Minimal Reservoir Computing

Kurzfassung

Minimal reservoir computing is a novel machine learning technique for predicting complex systems. It simplifies the classical reservoir computing approach by eliminating the need for randomness. Instead of a random embedding, it embeds its input into a high-dimensional space structurally. Additionally, the reservoir is no longer a random graph, but a block-diagonal matrix. The reservoir states are simply evolved linearly, and the nonlinearity is pushed to the readout layer. The output is then a linear combination of the reservoir states, determined by a simple linear regression. In this work we simplify the initial approach even further by utilizing a diagonal matrix as a reservoir, effectively dropping the notion of it. In classical reservoir computing the reservoir states bear no obvious interpretation, as they are a representation of the reservoir at the time. However, in this setup the reservoir states are interpretable and represent nonlinear combinations of input space. Using a small number of data points, it is possible to fully capture the dynamics of the attractor in the short- and long-term using this simple setup. In this work we show that the weights of the linear regression can be utilized to derive recursive equations of complex systems. We analyze the stability of the discovered equations with regards to various hyperparameters. In the end we test its applicability on financial markets and study the modelling of interest rates using this model