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Intro
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What is a dynamical system?
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Attractor states in state space
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Working memory tasks & persistent activity
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Memory patterns as attractor states
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Limit cycles ...
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Limit cycles in motor behavior
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Action/ thought sequences as "heteroclinic channels"
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Altered dynamics in psychiatric states
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Dynamical systems as a central layer of convergence
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Recurrent Neural Network → time series
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Making RNN deep in time
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Piecewise-Linear (PL) RNN
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Line-attractor regularization
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Performance on ML benchmarks
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Line-attractors and solving long-range tasks
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Sequential MNIST benchmark
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Generative PLRNN for dynamical systems
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Reconstructing dynamical systems
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Statistical inference for small data: Expectation.Maximization
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Expectation-Maximization Algorithm
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Statistical inference for big data: Sequential VAE & SGVB
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Simple ahead prediction errors may be meaningless
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Reconstructing DS benchmarks
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Reconstructing DS: Lorenz system
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Enforcing line attractor directions helps to capture multiple time scales
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Inferring PLRNN from fMRI data
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Does PLANN really capture measured dynamics?
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Example 1. Unstable neuronal representations in schizophrenia
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Example 2: Inference of dynamical systems from mobile data
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Prediction of medical intervention effects
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Take home's
Description:
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. Read more

Deep Learning of Dynamical Systems for Mechanistic Insight and Prediction in Psychiatry

Institute for Pure & Applied Mathematics (IPAM)
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