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New analytic formulas for memory and prediction functions in reservoir computers with time delays
Peyton Mullarkey1, Sarah Marzen1
1Department of Natural Sciences, Pitzer and Scripps College, Claremont, California 91711, USA.
None:
Time delays increase the effective dimensionality of reservoirs, thus suggesting that time delays in reservoirs can enhance their performance, particularly their memory and prediction abilities. We find new closed-form expressions for memory and prediction functions of linear time-delayed reservoirs in terms of the power spectrum of the input and the reservoir transfer function. We confirm this relationship numerically for some time-delayed reservoirs using simulations, including when the reservoir can be linearized but is actually nonlinear. Finally, we use these closed-form formulas to address the utility of multiple time delays in linear reservoirs in order to perform memory and prediction, finding similar results to previous work on nonlinear reservoirs. We hope that these closed-form formulas can be used to understand memory and predictive capabilities in time-delayed reservoirs.
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