Explore deep learning techniques for analyzing dynamical systems in computational psychiatry through this 58-minute lecture by Daniel Durstewitz from Ruprecht-Karls-Universität Heidelberg. Delve into the application of dynamical systems theory in understanding neural and behavioral phenomena, focusing on the use of deep generative recurrent neural networks to infer dynamical systems from empirical data. Learn about the potential of these AI-based tools in constructing generative models of individual brains and behaviors, obtaining diagnostic markers, forecasting disease trajectories, and simulating therapeutic interventions. Examine example applications on fMRI and ecological momentary assessment data, and gain insights into topics such as attractor states, limit cycles, and the role of dynamical systems in psychiatric states. Discover how recurrent neural networks can be used to reconstruct dynamical systems, and explore statistical inference methods for both small and big data scenarios. Investigate the challenges in predicting dynamical systems and the importance of capturing multiple time scales in neuronal representations.
Deep Learning of Dynamical Systems for Mechanistic Insight and Prediction in Psychiatry
Institute for Pure & Applied Mathematics (IPAM) via YouTube
Overview
Syllabus
Intro
What is a dynamical system?
Attractor states in state space
Working memory tasks & persistent activity
Memory patterns as attractor states
Limit cycles ...
Limit cycles in motor behavior
Action/ thought sequences as "heteroclinic channels"
Altered dynamics in psychiatric states
Dynamical systems as a central layer of convergence
Recurrent Neural Network → time series
Making RNN deep in time
Piecewise-Linear (PL) RNN
Line-attractor regularization
Performance on ML benchmarks
Line-attractors and solving long-range tasks
Sequential MNIST benchmark
Generative PLRNN for dynamical systems
Reconstructing dynamical systems
Statistical inference for small data: Expectation.Maximization
Expectation-Maximization Algorithm
Statistical inference for big data: Sequential VAE & SGVB
Simple ahead prediction errors may be meaningless
Reconstructing DS benchmarks
Reconstructing DS: Lorenz system
Enforcing line attractor directions helps to capture multiple time scales
Inferring PLRNN from fMRI data
Does PLANN really capture measured dynamics?
Example 1. Unstable neuronal representations in schizophrenia
Example 2: Inference of dynamical systems from mobile data
Prediction of medical intervention effects
Take home's
Taught by
Institute for Pure & Applied Mathematics (IPAM)
