# Learning Collective Dynamics with Differentiable Gaussian Representations

arXiv: https://arxiv.org/abs/2609.28405 · HTML: https://mlsanity.com/paper/2609.28405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 79 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 30 of 30)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Entire Space Multi-Task Model: An Effective Approach for Estimating Post-Click Conversion Rate](https://mlsanity.com/paper/1804.07931/) (2018)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility](https://mlsanity.com/paper/1710.11214/) (2017)
- [RecSim: A Configurable Simulation Platform for Recommender Systems](https://mlsanity.com/paper/1909.04847/) (2019)
- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [KuaiRand: An Unbiased Sequential Recommendation Dataset with Randomly Exposed Videos](https://mlsanity.com/paper/2208.08696/) (2022)
- [Modeling User Exposure in Recommendation](https://mlsanity.com/paper/1510.07025/) (2015)
- [Degenerate Feedback Loops in Recommender Systems](https://mlsanity.com/paper/1902.10730/) (2019)
- [GWM: Towards Scalable Gaussian World Models for Robotic Manipulation](https://mlsanity.com/paper/2508.17600/) (2025)
- [Learning from Aggregate Observations](https://mlsanity.com/paper/2004.06316/) (2020)
- [KuaiSim: A Comprehensive Simulator for Recommender Systems](https://mlsanity.com/paper/2309.12645/) (2023)
- [Quasi-Monte Carlo Variational Inference](https://mlsanity.com/paper/1807.01604/) (2018)
- [RecSim NG: Toward Principled Uncertainty Modeling for Recommender Ecosystems](https://mlsanity.com/paper/2103.08057/) (2021)
- [Differentiable Agent-based Epidemiology](https://mlsanity.com/paper/2207.09714/) (2022)
- [Differentiable Agent-Based Simulation for Gradient-Guided Simulation-Based Optimization](https://mlsanity.com/paper/2103.12476/) (2021)
- [ContactGaussian-WM: Learning Physics-Grounded World Model from Videos](https://mlsanity.com/paper/2602.11021/) (2026)
- [Automatic Differentiation of Agent-Based Models](https://mlsanity.com/paper/2509.03303/) (2025)
- [Learning Hidden Markov Models from Aggregate Observations](https://mlsanity.com/paper/2011.11236/) (2020)
- [SARN: Structurally-Aware Recurrent Network for Spatio-Temporal Disaggregation](https://mlsanity.com/paper/2306.07292/) (2023)

## Abstract (arXiv)

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.