Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914577169514496 |
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| author | Massoli, Fabio Valerio Kuzmin, Andrey Behboodi, Arash |
| author_facet | Massoli, Fabio Valerio Kuzmin, Andrey Behboodi, Arash |
| contents | \ac{CoT} prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing ``Budget Forcing'' methods reduce cost via fine-tuning with heuristic length penalties, suppressing both essential reasoning and redundant filler. We recast efficient reasoning as a lossy compression problem under the \ac{IB} principle, and identify a key theoretical gap when applying naive \ac{IB} to transformers: attention violates the Markov property between prompt, reasoning trace, and response. To resolve this issue, we model \ac{CoT} generation under the \ac{CIB} principle, where the reasoning trace $Z$ acts as a computational bridge that contains only the information about the response $Y$ that is not directly accessible from the prompt $X$. This yields a general Reinforcement Learning objective: maximize task reward while compressing completions under a prior over reasoning traces, subsuming common heuristics (e.g., length penalties) as special cases (e.g., uniform priors). In contrast to naive token-counting approaches, we introduce a semantic prior that measures token cost by surprisal under a language model. Crucially, the prior is queried only for token-level log-probabilities, adding negligible overhead to the training loop. Empirically, our \ac{CIB} objective prunes reasoning redundancy while preserving fluency and logic, improving accuracy at moderate compression and enabling aggressive compression with minimal accuracy drop. These gains generalize across model families and task domains, confirming \ac{CIB} as a domain-agnostic CoT compression framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck Massoli, Fabio Valerio Kuzmin, Andrey Behboodi, Arash Machine Learning I.2 \ac{CoT} prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing ``Budget Forcing'' methods reduce cost via fine-tuning with heuristic length penalties, suppressing both essential reasoning and redundant filler. We recast efficient reasoning as a lossy compression problem under the \ac{IB} principle, and identify a key theoretical gap when applying naive \ac{IB} to transformers: attention violates the Markov property between prompt, reasoning trace, and response. To resolve this issue, we model \ac{CoT} generation under the \ac{CIB} principle, where the reasoning trace $Z$ acts as a computational bridge that contains only the information about the response $Y$ that is not directly accessible from the prompt $X$. This yields a general Reinforcement Learning objective: maximize task reward while compressing completions under a prior over reasoning traces, subsuming common heuristics (e.g., length penalties) as special cases (e.g., uniform priors). In contrast to naive token-counting approaches, we introduce a semantic prior that measures token cost by surprisal under a language model. Crucially, the prior is queried only for token-level log-probabilities, adding negligible overhead to the training loop. Empirically, our \ac{CIB} objective prunes reasoning redundancy while preserving fluency and logic, improving accuracy at moderate compression and enabling aggressive compression with minimal accuracy drop. These gains generalize across model families and task domains, confirming \ac{CIB} as a domain-agnostic CoT compression framework. |
| title | Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck |
| topic | Machine Learning I.2 |
| url | https://arxiv.org/abs/2603.08462 |