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This paper introduces the Hamiltonian Spectral Recommender (HSR), which models user preference evolution in sequential recommendation as a second-order dynamical system, addressing the limitations of first-order models that fail to capture complex user behaviors. By leveraging a dissipative Hamiltonian framework, HSR incorporates inertia, periodicity, and sudden shifts in user preferences, leading to a more nuanced understanding of user dynamics. Experimental results across three benchmark datasets show that HSR significantly outperforms existing Transformer-based and state space model recommenders, highlighting its effectiveness in capturing the intricacies of user behavior.
HSR reveals that modeling user preferences as a second-order dynamical system can dramatically enhance recommendation accuracy by capturing complex behavioral patterns often overlooked by traditional methods.
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.
