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arxiv: 2601.03066 · v3 · submitted 2026-01-06 · 💻 cs.CL · cs.AI· cs.LG

Do LLMs Encode Functional Importance of Reasoning Tokens?

Janvijay Singh , Dilek Hakkani-T\"ur This is my paper

Pith reviewed 2026-05-16 17:00 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG
keywords LLMsreasoning chainstoken pruningattention scoresfunctional importancegreedy pruningknowledge distillationchain-of-thought
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The pith

LLMs encode a functional importance structure over tokens in their reasoning chains.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Large language models produce long reasoning chains to reach answers, yet many tokens can be removed with little effect on the model's own likelihood of outputting the correct final answer. The paper introduces greedy pruning, which iteratively deletes the token whose removal causes the smallest drop in that likelihood, producing shorter yet still effective chains. When these pruned chains are used to train smaller student models, the students outperform those trained on chains compressed by a stronger frontier model at the same length. Analysis of the pruned tokens reveals consistent patterns across examples, and the model's attention scores alone can predict the order in which tokens would be pruned.

Core claim

Greedy pruning reveals that models encode a nontrivial functional importance structure over reasoning tokens: attention scores predict the ranks at which tokens can be removed while preserving model likelihood, and chains shortened this way support more effective distillation than frontier-supervised compression at matched lengths.

What carries the argument

Greedy pruning: an iterative procedure that repeatedly removes the reasoning token whose deletion produces the smallest degradation in model likelihood under a chosen objective.

If this is right

  • Distilled student models trained on greedy-pruned chains outperform frontier-model-supervised compression at matched reasoning lengths.
  • Attention scores can be used as a fast proxy to rank token importance without running the full iterative pruning search.
  • Pruning follows systematic patterns that suggest models treat certain reasoning steps as more critical than others.
  • Length-controlled chains obtained this way reduce computation while retaining the ability to reach correct answers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Direct use of attention scores for pruning could replace the slower greedy search during inference.
  • The same importance structure might appear in non-text modalities or in tasks other than step-by-step reasoning.
  • Models that encode token importance explicitly could be edited or compressed by targeting only the high-importance tokens.

Load-bearing premise

Tokens whose removal minimally degrades model likelihood are functionally unimportant for producing the correct final answer rather than merely unimportant for the model's internal probability estimate.

What would settle it

A direct test on held-out problems where chains pruned by the greedy procedure yield lower final-answer accuracy than chains pruned by random selection or by attention scores at identical lengths.

Figures

Figures reproduced from arXiv: 2601.03066 by Dilek Hakkani-T\"ur, Janvijay Singh.

Figure 1
Figure 1. Figure 1: Greedy pruning as a diagnostic probe. A. A teacher model generates a full reasoning chain for a given question. B. A greedy pruning step scores candidate token deletions by post-deletion likelihood L del and removes the token whose deletion best preserves likelihood. C. Iterating this procedure over decreasing keep fractions ρ yields length-controlled chains and induces a pruning order π, where earlier-ran… view at source ↗
Figure 2
Figure 2. Figure 2: Distillation under reasoning token pruning. Accuracy of a Llama2-7B student trained on pruned reasoning at varying keep fractions, teacher, pruner, and dataset; dashed lines indicate zero-shot performance. Greedy pruning achieves the strongest performance at matched lengths, indicating preservation of important tokens. ing tokens using a learned notion of semantic im￾portance, with supervision from GPT-4 (… view at source ↗
Figure 3
Figure 3. Figure 3: Functional structure under greedy pruning. Each curve shows the fraction of tokens retained per category at a given keep fraction. Panels vary teacher, pruner, and pruning objective; the dashed line indicates uniform pruning. (a) Pruning preferentially preserves symbolic computation while removing referential, descriptive, and linguistic scaffolding. (b) Excluding reasoning likelihood in pruning objective … view at source ↗
Figure 5
Figure 5. Figure 5: Dynamics of pruning ranks. Hit@|S| align￾ment between tokens removed at keep fraction ρcurr and L del-based local ranks at the previous pruning stage. Dynamic rankings (ρprev = ρcurr + 0.1) consistently outperform frozen (ρprev=1.0) and random baselines across keep fractions, indicating that greedy pruning re-evaluates token importance as context contracts. ken importance as the retained context contracts,… view at source ↗
Figure 6
Figure 6. Figure 6: Distillation under reasoning token pruning. Accuracy of a Mistral-7B student trained on pruned reasoning at varying keep fractions, teacher, pruner, and dataset; dashed lines indicate zero-shot performance. Greedy pruning achieves the strongest performance at matched lengths, indicating preservation of important tokens. category. Furthermore, when a token could fit multiple categories, we resolve ties usin… view at source ↗
Figure 7
Figure 7. Figure 7: Functional structure under different pruning criteria. Each curve shows the fraction of tokens retained within a functional category at a given keep fraction; the dashed line denotes uniform pruning. (a) Greedy pruning with Llama3.1-8B preserves a clear functional ordering, strongly retaining symbolic computation while pruning referential, descriptive, and grammatical scaffolding. (b) TokenSkip exhibits we… view at source ↗
Figure 8
Figure 8. Figure 8: Token Category Distribution. Token-level functional category distribution over 1,000 randomly sampled GSM8K reasoning traces generated by (a) Qwen2.5-7B and (b) Llama3.1-8B. Percentages are computed over all reasoning tokens prior to pruning and provide additional context for our functional structure analysis. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that LLMs internally encode a nontrivial functional importance structure over reasoning tokens. It introduces greedy pruning, a likelihood-preserving iterative deletion procedure that removes tokens causing the smallest drop in model likelihood of the generated sequence, yielding length-controlled chains. In a distillation framework, students trained on these pruned chains outperform a frontier-model-supervised compression baseline at matched lengths. Analysis further shows systematic pruning patterns and that attention scores can predict greedy pruning ranks.

