# Uncovering the Representation Geometry of Minimal Cores in Overcomplete Reasoning Traces

arXiv: https://arxiv.org/abs/2605.14358 · HTML: https://mlsanity.com/paper/2605.14358/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 34 of its 79 references that are in the map.
- First posted on arXiv 14 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 34)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Robots That Ask For Help: Uncertainty Alignment for Large Language Model Planners](https://mlsanity.com/paper/2307.01928/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Question Decomposition Improves the Faithfulness of Model-Generated Reasoning](https://mlsanity.com/paper/2307.11768/) (2023)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [Don't Overthink it. Preferring Shorter Thinking Chains for Improved LLM Reasoning](https://mlsanity.com/paper/2505.17813/) (2025)
- [Atom of Thoughts for Markov LLM Test-Time Scaling](https://mlsanity.com/paper/2502.12018/) (2025)
- [Think Twice: Enhancing LLM Reasoning by Scaling Multi-round Test-time Thinking](https://mlsanity.com/paper/2503.19855/) (2025)
- [Consistent Paths Lead to Truth: Self-Rewarding Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08745/) (2025)
- [Tracing the Representation Geometry of Language Models from Pretraining to Post-training](https://mlsanity.com/paper/2509.23024/) (2025)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Overclocking LLM Reasoning: Monitoring and Controlling Thinking Path Lengths in LLMs](https://mlsanity.com/paper/2506.07240/) (2025)
- [Reason-to-Recommend: Using Interaction-of-Thought Reasoning to Enhance LLM Recommendation](https://mlsanity.com/paper/2506.05069/) (2025)
- [A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning](https://mlsanity.com/paper/2510.15444/) (2025)
- [AURA: A Fine-Grained Benchmark and Decomposed Metric for Audio-Visual Reasoning](https://mlsanity.com/paper/2508.07470/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Survey on Foundations and Frontiers of Multimodal Agentic Frameworks: Techniques and Applications](https://mlsanity.com/paper/2608.20379/) (2026)

## Abstract (arXiv)

Language models often generate long chain-of-thought traces, but it remains unclear how much of this reasoning is necessary for preserving the final prediction. We study this through the lens of overcomplete reasoning traces: generated traces that contain more intermediate steps than are needed to support the model's answer. We define the minimal core as the smallest subset of steps that preserves either the final answer or predictive distribution, and introduce metrics for compression ratio, redundancy mass, step necessity, and necessity concentration. Across six deliberative reasoning benchmarks spanning arithmetic, competition mathematics, expert scientific reasoning, and commonsense multi-hop QA, we find substantial overcompleteness: on average, 46% of steps are removable under greedy minimal-core extraction while preserving the original answer in 86% of cases. We also find that predictive support is concentrated: the top three steps account for 65% of measured necessity mass on average. Beyond compression, minimal cores expose a cleaner geometry of reasoning: compared with full traces, they improve correct-incorrect trace separation by 11 points, reduce estimated intrinsic dimensionality by 34%, and transfer across model families with 85% off-diagonal answer retention. Theoretically, we establish existence of minimal sufficient subsets, local irreducibility guarantees for greedy elimination, and certificates of overcompleteness and sparse necessity. Together, these results suggest that full reasoning traces are often verbose and overcomplete, while minimal cores isolate the effective support underlying language-model predictions.