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

Dynamical systems theory provides a promising framework for understanding neural activity. LFADS approximates neural recordings using a recurrent neural network (RNN) generator, but analyzing its dynamics has been challenging. We propose a simple modification to LFADS, adding a per-trial inferred bias, that dramatically improves interpretability by replacing complex multi-stable dynamics with simpler contextual dynamics. Both models were applied to neural activity recorded from macaque motor cortex during reaching movements. While the kinematic decoding was similar, they implemented contrasti

…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

…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

…From the perspective of dynamical systems theory, such critical transitions occur upon inconspicuous perturbations in highly interconnected systems presenting positive feedback loops and can be modeled as mathematical bifurcations between alternative regimes. Here, we sought to characterize dynamical signatures of impending seizures. We systematically verified the predictions of the model called ‘Epileptor’ that captures seizure dynamics in five differe

Anesthesia is ubiquitous in hospitals, yet a mechanistic understanding of how anesthetic drugs induce unconsciousness is lacking. A prominent hypothesis suggests that dynamic stability is critical to cortical function: awake brains are poised at a state that is sufficiently excitable for activity generation and propagation, yet controllable and stable. Measuring dynamic stability during the transition from consciousness to anesthetic unconsciousness could identify the neural mechanisms disrupted by anesthesia, and thus provide insight into the neural basis of consciousness. Related work sugges