex 3D objects from point clouds into editable Blender Python scripts. We develop a comprehensive set of expressive Blender Python APIs capable of synthesizing intricate geometries. Leveraging these APIs, we construct a large-scale paired object-code dataset, where the code for each object is decomposed into distinct semantic parts. Subsequently, we train a multimodal large language model (LLM) that translates 3D point cloud into executable Blender Python scripts. Our approach not only achieves superior performance in shape-to-code reconstruction tasks but also facilitates intuitive geometric and topological editing through convenient code modifications. Furthermore, our code-based representation enhances the reasoning capabilities of LLMs in 3D shape understanding tasks. Together, these contributions establish MeshCoder as a powerful and flexible solution for programmatic 3D shape reconstruction and understanding.

We present OSMGraphCLIP, a CLIP-style geospatial representation model that learns global location embeddings from freely available OpenStreetMap (OSM) data. OSMGraphCLIP represents geographic environments as heterogeneous graphs of typed OSM features, preserving the topological and semantic relationships among roads, buildings, land-use regions, and points of interest. A multi-scale graph encoder captures both fine-grained local structure and broader landscape composition, and supervises a spherical-harmonics location encoder through a contrastive alignment objective. We evaluate OSMGraphCLIP across a diverse suite of downstream geospatial regression and classification tasks spanning climate, ecology, socioeconomic indicators, public health, land cover, biodiversity, and wildfire forecasting, and show that structured OSM data alone supports strong global location representations across domains. OSMGraphCLIP matches or exceeds satellite-based baselines on the majority of benchmarks, with the most pronounced advantage on socioeconomic and public-health tasks, where OSM's explicit semantic annotation of the built environment encodes patterns of human activity that satellite pixels can only capture indirectly. On ecological and environmental tasks, the model remains closely competitive with imagery-based methods despite using no Earth observation data. Qualitative analysis confirms that the learned embeddings organize geographic space coherently, recovering biome boundaries, urban gradients, and tropical--temperate distinctions from map topology alone.

The generation of large-scale urban layouts has garnered substantial interest across various disciplines. Prior methods have utilized procedural generation requiring manual rule coding or deep learning needing abundant data. However, prior approaches have not considered the context-sensitive nature of urban layout generation. Our approach addresses this gap by leveraging a canonical graph representation for the entire city, which facilitates scalability and captures the multi-layer semantics inherent in urban layouts. We introduce a novel graph-based masked autoencoder (GMAE) for city-scale urban layout generation. The method encodes attributed buildings, city blocks, communities and cities into a unified graph structure, enabling self-supervised masked training for graph autoencoder. Additionally, we employ scheduled iterative sampling for 2.5D layout generation, prioritizing the generation of important city blocks and buildings. Our approach achieves good realism, semantic consistency, and correctness across the heterogeneous urban styles in 330 US cities. Codes and datasets are released at https://github.com/Arking1995/COHO.

Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize graphs by modeling higher-order relationships among multiple entities, enabling richer representations but introducing significant computational challenges. In this work, we extend the Loop Transformer architecture's neural algorithmic reasoning capability to simulate hypergraph algorithms, addressing the gap between neural networks and combinatorial optimization over hypergraphs. Specifically, we propose a novel degradation mechanism for reducing hypergraphs to graph representations, enabling the simulation of graph-based algorithms, such as Dijkstra's shortest path. Furthermore, we introduce a hyperedge-aware encoding scheme to simulate hypergraph-specific algorithms, exemplified by Helly's algorithm. We establish theoretical guarantees for these simulations, demonstrating the feasibility of processing high-dimensional and combinatorial data using Loop Transformers. This work highlights the potential of Transformers as general-purpose algorithmic solvers for structured data.

