Optimal Kronecker-Sum Approximation of Real Time Recurrent Learning

TL;DR

This paper introduces the Optimal Kronecker-Sum Approximation (OK), a new method for approximating Real Time Recurrent Learning (RTRL) that achieves optimality and reduces noise, enabling better long-term dependency learning in RNNs.

Contribution

The paper proposes the OK algorithm, proving its optimality for RTRL approximations and demonstrating its effectiveness in real-world and synthetic tasks.

Findings

OK matches TBPTT in character-level Penn TreeBank task.

OK outperforms TBPTT in a synthetic string memorization task.

OK has empirically negligible noise compared to previous methods.

Abstract

One of the central goals of Recurrent Neural Networks (RNNs) is to learn long-term dependencies in sequential data. Nevertheless, the most popular training method, Truncated Backpropagation through Time (TBPTT), categorically forbids learning dependencies beyond the truncation horizon. In contrast, the online training algorithm Real Time Recurrent Learning (RTRL) provides untruncated gradients, with the disadvantage of impractically large computational costs. Recently published approaches reduce these costs by providing noisy approximations of RTRL. We present a new approximation algorithm of RTRL, Optimal Kronecker-Sum Approximation (OK). We prove that OK is optimal for a class of approximations of RTRL, which includes all approaches published so far. Additionally, we show that OK has empirically negligible noise: Unlike previous algorithms it matches TBPTT in a real world task (character-level Penn TreeBank) and can exploit online parameter updates to outperform TBPTT in a synthetic string memorization task. Code availiable on github.