Geometric Representation Learning

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Overview

The field studies how to represent data whose structure is not well described by ordinary flat vectors, including point clouds, graphs, molecules, shapes, and signals. Approaches include rotation- and group-equivariant networks, learning directly on Riemannian, spherical, or hyperbolic spaces, and using geodesic distances, curvature, or spectral structure to guide training. These methods aim to preserve meaningful geometry so models can generalize across changes in viewpoint, sampling, or domain, with applications from 3D perception and robotics to biology and medical imaging. A central challenge is choosing geometry that fits the task: explicit geometric constraints can improve robustness and data efficiency, but may add computational cost or hinder downstream learning when the chosen structure is mismatched.

Latest papers

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259 papers32 papers in the last four weeks, up 7% on the four weeks before. 0.2% of all new papers.

Mar 2, 2026

Rigidity-Aware Geometric Pretraining for Protein Design and Conformational Ensembles

Generative models have recently advanced de novo\textit{de novo} protein design by learning the statistical regularities of natural structures. However, current approaches face three key limitations: (1) Existing methods cannot jointly learn protein geometry and design tasks, where pretraining can be a solution; (2) Current pretraining methods mostly rely on local, non-rigid atomic representations for property prediction downstream tasks, limiting global geometric understanding for protein generation tasks; and (3) Existing approaches have yet to effectively model the rich dynamic and conformational information of protein structures. To overcome these issues, we introduce RigidSSL\textbf{RigidSSL} (Rigidity-Aware Self-Supervised Learning\textit{Rigidity-Aware Self-Supervised Learning}), a geometric pretraining framework that front-loads geometry learning prior to generative finetuning. Phase I (RigidSSL-Perturb) learns geometric priors from 432K structures from the AlphaFold Protein Structure Database with simulated perturbations. Phase II (RigidSSL-MD) refines these representations on 1.3K molecular dynamics trajectories to capture physically realistic transitions. Underpinning both phases is a bi-directional, rigidity-aware flow matching objective that jointly optimizes translational and rotational dynamics to maximize mutual information between conformations. Empirically, RigidSSL variants improve designability by up to 43% while enhancing novelty and diversity in unconditional generation. Furthermore, RigidSSL-Perturb improves the success rate by 5.8% in zero-shot motif scaffolding and RigidSSL-MD captures more biophysically realistic conformational ensembles in G protein-coupled receptor modeling.

Zhanghan Ni, Yanjing Li, Zeju Qiu +4

University of Illinois Urbana-Champaign · University of Washington · MPI for Intelligent Systems, Tübingen +3

Protein Structure GenerationGenerative ModelingProtein DesignSelf-Supervised Pre-TrainingProtein Representation LearningGeometric Representation Learning
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Feb 28, 2026

Social-JEPA: Emergent Geometric Isomorphism

World models compress rich sensory streams into compact latent codes that anticipate future observations. We let separate agents acquire such models from distinct viewpoints of the same environment without any parameter sharing or coordination. After training, their internal representations exhibit a striking emergent property: the two latent spaces are related by an approximate linear isometry, enabling transparent translation between them. This geometric consensus survives large viewpoint shifts and scant overlap in raw pixels. Leveraging the learned alignment, a classifier trained on one agent can be ported to the other with no additional gradient steps, while distillation-like migration accelerates later learning and markedly reduces total compute. The findings reveal that predictive learning objectives impose strong regularities on representation geometry, suggesting a lightweight path to interoperability among decentralized vision systems. The code is available at https://anonymous.4open.science/r/Social-JEPA-5C57.

Youjin Wang

Renmin University of China

Representation LearningVisual Representation LearningLatent Space AlignmentGeometric Representation LearningWorld Model Learning
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Feb 28, 2026

Hereditary Geometric Meta-RL: Nonlocal Generalization via Task Symmetries

Meta-Reinforcement Learning (Meta-RL) commonly generalizes via smoothness in the task encoding. While this enables local generalization around each training task, it requires dense coverage of the task space and leaves richer task space structure untapped. In response, we develop a geometric perspective that endows the task space with a "hereditary geometry" induced by the inherent symmetries of the underlying system. Concretely, the agent reuses a policy learned at the train time by transforming states and actions through actions of a Lie group. This converts Meta-RL into symmetry discovery rather than smooth extrapolation, enabling the agent to generalize to wider regions of the task space. We show that when the task space is inherited from the symmetries of the underlying system, the task space embeds into a subgroup of those symmetries whose actions are linearizable, connected, and compact--properties that enable efficient learning and inference at the test time. To learn these structures, we develop a differential symmetry discovery method. This collapses functional invariance constraints and thereby improves numerical stability and sample efficiency over functional approaches. Empirically, on a two-dimensional navigation task, our method efficiently recovers the ground-truth symmetry and generalizes across the entire task space, while a common baseline generalizes only near training tasks.

