Probing for Representation Manifolds in Superposition

2026-05-18

AI Summary

This work addresses how to uncover interpretable concept manifolds embedded within the stacked representations of language models. The authors propose Manifold Probe, a method that generalizes traditional linear probing to manifold probing by integrating supervised manifold learning with linear predictability analysis. This approach identifies continuous geometric structures in representation space corresponding to high-level concepts—such as time or space—and determines their encoding directions. Beyond merely detecting the presence of such concepts, the method enables causal intervention: manipulating activations along discovered manifold directions directly alters model behavior. Experiments on Llama 2-7B demonstrate that perturbing representations along the extracted temporal manifold significantly shifts the model’s generated outputs regarding the release years of cultural works, thereby validating both the interpretability and causal efficacy of the recovered manifolds.

Abstract

This paper introduces the Manifold Probe, a supervised method for discovering representation manifolds in superposition. The method generalizes linear regression probes by learning the space of features of a concept that can be linearly predicted from the representations, and then learning the directions used to encode them. We demonstrate the probe on representations of time and space in Llama 2-7b, finding manifolds which linearly represent an interpretable set of features in each case. In the case of time, we show that by steering along the manifold, we can influence the model's completions about the years in which famous songs, movies and books were released, providing evidence that the Manifold Probe can discover manifolds which are causally involved in model behaviour.

Problem

• representation manifolds
• superposition
• probing
• interpretability
• language models

Innovation

• Manifold Probe
• representation manifold
• linear probing
• causal intervention
• interpretable features