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

Multimodal contrastive learning aims to train a general-purpose feature extractor, such as CLIP, on vast amounts of raw, unlabeled paired image-text data. This can greatly benefit various complex downstream tasks, including cross-modal image-text retrieval and image classification. Despite its promising prospect, the security issue of cross-modal pre-trained encoder has not been fully explored yet, especially when the pre-trained encoder is publicly available for commercial use. In this work, we propose AdvCLIP, the first attack framework for generating downstream-agnostic adversarial examples based on cross-modal pre-trained encoders. AdvCLIP aims to construct a universal adversarial patch for a set of natural images that can fool all the downstream tasks inheriting the victim cross-modal pre-trained encoder. To address the challenges of heterogeneity between different modalities and unknown downstream tasks, we first build a topological graph structure to capture the relevant positions between target samples and their neighbors. Then, we design a topology-deviation based generative adversarial network to generate a universal adversarial patch. By adding the patch to images, we minimize their embeddings similarity to different modality and perturb the sample distribution in the feature space, achieving unviersal non-targeted attacks. Our results demonstrate the excellent attack performance of AdvCLIP on two types of downstream tasks across eight datasets. We also tailor three popular defenses to mitigate AdvCLIP, highlighting the need for new defense mechanisms to defend cross-modal pre-trained encoders.

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.

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

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex hierarchical relationships in images with remarkably small dimensionality. To demonstrate hyperbolic embeddings' competence, we introduce a light-weight hyperbolic graph neural network for image segmentation, encompassing patch-level features in a very small embedding size. Our solution, Seg-HGNN, surpasses the current best unsupervised method by 2.5\%, 4\% on VOC-07, VOC-12 for localization, and by 0.8\%, 1.3\% on CUB-200, ECSSD for segmentation, respectively. With less than 7.5k trainable parameters, Seg-HGNN delivers effective and fast (approx 2 images/second) results on very standard GPUs like the GTX1650. This empirical evaluation presents compelling evidence of the efficacy and potential of hyperbolic representations for vision tasks.

We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined _Wave-Induced Rotary Encodings_ (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100\% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive accuracy, interpretability, and computational efficiency remains a major challenge. In this work, we introduce a novel Graph Neural Network (GNN) architecture that combines compressed higher-order topological signals with standard molecular features. Our approach captures global geometric information while preserving computational tractability and human-interpretable structure. We evaluate our model across a range of benchmarks, from small-molecule datasets to complex material datasets, and demonstrate superior performance using a parameter-efficient architecture. We achieve the best performing results in both accuracy and robustness across almost all benchmarks. We open source all code All code and results can be found on Github https://github.com/rahulkhorana/TFC-PACT-Net.

Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock "bump hunt" in which the autoencoder fails to identify an anomalous "signal" for reasons tied to the intrinsic topology of n-particle phase space.

Pre-routing timing prediction has been recently studied for evaluating the quality of a candidate cell placement in chip design. It involves directly estimating the timing metrics for both pin-level (slack, slew) and edge-level (net delay, cell delay), without time-consuming routing. However, it often suffers from signal decay and error accumulation due to the long timing paths in large-scale industrial circuits. To address these challenges, we propose a two-stage approach. First, we propose global circuit training to pre-train a graph auto-encoder that learns the global graph embedding from circuit netlist. Second, we use a novel node updating scheme for message passing on GCN, following the topological sorting sequence of the learned graph embedding and circuit graph. This scheme residually models the local time delay between two adjacent pins in the updating sequence, and extracts the lookup table information inside each cell via a new attention mechanism. To handle large-scale circuits efficiently, we introduce an order preserving partition scheme that reduces memory consumption while maintaining the topological dependencies. Experiments on 21 real world circuits achieve a new SOTA R2 of 0.93 for slack prediction, which is significantly surpasses 0.59 by previous SOTA method. Code will be available at: https://github.com/Thinklab-SJTU/EDA-AI.