Paul Nitschke, Shahriar Talebi

P. Nitschke is with the Paulson School Of Engineering And Applied Sciences, Harvard University, Cambridge, US. · S. Talebi is with the UCLA Samueli School of Engineering and Applied Science, University of California, Los Angeles, US.

Symmetry DiscoveryMeta-Reinforcement LearningGeneralization in RLGeometric Representation Learning
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Feb 27, 2026

Compositional Generalization Requires Linear, Orthogonal Representations in Vision Embedding Models

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the combinatorial space of possible inputs, raising the question of what structure representations must have to support generalization to unseen combinations. We formalize three desiderata for compositional generalization under standard training (divisibility, transferability, stability) and show they impose necessary geometric constraints: representations must decompose linearly into per-concept components, and these components must be orthogonal across concepts. This provides theoretical grounding for the Linear Representation Hypothesis: the linear structure widely observed in neural representations is a necessary consequence of compositional generalization. We further derive dimension bounds linking the number of composable concepts to the embedding geometry. Empirically, we evaluate these predictions across modern vision models (CLIP, SigLIP, DINO) and find that representations exhibit partial linear factorization with low-rank, near-orthogonal per-concept factors, and that the degree of this structure correlates with compositional generalization on unseen combinations. As models continue to scale, these conditions predict the representational geometry they may converge to. Code is available at https://github.com/oshapio/necessary-compositionality.

Arnas Uselis, Andrea Dittadi, Seong Joon Oh

Tübingen AI Center, University of Tübingen · Helmholtz · Technical University of Munich

Neural Representation GeometryVisual Representation LearningLinear Representation HypothesisOrthogonal Representation LearningGeometric Representation LearningCompositional Representation Learning+1
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Feb 26, 2026

RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs

Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning stands out as its theoretical underpinnings on symmetric positive definite (SPD) allows revealing structural connectivity analysis in a physics-grounded manner. However, current SPD-based methods focus predominantly on statistical aggregation of EEGs, with frequency-specific synchronization and local topological structures of brain regions neglected. Given this, we propose RepSPD, a novel geometric deep learning (GDL)-based model. RepSPD implements a cross-attention mechanism on the Riemannian manifold to modulate the geometric attributes of SPD with graph-derived functional connectivity features. On top of this, we introduce a global bidirectional alignment strategy to reshape tangent-space embeddings, mitigating geometric distortions caused by curvature and thereby enhancing geometric consistency. Extensive experiments demonstrate that our proposed framework significantly outperforms existing EEG representation methods, exhibiting superior robustness and generalization capabilities.

Haohui Jia, Zheng Chen, Lingwei Zhu +4

Information Science and Techinology, Hokkaido University, Japan · SANKEN, The University of Osaka, Japan · Great Bay University, China +1

EEG DecodingGeometric Representation LearningManifold Learning
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Feb 26, 2026

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold constraints and non-unified training setups, which hinders reproducibility and integration into modern deep-learning workflows. To address this gap, we introduce SPD Learn, a unified and modular Python package for geometric deep learning with SPD matrices. SPD Learn provides core SPD operators and neural-network layers, including numerically stable spectral operators, and enforces Stiefel/SPD constraints via trivialization-based parameterizations. This design enables standard backpropagation and optimization in unconstrained Euclidean spaces while producing manifold-constrained parameters by construction. The package also offers reference implementations of representative SPDNet-based models and interfaces with widely used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.