Significance. If the central results hold after addressing the noted gaps, the work offers a diagnostic tool for probing internal reasoning structure in LLMs and a practical, parameter-free compression method that improves downstream distillation. The independent attention-prediction finding strengthens the claim of encoded importance and could inform both interpretability and efficient inference techniques.

major comments (2)
  1. [§3] §3 (greedy pruning definition): functional importance is operationalized exclusively as minimal degradation in the model's likelihood of the generated sequence. This does not enforce that retained tokens are those required to reach the correct final answer, as the model may assign high likelihood to incorrect reasoning paths; the distillation results provide only indirect downstream evidence and do not directly test answer correctness preservation in the source model.
  2. [Evaluation] Evaluation section: the abstract and results report positive distillation outcomes but supply no implementation details, statistical tests, error bars, or controls for confounds (e.g., length matching rigor, baseline equivalence). This leaves the claim that pruned chains are functionally superior only weakly supported at the current level of description.
minor comments (1)
  1. [Abstract] Abstract: clarify the distinction between likelihood preservation and answer correctness earlier to avoid conflation with the weakest assumption.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive feedback. We address the major comments point by point below. We agree that additional experiments and details will strengthen the manuscript and will incorporate revisions accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (greedy pruning definition): functional importance is operationalized exclusively as minimal degradation in the model's likelihood of the generated sequence. This does not enforce that retained tokens are those required to reach the correct final answer, as the model may assign high likelihood to incorrect reasoning paths; the distillation results provide only indirect downstream evidence and do not directly test answer correctness preservation in the source model.

    Authors: We acknowledge that our operationalization of functional importance centers on likelihood preservation of the model's own generated sequence rather than explicit preservation of answer correctness. This choice is deliberate: the paper's focus is diagnostic—probing the internal structure the model assigns to its reasoning tokens—rather than extracting veridical or correct reasoning. Because the sequence includes both the reasoning chain and the final answer, preserving likelihood under the model's distribution maintains the path the model itself would follow. Nevertheless, the referee correctly notes that we provide only indirect evidence via distillation and do not directly measure whether the source model produces the same answer when conditioned on pruned chains. We will add a new experiment in the revised manuscript that evaluates answer accuracy preservation in the source model for pruned versus original chains across the evaluated tasks. revision: yes

  2. Referee: [Evaluation] Evaluation section: the abstract and results report positive distillation outcomes but supply no implementation details, statistical tests, error bars, or controls for confounds (e.g., length matching rigor, baseline equivalence). This leaves the claim that pruned chains are functionally superior only weakly supported at the current level of description.

    Authors: We agree that the current Evaluation section is insufficiently detailed for reproducibility and statistical confidence. In the revision we will expand this section to include: (i) full implementation details of the distillation procedure (hyperparameters, training steps, student architectures), (ii) the precise length-matching protocol and verification that baselines are matched at the token level, (iii) statistical tests (e.g., paired t-tests or Wilcoxon signed-rank tests with reported p-values), (iv) error bars (standard deviation across random seeds or multiple runs), and (v) additional controls confirming baseline equivalence. These additions will make the superiority claim more robustly supported. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines greedy pruning directly as iterative deletion of tokens that minimize degradation to the model's own likelihood under a specified objective, then reports downstream distillation gains and a post-hoc correlation with attention scores. This definition is not fitted to the final claim about functional importance for correct answers, nor does any prediction reduce by construction to the inputs; the attention-rank result is an independent observation. No load-bearing self-citations, uniqueness theorems, or ansatzes appear in the provided text, and the central results remain empirically grounded rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract, the work relies on standard LLM components (likelihood, attention) with no new free parameters, axioms, or invented entities introduced.

