SEAL: Steerable Reasoning Calibration of Large Language Models for Free

Thanks for the constructive suggestion. We provide detailed results below.

More Benchmark Results

Thank you for the insightful question. As the DeepSeek–Distilled model used in our study does not currently support tool use, we chose to evaluate our method on a planning task [1], deliberately selecting a scenario with a significant domain gap between math and code. To assess cross-domain generalization, we continued using the steering vector extracted from the MATH dataset. As shown in Table R1, SEAL achieves a consistent improvement of 3.7% in accuracy, along with a 44% reduction in token usage. These results further validate the effectiveness and generalizability of our approach. We’d be happy to include additional benchmark evaluations if the reviewer has specific suggestions.

Table R1. Results on the calendar planning task from the Natural Plan benchmark using Deepseek-Distill-7B.

[1] NaturalPlan: Benchmarking LLMs on Natural Language Planning

Dear Reviewer b7rX,

Thanks for your valuable time. As the deadline for the discussion period is nearing, we would greatly appreciate it if you could kindly let us know whether our responses have adequately addresses your concern. And we are eager to engage in further discussions before the discussion period ends if you still have remaining concerns. Thank you very much for your time and efforts!

Best wishes,

Authors

We’re glad that Reviewer ssbp acknowledged our work as “insightful” and “promising”, To address Reviewer ssbp’s concerns, we provide detailed responses in the following.

Q1: Robust Thinking Step Identification Method

In this work, we adopted a keyword-based identification method, as we found that reflection and transition steps in the thinking model exhibit relatively distinct patterns, making simple keyword matching both effective and efficient. That said, more robust methods, such as using a large language model (LLM) for step classification are certainly feasible.

Additionally, we experimented with LLM-based identification and observed an 87.15% agreement with our keyword-based method. While the LLM occasionally misclassifies execution steps as reflection or transition, it still provides a strong general-purpose alternative. To evaluate its effectiveness, we extracted new steering vectors using LLM-based annotations and applied them in our method. As shown in Table R1, SEAL with LLM-based identification achieves performance improvements comparable to the one obtained with keyword-based matching.

Table R1. Performance on MATH500 using Deepseek-distill-7B with different step identification methods.

Additionally, we’d like to emphasize that our mean-diff approach for vector extraction is inherently robust to light misclassification. As long as the positive samples (those containing the target step) are dominated by the correct category, and the negative samples contain few such instances, the resulting direction remains meaningful. Naturally, perfect classification would yield even higher-quality vectors, but our method is designed to tolerate some level of noise. In Appendix B.2, we conduct a keyword ablation study where we intentionally introduce misclassifications. While this slightly degrades vector quality, we are still able to extract effective steering directions. These findings further demonstrate the robustness of our approach to moderate classification noise.

Q2: Clarification of Lines 145–146

The statement, “This aligns with the expectation that shallow layers primarily capture low-level features, while deeper layers encode more abstract conceptual and semantic knowledge,” suggests that deeper layers are more likely to represent features associated with high-level semantics, as opposed to the token-level patterns captured by shallow layers. Since reflection and transition thoughts are inherently semantic in nature, it follows that the corresponding activation patterns are more salient in deeper layers. The visualization results in Figure 3 support this perspective and help explain why mid-to-late layers in our experiments tend to produce higher-quality directions for steering reflection and transition behaviors.

Q3: Selective Reasoning Calibration

Thanks for the question. We would like to clarify that our method preserves essential reflection and transition steps when the model exhibits a strong tendency toward them. By applying a moderate steering strength, the method primarily suppresses unnecessary or marginal cases when the hidden representations lie near the boundary between execution and reflection/transition thoughts. When the hidden representations are far from this boundary, the model continues to perform necessary reflection and transition behaviors as originally intended. Our goal is not to eliminate all reflection and transition, but rather to reduce redundant instances.

For example, in Table R2, we compare the average number of reflection/transition steps before and after applying SEAL. For correctly answered samples where redundancy is low, SEAL leads to only a modest reduction (3.43 steps). In contrast, for incorrectly answered samples, which exhibit more redundant reflection/transition behavior, SEAL reduces the number of steps by a significant average of 55.43. This demonstrates that our method selectively suppresses redundant behaviors without impairing effective reasoning.

Table R2. Average number of reflection/transition steps before and after applying SEAL.

While we believe our lightweight, training-free method is practical and effective, we agree that a more adaptive steering mechanism would be a promising direction. Such adaptability could potentially be achieved through reinforcement learning, and we consider this a promising direction for future work.

Q4: Typo

Thank you for pointing it out. We will correct the typo in the revised version.

Dear Reviewer ssbp,

Thanks for your valuable time. As the deadline for the discussion period is nearing, we would greatly appreciate it if you could kindly let us know whether our responses have adequately addresses your concern. And we are eager to engage in further discussions before the discussion period ends if you still have remaining concerns. Thank you very much for your time and efforts!

