Learning Collective Dynamics with Differentiable Gaussian Representations
Researchers propose Differentiable Gaussian Dynamics to learn population behavior from aggregate counts, beating a DeepAR baseline.
The paper introduces Differentiable Gaussian Dynamics, which represents heterogeneous response propensities with a Gaussian mixture, aggregates contact intensity and behavior probabilities differentiably, and updates later responses through feedback recurrence. On windows from KuaiRand-Pure and Online Retail II, it reports lower joint behavioral negative log-likelihood than a DeepAR adaptation with a joint-behavior head. In Retail 2010, one-day behavioral-count MAE is 4.71 versus 6.88. Learning the distribution reduces behavioral NLL by 10.82% versus a fixed Gaussian on one KuaiRand window, and removing feedback raises joint KL from 0.0340 to 0.2577.
- DGD learns population response distributions from aggregate counts.
- Retail 2010 one-day count MAE is 4.71 versus 6.88 for DeepAR.
- Learned distribution cuts behavioral NLL 10.82% versus a fixed Gaussian.
- Removing feedback raises joint KL from 0.0340 to 0.2577.
Full article174 words · extracted from arxiv.org · click to collapse
Collective responses depend on individual differences, contact opportunities, and accumulated experience. Learning their dynamics from aggregate counts requires connecting a population's response distribution to both current observations and future behavior. We introduce Differentiable Gaussian Dynamics (DGD), which learns this connection through three components: a Gaussian mixture representing heterogeneous response propensities, differentiable aggregation of contact intensity and behavioral probabilities, and feedback recurrence that updates subsequent responses. Reparameterized integration and temporal recurrence let aggregate prediction errors jointly train the distribution, observation functions, and feedback parameters. On four windows from KuaiRand-Pure and Online Retail II, DGD achieves lower joint behavioral negative log-likelihood than a DeepAR adaptation with a joint-behavior head. In Retail 2010, its one-day behavioral-count MAE is 4.71 versus 6.88 for this adaptation. Learning the distribution reduces behavioral negative log-likelihood by 10.82% relative to a fixed Gaussian in KuaiRand's standard-recommendation window; removing feedback dynamics raises joint KL from 0.0340 to 0.2577 in a controlled experiment. These results establish the value of learning population representations and their feedback process from aggregate observations. Code is available at https://github.com/OranAi-Ltd/oransim.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.28405