Hodge Decomposition

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3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling
Sep 29, 2026Zeyu JiaHodge Decomposition Inference-Time Scaling
School of Biomedical Engineering and Technology, Tianjin Medical University, Medical School, Tianjin University
Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies
Sep 27, 2026Xiang Li, Yue SongHodge Decomposition PDE Operator Learning
Tsinghua University · Beijing University of Chemical Technology
Human mutation field reveals an equilibrium-like structure with irreversible circulation
Sep 7, 2026Isabella Caranzano, Daniel Maria Busiello, Stefano Priorelli +2Hodge Decomposition Genomics
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
Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors
Jun 4, 2026Naïl B. Khelifa, Richard E. Turner, Ramji VenkataramananScore Matching Hodge Decomposition
University of Cambridge
A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery
May 18, 2026Diego CasadeiDynamical Systems Hodge Decomposition
Fly High Engineering AG, Badenerstrasse 13, 5200 Brugg AG, Switzerland
HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts
May 13, 2026Tao Zhong, Dongzhe Zheng, Christine Allen-BlanchetteMixture-of-Experts Pruning Hodge Decomposition
Princeton University
Topology-Preserving Neural Operator Learning via Hodge Decomposition
May 13, 2026Dongzhe Zheng, Tao Zhong, Christine Allen-BlanchetteHodge Decomposition PDE Operator Learning
Princeton University
Metric-Gradient Projection for Stable Multi-Agent Policy Learning
May 12, 2026Zuyuan Zhang, Sizhe Tang, Mahdi Imani +1Hodge Decomposition Multi-Agent Systems
The George Washington University · Northeastern University

Sep 29, 2026, cs.LGJ/K move · Enter open · S save

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

Zeyu Jia

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

Hodge Decomposition Inference-Time Scaling Port-Hamiltonian Systems

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Test-time compute scaling has emerged as a cornerstone of advanced machine reasoning, yet performing iterative deliberation directly within continuous latent representation spaces reveals a catastrophic pathology: the Deliberation Drift Cliff. While unconstrained recurrent latent models achieve initial reasoning gains at short horizons (K <= 4), their reasoning collapses when extrapolated to deeper thinking steps (K >= 16), dropping by 22% to 62% across standard logical benchmarks. We resolve the trilemma among expressivity, Lyapunov stability, and computational efficiency in test-time latent reasoning through a 22-round empirical and theoretical investigation. We demonstrate that strictly conservative scalar potential gradient flows suppress long-range drift (cliff 3.40%) but bottleneck peak reasoning accuracy at 32.73%, whereas unconstrained rotational flows achieve high symbolic expressivity (82.33%) but suffer a severe 36.87% drift cliff. To resolve this geometric duality, we establish Port-Hamiltonian Latent Deliberation (PH-LD) and propose the Direct-Gradient Pure-Tensor Helmholtz-Hodge Decomposition (DG-HHD). DG-HHD parameterizes the attracting flow as a tangent projection tensor network while orthogonally decoupling non-zero circulation (Hodge machine error 1.65e-17, contraction error 5.55e-17), eliminating runtime autograd dependencies to achieve 1.84x vector field and 2.09x RK45 rollout speedups. In a 15-arm symmetrical Pareto benchmark, DG-HHD achieves 58.67% peak accuracy (+25.94% absolute gain over conservative HHD) and retains 35.27% at K=32. Transferred to small language model (SLM) multi-hop causal reasoning, DG-HHD delivers monotonic compute scaling (49.33% to 51.56%) and suppresses out-of-distribution drift (cliff -0.66%). All 30 Level 0 deterministic invariants are certified.

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