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

2024/08/20 by Róbert Csordás, Csordás, Róbert, Christopher Potts +5 · 7 citations
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Handwritten Text Recognition Techniques #Image Processing and 3D Reconstruction #Machine Learning (cs.LG) #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE)

paper · pdf · doi:10.48550/arxiv.2408.10920

openalex publication_date 2024/08/20 · openalex created_date 2024/10/01 · openalex updated_date 2026/07/28

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.

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