# Do LLMs Encode Functional Importance of Reasoning Tokens?

arXiv: https://arxiv.org/abs/2601.03066 · HTML: https://mlsanity.com/paper/2601.03066/

## Key facts

- Cited by 5 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 12 of its 45 references that are in the map.
- First posted on arXiv 6 Jan 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, 12 of 12)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [Don't Overthink it. Preferring Shorter Thinking Chains for Improved LLM Reasoning](https://mlsanity.com/paper/2505.17813/) (2025)
- [Stepwise Perplexity-Guided Refinement for Efficient Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2502.13260/) (2025)
- [Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models](https://mlsanity.com/paper/2310.14491/) (2023)
- [Analyzing Chain-of-Thought Prompting in Large Language Models via Gradient-based Feature Attributions](https://mlsanity.com/paper/2307.13339/) (2023)
- [Pruning the Unsurprising: Efficient LLM Reasoning via First-Token Surprisal](https://mlsanity.com/paper/2508.05988/) (2025)
- [Learning to Attribute with Attention](https://mlsanity.com/paper/2504.13752/) (2025)
- [Breadcrumbs Reasoning: Memory-Efficient Reasoning with Compression Beacons](https://mlsanity.com/paper/2510.13797/) (2025)

## Built on by (most cited first, 5 of 5)

- [When Does Value-Aware KV Eviction Help? A Fixed-Contract Diagnostic for Non-Monotone Cache Compression](https://mlsanity.com/paper/2605.08234/) (2026)
- [On-Policy Supervised Fine-Tuning for Efficient Reasoning](https://mlsanity.com/paper/2602.13407/) (2026)
- [Less is More: Early Stopping Rollout for On-Policy Distillation](https://mlsanity.com/paper/2605.27028/) (2026)
- [How Far Ahead Do LLMs Plan? Uncovering the Latent Horizon in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.02103/) (2026)
- [Every Token Leaves a Ripple in the Stream of Thought: Eliciting Model-Internal Token Saliency for Chain-of-Thought Compression](https://mlsanity.com/paper/2608.31066/) (2026)

## Abstract (arXiv)

Large language models solve complex tasks by generating long reasoning chains, achieving higher accuracy at the cost of increased computational cost and reduced ability to isolate functionally relevant reasoning. Prior work on compact reasoning shortens such chains through probabilistic sampling, heuristics, or supervision from frontier models, but offers limited insight into whether models internally encode token-level functional importance for answer generation. We address this gap diagnostically and propose greedy pruning, a likelihood-preserving deletion procedure that iteratively removes reasoning tokens whose removal minimally degrades model likelihood under a specified objective, yielding length-controlled reasoning chains. We evaluate pruned reasoning in a distillation framework and show that students trained on pruned chains outperform a frontier-model-supervised compression baseline at matched reasoning lengths. Finally, our analysis reveals systematic pruning patterns and shows that attention scores can predict greedy pruning ranks, further suggesting that models encode a nontrivial functional importance structure over reasoning tokens.