Bruno Aristimunha, Ce Ju, Antoine Collas +5

A&O, LISN, Université Paris-Saclay, CNRS, Inria TAU/NERV, France · Yneuro, France · University of San Diego, EUA +6

Geometric Representation LearningNeural Decoding
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Feb 25, 2026

What Topological and Geometric Structure Do Biological Foundation Models Learn? Evidence from 141 Hypotheses

When biological foundation models such as scGPT and Geneformer process single-cell gene expression, what geometric and topological structure forms in their internal representations? Is that structure biologically meaningful or a training artifact, and how confident should we be in such claims? We address these questions through autonomous large-scale hypothesis screening: an AI-driven executor-brainstormer loop that proposed, tested, and refined 141 geometric and topological hypotheses across 52 iterations, covering persistent homology, manifold distances, cross-model alignment, community structure, and directed topology, all with explicit null controls and disjoint gene-pool splits. Three principal findings emerge. First, the models learn genuine geometric structure. Gene embedding neighborhoods exhibit non-trivial topology, with persistent homology significant in 11 of 12 transformer layers at p < 0.05 in the weakest domain and 12 of 12 in the other two. A multi-level distance hierarchy shows that manifold-aware metrics outperform Euclidean distance for identifying regulatory gene pairs, and graph community partitions track known transcription factor target relationships. Second, this structure is shared across independently trained models. CCA alignment between scGPT and Geneformer yields canonical correlation of 0.80 and gene retrieval accuracy of 72 percent, yet none of 19 tested methods reliably recover gene-level correspondences. The models agree on the global shape of gene space but not on precise gene placement. Third, the structure is more localized than it first appears. Under stringent null controls applied across all null families, robust signal concentrates in immune tissue, while lung and external lung signals weaken substantially.

Ihor Kendiukhov

Department of Computer Science, University of Tübingen, Tübingen, Germany

Neural Representation GeometryGenomic Foundation ModelsGeometric Representation LearningTopological Representation LearningSingle-Cell Transcriptomics
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Feb 21, 2026

IRIS-SLAM: Unified Geo-Instance Representations for Robust Semantic Localization and Mapping

Geometry foundation models have significantly advanced dense geometric SLAM, yet existing systems often lack deep semantic understanding and robust loop closure capabilities. Meanwhile, contemporary semantic mapping approaches are frequently hindered by decoupled architectures and fragile data association. We propose IRIS-SLAM, a novel RGB semantic SLAM system that leverages unified geometric-instance representations derived from an instance-extended foundation model. By extending a geometry foundation model to concurrently predict dense geometry and cross-view consistent instance embeddings, we enable a semantic-synergized association mechanism and instance-guided loop closure detection. Our approach effectively utilizes viewpoint-agnostic semantic anchors to bridge the gap between geometric reconstruction and open-vocabulary mapping. Experimental results demonstrate that IRIS-SLAM significantly outperforms state-of-the-art methods, particularly in map consistency and wide-baseline loop closure reliability.

Tingyang Xiao, Liu Liu, Wei Feng +6

Horizon Robotics · D-Robotics · S-Lab, Nanyang Technological University +1

Open-Vocabulary Semantic MappingSimultaneous Localization and MappingSemantic MappingLoop Closure DetectionGeometric Representation Learning
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Feb 16, 2026

Spectral Convolution on Orbifolds for Geometric Deep Learning

Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to identify further topological and geometric structures with which these use cases can be made accessible to machine learning. There are various techniques, such as spectral convolution, that form the basic building blocks for some convolutional neural network-like architectures on non-Euclidean data. In this paper, the concept of spectral convolution on orbifolds is introduced. This provides a building block for making learning on orbifold structured data accessible using GDL. The theory discussed is illustrated using an example from music theory.

Tim Mangliers, Bernhard Mössner, Benjamin Himpel

Department of Computer Science Reutlingen University, Germany

Geometric Representation LearningSpectral Graph Convolution
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Feb 3, 2026

Geometry-Preserving Neural Architectures on Manifolds with Boundary

A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs. We provide a unified framework for these geometry-preserving architectures by organizing them according to where and how constraints are enforced, either throughout the intermediate layers or only at the final output. This perspective reveals several gaps in the existing theory. To address these gaps, we prove high-level approximation theorems for projected neural ODEs, intermediate augmented architectures, and final augmented architectures on prox-regular constraint sets, including smooth manifolds with boundary. Numerical experiments on synthetic dynamics over S^2, the disk, SO(3), together with real-world protein backbone data on SE(3), demonstrate exact feasibility for analytic updates and show that the final augmentation have simpler architecture and outperform in most tasks considered. When the constraint set is unknown, we learn projections via small-time heat-kernel limits, showing diffusion/flow-matching can be used as data-based projections. Moreover, we also the demonstrate the usefulness of the architectures that enforce non-convex constraints for path planning on manifolds with boundary.

Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum +4

Los Alamos National Laboratory · Boston College

Geometric Representation LearningNeural Network Approximation TheoryNeural ODEs
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Feb 2, 2026

Discovering Data Manifold Geometry through Geometric Properties

A prevailing paradigm in modern representation learning is the map-first approach, in which a representation map is learned from reconstruction, embedding, or task objectives. At the optimum, when the learned map accurately recovers a global coordinate chart, it should exhibit three structural properties whose geometric meaning can be illustrated through a face-editing example: Commutativity requires that changing pose and then expression gives the same result as applying them in the reverse order; Time Coherence requires that the same variation along one coordinate induces the same expression change across faces; Common-Reference requires that all faces are organized relative to a common reference face. However, small approximation errors in the learned map need not translate into small errors in these structural properties, and can therefore disrupt the global organization of the representation. Based on this observation, we consider the converse of the map-first formulation and ask whether a global representation can instead emerge by directly learning these properties. We represent variations along individual coordinates through vector fields defined in the ambient space and introduce a non-contraction condition preventing one transformation from destroying directions associated with the others. We derive an unsupervised objective that learns these structural properties and establish theoretical results connecting its minimization to tangent-space recovery. Experiments on controlled manifolds validate the predicted tangent-space recovery and global structure, while an autoencoder baseline shows that small map-first errors can still produce substantial violations of the targeted properties.

David Vigouroux, Lucas Drumetz, Ronan Fablet +1

ANITI, IMT Atlantique - DSD, LaTIM · IRT Saint Exupery, ANITI, Toulouse, France · IMT Atlantique, LaTIM UMR 1101 INSERM, Brest, France +5

Unsupervised Representation LearningGeometric Representation LearningManifold Learning
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Jan 14, 2026

Geometric Stability: The Missing Axis of Representations

Representational similarity methods compare the geometries of neural representations, but they do not measure how consistently the geometry of a single representation is recovered from subsets of its feature coordinates. We call this property geometric stability and introduce Shesha, which estimates it by correlating representational dissimilarity matrices from complementary random feature subsets. Shesha is not invariant to orthogonal rotations: representations with identical Gram matrices, and therefore identical linear CKA, can have different geometric stability. Controlled transformations further separate the quantities. Across 2,4632{,}463 encoder configurations spanning seven domains, similarity and stability are positively associated across non-PCA transformations (ρ=+0.75ρ=+0.75) but negatively associated under PCA-coordinate compression (ρ=−0.47ρ=-0.47). We further evaluate 170 pretrained vision models across six datasets. DINOv2 combines strong transfer performance with bottom-quartile stability on five of six datasets, showing that transferability and feature-split stability need not coincide. Across random feature subsets, the marginal relationship between Shesha and linear-probe variability is dataset-dependent; after controlling for task alignment with LogME, higher Shesha is associated with lower variability on five of six datasets. These results identify geometric stability as a basis-dependent property that complements representational similarity and task alignment.

Prashant C. Raju

Representational Similarity AnalysisNeural Representation GeometryVisual Representation LearningGeometric Representation Learning
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Jan 12, 2026

GeoMotionGPT: Geometry-Aligned Motion Understanding with Large Language Models

Discrete motion tokenization has recently enabled Large Language Models (LLMs) to serve as versatile backbones for motion understanding and motion-language reasoning. However, existing pipelines typically decouple motion quantization from semantic embedding learning, linking them solely via token IDs. This approach fails to effectively align the intrinsic geometry of the motion space with the embedding space, thereby hindering the LLM's capacity for nuanced motion reasoning. We argue that alignment is most effective when both modalities share a unified geometric basis. Therefore, instead of forcing the LLM to reconstruct the complex geometry among motion tokens from scratch, we present a novel framework that explicitly enforces orthogonality on both the motion codebook and the LLM embedding space, ensuring that their relational structures naturally mirror each other. Specifically, we employ a decoder-only quantizer with Gumbel-Softmax for differentiable training and balanced codebook usage. To bridge the modalities, we use a sparse projection that maps motion codes into the LLM embedding space while preserving orthogonality. Finally, a two-stage orthonormal regularization schedule enforces soft constraints during tokenizer training and LLM fine-tuning to maintain geometric alignment without hindering semantic adaptation. Extensive experiments show that our framework improves the aggregated Average by 22.4% over the strongest baseline on HumanML3D and by 14.4% on KIT-ML, while ablations confirm the effectiveness of the tokenizer, projection, and regularization designs.

