Hamiltonian Spectral-Temporal Dissipative Dynamics for Sequential Recommendation

• URL: http://arxiv.org/abs/2608.25755v1
• Date: Wed, 26 Aug 2026 13:04:04 GMT
• Title: Hamiltonian Spectral-Temporal Dissipative Dynamics for Sequential Recommendation
• Abstract summary: We introduce the Hamiltonian Spectral Recommender (HSR), which recasts preference evolution as a dissipative Hamiltonian system.<n>HSR consistently outperforms state-of-the-art Transformer-based and state space model (SSM)-based recommenders.
• Score: 4.649779668774962
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sequential recommendation requires understanding how user preferences evolve over time, yet most existing models treat such evolution as a first order process where the next state depends solely on the current latent representation. Nevertheless, real user behavior often exhibits richer dynamics, including inertia, periodicity, and sudden shifts that cannot be fully captured by these first order assumptions. Motivated by these behavioral characteristics, we reconceptualize sequential recommendation through the lens of second order dynamical systems and introduce the Hamiltonian Spectral Recommender (HSR), which recasts preference evolution as a dissipative Hamiltonian system in a latent phase space of position (stable preference) and momentum (short-term tendency). The linear time-invariant structure of the governing equation admits a closed-form solution in the frequency domain. A learnable dissipation mechanism further captures natural interest decay, while a short local impulse refinement module models abrupt behavioral fluctuations commonly observed in sparse interaction logs. This design jointly accounts for global periodic patterns, inertial evolution, and localized shocks, where three phenomena that are underrepresented in existing sequential models. Extensive experiments on three benchmark datasets demonstrate that HSR consistently outperforms state-of-the-art Transformer-based and state space model (SSM)-based recommenders.

Related papers

• Unlocking Temporal Generalization in Hamiltonian Video Dynamics Models [0.0]
  Hamiltonian Generative Networks (HGN) offer a principled path forward.<n>We show that HGN rollouts at step sizes beyond the training regime fail due to distinct failure modes.<n>In a detailed analysis, we recommend several strategies for enabling temporal generalization in continuous-time video generation.
  arXiv  Detail & Related papers  (2026-07-08T15:31:53Z)
• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• Forecasting as Rendering: A 2D Gaussian Splatting Framework for Time Series Forecasting [79.37674445572462]
  Time series forecasting (TSF) remains a challenging problem due to the intricate entanglement of intraperiod-fluctuations and interperiod-trends.<n>Treating reshaped tensors as static images results in a topological mismatch.<n> relying on uniform fixed-size representations allocates modeling capacity inefficiently.<n>TimeGS is a novel framework that fundamentally shifts the forecasting paradigm from regression to 2D generative rendering.
  arXiv  Detail & Related papers  (2026-02-10T14:13:36Z)
• A Mechanistic Analysis of Transformers for Dynamical Systems [4.590170084532207]
  We study the representational capabilities and limitations of single-layer Transformers when applied to dynamical data.<n>For linear systems, we show that the convexity constraint imposed by softmax attention fundamentally restricts the class of dynamics that can be represented.<n>For nonlinear systems under partial observability, attention instead acts as an adaptive delay-embedding mechanism.
  arXiv  Detail & Related papers  (2025-12-24T11:21:07Z)
• Forecasting Continuous Non-Conservative Dynamical Systems in SO(3) [51.510040541600176]
  We propose a novel approach to modeling the rotation of moving objects in computer vision.<n>Our approach is agnostic to energy and momentum conservation while being robust to input noise.<n>By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings.
  arXiv  Detail & Related papers  (2025-08-11T09:03:10Z)
• Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations [51.510040541600176]
  This work proposes modeling continuous-time rotational object dynamics on $SO(3)$.<n>Unlike existing methods that rely on simplified motion assumptions, our method learns a general latent dynamical system of the underlying object trajectory.<n> Experimental results on real-world data demonstrate compelling forecasting capabilities compared to existing approaches.
  arXiv  Detail & Related papers  (2025-06-07T12:41:50Z)
• Learning Robust Spectral Dynamics for Temporal Domain Generalization [35.98513351187109]
  Temporal Domain Generalization seeks to enable model generalization across evolving domains.<n>We introduce FreKoo, which tackles these challenges via a novel frequency-domain analysis of parameter trajectories.<n>FreKoo excels in real-world streaming scenarios with complex drifts and uncertainties.
  arXiv  Detail & Related papers  (2025-05-19T00:38:18Z)
• Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling [0.0]
  We present a data-driven framework for estimating the response of higher-order moments of nonlinear systems to small external perturbations.<n>We combine GFDT with score-based generative modeling to estimate the system's score function directly from data.<n>Our method is validated on several models relevant to climate dynamics.
  arXiv  Detail & Related papers  (2025-04-17T20:54:33Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences.<n>We train the model using maximum likelihood estimation with Markov chain Monte Carlo.<n> Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving [0.0]
  We investigate the dynamics of a quasiperiodically driven Rydberg atom chain in the strong Rydberg blockage regime. Even without driving, the PXP model exhibits many-body scarring and resultant persistent oscillations. Our results demonstrate that continuous quasi-periodic drive protocols can provide a promising route to realize prethermal phases of matter.
  arXiv  Detail & Related papers  (2024-06-03T15:30:02Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

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.