# Predicting Performance using Approximate State Space Model for Liquid State Machines

arXiv: https://arxiv.org/abs/1901.06240 · HTML: https://mlsanity.com/paper/1901.06240/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [Temporal and Spatial Reservoir Ensembling Techniques for Liquid State Machines](https://mlsanity.com/paper/2411.11414/) (2024)

## Abstract (arXiv)

Liquid State Machine (LSM) is a brain-inspired architecture used for solving problems like speech recognition and time series prediction. LSM comprises of a randomly connected recurrent network of spiking neurons. This network propagates the non-linear neuronal and synaptic dynamics. Maass et al. have argued that the non-linear dynamics of LSMs is essential for its performance as a universal computer. Lyapunov exponent (mu), used to characterize the "non-linearity" of the network, correlates well with LSM performance. We propose a complementary approach of approximating the LSM dynamics with a linear state space representation. The spike rates from this model are well correlated to the spike rates from LSM. Such equivalence allows the extraction of a "memory" metric (tau_M) from the state transition matrix. tau_M displays high correlation with performance. Further, high tau_M system require lesser epochs to achieve a given accuracy. Being computationally cheap (1800x time efficient compared to LSM), the tau_M metric enables exploration of the vast parameter design space. We observe that the performance correlation of the tau_M surpasses the Lyapunov exponent (mu), (2-4x improvement) in the high-performance regime over multiple datasets. In fact, while mu increases monotonically with network activity, the performance reaches a maxima at a specific activity described in literature as the "edge of chaos". On the other hand, tau_M remains correlated with LSM performance even as mu increases monotonically. Hence, tau_M captures the useful memory of network activity that enables LSM performance. It also enables rapid design space exploration and fine-tuning of LSM parameters for high performance.