# Probing for Representation Manifolds in Superposition

arXiv: https://arxiv.org/abs/2605.18537 · HTML: https://mlsanity.com/paper/2605.18537/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 18 May 2026.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 22 of 22)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Emotion Concepts and their Function in a Large Language Model](https://mlsanity.com/paper/2604.07729/) (2026)
- [The Origins of Representation Manifolds in Large Language Models](https://mlsanity.com/paper/2505.18235/) (2025)
- [When Models Manipulate Manifolds: The Geometry of a Counting Task](https://mlsanity.com/paper/2601.04480/) (2026)
- [Symmetry in language statistics shapes the geometry of model representations](https://mlsanity.com/paper/2602.15029/) (2026)
- [Vintage Factor Analysis with Varimax Performs Statistical Inference](https://mlsanity.com/paper/2004.05387/) (2020)
- [Valence-Arousal Subspace in LLMs: Circular Emotion Geometry and Multi-Behavioral Control](https://mlsanity.com/paper/2604.03147/) (2026)
- [The Geometry of Representational Failures in Vision Language Models](https://mlsanity.com/paper/2602.07025/) (2026)
- [Latent Structure of Affective Representations in Large Language Models](https://mlsanity.com/paper/2604.07382/) (2026)

## Built on by (most cited first, 1 of 1)

- [Beyond the Linear Representation Hypothesis: Non-Linear Activation Steering in Text-to-Image Models](https://mlsanity.com/paper/2610.06945/) (2026)

## Abstract (arXiv)

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.