# Hypothesis-Driven Feature Manifold Analysis in LLMs via Supervised Multi-Dimensional Scaling

arXiv: https://arxiv.org/abs/2510.01025 · HTML: https://mlsanity.com/paper/2510.01025/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 98 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 30 of 57)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [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)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (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)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [On the Cross-lingual Transferability of Monolingual Representations](https://mlsanity.com/paper/1910.11856/) (2019)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [The Unlocking Spell on Base LLMs: Rethinking Alignment via In-Context Learning](https://mlsanity.com/paper/2312.01552/) (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)
- [Emerging Cross-lingual Structure in Pretrained Language Models](https://mlsanity.com/paper/1911.01464/) (2019)
- [What do Neural Machine Translation Models Learn about Morphology?](https://mlsanity.com/paper/1704.03471/) (2017)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [A Dataset for Answering Time-Sensitive Questions](https://mlsanity.com/paper/2108.06314/) (2021)
- ["Going on a vacation" takes longer than "Going for a walk": A Study of Temporal Commonsense Understanding](https://mlsanity.com/paper/1909.03065/) (2019)

## Built on by (most cited first, 8 of 8)

- [All Circuits Lead to Rome: Rethinking Functional Anisotropy in Circuit and Sheaf Discovery for LLMs](https://mlsanity.com/paper/2605.12671/) (2026)
- [Relational Rank Geometry in Transformers: Detecting and Steering Hidden-State Relation Frames](https://mlsanity.com/paper/2605.29634/) (2026)
- [The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models](https://mlsanity.com/paper/2606.03645/) (2026)
- [Temporal Preference Concepts and their Functions in a Large Language Model](https://mlsanity.com/paper/2606.05194/) (2026)
- [Subliminal Clocks: Latent Time Modelling in Diffusion Language Models](https://mlsanity.com/paper/2607.01774/) (2026)
- [Some Tokens Behave like Magnets: Revealing Linguistic Organization in the Layers of Language Models](https://mlsanity.com/paper/2609.05743/) (2026)
- [MAxBench: A Multinomial Concept Recovery Benchmark](https://mlsanity.com/paper/2609.13072/) (2026)
- [Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable](https://mlsanity.com/paper/2610.06897/) (2026)

## Abstract (arXiv)

The linear representation hypothesis states that language models (LMs) encode concepts as directions in their latent space, forming organized, multidimensional manifolds. Prior work has largely focused on identifying specific geometries for individual features, limiting its ability to generalize. We introduce Supervised Multi-Dimensional Scaling (SMDS), a model-agnostic method for evaluating and comparing competing feature manifold hypotheses. We apply SMDS to temporal reasoning as a case study and find that different features instantiate distinct geometric structures, including circles, lines, and clusters. SMDS reveals several consistent characteristics of these structures: they reflect the semantic properties of the concepts they represent, remain stable across model families and sizes, actively support reasoning, and dynamically reshape in response to contextual changes. Together, our findings shed light on the functional role of feature manifolds, supporting a model of entity-based reasoning in which LMs encode and transform structured representations.