Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representations

TL;DR

This paper challenges the Linear Representation Hypothesis by showing that RNNs use non-linear, magnitude-based representations for sequence storage, especially in smaller models, highlighting the complexity of neural encoding.

Contribution

The study provides a counterexample to the strong LRH, demonstrating that RNNs can learn non-linear, magnitude-based representations rather than solely linear directions.

Findings

Small RNNs encode tokens by magnitude rather than direction

Larger RNNs develop linear, direction-based representations

Interpretability should consider non-linear encoding mechanisms

Abstract

The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a counterexample to this strong LRH: when trained to repeat an input token sequence, gated recurrent neural networks (RNNs) learn to represent the token at each position with a particular order of magnitude, rather than a direction. These representations have layered features that are impossible to locate in distinct linear subspaces. To show this, we train interventions to predict and manipulate tokens by learning the scaling factor corresponding to each sequence position. These interventions indicate that the smallest RNNs find only this magnitude-based solution, while larger RNNs have linear representations. These findings strongly indicate that interpretability research should not be confined by the LRH.