# Reasoning emerges from constrained inference manifolds in large language models

arXiv: https://arxiv.org/abs/2605.08142 · HTML: https://mlsanity.com/paper/2605.08142/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 2 May 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (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)
- [Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey](https://mlsanity.com/paper/2404.01869/) (2024)
- [On the Hardness of Faithful Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2406.10625/) (2024)
- [Densing Law of LLMs](https://mlsanity.com/paper/2412.04315/) (2024)
- [Mechanistic understanding and validation of large AI models with SemanticLens](https://mlsanity.com/paper/2501.05398/) (2025)
- [Toward Generalizable Evaluation in the LLM Era: A Survey Beyond Benchmarks](https://mlsanity.com/paper/2504.18838/) (2025)
- [Predicting and Enhancing the Fairness of DNNs with the Curvature of Perceptual Manifolds](https://mlsanity.com/paper/2303.12307/) (2023)
- [Geometry of Decision Making in Language Models](https://mlsanity.com/paper/2511.20315/) (2025)
- [Inversion dynamics of class manifolds in deep learning reveals tradeoffs underlying generalisation](https://mlsanity.com/paper/2303.05161/) (2023)
- [Unveiling and Mitigating Generalized Biases of DNNs through the Intrinsic Dimensions of Perceptual Manifolds](https://mlsanity.com/paper/2404.13859/) (2024)
- [Sampling-enabled scalable manifold learning unveils the discriminative cluster structure of high-dimensional data](https://mlsanity.com/paper/2401.01100/) (2024)

## Built on by (most cited first, 6 of 6)

- [FutureNav: Unified World-Action Modeling for Vision-and-Language Navigation](https://mlsanity.com/paper/2606.30367/) (2026)
- [GeoFaith: A Spatio-Temporal Dual View of Faithful Chain-of-Thought](https://mlsanity.com/paper/2605.26893/) (2026)
- [Hybrid NARX-LLM for Greenland Iceberg Discharge: Prompt-Driven Residual Correction](https://mlsanity.com/paper/2606.15288/) (2026)
- [From Brewing to Resolution: Tracing the Internal Lifecycle of Code Reasoning in LLMs](https://mlsanity.com/paper/2606.17648/) (2026)
- [Can We Trust the Teacher? Decoupled Credit Direction-Magnitude for Self-Distillation](https://mlsanity.com/paper/2609.34848/) (2026)
- [Geometric Similarity in VLM Low-Level Vision Representations](https://mlsanity.com/paper/2610.00848/) (2026)

## Abstract (arXiv)

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the evolution of internal representations during inference. We find that inference-time dynamics consistently self-organize into low-dimensional manifolds embedded within high-dimensional representation spaces. we find that such geometric compression, although pervasive, is not sufficient for stable or reliable reasoning. Instead, effective reasoning dynamics emerge within a constrained structural regime characterized by three conditions: adequate representational expressivity, spontaneous manifold compression, and preservation of non-degenerate information volume within the compressed subspace. Models outside this regime exhibit characteristic pathological inference dynamics. Based on these insights, we introduce a unified, label-free diagnostic computed solely from internal dynamics. These findings suggest that reasoning in LLMs is fundamentally governed by geometric and informational constraints, offering a complementary framework to benchmark-centric assessment.