Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals.

We wish to thank all of the reviewers for their time and thorough reading of our paper! We appreciate the reviewer's suggestions regarding clarity. We have added the suggested summary sentence "the key We started with binary sentiment classification, but are actively working on more tasks. RNN hidden states onto the top two PCs for two different input sequences that differ only by two tokens (replacing ' The trajectories start out the same as the initial tokens are identical. We have added a footnote noting this in the main text.

Y et in recurrent networks, computations are implemented at the level of dynamics, and two networks performing the same computation with equivalent dynamics need not exhibit the same geometry.

In this setting, neural operators trained to minimize squared error losses, while capable of accurate short-term forecasts, often fail to reproduce statistical or structural properties of the dynamics over longer time horizons and can yield degenerate results.

However,givenlimited data, classical GANs have struggled, and strategies like output-regularization, data-augmentation, use of pre-trained models and pruning have been shown to lead to improvements. Notably, the applicability of these strategies is 1) often constrained to particular settings, e.g., availability of a pretrained GAN; or 2) increases training time, e.g., when using pruning.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations.

Note that a metric space is calledcompact if X is closed and bounded.