Best wishes,

Authors

Thank you for the positive evaluation and for acknowledging that our work “identifies a meaningful problem” and that our method shows “robustness and practical utility.” We provide point-by-point responses below.

Q1: Theoretical Justification of Steering Methods

Thanks for pointing it out. The theoretical analysis of activation-based intervention methods remains an open research challenge. Existing theoretical work on neural networks is often limited to small-scale models and simplified settings (e.g., omitting positional encodings), which makes it difficult to extend such analyses to large language models (LLMs). Moreover, reasoning behavior in LLMs involves complex interactions across multiple tokens, further complicating theoretical justification. For these reasons, we consider a full theoretical treatment beyond the scope of this work.

That said, there is strong intuitive and empirical support for our approach. A growing body of interpretability research has shown that LLM activations encode meaningful semantic directions. For instance, prior work [1–3] demonstrates that specific features, such as concepts, refusals, or reasoning patterns, can be extracted from activation vectors, and that manipulating these directions can systematically influence model behavior. In our study, we observe that similar activation directions correspond to reflection and transition behaviors, and we show that modifying these directions leads to measurable changes in reasoning performance.

References

[1] Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet

[2] Refusal in Language Models Is Mediated by a Single Direction

[3] AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders

Q2: Comparison with Simply Shortening Sequences

Great question! To isolate the effect of SEAL from simple response shortening, we conducted a comparison with a baseline method that truncates the thinking process. Specifically, we introduced a fixed “think budget,” forcing the model to insert an end-of-think token (</think>) once the generated thinking sequence exceeds the budget. This transition moves the model into the summarization phase, resulting in a final answer. By setting the reasoning budget to 3500 tokens, we aligned the average response length with that of SEAL for a fair comparison.

As shown in Table R1, this truncation-based approach underperforms SEAL, despite producing similarly shorter outputs. This indicates that SEAL’s advantage stems not merely from shortening the response, but from guiding the model to reduce unnecessary reflection and transition steps, effectively altering its reasoning behavior.

Table R1. Comparison between SEAL and simple truncation on Deepseek-distill-7B (MATH500).

Q3: Robustness of the Ablation Study

In our experiments, we used a fixed steering coefficient of 1.0 across all tasks and models, as this value consistently delivered strong performance across diverse settings. To assess robustness, we repeated the ablation study over three runs and observed stable results, with low variance in accuracy. The average performance and standard deviation for different coefficients and layers are reported in Table R2 and Table R3.

Table R2. Ablation results on steering coefficient using Deepseek-Distill-7B on the MATH500 dataset.

Table R3. Ablation results on the target steering layer using Deepseek-Distill-7B on the MATH500 dataset.

We appreciate Reviewer hU5P’s positive initial evaluation and are grateful for the recognition of our work as providing “insightful analysis,” introducing “new” methods, and achieving “notable improvements.” To address the reviewer’s concerns, we provide point-by-point responses below.

Q1: Generalization of Thought Labeling Methods

Thank you for the question. We adopt a keyword-based identification approach, as we observed that reflection and transition steps in the reasoning process tend to follow relatively distinct and recognizable patterns. These can be effectively captured through simple keyword matching. To support generalization across different domains or writing styles, large language models (LLMs) can also be used to identify thought types. In our analysis, the keyword-based method showed a high degree of consistency with LLM-based identification, achieving an 87.1% agreement. Furthermore, the end-to-end performance improvements achieved using keyword matching are similar to those obtained with LLM-based identification. This demonstrates the robustness and generalizability of our approach across different classification strategies.

Results: As shown in Table R1, both identification methods lead to significant improvements over the baseline full model, with accuracy gains ranging from 2.80% to 3.60%.

Table R1. End-to-end performance with different thought identification methods. Evaluated on Deepseek-Distill-7B and the MATH500 test set.

Q2: Improvements on Advanced Models

Thanks for pointing it out. First, we would like to clarify that our method is not limited to small models. The QWQ-32B-preview model (used in our manuscript) is an early-stage reasoning model that has not undergone large-scale reinforcement learning (RL) training, which explains why the over-reflection and over-transition phenomena are less prominent. Furthermore, we evaluated our method on the newly released QWQ-32B model, which has been extensively trained with RL. Our method remains highly effective on this more advanced model, as shown in Table R2

Table R2. Performance on QWQ-32B across Math500 and LiveCodeBench datasets.

Second, it is indeed the case that over-reflection and over-transition behaviors are more pronounced in smaller models. However, smaller reasoning models remain widely used in practice due to resource constraints. The fact that our method effectively mitigates these behaviors in small models makes it especially valuable and practical for a broader range of use cases. Therefore, we believe our method holds strong practical value for improving the performance and efficiency of current reasoning models.

Dear Reviewer hU5P,

Thanks for your valuable time. As the deadline for the discussion period is nearing, we would greatly appreciate it if you could kindly let us know whether our responses have adequately addresses your concern. And we are eager to engage in further discussions before the discussion period ends if you still have remaining concerns. Thank you very much for your time and efforts!

Best wishes,

Authors