On Reasoning Strength Planning in Large Reasoning Models

Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (i.e., the number of reasoning tokens) for harder problems, exhibiting difficulty-awareness for better task performance. While this automatic reasoning strength allocation phenomenon has been widely observed, its underlying mechanism remains largely unexplored. To this end, we provide explanations for this phenomenon from the perspective of model activations. We find evidence that LRMs pre-plan the reasoning strengths in their activations even before generation, with this reasoning strength causally controlled by the magnitude of a pre-allocated directional vector. Specifically, we show that the number of reasoning tokens is predictable solely based on the question activations using linear probes, indicating that LRMs estimate the required reasoning strength in advance. We then uncover that LRMs encode this reasoning strength through a pre-allocated directional vector embedded in the activations of the model, where the vector’s magnitude modulates the reasoning strength. Subtracting this vector can lead to reduced reasoning token number and performance, while adding this vector can lead to increased reasoning token number and even improved performance. We further reveal that this direction vector consistently yields positive reasoning length prediction, and it modifies the logits of end-of-reasoning token to affect the reasoning length. Finally, we demonstrate two potential applications of our findings: overthinking behavior detection and enabling efficient reasoning on simple problems. Our work provides new insights into the internal mechanisms of reasoning in LRMs and offers practical tools for controlling their reasoning behaviors. Our code is available at https://github.com/AlphaLab-USTC/LRM-plans-CoT.

💡 Research Summary

The paper investigates why large reasoning models (LRMs) automatically allocate more reasoning tokens for harder problems and how this allocation is internally represented. The authors pose two questions: (1) Do LRMs pre‑plan the amount of reasoning (i.e., the length of the chain‑of‑thought) before generation begins? (2) If so, how is this plan encoded? To answer these, they conduct a series of probing and activation‑steering experiments on several open‑source LRMs ranging from 1.5 B to 32 B parameters, using the MA​TH math dataset that contains five difficulty levels.

First, they extract the residual‑stream activation at the position of the start‑of‑reasoning token for each question and train a Lasso linear regression model to predict the number of subsequent reasoning tokens. Across all models and layers, the probe achieves Pearson correlations above 0.8, with deeper layers yielding even stronger signals. This demonstrates that the required reasoning length is already predictable from the question’s activation, implying that the model forms a plan before any reasoning token is emitted.

Next, the authors search for a “pre‑allocated direction vector” that could carry this plan. Using a difference‑in‑means method, they compute vectors between the mean activations of the easiest and progressively harder difficulty groups (r₅←₁, r₄←₁, r₃←₁, r₂←₁). Cosine similarity analysis shows that these vectors are almost identical in direction (≈0.99 similarity in the highest‑similarity layer, >0.9 across all layers) while their L2 norms increase monotonically with difficulty. Thus, a single shared direction encodes difficulty, and the magnitude of the vector encodes the exact amount of reasoning needed.

To test causality, they perform activation steering: adding the direction vector with a positive magnitude to the question activation leads to later generation of the end‑of‑reasoning token , longer chain‑of‑thoughts, and higher task accuracy; subtracting the vector shortens the chain and degrades performance. Logit analysis reveals that the vector directly modulates the logits of , confirming that the model’s termination decision is linearly influenced by this latent direction.

Finally, the paper demonstrates two practical applications. (1) Overthinking detection: the linear probe can flag inputs where the predicted reasoning length far exceeds the typical range, indicating potentially wasteful computation. (2) Efficient reasoning for simple problems: by reducing the vector’s magnitude for easy questions, one can force the model to stop reasoning early, saving compute without sacrificing accuracy.

Overall, the study uncovers a concrete internal mechanism: LRMs embed a pre‑planned reasoning length as the magnitude of a single linear direction in activation space, discovered at the moment the question is processed. This insight bridges the gap between observed difficulty‑aware behavior and model internals, offering new tools for interpretability, safety, and resource‑efficient inference. The code and data are publicly released at the provided GitHub repository.