# Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics

arXiv: https://arxiv.org/abs/2408.16862 · HTML: https://mlsanity.com/paper/2408.16862/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 13 of 13)

- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [Smooth Loss Functions for Deep Top-k Classification](https://mlsanity.com/paper/1802.07595/) (2018)
- [Loss Functions for Top-k Error: Analysis and Insights](https://mlsanity.com/paper/1512.00486/) (2015)
- [Recurrent switching linear dynamical systems](https://mlsanity.com/paper/1610.08466/) (2016)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [The Dynamics of Functional Brain Networks: Integrated Network States during Cognitive Function](https://mlsanity.com/paper/1511.02976/) (2015)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [Dynamic Filtering of Time-Varying Sparse Signals via l1 Minimization](https://mlsanity.com/paper/1507.06145/) (2015)
- [Unifying and generalizing models of neural dynamics during decision-making](https://mlsanity.com/paper/2001.04571/) (2020)
- [Switching Autoregressive Low-rank Tensor Models](https://mlsanity.com/paper/2306.03291/) (2023)
- [Sparse Bayesian Learning with Dynamic Filtering for Inference of Time-Varying Sparse Signals](https://mlsanity.com/paper/1902.05362/) (2019)
- [Bayesian Dynamic Fused LASSO](https://mlsanity.com/paper/1905.12275/) (2019)
- [Bayesian Fused Lasso Modeling via Horseshoe Prior](https://mlsanity.com/paper/2201.08053/) (2022)

## Built on by (most cited first, 6 of 6)

- [Self-Supervised Dynamical System Representations for Physiological Time-Series](https://mlsanity.com/paper/2512.00239/) (2025)
- [Multi-Integration of Labels across Categories for Component Identification (MILCCI)](https://mlsanity.com/paper/2602.04270/) (2026)
- [MANGO: Learning Disentangled Image Transformation Manifolds with Grouped Operators](https://mlsanity.com/paper/2409.09542/) (2024)
- [Interpretable time series analysis with Gumbel dynamics](https://mlsanity.com/paper/2509.21578/) (2025)
- [Learning Mixtures of Linear Dynamical Systems via Hybrid Tensor-EM Method](https://mlsanity.com/paper/2510.06091/) (2025)
- [Behavior-dLDS: A decomposed linear dynamical systems model for neural activity partially constrained by behavior](https://mlsanity.com/paper/2603.05612/) (2026)

## Abstract (arXiv)

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve according to simple locally linear dynamics. However, existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity due to noise-sensitive inference procedures and limited model formulations. This can lead to inconsistent results on signals with similar dynamics, limiting the model's ability to provide scientific insight. In this work, we address these limitations and propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise. Additionally, we introduce an extended latent dynamics model to improve robustness against system nonlinearities. We evaluate our approach on several synthetic dynamical systems, including an empirically-derived brain-computer interface experiment, and demonstrate more accurate latent variable inference in nonlinear systems with diverse noise conditions. Furthermore, we apply our method to a real-world clinical neurophysiology dataset, illustrating the ability to identify interpretable and coherent structure where previous models cannot.