A novel Reservoir Architecture for Periodic Time Series Prediction

TL;DR

This work tackles quasi-periodic time series prediction, focusing on human-perceived rhythm to enable accurate beat anticipation. It introduces a physics-inspired reservoir whose weights derive from a 2D-FDTD discretization of wave dynamics, with two neuron types and tunable parameters $c$ and $k$, plus a dynamic selection mechanism. A synchronization-based loss and DS procedure adjust $c$ during inference and selectively modulate $k$ to align predictions with targets. On a rhythmic beat dataset, the approach achieves mean timing errors under $1\%$ of the inter-beat interval after adaptation, outperforming a random reservoir and a motor-generator baseline, highlighting its potential for real-time rhythm processing and hardware-friendly implementations.

Abstract

This paper introduces a novel approach to predicting periodic time series using reservoir computing. The model is tailored to deliver precise forecasts of rhythms, a crucial aspect for tasks such as generating musical rhythm. Leveraging reservoir computing, our proposed method is ultimately oriented towards predicting human perception of rhythm. Our network accurately predicts rhythmic signals within the human frequency perception range. The model architecture incorporates primary and intermediate neurons tasked with capturing and transmitting rhythmic information. Two parameter matrices, denoted as c and k, regulate the reservoir's overall dynamics. We propose a loss function to adapt c post-training and introduce a dynamic selection (DS) mechanism that adjusts $k$ to focus on areas with outstanding contributions. Experimental results on a diverse test set showcase accurate predictions, further improved through real-time tuning of the reservoir via c and k. Comparative assessments highlight its superior performance compared to conventional models.

Figures (6)

• Figure 1: Overview of the model structure: This figure illustrates the components $p$, and $\mathbf{o}$ of the reservoir. Fast Fourier Transform spectra of select samples for both fast and slow segments are presented to highlight the resonances.
• Figure 2: Comparing the time offset ratios pre- and post-adaptation through the assessment of mean and variance measurements.
• Figure 3: Evaluating Synchronized Time Intervals: Mean error and variance calculations are performed on the discrepancies between intervals generated by the motor generator and the target intervals, alongside predictions made by our model.
• Figure 4: An illustration showcasing the effectiveness of adapting matrix c is presented. Various constant values of $\delta_c$ are employed for the adaptation process, and the resulting mean error and variance between predictions and targets are computed to highlight the performance of the adaptation.
• Figure 5: (a) The comparative panel between predictions and targets before and after adjusting parameter $k$.