# Optimal short-term memory before the edge of chaos in driven random recurrent networks

arXiv: https://arxiv.org/abs/1912.11213 · HTML: https://mlsanity.com/paper/1912.11213/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [Edge of chaos as a guiding principle for modern neural network training](https://mlsanity.com/paper/2107.09437/) (2021)
- [Learning Temporal Quantum Tomography](https://mlsanity.com/paper/2103.13973/) (2021)
- [Designing Chaotic Attractors: A Semi-supervised Approach](https://mlsanity.com/paper/2407.09545/) (2024)
- [How noise affects memory in linear recurrent networks](https://mlsanity.com/paper/2409.03187/) (2024)
- [Attractor-merging Crises and Intermittency in Reservoir Computing](https://mlsanity.com/paper/2504.12695/) (2025)
- [Neuronal correlations shape the scaling behavior of memory capacity and nonlinear computational capability of reservoir recurrent neural networks](https://mlsanity.com/paper/2504.19657/) (2025)

## Abstract (arXiv)

The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to derive an approximate expression for the conditional probability density of the state of a neuron given a past input signal. From this conditional probability density, we can analytically calculate short-term memory measures, such as memory capacity, mutual information, and Fisher information, and determine the relationships among these measures, which have not been clarified to date to the best of our knowledge. We show that the network contribution of these short-term memory measures peaks before the edge of chaos, where the dynamics of input-driven networks is stable but corresponding systems without input signals are unstable.