Stagnation detection and reasoning trace reinitialization in CGR

Develop and evaluate a mechanism within Certainty-Guided Reasoning (CGR) to detect stagnation in the reasoning trace and perform flush-and-reinitialize using sampling randomness to explore alternate solution paths, and determine its effects on accuracy and token efficiency.

Background

Reasoning trajectories can stagnate, leading to wasted tokens without improving solutions. CGR currently relies on certainty thresholds and probing to decide when to stop but does not explicitly handle stagnation.

The authors propose a future mechanism to detect stagnation and reinitialize the reasoning process, potentially improving exploration and outcomes. Whether this improves performance and efficiency remains unsettled.

References

Several promising directions remain open for exploration. We also consider a future mechanism for flushing and reinitializing reasoning traces when stagnation is detected, leveraging sampling randomness to explore alternate solution paths.

— Certainty-Guided Reasoning in Large Language Models: A Dynamic Thinking Budget Approach  (2509.07820 - Nogueira et al., 9 Sep 2025) in Conclusions and Future Work