Abstract
Reservoir computers (RCs) are biology-inspired computational frameworks for signal processing that are typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying the factors that determine the effective approximation of Boolean functions applied in a sliding-window fashion over a binary signal, both non-recursively and recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate three-bit, five-bit, and three-bit recursive binary functions, respectively. We analyze how BN RC parameters and function average sensitivity, which is a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible, and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity.
Highlights
Many biological systems are regarded as non-linear dynamical systems [1] operating in high-dimensional spaces
We found that the flexibility of a particular Boolean networks (BN) Reservoir computers (RCs) instantiation is a function of the topology and size of the reservoir, as encoded by the parameter set (N, L, K)
As noted in research concerning BN RCs, the optimal parameter set includes tuning the dynamics toward criticality, which leads to more flexible systems
Summary
Many biological systems are regarded as non-linear dynamical systems [1] operating in high-dimensional spaces. Genes, and macromolecules interact in a variety of ways to create the dynamics of cells [2]. Collections of cells interact and coordinate activity, forming cohesive units such as bacterial colonies, simple multicellular organisms, or tissues in more complex multicellular organisms. At each level of organization, ‘input’ signals (e.g., odors or hormones) are introduced into the system, processed by means of the system’s dynamics, and responded to sometimes generating new ‘output’ signals as a by-product [3]. Biological systems must process external signals in real time to inform a wide variety of response decisions. The fruit fly olfactory system projects an input to a high-dimensional space before classifying an odor [4]
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