Predicting Performance using Approximate State Space Model for Liquid State Machines
This work provides a computationally efficient method for exploring the design space of LSMs, which are used in tasks like speech recognition and time series prediction, though it is incremental as it builds on existing metrics like the Lyapunov exponent.
The paper tackles the problem of predicting Liquid State Machine (LSM) performance by proposing a linear state space model approximation, which extracts a memory metric (tau_M) that correlates better with performance than the Lyapunov exponent (mu), achieving a 2-4x improvement in correlation in high-performance regimes and being 1800x more time-efficient.
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.