Transformation of ReLU-based recurrent neural networks from discrete-time to continuous-time

Authors: Zahra Monfared, Daniel Durstewitz

ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Here we show how to perform such a translation from discrete to continuous time for a particular class of Re LU-based RNN. We prove three theorems on the mathematical equivalence between the discrete and continuous time formulations under a variety of conditions, and illustrate how to use our mathematical results on different machine learning and nonlinear dynamical systems examples. ... We will exemplify these results on a couple of machine learning and DS models, including an ODE solution to the well-known addition problem (Hochreiter & Schmidhuber, 1997), limit cycle and chaotic dynamics, and on a PLRNN inferred from empirical time series (human functional magnetic resonance imaging [f MRI] data; (Koppe et al., 2019)).
Researcher Affiliation Academia 1Department of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany 2Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany.
Pseudocode No The paper does not contain any pseudocode or algorithm blocks.
Open Source Code Yes Matlab code for all these examples is available at github.com/Durstewitz Lab/cont PLRNN.
Open Datasets Yes Example 1. Consider a discrete-time PLRNN emulation of the nonlinear van-der-Pol oscillator, derived by training a discrete PLRNN with M = 10 units on time series generated by the van-der-Pol equations (taken from (Koppe et al., 2019), provided online at github.com/Durstewitz Lab). ... Example 4. As a final example we applied the continuous-time transform developed here to a PLRNN inferred from empirical time series, namely human f MRI data. ... Details on the experimental procedure and task and on PLRNN training can be found in (Koppe et al., 2019).
Dataset Splits No The paper does not provide explicit training/validation/test dataset splits.
Hardware Specification No No specific hardware used for experiments is mentioned.
Software Dependencies No The paper mentions "Matlab code" but does not specify version numbers or other software dependencies with versions.
Experiment Setup Yes Example 1. Consider a discrete-time PLRNN emulation of the nonlinear van-der-Pol oscillator, derived by training a discrete PLRNN with M = 10 units... Example 2. A simple discrete-time 2-unit PLRNN which (approximately) solves this task is the one with parameters A = [0.99 0; 0 0.99], W = [0 0; 0 0.01], h = [0; 0]... Inputs were accommodated by adding a term Cst to eq. (6), with C = [0 0; 1 1]. ... Example 3. As an example for a system with chaotic dynamics we chose a PLRNN emulation (M = 10)... Example 4. A discrete PLRNN with M = 10 latent states was used for this purpose...