Topic: dynamical systems theory

For decades dynamical systems theory played a pivotal role in theoretical and computational neuroscience, as it links biophysical and biochemical processes to neural computation. In fact, dynamical systems are computationally universal. Rather than hand-crafting computational theories of neural function based on dynamical systems, recent developments in scientific machine learning (ML) and AI suggest that we may be able to infer such dynamical-computational models directly from neurophysiological and behavioral observations. This is called dynamical systems reconstruction (DSR), the learning o

A long-standing premise in theoretical neuroscience holds that the complex interactions between neurons or, at a different systems level, between networks in the nervous system can be expressed in terms of an underlying system of nonlinear dynamics. A classical approach has been dynamical systems theory, whereby biophysical processes in the brain can be naturally formalized in terms of differential equations (ODEs) that may be capable of offering an explicit and interpretable account of how different biochemical and physiological processes in the brain evolve to produce the complex repertoire

Perception of external stimuli slowly drifts between phases of increased and decreased sensitivity in sustained attention tasks. This phenomenon may represent a deliberate cognitive strategy to balance evidence accumulation against evidence gathering according to the predictive coding hypothesis, or it might simply indicate computational bottlenecks. Here, we claim that dynamical systems theory and large-scale network modeling may offer crucial insights to adjudicate this debate. We attempt to harmonize brain dynamics with dual processing modes by suggesting a link with another aspect of neuro

Spiking Neural Networks (SNNs) promise energy efficiency and offer a more brain-like alternative to artificial neural networks. A major challenge to unleashing their potential, however, is to make them trainable on challenging tasks that require credit assignment across long time horizons. Gradient-based learning, which has driven much of the recent success in ANNs, is hampered in spiking networks by their discrete spiking interactions, which make the error landscape non-differentiable. A recent approach to this challenge is to replace the spike interaction with a surrogate gradient in the bac