Zhankai Ye, Bofan Li, Yukai Jin +5

Florida State University · Texas Tech University · William & Mary University

Motion Representation LearningCross-Modal AlignmentLatent Space AlignmentGeometric Representation Learning
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Dec 29, 2025

PGOT: A Physics-Geometry Operator Transformer for Complex PDEs

While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures often employ feature dimensionality reduction strategies, which inadvertently induces Geometric Aliasing, resulting in the loss of critical physical boundary information. To address this, we propose the Physics-Geometry Operator Transformer (PGOT), designed to reconstruct physical feature learning through explicit geometry awareness. Specifically, we propose Spectrum-Preserving Geometric Attention (SpecGeo-Attention). Utilizing a ``physics slicing-geometry injection" mechanism, this module incorporates multi-scale geometric encodings to explicitly preserve multi-scale geometric features while maintaining linear computational complexity O(N)O(N). Furthermore, PGOT dynamically routes computations to low-order linear paths for smooth regions and high-order non-linear paths for shock waves and discontinuities based on spatial coordinates, enabling spatially adaptive and high-precision physical field modeling. PGOT achieves consistent state-of-the-art performance across four standard benchmarks and excels in large-scale industrial tasks including airfoil and car designs.

Zhuo Zhang, Xi Yang, Ying Miao +5

National University of Defense Technology · Peking University · National University of Singapore +2

Neural PDE SolversPDE Surrogate ModelingGeometric Representation LearningPDE Operator LearningNeural Operators
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Nov 28, 2025

Freeze, Diffuse, Decode: Task-Aware Adaptation of Transformer Embeddings for Antimicrobial Peptide Design

Pretrained transformers provide rich, general-purpose embeddings, which are transferred to downstream tasks. However, current transfer strategies: fine-tuning and probing, either distort the pretrained geometric structure of the embeddings or lack sufficient expressivity to capture task-relevant signals. These issues become even more pronounced when supervised data are scarce. Here, we introduce Freeze, Diffuse, Decode (FDD), a novel diffusion-based framework that adapts pre-trained embeddings to downstream tasks while preserving their underlying geometric structure. FDD propagates supervised signal along the intrinsic manifold of frozen embeddings, enabling a geometry-aware adaptation of the embedding space. Applied to antimicrobial peptide design, FDD yields low-dimensional, predictive, and interpretable representations that support property prediction, retrieval, and latent-space interpolation.

Pankhil Gawade, Adam Izdebski, Myriam Lizotte +4

Institute of AI for Health, Helmholtz Munich · School of Computation, Information and Technology, Technical University of Munich · Mila - Quebec AI institute; Univ. de Montreal +3

Representation LearningGeometric Representation LearningMolecular Property Prediction
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Nov 24, 2025

Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery

Cross-subject motor imagery decoding remains a fundamental challenge in EEG-based brain-computer interfaces due to substantial inter-subject variability. Recent approaches have leveraged Riemannian geometry by representing EEG signals as covariance matrices on the symmetric positive definite (SPD) manifold. However, existing methods primarily focus on manifold-based representations while largely overlooking subject-specific variations in covariance dispersion and orientation. In this work, we address these challenges through geometry-aware congruence transformations and propose three complementary models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). The proposed models are evaluated both as manifold alignment modules for downstream classifiers and as end-to-end discriminative architectures optimized via cross-entropy with a custom logistic regression head. Experiments on challenging cross-subject motor imagery benchmarks demonstrate consistent improvements in transductive decoding performance, achieving 2-3% higher accuracy than strong baselines. These results highlight the effectiveness of geometry-aware congruence learning for mitigating inter-subject variability in EEG decoding.

