# Reasoning Models Don't Just Think Longer, They Move Differently

arXiv: https://arxiv.org/abs/2605.15454 · HTML: https://mlsanity.com/paper/2605.15454/

## Key facts

- Cited by 2 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 23 of its 29 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, 23 of 23)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Lost in Benchmarks? Rethinking Large Language Model Benchmarking with Item Response Theory](https://mlsanity.com/paper/2505.15055/) (2025)
- [SATBench: Benchmarking LLMs' Logical Reasoning via Automated Puzzle Generation from SAT Formulas](https://mlsanity.com/paper/2505.14615/) (2025)
- [Mitigating Overthinking in Large Reasoning Models via Manifold Steering](https://mlsanity.com/paper/2505.22411/) (2025)
- [Large language models implicitly learn to straighten neural sentence trajectories to construct a predictive representation of natural language](https://mlsanity.com/paper/2311.04930/) (2023)
- [The LLM Already Knows: Estimating LLM-Perceived Question Difficulty via Hidden Representations](https://mlsanity.com/paper/2509.12886/) (2025)
- [Easy2Hard-Bench: Standardized Difficulty Labels for Profiling LLM Performance and Generalization](https://mlsanity.com/paper/2409.18433/) (2024)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [The Geometry of Reasoning: Flowing Logics in Representation Space](https://mlsanity.com/paper/2510.09782/) (2025)
- [Aligned and oblique dynamics in recurrent neural networks](https://mlsanity.com/paper/2307.07654/) (2023)
- [Truth as a Trajectory: What Internal Representations Reveal About Large Language Model Reasoning](https://mlsanity.com/paper/2603.01326/) (2026)
- [Probing the Difficulty Perception Mechanism of Large Language Models](https://mlsanity.com/paper/2510.05969/) (2025)
- [LLMs Encode How Difficult Problems Are](https://mlsanity.com/paper/2510.18147/) (2025)
- [Latency-Response Theory Model: Evaluating Large Language Models via Response Accuracy and Chain-of-Thought Length](https://mlsanity.com/paper/2512.07019/) (2025)

## Built on by (most cited first, 2 of 2)

- [It's the Problem, Not the Path: Budget and Difficulty Confounds in LLM Reasoning Trajectories](https://mlsanity.com/paper/2609.03436/) (2026)
- [MetaSteer: Context-Conditioned, nonlinear Steering via Attention-Projection Adaptation](https://mlsanity.com/paper/2609.38718/) (2026)

## Abstract (arXiv)

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.