Dynamic K-Head: Difficulty-Supervised Budget Selection for Continuous Latent Reasoning

arXiv:2610.17679v1 Announce Type: cross Abstract: Chain-of-thought (CoT) improves reasoning but incurs substantial autoregressive rationale cost. Continuous CoT moves intermediate computation into recurrent hidden states, yet typically uses a fixed number of updates even though the best budget varies across questions and accuracy need not improve monotonically with $K$. We introduce Dynamic K-Head, a question-conditioned, pre-rollout budget selector. It is jointly trained with the reasoner under selected budgets, using difficulty supervision based on scores assigned from the question alone. We also show that latent-update count can misrepresent end-to-end cost because a short latent rollout can shift computation into a longer explicit continuation. We therefore count latent updates, implementation-specific special tokens, and all decoded text. Instantiated with CoDI on Llama 3.2 1B and GSM8K, Dynamic K-Head reaches 54.44% exact-match accuracy at 12.03 average reasoning/output tokens, compared with 52.31% at 15.21 tokens for fixed-$K=6$ CoDI---a 2.12-point gain with 20.9% lower token cost. Across three out-of-distribution arithmetic datasets, it reduces cost by 19.3--25.7% while improving accuracy by 0.30--2.22 points. These results demonstrate that difficulty-supervised budget selection can improve both accuracy and efficiency, while stable budget selection remains a central challenge.

Abstract:Chain-of-thought (CoT) improves reasoning but incurs substantial autoregressive rationale cost. Continuous CoT moves intermediate computation into recurrent hidden states, yet typically uses a fixed number of updates even though the best budget varies across questions and accuracy need not improve monotonically with $K$. We introduce Dynamic K-Head, a question-conditioned, pre-rollout budget selector. It is jointly trained with the reasoner under selected budgets, using difficulty supervision based on scores assigned from the question alone. We also show that latent-update count can misrepresent end-to-end cost because a short latent rollout can shift computation into a longer explicit continuation. We therefore count latent updates, implementation-specific special tokens, and all decoded text. Instantiated with CoDI on Llama 3.2 1B and GSM8K, Dynamic K-Head reaches 54.44% exact-match accuracy at 12.03 average reasoning/output tokens, compared with 52.31% at 15.21 tokens for fixed-$K=6$ CoDI---a 2.12-point gain with 20.9% lower token cost. Across three out-of-distribution arithmetic datasets, it reduces cost by 19.3--25.7% while improving accuracy by 0.30--2.22 points. These results demonstrate that difficulty-supervised budget selection can improve both accuracy and efficiency, while stable budget selection remains a central challenge.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.17679 [cs.LG]

(or arXiv:2610.17679v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.17679 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Dynamic K-Head: Difficulty-Supervised Budget Selection for Continuous Latent Reasoning

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