Sanjeev Manivannan, Chandra Shekar Lakshminarayan

Department of Biotechnology · Department of Data Science and Artificial Intelligence

Cross-Subject EEG DecodingMI ClassificationBrain-Computer InterfacesNeural DecodingEEG DecodingGeometric Representation Learning+1
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Nov 4, 2025

Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity

We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (φ), we define (Q_{β,γ}(φ)=I(φ(X);Y)-β\mathcal C(φ)-γd_{\mathrm{int}}(φ)), combining task-relevant information with penalties for curvature and intrinsic latent dimension. Thus geometry becomes part of the bottleneck criterion, not only a post hoc diagnostic. Under smooth-manifold, loss-transfer, and estimator-concentration assumptions, we derive non-asymptotic low-label generalization bounds where intrinsic dimension and covering complexity enter explicitly. We characterize the information--geometry frontier and prove empirical-surrogate consistency. The analysis links encoder geometry to learning through latent covering numbers, loss-class entropy, and uniform deviation. We instantiate the theory as V-GIB, adding curvature and dimension penalties to variational bottleneck training. Real low-label benchmarks compare V-GIB with ERM, VIB, and ablations across (1%)--(20%) label fractions. Results show improved performance and reduced geometric complexity in several regimes, especially FashionMNIST and CIFAR-10, while confirming that no fixed regularizer is universally dominant.

Ronald Katende

Department of Mathematics, Kabale University, Katuna Road, Kikungiri Hill, Kabale, 317, Uganda

Intrinsic DimensionalityInformation BottleneckGeometric Representation LearningVariational Information BottleneckData-Efficient LearningLatent Space Geometry
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Sep 19, 2025

eVGGT: An Efficient Geometry-Aware Vision Encoder for Visuomotor Policies

Geometry-grounded vision models, such as VGGT, have emerged as robust visual encoders, providing essential geometric priors for robotic manipulation. However, the high computational cost of these models often leads to slow inference, limiting their practical applications in real-world robotics. This paper introduces eVGGT, a lightweight geometry-aware vision encoder distilled from the high-performing VGGT. Our findings demonstrate two primary advantages: i) integrating eVGGT into imitation learning frameworks (including ACT and Diffusion Policy) yields up to a 6.3% improvement in success rate over standard 2D encoders across bimanual and single-arm tasks in both simulation and real-world settings with variable viewpoints; ii) eVGGT achieves a nearly 5 times speedup and a 63% reduction in memory usage compared to state-of-the-art geometry-aware encoders while maintaining comparable task performance. These results suggest that eVGGT substantially alleviates the performance-latency bottleneck that has limited geometry-aware visuomotor policies in real-world deployment.

An Dinh Vuong, Minh Nhat Vu, Ian Reid

Department of Computer Vision, Mohammed bin Zayed University of Artificial Intelligence, UAE · AIT Austrian Institute of Technology GmbH, Austria

Visual Representation LearningVisuomotor Policy LearningGeometric Representation LearningRobotic Manipulation
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Dec 13, 2023

Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches

Detecting partial extrinsic symmetry in 3D geometry is a fundamental yet persistent challenge in computer vision and graphics, critical for tasks ranging from shape completion to procedural generation. Classical transformation-space voting methods rely on pairwise matching, scaling as O(n^2) and struggling to resolve coherent multi-instance groups. Recent learning approaches advance global symmetry detection but restrict the solution space to reflection planes, failing to capture rotational or translational repetitions such as the legs of a chair or the steps of a staircase. We propose SymCL, a self-supervised contrastive learning framework that detects partial symmetries across rotation, translation, and reflection (with scale-invariant features) and requires no ground truth annotations. By mapping local geodesic patches to a latent space invariant to the Euclidean group, we reformulate symmetry detection as a density-based clustering problem, enabling the simultaneous discovery of multi-instance symmetric relationships in a single forward pass. We evaluate quantitatively on SymPartNet, a new benchmark annotating all PartNet categories with partial symmetry relations, and demonstrate class-agnostic generalization qualitatively on everyday objects outside the training distribution.

Gregor Kobsik, Isaak Lim, Leif Kobbelt

Visual Computing Institute, RWTH Aachen University, Germany

Point Cloud LearningGeometric Representation LearningSymmetry Discovery
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