# Steering by Influence: Curvature Aware Data Weighting for Activation Steering

arXiv: https://arxiv.org/abs/2610.06383 · HTML: https://mlsanity.com/paper/2610.06383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Activation steering methods, one of 13 directions in Mechanistic interpretability.
- Builds on 23 of its 62 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (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)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [The rising costs of training frontier AI models](https://mlsanity.com/paper/2405.21015/) (2024)
- [Improving Activation Steering in Language Models with Mean-Centring](https://mlsanity.com/paper/2312.03813/) (2023)
- [Representation Surgery: Theory and Practice of Affine Steering](https://mlsanity.com/paper/2402.09631/) (2024)
- [On Effects of Steering Latent Representation for Large Language Model Unlearning](https://mlsanity.com/paper/2408.06223/) (2024)
- [ASDL: A Unified Interface for Gradient Preconditioning in PyTorch](https://mlsanity.com/paper/2305.04684/) (2023)
- [Delta-Influence: Unlearning Poisons via Influence Functions](https://mlsanity.com/paper/2411.13731/) (2024)
- [The Blessing and Curse of Dimensionality in Safety Alignment](https://mlsanity.com/paper/2507.20333/) (2025)
- [Concept Heterogeneity-aware Representation Steering](https://mlsanity.com/paper/2603.02237/) (2026)
- [Infusion: Shaping Model Behavior by Editing Training Data via Influence Functions](https://mlsanity.com/paper/2602.09987/) (2026)
- [Detecting Contaminated Code-Generation Prompt Batches via Influence Functions](https://mlsanity.com/paper/2608.14303/) (2026)

## Abstract (arXiv)

Inference-time steering offers cheap, fine-grained control over a language model's outputs by estimating a concept's representation in activation space and shifting activations towards it. Existing methods build these representations from activation averages over contrastive datasets. These averages incorporate unrelated concepts and noise, and are dominated by a few tokens, meaning the activation transport encodes token-level rather than thematic concepts. In this work, we steer towards examples that most express a concept thematically, rather than towards an expectation over all. We identify these examples using influence functions, which estimate how much each data point contributes to a model's representation of a concept. Unlike simple model activation similarity, they incorporate the curvature of the model's loss landscape, allowing them to capture concept-relevant relationships beyond superficial token-level similarity. We then propose influence-weighted activation transport, which uses optimal transport to steer activations of non-concept text towards those of concept text, weighting concept examples by their influence scores. We evaluate on toxicity suppression (Jigsaw), object-based concept induction (OneSec) and truthfulness induction (TruthfulQA), outperforming existing activation-transport baselines. We track capability after steering using perplexity and MMLU accuracy, finding that our method improves steering while largely preserving model quality. We further show that influence functions capture concept-relevant information that activation-based methods miss with the two approaches ranking data points significantly differently. Together, these results demonstrate the value of curvature-aware influence information for activation steering.