# Hierarchical Temporal Representation in Linear Reservoir Computing

## TL;DR

This paper demonstrates how linear reservoir computing models exhibit hierarchical temporal representations, analyzed through frequency analysis, with potential applications in complex oscillatory tasks and insights into deep learning's temporal dynamics.

## Contribution

It provides evidence of hierarchical temporal encoding in deep RNNs using linear units and frequency analysis, advancing understanding of temporal processing in neural networks.

## Key findings

- Hierarchical temporal representations are observable in linear RC models.
- Frequency analysis reveals layered temporal features.
- Models perform well on Multiple Superimposed Oscillator tasks.

## Abstract

Recently, studies on deep Reservoir Computing (RC) highlighted the role of layering in deep recurrent neural networks (RNNs). In this paper, the use of linear recurrent units allows us to bring more evidence on the intrinsic hierarchical temporal representation in deep RNNs through frequency analysis applied to the state signals. The potentiality of our approach is assessed on the class of Multiple Superimposed Oscillator tasks. Furthermore, our investigation provides useful insights to open a discussion on the main aspects that characterize the deep learning framework in the temporal domain.