We present a conceptually simple yet effective algorithm to detect wireframes in a given image. Compared to the previous methods which first predict an intermediate heat map and then extract straight lines with heuristic algorithms, our method is end-to-end trainable and can directly output a vectorized wireframe that contains semantically meaningful and geometrically salient junctions and lines. To better understand the quality of the outputs, we propose a new metric for wireframe evaluation that penalizes overlapped line segments and incorrect line connectivities. We conduct extensive experiments and show that our method significantly outperforms the previous state-of-the-art wireframe and line extraction algorithms. We hope our simple approach can be served as a baseline for future wireframe parsing studies. Code has been made publicly available at https://github.com/zhou13/lcnn.

Accurately predicting road networks from satellite images requires a global understanding of the network topology. We propose to capture such high-level information by introducing a graph-based framework that simulates the addition of sequences of graph edges using a reinforcement learning (RL) approach. In particular, given a partially generated graph associated with a satellite image, an RL agent nominates modifications that maximize a cumulative reward. As opposed to standard supervised techniques that tend to be more restricted to commonly used surrogate losses, these rewards can be based on various complex, potentially non-continuous, metrics of interest. This yields more power and flexibility to encode problem-dependent knowledge. Empirical results on several benchmark datasets demonstrate enhanced performance and increased high-level reasoning about the graph topology when using a tree-based search. We further highlight the superiority of our approach under substantial occlusions by introducing a new synthetic benchmark dataset for this task.

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 this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination of two optimization objectives, we propose a novel semantic graph representation (SGR) method to formulate the joint optimization of the two heterogeneous sources into a common high-order proximity based framework. Concretely, we first construct an auxiliary weighted graph, where the complex homogeneous and heterogeneous relations among nodes and attributes in the original graph are comprehensively encoded. Conventional embedding methods that consider high-order topology proximities can then be easily applied to the newly constructed graph to learn the representations of both node and attribute while capturing the nonlinear high-order intrinsic correlation inside or among graph structure and semantic. The learned attribute embeddings can also effectively support some semantic-oriented inference tasks (e.g., semantic community detection), helping to reveal the graph's deep semantic. The effectiveness of SGR is further verified on a series of real graphs, where it achieves impressive performance over other baselines.

Autoregressive mesh generation has gained attention by tokenizing meshes into sequences and training models in a language-modeling fashion. However, existing approaches suffer from two fundamental limitations: (i) low tokenization efficiency, which yields long token sequences and prevents scaling to high-poly meshes, and (ii) absence of geometry-aware guidance, as generation is conditioned only on global shape embeddings rather than local surface cues. We introduce MeshWeaver, an autoregressive framework that treats mesh generation as a surface weaving process by directly predicting the next vertex instead of independent coordinates. At its core is a multi-level sparse-voxel encoder that injects geometric context into the generative process in three complementary ways: providing voxel features as vertex representations, guiding token prediction via cross-attention to voxel features, and serving as a structural scaffold that constrains generation around the input surface. Our hierarchical design enables coarse-to-fine vertex prediction in a single decoding step, while tightly coupling the generative model with 3D geometry. Extensive experiments demonstrate that MeshWeaver achieves a state-of-the-art compression ratio of 18%, can generate meshes with up to 16K faces, and significantly improves geometric fidelity over prior approaches.

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

Recently, 3D Gaussian Spatting (3DGS) has gained widespread attention in Novel View Synthesis (NVS) due to the remarkable real-time rendering performance. However, the substantial cost of storage and transmission of vanilla 3DGS hinders its further application (hundreds of megabytes or even gigabytes for a single scene). Motivated by the achievements of prediction in video compression, we introduce the prediction technique into the anchor-based Gaussian representation to effectively reduce the bit rate. Specifically, we propose a spatial condition-based prediction module to utilize the grid-captured scene information for prediction, with a residual compensation strategy designed to learn the missing fine-grained information. Besides, to further compress the residual, we propose an instance-aware hyper prior, developing a structure-aware and instance-aware entropy model. Extensive experiments demonstrate the effectiveness of our prediction-based compression framework and each technical component. Even compared with SOTA compression method, our framework still achieves a bit rate savings of 24.42 percent. Code is to be released!