Test-time Prompt Intervention

Test-time compute has led to remarkable success in the large language model (LLM) community, particularly for complex tasks, where longer chains of thought (CoTs) are generated to enhance reasoning capabilities. However, growing evidence reveals that such reasoning models often produce CoTs plagued by excessive redundancy, including repetitive verification steps and unnecessary reasoning shifts. The root cause lies in post-training of them that overly rely on outcome reward paradigms, as the data of process reward paradigms, which regulate intermediate reasoning steps, is difficult to construct at scale. To address this, we propose PI (π), a novel framework for Test-time Prompt Intervention. PI provides an interface to dynamically guide and regulate reasoning paths during inference through timely (When module) and proper (How module) interventions and post-intervention sampling (Which module). This allows human problem-solving expertise and cognitive science principles to be seamlessly integrated into LLMs’ reasoning processes, enhancing controllability and interpretability. Extensive experiments across multiple models and datasets demonstrate that PI significantly shortens CoTs while reducing hallucination, yielding more concise and reliable reasoning.

question: What is the logical structure of CoT when expanded into reasoning steps? To investigate this question, we visualize attention maps to reveal how reasoning steps interconnect, providing an intuitive view of dependency structures in the CoTs.

Examining Figure 2 collectively, we observe distinct attention patterns throughout the reasoning process. Early stages focus primarily on step 2, which explores the problem-solving approach, while backtracking and verification steps (steps 7-8) receive minimal subsequent attention. After generating step 9 with the correct answer, all following steps predominantly attend to this pivotal moment. However, the model performs several redundant checks with low attention scores (e.g., step 12) before reaching the final conclusion. We consider steps receiving negligible attention during subsequent reasoning as redundant. Bypassing these through generation intervention could substantially enhance efficiency. Using the graph structure in Figure 2(b), we formalize this analysis by identifying critical steps: a subset where each node includes all its highly-attended predecessors. If the model generated only these critical steps (2, 9, and 13), as shown in Figure 2(c), it would achieve a 75% reduction in computational overhead.

we first analyze their reasoning behaviors. Inspired by recent work (Gandhi et al. 2025; Luo et al. 2025) and based on observations of the generated CoTs, we categorize reasoning steps into six types: Progression, Summary, Exploration, Verification, Backtracking, and Conclusion.

• Progression involves advancing further along the current line of reasoning based on known information and inference rules, often accompanied by connective words such as “Next”, “Then” or phrases like “Okay, moving on”.

• Summary involves organizing and integrating key information obtained from existing reasoning steps to lay the foundation for subsequent reasoning, often accompanied by summarizing phrases such as “Putting it together”.

• Exploration involves actively generating new hypotheses or seeking alternative solution approaches when the current reasoning trajectory fails to yield progress, often accompanied by connective words like “Alternatively”.

• Verification involves checking and confirming the logical consistency and accuracy of recently generated reasoning steps, typically accompanied by “Wait”.

• Backtracking enables the system to revert to earlier decision points and select new paths when the current reasoning approach is incorrect, facilitating error correction.

• Conclusion delivers the final answer once adequate and accurate reasoning information has been gathered.

Static Intervention. S1 (Muennighoff et al. 2025) represents a special case of static intervention, which incorporates additional verification and exploration steps. To address the overthinking problem, developed several static PI strategies as shown in Figure 4 to reduce verification. Figure 5 shows the performance of multiple predefined static intervention strategies, including progressive priority (πs(p)), progressive with verification (πs(p, v)), progressive with summarization (πs(p, s)). Experimental results demonstrate length declines on simple problems, whereas accuracy drops on challenging questions. This suggests that while static PI mitigates overthinking issues in simple cases, the rigid predefined intervention patterns hinder the model’s reasoning ability when dealing with complex problems.

Dynamic Intervention. Given the substantial variability across problems, it becomes challenging to predetermine the optimal reasoning trajectory for each specific instance. To address these limitations, we develop dynamic PI strategies that mitigate the risk of over-intervention. Specifically, upon completion of a reasoning step, dynamic PI concurrently extends multiple branches that generate diverse reasoning behaviors. These are combined with the model’s naturally generated reasoning steps as candidate options, with the optimal path selected using the Which module design.

St+1 = {St+1 i }, St+1 i = LRM(S≤t,Ti), Ti ∈ T , (1)

where Si is the candidate step and T denotes trigger sets. A key advantage of dynamic PI lies in its ability to flexibly adapt intervention actions based on varying task demands. When prioritizing reasoning efficiency, we designate progression behavior as a constant candidate action, invoke summary behavior less frequently, and preserve other reasoning behaviors that emerge naturally from the model, thus promoting depth-first reasoning in CoT (πd(p, s)). For simple tasks, conclusion behavior can be added to facilitate early exit, further mitigating overthinking (πd(p, s, c)). For trust-critical applications, verification branch can be incorporated to reduce hallucinations (πd(p, s, v)). Once dynamic PI generates multiple branches, the choice of optimal branch (determined by the Which module) and intervention timing (governed by the When module) becomes crucial.

Which Module

branch selection based purely on perplexity can lead the model into degenerative behaviors such as repetitive patterns. To address this limitation, we seek a metric that captures “reasoning depth” to guide branch selection. By prioritizing branches with deeper reasoning, the Which module minimizes superficial information propagation and accelerates the reasoning process

When Module

These limitations arise from two key factors: first, the inherent uncertainty in step granularity, as a single major step may encompass multiple sub-steps; and second, the potential strong correlations between adjacent steps, where subsequent steps often represent logical consequences of their predecessors. Inspired by Wang et al. (2025b), we combine the model’s internal state, specifically entropy, to determine optimal intervention timing.