Token Budget Saturation and Mechanistic Early Detection of Reasoning Non-Convergence in Chain-of-Thought Models

arXiv:2607.21433v1 Announce Type: new Abstract: Chain-of-thought reasoning models such as DeepSeek-R1-Distill-Qwen-7B exhibit a bimodal convergence pattern: generations either terminate within a token budget (converged) or exhaust it without reaching a conclusion (non-converged). We characterize this phenomenon empirically, showing that converged generations achieve 90.3% accuracy on AIME 1983-2024 while non-converged ones achieve only 6.6%, with an overall convergence rate of 62.0%. We then ask whether this outcome is detectable early in the thinking chain using internal model representations. Training linear probes on hidden-state activations at token positions 50-300, we find that layer-20 activations at token 150 achieve AUC 0.608 (+-0.080, 5-fold CV), reliably above chance even at token 50. Activation probes consistently outperform behavioral baselines derived from token entropy and repetition statistics. A sweep-level permutation test yields p=0.063 (100,000 permutations), consistent with a modest signal that our sample size cannot confirm at conventional thresholds. These findings suggest that convergence fate is partially encoded in intermediate representations well before the generation ends, opening a path toward early-exit inference and adaptive compute allocation.

Abstract:Chain-of-thought reasoning models such as DeepSeek-R1-Distill-Qwen-7B exhibit a bimodal convergence pattern: generations either terminate within a token budget (converged) or exhaust it without reaching a conclusion (non-converged). We characterize this phenomenon empirically, showing that converged generations achieve 90.3% accuracy on AIME 1983-2024 while non-converged ones achieve only 6.6%, with an overall convergence rate of 62.0%. We then ask whether this outcome is detectable early in the thinking chain using internal model representations. Training linear probes on hidden-state activations at token positions 50-300, we find that layer-20 activations at token 150 achieve AUC 0.608 (+-0.080, 5-fold CV), reliably above chance even at token 50. Activation probes consistently outperform behavioral baselines derived from token entropy and repetition statistics. A sweep-level permutation test yields p=0.063 (100,000 permutations), consistent with a modest signal that our sample size cannot confirm at conventional thresholds. These findings suggest that convergence fate is partially encoded in intermediate representations well before the generation ends, opening a path toward early-exit inference and adaptive compute allocation.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2607.21433 [cs.CL]

(or arXiv:2607.21433v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2607.21433 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

Token Budget Saturation and Mechanistic Early Detection of Reasoning Non-Convergence in Chain-of-Thought Models

Related coverage