# The Information Geometry of Softmax: Probing and Steering

arXiv: https://arxiv.org/abs/2602.15293 · HTML: https://mlsanity.com/paper/2602.15293/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 66 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 30 of 56)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (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)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [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)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)

## Built on by (most cited first, 11 of 11)

- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)
- [FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers](https://mlsanity.com/paper/2605.17231/) (2026)
- [Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds](https://mlsanity.com/paper/2606.25234/) (2026)
- [How Controllable Are Large Language Models? A Unified Evaluation across Behavioral Granularities](https://mlsanity.com/paper/2603.02578/) (2026)
- [Stream separation improves Bregman conditioning in transformers](https://mlsanity.com/paper/2603.21317/) (2026)
- [MAxBench: A Multinomial Concept Recovery Benchmark](https://mlsanity.com/paper/2609.13072/) (2026)
- [The Answer-Basin Representation Hypothesis: We Are Not Probing or Steering Concepts](https://mlsanity.com/paper/2609.24821/) (2026)
- [The Linear Representation Hypothesis for Vision-Language-Action Models](https://mlsanity.com/paper/2609.30996/) (2026)
- [Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable](https://mlsanity.com/paper/2610.06897/) (2026)
- [Anchor Divergence for Semantic Geometry in Contrastive Learning](https://mlsanity.com/paper/2610.06919/) (2026)

## Abstract (arXiv)

This paper concerns the question of how AI systems encode semantic structure into the geometric structure of their representation spaces. The motivating observation is that the natural geometry of these representation spaces should reflect the way models use representations to produce behavior. We focus on the important special case of representations that define softmax distributions. In this case, we argue that the natural geometry is information geometry. Our focus is on the role of information geometry on semantic encoding and the linear representation hypothesis. As an illustrative application, we develop "dual steering", a method for robustly steering representations to exhibit a particular concept using linear probes. We prove that dual steering optimally modifies the target concept while minimizing changes to off-target concepts. Empirically, we find that dual steering enhances the controllability and stability of concept manipulation.