Learning Collective Dynamics with Differentiable Gaussian Representations

Summary

The paper introduces Differentiable Gaussian Dynamics (DGD), a model that learns population-level collective response dynamics from aggregate counts. It represents a population as a Gaussian mixture over a latent response propensity, aggregates contact intensity and joint behavioral probabilities differentiably at quadrature nodes, and advances a state via feedback recurrence (memory, fatigue, response shifts, arrival environment). Training combines daily negative-binomial count losses and event-normalized joint-pattern losses through both observed and expected-feedback branches. On four windows from KuaiRand-Pure and Online Retail II, DGD achieves lower joint behavioral NLL than an adapted DeepAR with a joint-behavior head (e.g., 1.1232 vs 1.3466 in the standard-recommendation window); one-day behavioral-count MAE in Retail 2010 is 4.71 vs 6.88. Ablations attribute gains to distribution learning (10.82% NLL reduction vs a fixed Gaussian) and feedback (one-day count MAE 34.08 to 16.47 under random exposure). Controlled experiments recover known cross-day dynamics and predict choice distributions under new attributes and prices. Main limitations: no significance testing, with some seed standard deviations overlapping the reported gaps; short test windows (7-17 days); a partly post-hoc baseline set whose timing the authors disclose; KuaiRand experiments restricted to one user hash bucket (~354-381 users); and no comparison against the aggregate-HMM, Hawkes, or differentiable-ABM methods the paper cites as nearest neighbors.