# Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable

arXiv: https://arxiv.org/abs/2610.06897 · HTML: https://mlsanity.com/paper/2610.06897/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 30 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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 Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [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)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [What do Neural Machine Translation Models Learn about Morphology?](https://mlsanity.com/paper/1704.03471/) (2017)
- [Probing the Probing Paradigm: Does Probing Accuracy Entail Task Relevance?](https://mlsanity.com/paper/2005.00719/) (2020)
- [SAEs Are Good for Steering -- If You Select the Right Features](https://mlsanity.com/paper/2505.20063/) (2025)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [The Information Geometry of Softmax: Probing and Steering](https://mlsanity.com/paper/2602.15293/) (2026)
- [HyperDAS: Towards Automating Mechanistic Interpretability with Hypernetworks](https://mlsanity.com/paper/2503.10894/) (2025)
- [Decomposing Representation Space into Interpretable Subspaces with Unsupervised Learning](https://mlsanity.com/paper/2508.01916/) (2025)
- [Hypothesis-Driven Feature Manifold Analysis in LLMs via Supervised Multi-Dimensional Scaling](https://mlsanity.com/paper/2510.01025/) (2025)
- [FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers](https://mlsanity.com/paper/2605.17231/) (2026)
- [Perfect Detection, Failed Control: The Geometry of Knowing vs. Steering in Language Models](https://mlsanity.com/paper/2606.24952/) (2026)
- [Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effects](https://mlsanity.com/paper/2607.24645/) (2026)

## Abstract (arXiv)

Localizing latent structures in the activation space of language models (LMs) is central to understanding and controlling their behavior. Yet, localized structures can differ substantially in their causal influence, raising the question of what makes a structure actionable. We tackle this question by casting causal influence as a product of three factors and showing empirically that they act as interpretable, distinct constraints: capacity, measuring the sensitivity of the model's output to movement along the structure, responsiveness, capturing how promotable the concept is given the current context, and alignment, reflecting how well the structure aligns with the context-specific representation of the concept. Across 4 LM families and 50 concepts, we observe that causal effectiveness requires all factors to be high; low capacity and responsiveness reduce it by 84% and 95%, respectively, while low alignment can reverse it, suppressing concept expression. Moreover, we find that causality is context-dependent rather than an intrinsic property of the structure, with causally effective directions forming a low-dimensional subspace that varies across contexts. By restricting the training of linear probes to this subspace, we introduce causal probes that achieve 17%-118% improvement in steering across models, with only 3% reduction in concept detection.