# FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers

arXiv: https://arxiv.org/abs/2605.17231 · HTML: https://mlsanity.com/paper/2605.17231/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Activation steering methods, one of 13 directions in Mechanistic interpretability.
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 17 May 2026.

## Placed in

- Mechanistic interpretability / [Activation steering methods](https://mlsanity.com/mechinterp/activation-steering-methods/)

## Builds on (most cited first, 19 of 19)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [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)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [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)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Angular Steering: Behavior Control via Rotation in Activation Space](https://mlsanity.com/paper/2510.26243/) (2025)
- [Representation Surgery: Theory and Practice of Affine Steering](https://mlsanity.com/paper/2402.09631/) (2024)
- [Understanding (Un)Reliability of Steering Vectors in Language Models](https://mlsanity.com/paper/2505.22637/) (2025)
- [Extending Activation Steering to Broad Skills and Multiple Behaviours](https://mlsanity.com/paper/2403.05767/) (2024)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)
- [The Information Geometry of Softmax: Probing and Steering](https://mlsanity.com/paper/2602.15293/) (2026)
- [Curveball Steering: The Right Direction To Steer Isn't Always Linear](https://mlsanity.com/paper/2603.09313/) (2026)

## Built on by (most cited first, 6 of 6)

- [When Do Concepts Become Functionally Sufficient During Language-Model Training?](https://mlsanity.com/paper/2608.15323/) (2026)
- [Activation Flow: Manufacturing Activations for Steering](https://mlsanity.com/paper/2609.32530/) (2026)
- [Fisher-IRG: Fisher-Induced Local Invariant Representation Geometry across Language and Vision Models](https://mlsanity.com/paper/2609.36458/) (2026)
- [Language Model Activations Inhabit Privileged Error-Correcting Basins](https://mlsanity.com/paper/2610.04183/) (2026)
- [JLD: Perceptual Distance Through A Jacobian Lens](https://mlsanity.com/paper/2610.05967/) (2026)
- [Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable](https://mlsanity.com/paper/2610.06897/) (2026)

## Abstract (arXiv)

Activation steering has emerged as a lightweight approach for modifying language model behavior without parameter updates, yet existing methods remain brittle: unstable across layers and prone to disturbing behavior unrelated to the target concept. We trace these failures to a hidden assumption shared by widely-used methods such as CAA, ActAdd, and ITI: that the intermediate activation space is Euclidean. We show this assumption is fundamentally flawed. The metric that actually governs how a hidden-state perturbation changes the output is the Fisher information metric of the softmax layer, pulled back to the intermediate layer through the Jacobian of the intervening layers. From it we derive a closed-form steering direction, applied to a hidden state at an intermediate layer, that reaches a target concept change with the least non-target distortion. The framework is sharpest in the early and middle intermediate layers, where the metric is strongly non-Euclidean and geometric correction matters most. We evaluate it on three verb-morphology concepts: third-person-singular, progressive, and past-tense inflection, following standard counterfactual-concept evaluation. On GPT-2 Small, this non-Euclidean geometry is borne out empirically, and our method lowers off-target KL divergence by median factors of 1.4--6.5x against individual steering baselines. On Llama-3-8B and Qwen3-8B, it lowers off-target KL by median factors of 1.8--3.6x against individual baselines at the early and middle layers. These results show that geometric correction retains its advantage on larger models with more complex internal structure.