Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Slow Transition to Low-Dimensional Chaos in Heavy-Tailed Recurrent Neural Networks
Authors: Eva Xie, Stefan Mihalas, Łukasz Kuśmierz
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We theoretically predict the gain at which the finite system transitions from quiescent to chaotic dynamics, and validate it through simulations. [...] Our simulations of autonomous RNNs (Fig. 2; similar results for noisy stimulus-driven RNNs shown in Fig. 5) reveal that although networks with α <= 1 exhibit a transition to chaos as predicted, the sharpness and location of the transition vary substantially with α [...]. To probe the structure of the dynamical landscape near the transition to chaos, we examine the full Lyapunov spectrum of the networks. [...] Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 all show simulation results, plots, and error bars. |
| Researcher Affiliation | Collaboration | Eva Yi Xie1,2 Stefan Mihalas1 Łukasz Ku smierz1 1 Allen Institute, Seattle, WA, USA 2 Princeton Neuroscience Institute, Princeton University, NJ, USA |
| Pseudocode | Yes | C Algorithm to compute Lyapunov exponents for RNNs [...] Algorithm 1: Lyapunov Exponents Calculation 1 Initialize h, Q; 2 for t = 1 to T do 3 h <- f(h, xt); 4 if t > warmup then 5 J <- Jacobian_fn(h, xt); 6 Q_prev <- Q; 7 Q, R <- qr(Q); 8 gamma_i += log(R_ii); 9 lambda_i = gamma_i/(T - warmup) |
| Open Source Code | Yes | *The codebase is publicly available at https://github.com/Allen Institute/Heavy RNN_public. |
| Open Datasets | No | This paper focuses on theoretical modeling and simulations of recurrent neural networks. The data for analysis is generated through these simulations, not sourced from external datasets. The NeurIPS Paper Checklist also explicitly states: "no dataset is involved." |
| Dataset Splits | No | The paper does not use any external datasets, therefore, there are no dataset splits to describe. The data used for analysis is generated internally through simulations. |
| Hardware Specification | No | All experiments reported in this paper can be reproduced using CPUs only; no GPUs are required. The only exception is Fig. 1, for which we strongly recommend using a single GPU to avoid potential compatibility issues with the JAX package. Jobs were executed on a compute cluster using a maximum of 4 CPU cores and 20 GB of memory per task (which is a very conservative allocation; for networks of size N = 1000, for example, 5 GB is likely sufficient). |
| Software Dependencies | Yes | M.2 Licenses for existing assets This project makes use of several open-source Python packages. While the main paper does not formally cite each package, we acknowledge their use here and ensure full transparency by providing all code and dependencies in the released repository. Below we list each core package, its version, license, and citation if applicable: jax, jaxlib v0.4.38; numpy v1.26.4; scipy v1.15.2; torch v2.7.0; tensorflow, keras v2.19.0, v3.9.2; matplotlib v3.10.1; tqdm v4.67.1. Python versions >=3.10 and <3.13 are recommended. All software dependencies are installable via pip using the provided requirements.txt. |
| Experiment Setup | Yes | We study recurrent neural networks that evolve in discrete time according to the update rule xi(t + 1) = ϕ( Pj=1 Wijxj(t) + Ii(t)) where ϕ = tanh is the activation function, Ii(t) is the external input to neuron i at time t, and N is the number of neurons. The synaptic weights Wij are independently drawn from a symmetric Lévy α-stable distribution [...] with scale parameter σ = g/N^1/α, where the gain g acts as the control parameter in our analysis. [...] In the latter case (see Appendix E), inputs at each time step are sampled i.i.d. from a Gaussian distribution with zero mean and variance 0.01. [...] To avoid transient effects, we include a short warmup period during which the network state evolves but Lyapunov exponents are not accumulated. The MLE is then averaged over multiple random input sequences to obtain a robust estimate. [...] We let the networks evolve for T = 3000 steps, among which the Lyapunov exponents are accumulated over the last K = 100 steps. |