Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction

Authors: Manuel Brenner, Christoph Jürgen Hemmer, Zahra Monfared, Daniel Durstewitz

NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental 5 Experimental Results To assess the quality of DSR, we employed established performance criteria based on long-term, invariant topological, geometrical, and temporal features of DS [51, 11, 39]. ... We then tested AL-RNNs on two commonly employed benchmark DS for which minimal PWL representations are known, the famous Lorenz-63 model of atmospheric convection [61] and the chaotic Rössler system [85]. We finally explored the suitability of our approach on two real-world examples, human electrocardiogram (ECG) and human functional magnetic resonance imaging (f MRI) data.
Researcher Affiliation Academia Manuel Brenner1,2 , Christoph Jürgen Hemmer1,3 , Zahra Monfared2, Daniel Durstewitz1,2,3 1Dept. of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty, Heidelberg University, Germany 2Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany 3Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
Pseudocode No The paper does not contain pseudocode or clearly labeled algorithm blocks.
Open Source Code Yes All code created is available at https://github.com/Durstewitz Lab/ALRNN-DSR.
Open Datasets Yes The electrocardiogram (ECG) time series was taken from the PPGDa Li A dataset [82]. The functional magnetic resonance imaging (f MRI) data from human subjects performing three cognitive tasks is publicly available on Git Hub [52].
Dataset Splits No The paper mentions training sequence lengths and test set lengths, but does not specify explicit train/validation/test dataset splits with percentages or sample counts, nor does it refer to standard predefined splits for the datasets used.
Hardware Specification No Each individual training run of the AL-RNN was performed on a single CPU. Depending on the training sequence length, a single epoch took between 0.5 to 3 seconds.
Software Dependencies No The system was solved numerically with integration time step t = 0.01 using scipy.integrate with the default RK45 solver. The electrocardiogram (ECG) time series was taken from the PPGDa Li A dataset [82]. ... We standardized the time series and applied temporal delay embedding using the Dynamical Systems.jl Julia library, resulting in an embedding dimension of m = 5.
Experiment Setup Yes We used rectified adaptive moment estimation (RADAM) [59] as the optimizer, with L = 50 batches with S = 16 sequences per epoch. Further, we chose M = {20, 20, 100, 100, 100, 130}, τ = {16, 8, 10, 7, 20, 10}, T = {200, 300, 50, 72, 50, 100}, initial learning rates ηstart = {10^-3, 5*10^-3, 2*10^-3, 5*10^-3, 10^-3, 10^-3}, ηend = 10^-5 and epochs = {2000, 3000, 4000, 2000, 3000, 2000} for the {Lorenz-63, Rössler, ECG, f MRI,Lorenz96,EEG} dataset, respectively. Parameters in W were initialized using a Gaussian initialization with σ = 0.01, h as a vector of zeros, and A as the diagonal of a normalized positive-definite random matrix [11, 97]. ... Additionally, for the Rössler and Lorenz systems, we added 5% observation noise during training.