# MAxBench: A Multinomial Concept Recovery Benchmark

arXiv: https://arxiv.org/abs/2609.13072 · HTML: https://mlsanity.com/paper/2609.13072/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 57 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 30 of 43)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [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)
- [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)
- [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)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [SAEs Are Good for Steering -- If You Select the Right Features](https://mlsanity.com/paper/2505.20063/) (2025)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [The Origins of Representation Manifolds in Large Language Models](https://mlsanity.com/paper/2505.18235/) (2025)
- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representations](https://mlsanity.com/paper/2408.10920/) (2024)
- [When Models Manipulate Manifolds: The Geometry of a Counting Task](https://mlsanity.com/paper/2601.04480/) (2026)
- [Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry](https://mlsanity.com/paper/2510.08638/) (2025)
- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Interpretability in Parameter Space: Minimizing Mechanistic Description Length with Attribution-based Parameter Decomposition](https://mlsanity.com/paper/2501.14926/) (2025)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)

## Abstract (arXiv)

Fine-grained control of language model behaviors (e.g., steering) is among the more actionable outcomes of interpretability research. For binary concepts such as refusal, a single direction in activation space often suffices for steering. However, many concepts are not binary: Animals and Countries contain many subcategories, each with multiple instances. For these concepts, the search space over possible representation geometries is far larger than for binary concepts; it is thus not clear what geometries are most appropriate, nor what methods are most effective at recovering them. In this work, we introduce MAxBench, a geometry-agnostic evaluation framework for multinomial concept representations based on sampling from the recovered concept representation. We use MAxBench to compare 10 localization methods (covering 5 geometry types) across 6 concepts and 4 models. Using this framework, we find that (i) affine subspaces steer more reliably and have greater recall than rank-one or linear subspaces; (ii) much of this advantage is due to better non-zero offsets rather than the choice of bases; (iii) manifold steering is competitive with the best methods when applicable; and (iv) no method consistently outperforms prompting, in alignment with prior findings on binary concepts. These findings underscore the importance of expanding the scope of interpretability research and meta-evaluation to concepts with more varied structure.