# Interpretable Nonlinear Dynamic Modeling of Neural Trajectories

arXiv: https://arxiv.org/abs/1608.06546 · HTML: https://mlsanity.com/paper/1608.06546/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2016.

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

- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [Building population models for large-scale neural recordings: opportunities and pitfalls](https://mlsanity.com/paper/2102.01807/) (2021)
- [Mesoscopic modeling of hidden spiking neurons](https://mlsanity.com/paper/2205.13493/) (2022)
- [Bubblewrap: Online tiling and real-time flow prediction on neural manifolds](https://mlsanity.com/paper/2108.13941/) (2021)
- [Langevin Flows for Modeling Neural Latent Dynamics](https://mlsanity.com/paper/2507.11531/) (2025)
- [Integrative neurocybernetic modeling in the era of large-scale neuroscience](https://mlsanity.com/paper/2604.23903/) (2026)

## Abstract (arXiv)

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable long-term future predictions in a variety of dynamical models and in real neural data.