When Learning Hurts: Fixed-Pole RNN for Real-Time Online Training

TL;DR

This paper demonstrates that fixing recurrent poles in RNNs leads to more stable, efficient, and effective online learning in data-constrained scenarios, compared to learning the poles.

Contribution

The work provides both analytical and empirical evidence that fixing recurrent poles in RNNs improves stability and reduces training complexity in real-time online learning.

Findings

Fixed-pole RNNs outperform learned-pole RNNs in data-limited settings.

Learning poles increases non-convexity and training difficulty.

Fixed-pole architectures yield better performance with less training data.

Abstract

Recurrent neural networks (RNNs) can be interpreted as discrete-time state-space models, where the state evolution corresponds to an infinite-impulse-response (IIR) filtering operation governed by both feedforward weights and recurrent poles. While, in principle, all parameters including pole locations can be optimized via backpropagation through time (BPTT), such joint learning incurs substantial computational overhead and is often impractical for applications with limited training data. Echo state networks (ESNs) mitigate this limitation by fixing the recurrent dynamics and training only a linear readout, enabling efficient and stable online adaptation. In this work, we analytically and empirically examine why learning recurrent poles does not provide tangible benefits in data-constrained, real-time learning scenarios. Our analysis shows that pole learning renders the weight optimization problem highly non-convex, requiring significantly more training samples and iterations for gradient-based methods to converge to meaningful solutions. Empirically, we observe that for complex-valued data, gradient descent frequently exhibits prolonged plateaus, and advanced optimizers offer limited improvement. In contrast, fixed-pole architectures induce stable and well-conditioned state representations even with limited training data. Numerical results demonstrate that fixed-pole networks achieve superior performance with lower training complexity, making them more suitable for online real-time tasks.