HSR, a model for predicting the next item in a user's interaction sequence, was reported to deliver the best results across most of the main ranking measures tested on three benchmark datasets. The reported gains ranged from -0.39% to 17.42%, with the only negative result in the nine dataset-metric comparisons occurring for MovieLens-1M Hit@10.
The largest reported gain was 17.42% for MRR@10 on Amazon-Video-Games. On Amazon-Beauty, HSR's reported scores were 0.0952 for Hit@10, 0.0566 for NDCG@10, and 0.0448 for MRR@10.
A recommender built around momentum
The paper frames preference evolution as a dissipative Hamiltonian system, meaning it tracks a stable preference state and a short-term tendency while allowing the system's motion to be damped. In this formulation, position represents stable preference and momentum represents short-term tendency.
HSR combines a learnable frequency-domain propagator for sequence-wide patterns, computed with fast Fourier transforms at O(T log T) complexity, with a parallel local impulse branch for abrupt deviations. It then makes a one-step prediction using phase-space extrapolation.
Three sparse benchmarks
The evaluation used MovieLens-1M, Amazon-Beauty and Amazon-Video-Games. They contained 6,041, 22,364 and 24,304 users respectively; the corresponding interaction counts were 999,611, 198,502 and 231,780. Their reported sparsity was 95.53%, 99.93% and 99.91% respectively.
For each dataset, the final interaction was held out for testing and the penultimate interaction for validation, under a leave-one-out protocol. The maximum sequence length was 200 for MovieLens-1M and 50 for each Amazon dataset.
The efficiency case
On Amazon-Beauty, HSR was reported to use 4.74 million parameters and an 18.07 MB model, train in 6.8 seconds per epoch, respond to a single user in 0.014 milliseconds, and reach 60,113 queries per second. Compared with Mamba4Rec, the paper reported 21.91% lower parameter count and model size, 48.87% less training time, 44.00% lower latency and 77.09% higher throughput.
Those efficiency figures came from Amazon-Beauty only, and peak GPU memory was reported to be higher than DIFF. The component tests also found that removing any single HSR component degraded at least one metric, with the largest reported drops after removal of the Hamiltonian structure or local impulse refinement.
The ablation comparison was summarized qualitatively rather than through a complete numeric table, so the size of each component's contribution is not fully reported in the supplied results.
Stress tests favored HSR
As synthetic interaction noise rose from 0% to 30%, all baselines degraded substantially, while HSR was described as having the flattest degradation curve. No plotted numeric values or uncertainty estimates were reported for that analysis.
HSR was reported to have its largest margin over competing methods in the cold-start regime, when only a few interactions were available. In a separate MovieLens-1M average-reward comparison using the K most popular candidate items, HSR scored 0.0048 versus BMAB's 0.0028 at K=5, 0.0154 versus 0.0112 at K=20, and 0.0429 versus 0.0220 at K=100.
What remains untested
The evidence is confined to offline computational experiments on three benchmark interaction logs, rather than a prospective deployment with real users. The analysis reports no confidence intervals, standard errors, repeated-run variability, hypothesis tests or statistical significance results, so the percentage gains are point comparisons rather than estimates with stated uncertainty.
The study does not establish whether the pattern will generalize to other datasets, domains or deployment environments. It also does not show that HSR changes user preferences, engagement, satisfaction or welfare, or that learned mass and damping are direct measurements of human behavior.
Paper data and sources
Original title: Hamiltonian Spectral-Temporal Dissipative Dynamics for Sequential Recommendation
Authors: Shuiying Liao, P. Y. Mok
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: 10.1145/3773078.3831793
Original paper · Full text