General Covariant Action Modeling: Constructing Generalized Manifolds via Spatio-Temporal Decoupling

• URL: http://arxiv.org/abs/2606.00110v1
• Date: Wed, 27 May 2026 03:38:15 GMT
• Title: General Covariant Action Modeling: Constructing Generalized Manifolds via Spatio-Temporal Decoupling
• Abstract summary: Generalized Action Manifold (GAM) framework enforces general covariance through structural disentanglement.<n>GAM enables superior transfer and robustness capabilities, outperforming geometry-agnostic baselines.
• Score: 48.559681359374146
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Achieving robust generalization from limited data is a central challenge in embodied intelligence. Prevailing methods fail by regressing absolute coordinates, which violates the principle of general covariance. Fundamentally, this conflates the intrinsic task geometry with rigid execution patterns, binding policies to specific motion styles and fixed speeds. To resolve this, we propose the Generalized Action Manifold (GAM) framework that enforces general covariance through structural disentanglement. Specifically, GAM realizes the manifold by enforcing invariance across two orthogonal dimensions: (1) Temporal Invariance, utilizing an Arc-Length Parameterizer to orthogonalize the spatial path geometry from temporal dynamics, ensuring robustness to velocity variations; (2) Geometric Invariance, where a Schema-Affine-Factorization mechanism maps trajectories to canonical ``world lines'' in a pose-normalized coordinate frame. This distinguishes invariant geometric schemas from affine modulations, ensuring spatial generalizability. By integrating GAM within a structured Vision-Language-Action (VLA) architecture, we enable sparse demonstrations to densely populate a continuous, valid action manifold. Empirical results demonstrate that GAM enables superior transfer and robustness capabilities, outperforming geometry-agnostic baselines.

Related papers

• Prototype-Anchored Generalized Manifold Regression for Unknown-Domain Object Detection [58.25418970608328]
  We study Single-Domain Generalized Object Detection (Single-DGOD), which aims to transfer a detector trained on a single source domain to multiple unseen domains.<n>Existing methods mainly rely on simulation-driven strategies, such as data augmentation or textual prompts, to enlarge the training distribution.<n>We propose Manifold Regression with Visual-Text Dual Chain-of-Thought (MR-DCoT), which formulates unknown-domain generalization as a manifold regression problem.
  arXiv  Detail & Related papers  (2026-07-08T09:27:15Z)
• SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting [15.612678669559516]
  Multivariable time series forecasting requires capturing the continuously evolving correlation structure among interacting variables.<n>We address this limitation by introducing manifold constraints into state-space modeling.<n>We propose SPDM, a geometry-aware SSM architecture that realizes this principle through two cooperating mechanisms.
  arXiv  Detail & Related papers  (2026-06-06T17:04:57Z)
• LAST: Bridging Vision-Language and Action Manifolds via Gromov-Wasserstein Alignment [71.3712075841632]
  LAST reconstructs the action space to establish local metric compatibility with the Vision-Language-Action modality.<n> LAST enables VLA models with superior convergence and generalizability.
  arXiv  Detail & Related papers  (2026-05-27T03:48:10Z)
• Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learning [2.704566511657017]
  In this paper, we introduce the Spline-Pullback Metric (SPM), instantiated as Spectral-SPM and Cholesky-SPM.<n>By parameterizing the global diffeomorphism via a rank-invariant, B-spline, SPM acts as a dense universal approximator for strictly increasing $C1$ diffeomorphisms.<n>SPM achieves a state-of-the-art performance across 3 datasets utilizing Linear Probes, SPDNets, and deep Riemannian ResNets.
  arXiv  Detail & Related papers  (2026-05-06T01:55:45Z)
• Multi-Way Representation Alignment [19.53606443098969]
  Current strategies for mapping representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference.<n>We first adapt Generalized Procrustes Analysis (GPA) to construct a shared universe that preserves the internal geometry essential for tasks like model stitching.<n>We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail.<n>To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-
  arXiv  Detail & Related papers  (2026-02-05T21:33:45Z)
• Orthogonal Model Merging [21.902153344111223]
  Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model.<n>We propose Orthogonal Model Merging (OrthoMerge) to preserve the geometric structure of the model's weights.
  arXiv  Detail & Related papers  (2026-02-05T17:57:14Z)
• Riemannian Flow Matching for Disentangled Graph Domain Adaptation [51.98961391065951]
  Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space.<n>DisRFM is a geometry-aware GDA framework that unifies embedding and flow-based transport.
  arXiv  Detail & Related papers  (2026-01-31T11:05:35Z)
• GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters [61.51810815162003]
  We propose an SE(3)-equivariant adapter framework ( GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks.<n>GeoAda preserves the model's geometric consistency while mitigating overfitting and catastrophic forgetting.<n>We demonstrate the wide applicability of GeoAda across diverse geometric control types, including frame control, global control, subgraph control, and a broad range of application domains.
  arXiv  Detail & Related papers  (2025-07-02T18:44:03Z)
• GAMA: Geometry-Aware Manifold Alignment via Structured Adversarial Perturbations for Robust Domain Adaptation [0.0]
  GAMA is a structured framework that achieves explicit manifold alignment via adversarial perturbation guided by geometric information.<n>GAMA tightens the generalization bound via structured regularization and explicit alignment.<n> Empirical results on DomainNet, VisDA, and Office-Home demonstrate that GAMA consistently outperforms existing adversarial and adaptation methods.
  arXiv  Detail & Related papers  (2025-05-21T07:16:42Z)
• Continuous Domain Generalization [32.29899595196802]
  This paper introduces the task of Continuous Domain Generalization (CDG), which aims to generalize predictive models to unseen domains.<n>We present a principled framework grounded in geometric and algebraic theories, showing that optimal model parameters across domains lie on a low-dimensional manifold.<n>Experiments on synthetic and real-world datasets, including remote sensing, scientific documents, and traffic forecasting, demonstrate that our method significantly outperforms existing baselines in both generalization accuracy and robustness.
  arXiv  Detail & Related papers  (2025-05-17T12:39:45Z)
• Bridging Geometric States via Geometric Diffusion Bridge [79.60212414973002]
  We introduce the Geometric Diffusion Bridge (GDB), a novel generative modeling framework that accurately bridges initial and target geometric states. GDB employs an equivariant diffusion bridge derived by a modified version of Doob's $h$-transform for connecting geometric states. We show that GDB surpasses existing state-of-the-art approaches, opening up a new pathway for accurately bridging geometric states.
  arXiv  Detail & Related papers  (2024-10-31T17:59:53Z)
• Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds [70.32518963244466]
  A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold. We argue that the particular choice of coordinatization should not affect a network's inference -- it should be coordinate independent. A simultaneous demand for coordinate independence and weight sharing is shown to result in a requirement on the network to be equivariant.
  arXiv  Detail & Related papers  (2021-06-10T19:54:19Z)
• Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs [81.12344211998635]
  A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs) We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.
  arXiv  Detail & Related papers  (2020-03-11T17:21:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.