How Well do LLMs Compress Their Own Chain-of-Thought?
Free while signed in. Answers cite the passages they came from.
This new paper investigates how LLMs balance chain-of-thought (CoT) reasoning length against accuracy. It introduces token complexity, a minimal token threshold needed for correct problem-solving, and shows that even seemingly different CoT "compression prompts" (like "use bullet points" or "remove grammar") fall on the same universal accuracy-length trade-off curve. Key highlights include:
Universal accuracy-length trade-off - Despite prompting LLMs in diverse ways to shorten reasoning (e.g. "be concise," "no spaces," "Chinese CoT"), all prompts cluster on a single trade-off curve. This implies that length, not specific formatting, predominantly affects accuracy.
Token complexity as a threshold - For each question, there's a sharp cutoff in tokens required to yield the correct answer. If the LLM's CoT is shorter than this "token complexity," it fails. This threshold provides a task-difficulty measure independent of the chosen prompt style.
Information-theoretic upper bound - By treating CoT compression as a "lossy coding" problem, the authors derive theoretical limits on how short a correct reasoning chain can be. Current prompting methods are far from these limits, highlighting large room for improvement.
Importance of adaptive compression - The best strategy would match CoT length to problem difficulty, using minimal tokens for easy questions and more thorough CoTs for harder ones. Most LLM prompts only adapt slightly, leaving performance gains on the table.
Get next week’s papers.
The same picks and the same summaries, in your inbox. Free, and 176 issues deep.
Subscribe on Substack