pith-pipeline@v0.9.0 · 5441 in / 1019 out tokens · 62224 ms · 2026-05-16T17:00:36.373583+00:00 · methodology

discussion (0)

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Forward citations

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Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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    work page internal anchor Pith review Pith/arXiv arXiv 2023

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    InProceedings of the 2023 Conference on Empirical Methods in Natu- ral Language Processing, pages 6342–6353, Singa- pore

    Compressing context to enhance inference ef- ficiency of large language models. InProceedings of the 2023 Conference on Empirical Methods in Natu- ral Language Processing, pages 6342–6353, Singa- pore. Association for Computational Linguistics. Tengxiao Liu, Qipeng Guo, Xiangkun Hu, Cheng Ji- ayang, Yue Zhang, Xipeng Qiu, and Zheng Zhang

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    O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning.arXiv preprint arXiv:2501.12570, 2025

    Can language models learn to skip steps? In Proceedings of the 38th International Conference on Neural Information Processing Systems, NIPS ’24, Red Hook, NY , USA. Curran Associates Inc. Haotian Luo, Li Shen, Haiying He, Yibo Wang, Shi- wei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. 2025. O1-pruner: Length- harmonizing fine-tuning for o1-l...

    work page arXiv 2025

  4. [4]

    SYMBOLIC_MATH - Explicit numeric or symbolic computation - Includes: digits, currency symbols, arithmetic operators, equations, fractions, numeric constants

    work page

  5. [5]

    to find",

    META_DISCOURSE - Tokens that organize, narrate, or scaffold the reasoning process - Includes instructional or planning language rather than mathematical content - Examples: "to find", "we need to", "step", "first", "now", "so", "let's", "calculate", "find", "the final answer is", step numbers, list markers - Arithmetic verbs (e.g., "add", "subtract") are ...

    work page

  6. [6]

    COREFERENCE - Pronouns or references pointing to previously mentioned entities or quantities - Includes: she, her, he, it, they, we, him, this - "this" is COREFERENCE ONLY when referential, not when used as a grammatical filler

    work page

  7. [7]

    Natalia",

    ENTITY_NAME - Proper names or concrete entities central to the problem - Includes: people's names, objects, units, or concrete nouns being counted - Examples: "Natalia", "Julie", "wallet", "book", "pages", "year"

    work page

  8. [8]

    half", "twice

    VERBAL_MATH - Natural-language descriptions of arithmetic relationships or quantities - Includes: "half", "twice", "total", "remaining", "more", "per", "rate" - Arithmetic verbs (e.g., "add", "multiply", "divide") belong here ONLY when describing the operation itself, not when narrating steps

    work page

  9. [9]

    GRAMMATICAL - Grammatical glue with little standalone semantic content - Includes: articles, prepositions, conjunctions, auxiliary verbs, punctuation, formatting tokens, whitespace -------------------------------------------------- IMPORTANT NOTES --------------------------------------------------

    work page

  10. [10]

    Adjectives are NOT a separate category. Assign adjectives based on function: - Arithmetic-modifying adjectives -> VERBAL_MATH - Discourse or narrative adjectives -> META_DISCOURSE - Entity-identifying adjectives -> ENTITY_NAME - Otherwise -> FUNCTION

    work page

  11. [11]

    pages",

    ENTITY_NAME vs VERBAL_MATH: When a noun denotes a concrete object being counted (e.g., "pages", "wallet"), label it ENTITY_NAME. Mathematical relations involving those nouns are captured by VERBAL_MATH or SYMBOLIC_MATH. -------------------------------------------------- PRIORITY RULES (STRICT) -------------------------------------------------- If a token ...

    work page

  12. [12]

    If part of an explicit numeric or symbolic expression -> SYMBOLIC_MATH

    work page

  13. [13]

    Else if it narrates or structures reasoning -> META_DISCOURSE

    work page

  14. [14]

    Else if it is referential -> COREFERENCE

    work page

  15. [15]

    Else if it names a concrete entity -> ENTITY_NAME

    work page

  16. [16]

    Else if it describes arithmetic verbally -> VERBAL_MATH

    work page

  17. [17]

    token_position

    Else -> GRAMMATICAL -------------------------------------------------- CONSISTENCY CONSTRAINT -------------------------------------------------- If the same surface word appears multiple times with the same functional role, assign it the SAME category across occurrences unless its role clearly changes. 19 Prompt: Functional Role Annotation (continued) ---...

    work page