# Langevin Flows for Modeling Neural Latent Dynamics

arXiv: https://arxiv.org/abs/2507.11531 · HTML: https://mlsanity.com/paper/2507.11531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 52 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [A Unified, Scalable Framework for Neural Population Decoding](https://mlsanity.com/paper/2310.16046/) (2023)
- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Representation learning for neural population activity with Neural Data Transformers](https://mlsanity.com/paper/2108.01210/) (2021)
- [Linear dynamical neural population models through nonlinear embeddings](https://mlsanity.com/paper/1605.08454/) (2016)
- [LFADS - Latent Factor Analysis via Dynamical Systems](https://mlsanity.com/paper/1608.06315/) (2016)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [Making brain-machine interfaces robust to future neural variability](https://mlsanity.com/paper/1610.05872/) (2016)
- [Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains](https://mlsanity.com/paper/1604.03053/) (2016)
- [Enabling hyperparameter optimization in sequential autoencoders for spiking neural data](https://mlsanity.com/paper/1908.07896/) (2019)
- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [Interpretable Nonlinear Dynamic Modeling of Neural Trajectories](https://mlsanity.com/paper/1608.06546/) (2016)

## Abstract (arXiv)

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation. Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and stochastic forces -- to represent both autonomous and non-autonomous processes in neural systems. Crucially, the potential function is parameterized as a network of locally coupled oscillators, biasing the model toward oscillatory and flow-like behaviors observed in biological neural populations. Our model features a recurrent encoder, a one-layer Transformer decoder, and Langevin dynamics in the latent space. Empirically, our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor, closely matching ground-truth firing rates. On the Neural Latents Benchmark (NLB), the model achieves superior held-out neuron likelihoods (bits per spike) and forward prediction accuracy across four challenging datasets. It also matches or surpasses alternative methods in decoding behavioral metrics such as hand velocity. Overall, this work introduces a flexible, physics-inspired, high-performing framework for modeling complex neural population dynamics and their unobserved influences.