# BRAID: Input-Driven Nonlinear Dynamical Modeling of Neural-Behavioral Data

arXiv: https://arxiv.org/abs/2509.18627 · HTML: https://mlsanity.com/paper/2509.18627/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 23 Sep 2025.

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

- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE](https://mlsanity.com/paper/2011.04798/) (2020)
- [Linear dynamical neural population models through nonlinear embeddings](https://mlsanity.com/paper/1605.08454/) (2016)
- [Adversarial Domain Adaptation for Stable Brain-Machine Interfaces](https://mlsanity.com/paper/1810.00045/) (2018)
- [A State Space Approach for Piecewise-Linear Recurrent Neural Networks for Reconstructing Nonlinear Dynamics from Neural Measurements](https://mlsanity.com/paper/1612.07846/) (2016)
- [Making brain-machine interfaces robust to future neural variability](https://mlsanity.com/paper/1610.05872/) (2016)
- [Targeted Neural Dynamical Modeling](https://mlsanity.com/paper/2110.14853/) (2021)
- [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021)
- [Demixed principal component analysis of population activity in higher cortical areas reveals independent representation of task parameters](https://mlsanity.com/paper/1410.6031/) (2014)
- [Multi-modal Gaussian Process Variational Autoencoders for Neural and Behavioral Data](https://mlsanity.com/paper/2310.03111/) (2023)
- [Learning Optimal Filters Using Variational Inference](https://mlsanity.com/paper/2406.18066/) (2024)

## Built on by (most cited first, 8 of 8)

- [BaRISTA: Brain Scale Informed Spatiotemporal Representation of Human Intracranial Neural Activity](https://mlsanity.com/paper/2512.12135/) (2025)
- [Cross-Modal Representational Knowledge Distillation for Enhanced Spike-Informed LFP Modeling](https://mlsanity.com/paper/2512.12461/) (2025)
- [Dynamical modeling of nonlinear latent factors in multiscale neural activity with real-time inference](https://mlsanity.com/paper/2512.12462/) (2025)
- [SpikeProphecy: A Large-Scale Benchmark for Autoregressive Neural Population Forecasting](https://mlsanity.com/paper/2605.12992/) (2026)
- [Benchmarking Probabilistic Time Series Forecasting Models on Neural Activity](https://mlsanity.com/paper/2510.18037/) (2025)
- [Cross-Subject Modeling for Widefield Calcium Imaging via Atlas-Aligned Spatiotemporal Tokenization](https://mlsanity.com/paper/2607.09754/) (2026)
- [Nonlinear Dynamical Modeling of Human Intracranial Brain Activity with Flexible Inference](https://mlsanity.com/paper/2512.22785/) (2025)
- [Machine Learning Methods for Studying Latent Neural Activity Dynamics](https://mlsanity.com/paper/2606.10530/) (2026)

## Abstract (arXiv)

Neural populations exhibit complex recurrent structures that drive behavior, while continuously receiving and integrating external inputs from sensory stimuli, upstream regions, and neurostimulation. However, neural populations are often modeled as autonomous dynamical systems, with little consideration given to the influence of external inputs that shape the population activity and behavioral outcomes. Here, we introduce BRAID, a deep learning framework that models nonlinear neural dynamics underlying behavior while explicitly incorporating any measured external inputs. Our method disentangles intrinsic recurrent neural population dynamics from the effects of inputs by including a forecasting objective within input-driven recurrent neural networks. BRAID further prioritizes the learning of intrinsic dynamics that are related to a behavior of interest by using a multi-stage optimization scheme. We validate BRAID with nonlinear simulations, showing that it can accurately learn the intrinsic dynamics shared between neural and behavioral modalities. We then apply BRAID to motor cortical activity recorded during a motor task and demonstrate that our method more accurately fits the neural-behavioral data by incorporating measured sensory stimuli into the model and improves the forecasting of neural-behavioral data compared with various baseline methods, whether input-driven or not.