# Suppression of chaos in a partially driven recurrent neural network

arXiv: https://arxiv.org/abs/2306.00900 · HTML: https://mlsanity.com/paper/2306.00900/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2023.

## Built on by (most cited first, 3 of 3)

- [Universal Scaling Laws of Absorbing Phase Transitions in Artificial Deep Neural Networks](https://mlsanity.com/paper/2307.02284/) (2023)
- [Oscillations enhance time-series prediction in reservoir computing with feedback](https://mlsanity.com/paper/2406.02867/) (2024)
- [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 dynamics of recurrent neural networks (RNNs), and particularly their response to inputs, play a critical role in information processing. In many applications of RNNs, only a specific subset of the neurons generally receive inputs. However, it remains to be theoretically clarified how the restriction of the input to a specific subset of neurons affects the network dynamics. Considering RNNs with such restricted input, we investigate how the proportion, p, of the neurons receiving inputs (the "inputs neurons") and the strength of the input signals affect the dynamics by analytically deriving the conditional maximum Lyapunov exponent. Our results show that for sufficiently large p, the maximum Lyapunov exponent decreases monotonically as a function of the input strength, indicating the suppression of chaos, but if p is smaller than a critical threshold, pc, even significantly amplified inputs cannot suppress spontaneous chaotic dynamics. Furthermore, although the value of pc is seemingly dependent on several model parameters, such as the sparseness and strength of recurrent connections, it is proved to be intrinsically determined solely by the strength of chaos in spontaneous activity of the RNN. This is to say, despite changes in these model parameters, it is possible to represent the value of pc as a common invariant function by appropriately scaling these parameters to yield the same strength of spontaneous chaos. Our study suggests that if p is above pc, we can bring the neural network to the edge of chaos, thereby maximizing its information processing capacity, by amplifying inputs.