Activation Bottleneck: Sigmoidal Neural Networks Cannot Forecast a Straight Line

TL;DR

This paper demonstrates that neural networks with activation bottlenecks, especially sigmoidal ones like LSTM and GRU, cannot accurately forecast unbounded sequences such as straight lines or random walks, due to their bounded hidden layer representations.

Contribution

The paper characterizes activation bottlenecks in neural networks and explains their impact on forecasting unbounded sequences, providing insights into architectural limitations.

Findings

Sigmoidal networks cannot forecast unbounded sequences.

Activation bottlenecks cause prediction errors to grow arbitrarily large.

Modifications to architectures can mitigate bottleneck effects.

Abstract

A neural network has an activation bottleneck if one of its hidden layers has a bounded image. We show that networks with an activation bottleneck cannot forecast unbounded sequences such as straight lines, random walks, or any sequence with a trend: The difference between prediction and ground truth becomes arbitrary large, regardless of the training procedure. Widely-used neural network architectures such as LSTM and GRU suffer from this limitation. In our analysis, we characterize activation bottlenecks and explain why they prevent sigmoidal networks from learning unbounded sequences. We experimentally validate our findings and discuss modifications to network architectures which mitigate the effects of activation bottlenecks.