A scalable generative model for dynamical system reconstruction from neuroimaging data

TL;DR

This paper introduces a scalable generative model for reconstructing dynamical systems from neuroimaging data, specifically addressing challenges posed by filtered signals like fMRI, and demonstrates its effectiveness on short BOLD time series.

Contribution

The paper presents a novel algorithm that enables dynamical system reconstruction from filtered neuroimaging signals, overcoming limitations of previous methods and scaling well with model complexity.

Findings

Successfully reconstructs system dynamics from short BOLD signals.

Accurately captures state space geometry and long-term properties.

Scales efficiently with model size and filter length.

Abstract

Data-driven inference of the generative dynamics underlying a set of observed time series is of growing interest in machine learning and the natural sciences. In neuroscience, such methods promise to alleviate the need to handcraft models based on biophysical principles and allow to automatize the inference of inter-individual differences in brain dynamics. Recent breakthroughs in training techniques for state space models (SSMs) specifically geared toward dynamical systems (DS) reconstruction (DSR) enable to recover the underlying system including its geometrical (attractor) and long-term statistical invariants from even short time series. These techniques are based on control-theoretic ideas, like modern variants of teacher forcing (TF), to ensure stable loss gradient propagation while training. However, as it currently stands, these techniques are not directly applicable to data modalities where current observations depend on an entire history of previous states due to a signal's filtering properties, as common in neuroscience (and physiology more generally). Prominent examples are the blood oxygenation level dependent (BOLD) signal in functional magnetic resonance imaging (fMRI) or Ca$^{2+}$ imaging data. Such types of signals render the SSM's decoder model non-invertible, a requirement for previous TF-based methods. Here, exploiting the recent success of control techniques for training SSMs, we propose a novel algorithm that solves this problem and scales exceptionally well with model dimensionality and filter length. We demonstrate its efficiency in reconstructing dynamical systems, including their state space geometry and long-term temporal properties, from just short BOLD time series.