# How noise affects memory in linear recurrent networks

arXiv: https://arxiv.org/abs/2409.03187 · HTML: https://mlsanity.com/paper/2409.03187/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 56 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [A Unifying Framework for Information Processing in Stochastically Driven Dynamical Systems](https://mlsanity.com/paper/1906.04608/) (2019)
- [Memory and forecasting capacities of nonlinear recurrent networks](https://mlsanity.com/paper/2004.11234/) (2020)
- [Optimal short-term memory before the edge of chaos in driven random recurrent networks](https://mlsanity.com/paper/1912.11213/) (2019)
- [Memory of recurrent networks: Do we compute it right?](https://mlsanity.com/paper/2305.01457/) (2023)

## Built on by (most cited first, 2 of 2)

- [Memory Determines Learning Direction: A Theory of Gradient-Based Optimization in State Space Models](https://mlsanity.com/paper/2510.00563/) (2025)
- [Finite-Horizon Fisher Memory in Two-Sided Power-Bounded Recurrent Systems](https://mlsanity.com/paper/2609.39800/) (2026)

## Abstract (arXiv)

The effects of noise on memory in a linear recurrent network are theoretically investigated. Memory is characterized by its ability to store previous inputs in its instantaneous state of network, which receives a correlated or uncorrelated noise. Two major properties are revealed: First, the memory reduced by noise is uniquely determined by the noise's power spectral density (PSD). Second, the memory will not decrease regardless of noise intensity if the PSD is in a certain class of distribution (including power law). The results are verified using the human brain signals, showing good agreement.