# Isotropy Cliffs: The Geometric Signature of Decision-Making in Large Language Models

arXiv: https://arxiv.org/abs/2608.00828 · HTML: https://mlsanity.com/paper/2608.00828/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 1 Aug 2026.

## Builds on (most cited first, 30 of 32)

- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [PromptRobust: Towards Evaluating the Robustness of Large Language Models on Adversarial Prompts](https://mlsanity.com/paper/2306.04528/) (2023)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [Leveraging Large Language Models for Multiple Choice Question Answering](https://mlsanity.com/paper/2210.12353/) (2022)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)
- [ProSA: Assessing and Understanding the Prompt Sensitivity of LLMs](https://mlsanity.com/paper/2410.12405/) (2024)
- [HEAD-QA: A Healthcare Dataset for Complex Reasoning](https://mlsanity.com/paper/1906.04701/) (2019)
- [How Alignment and Jailbreak Work: Explain LLM Safety through Intermediate Hidden States](https://mlsanity.com/paper/2406.05644/) (2024)
- [Emergence of a High-Dimensional Abstraction Phase in Language Transformers](https://mlsanity.com/paper/2405.15471/) (2024)
- [IsoScore: Measuring the Uniformity of Embedding Space Utilization](https://mlsanity.com/paper/2108.07344/) (2021)
- [Exploring the Sensitivity of LLMs' Decision-Making Capabilities: Insights from Prompt Variation and Hyperparameters](https://mlsanity.com/paper/2312.17476/) (2023)
- [Beyond Probabilities: Unveiling the Misalignment in Evaluating Large Language Models](https://mlsanity.com/paper/2402.13887/) (2024)
- [The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models](https://mlsanity.com/paper/2501.10573/) (2025)
- [On Isotropy, Contextualization and Learning Dynamics of Contrastive-based Sentence Representation Learning](https://mlsanity.com/paper/2212.09170/) (2022)
- [Outlier Dimensions Encode Task-Specific Knowledge](https://mlsanity.com/paper/2310.17715/) (2023)
- [Low Anisotropy Sense Retrofitting (LASeR) : Towards Isotropic and Sense Enriched Representations](https://mlsanity.com/paper/2104.10833/) (2021)
- [Redundancy, Isotropy, and Intrinsic Dimensionality of Prompt-based Text Embeddings](https://mlsanity.com/paper/2506.01435/) (2025)
- [Geometry of Decision Making in Language Models](https://mlsanity.com/paper/2511.20315/) (2025)

## Abstract (arXiv)

We investigate the geometry of decision-making in Multiple Choice Question Answering (MCQA) through the lens of isotropy. Analyzing five open-weight models across diverse datasets, we identify decision-critical transition layers characterized by a shift in isotropy, coinciding with a major representational change and the emergence of task-relevant clusters. We demonstrate that this synchronized geometric behavior is strongly correlated with downstream accuracy (r≈0.84), displaying its relevance for successful decision-making. Furthermore, we show that this transition is robust to prompt variations, suggesting that it reflects a general mechanism of model behavior.