Fast Parameter Optimization of Delayed Feedback Reservoir with Backpropagation and Gradient Descent

TL;DR

This work tackles the slow offline hyperparameter tuning of delayed feedback reservoirs (DFRs) by introducing a backpropagation-based optimization framework built on a modular DFR. By decomposing the nonlinear element into blocks and learning the two scalars $A$ and $B$ alongside the output regularization, the approach enables fast, online adaptation with gradient descent and a truncated backpropagation strategy to curb memory usage. The authors demonstrate that their method achieves comparable or superior accuracy to grid search while reducing computation time by up to about 700x and cutting memory by roughly half in many cases. The practical impact is enabling scalable, hardware-friendly reservoir learning with online capabilities for time-series classification tasks.

Abstract

A delayed feedback reservoir (DFR) is a reservoir computing system well-suited for hardware implementations. However, achieving high accuracy in DFRs depends heavily on selecting appropriate hyperparameters. Conventionally, due to the presence of a non-linear circuit block in the DFR, the grid search has only been the preferred method, which is computationally intensive and time-consuming and thus performed offline. This paper presents a fast and accurate parameter optimization method for DFRs. To this end, we leverage the well-known backpropagation and gradient descent framework with the state-of-the-art DFR model for the first time to facilitate parameter optimization. We further propose a truncated backpropagation strategy applicable to the recursive dot-product reservoir representation to achieve the highest accuracy with reduced memory usage. With the proposed lightweight implementation, the computation time has been significantly reduced by up to 1/700 of the grid search.

Figures (6)

• Figure 1: Conceptual diagram of DFR. The reservoir consists of a nonlinear element (NL) and a feedback loop with a total delay $\tau$. The feedback loop comprises $N_x$ virtual nodes with a time interval $\theta$.
• Figure 2: Block diagram of reservoir processing in the modular DFR model. The block labeled "$f$" operates as a one-input, one-output function $f$ in Eq. (\ref{['eq:MG']}). Only two parameters, $A$ and $B$, have to be optimized.
• Figure 3: Computation graph of forward and backward propagation in the output layer.
• Figure 4: Computation graph of forward and backward propagation in the DPRR layer.
• Figure 5: Computation graph of forward and backward propagation in the reservoir layer.