Hodge Decomposition

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Overview

Hodge decomposition studies how vector fields and graph flows can be separated into gradient-driven, cyclic, and topology-dependent components. Common approaches use graph or simplicial Laplacians, discrete differential forms, and projection layers to isolate these components. Researchers apply the decomposition to multi-agent learning, neural operators for physical systems, diffusion-model error analysis, and flows represented in transformer attention. A central open question is when the separation provides useful stability or interpretability, since harmonic and cyclic components can be hard to assign a clear meaning in each application.

Latest papers

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9 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. HodgePhaseNet: Discrete Hodge Decomposition of Semantic Flows in Transformer Attention

    Oct 10, 2026Kiyotaka Kasubuchi, Kazuo FukiyaTransformer AttentionHodge Decomposition

  2. Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling

    Sep 29, 2026Zeyu JiaHodge DecompositionInference-Time Scaling

    School of Biomedical Engineering and Technology, Tianjin Medical University, Medical School, Tianjin University

  3. Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies

    Sep 27, 2026Xiang Li, Yue SongKuramoto ModelHodge Decomposition

    Tsinghua University · Beijing University of Chemical Technology

  4. Human mutation field reveals an equilibrium-like structure with irreversible circulation

    Sep 7, 2026Isabella Caranzano, Daniel Maria Busiello, Stefano Priorelli +2Hodge DecompositionGenomics

    AI and Computational Biomedicine Unit, Department of Medical Sciences, University of Torino, Torino, Italy · Department of Physics, University of Padova, Padova, Italy · Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

  5. Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors

    Jun 4, 2026Naïl B. Khelifa, Richard E. Turner, Ramji VenkataramananScore MatchingHodge Decomposition

    University of Cambridge

  6. A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery

    May 18, 2026Diego CasadeiDynamical SystemsHodge Decomposition

    Fly High Engineering AG, Badenerstrasse 13, 5200 Brugg AG, Switzerland

  7. HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts

    May 13, 2026Tao Zhong, Dongzhe Zheng, Christine Allen-BlanchetteMixture-of-Experts PruningHodge Decomposition

    Princeton University

  8. Topology-Preserving Neural Operator Learning via Hodge Decomposition

    May 13, 2026Dongzhe Zheng, Tao Zhong, Christine Allen-BlanchetteHodge DecompositionPDE Operator Learning

    Princeton University

  9. Metric-Gradient Projection for Stable Multi-Agent Policy Learning

    May 12, 2026Zuyuan Zhang, Sizhe Tang, Mahdi Imani +1Hodge DecompositionMulti-Agent Systems

    The George Washington University · Northeastern University