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

arXiv: https://arxiv.org/abs/2607.21433 · HTML: https://mlsanity.com/paper/2607.21433/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 6 of 6)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Wait, Wait, Wait... Why Do Reasoning Models Loop?](https://mlsanity.com/paper/2512.12895/) (2025)

## Abstract (arXiv)

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.