Title: On Reasoning Strength Planning in Large Reasoning Models
Venue: NeurIPS 2025
Accepted: yes
Keywords: Large reasoning models

mechanism explanation

reasoning strength

activation steering
Abstract: Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (\ie 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.
\textbf{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 \texttt{</think>} 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 \url{https://anonymous.4open.science/r/LRM-plans-CoT-7E04}.

On Reasoning Strength Planning in Large Reasoning Models

Abstract

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 </think> 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 .

1 Introduction

Large reasoning models (LRMs) [1-3] have demonstrated exceptional performance across a variety of complex reasoning tasks, such as mathematical problem solving [4-6], code generation [7, 8], and scientific question answering [9]. Here we take a closer look at LRMs' ability to allocate reasoning strength commonly quantified by the number of reasoning tokens generated during inference. Increasing reasoning strength has been shown to substantially improve model performance on

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complex reasoning tasks [2, 10]. As a result, it has emerged as a critical factor for both performance optimization and controllable model behavior [11-13].

Recent findings have revealed two key properties of reasoning strength in LRMs: it can be automatically allocated based on problem difficulty [1, 14, 2, 15] and it can be manually controlled through intervention [16-20]. On the one hand, LRMs tend to allocate more reasoning tokens to harder questions, reflecting an implicit adaptation to task complexity [12, 21-24]. On the other hand, reasoning strength can also be explicitly manipulated by prompting a desired length, typically enabled through supervised fine-tuning (SFT) [17] or reinforcement learning (RL) [16] with strength-aware objectives. These empirical observations suggest that LRMs may have automatic and controllable mechanisms for reasoning strength modulation. However, the underlying nature and internal structure of these mechanisms remain largely unexplored.

To fill this research gap, we investigate the underlying mechanism of reasoning strength in LRMs by asking two key questions: (1) Do LRMs pre-plan their reasoning strength before generation? (2) If so, in what form is this control encoded in advance? We approach these questions from the perspective of model activations - that is, how the activations ( i.e., latent representations of the question prompt) vary in response to different levels of reasoning strength. For the first, we examine whether the number of reasoning tokens can be predicted solely from the activations corresponding to the input question. For the second, we explore how LRMs encode pre-allocation signals within activations that modulate reasoning strength. Specifically, we employ a linear probe to predict the reasoning token count from question activations, and further extract a pre-allocated direction vector ( i.e., pre-allocation vector), such that manipulating this vector within the activation space enables control over the reasoning strength. Positive findings would indicate that LRMs plan reasoning strength ahead of generation through specific pre-allocated activations.

Here we conduct preliminary experiments using DeepSeek-R1-distilled-Qwen on the MATH [5] dataset, which contains math questions across five difficulty levels. As visualized in Figure 1, we summarize three key empirical findings from the activation distribution of the LRM:

Figure 1a shows that a well-trained linear predictor can estimate the number of reasoning tokens from input activations, achieving a correlation of 0.84 between predicted and actual values. This result indicates that the number of reasoning tokens is predictable prior to generation, suggesting that LRMs pre-plan their reasoning strength in advance.

As the question difficulty increases, activations consistently shift in a shared direction, as Figure 1b depicts. The activations of math problems exhibit a consistent trend shifting towards the same direction. Specifically, mean difference vectors between high- and low-difficulty questions consistently point in a similar direction, with magnitudes that correlate with question difficulty.

As shown in Figure 1c, manipulating activations along this direction vector - with varying magnitudes - causally modulates reasoning strength, leading to corresponding changes in LRM performance on reasoning tasks.

These findings suggest that LRMs pre-plan their reasoning strength through pre-allocating a direction vector, whose magnitude encodes the intended strength. To further investigate, we show that this direction vector consistently produces positive predictions of reasoning token numbers, closely aligning with actual values. Moreover, we observe that manipulating activations along this direction influences the logit of the end-of-reasoning token </think> , indicating a causal role in terminating the reasoning process. Based on these findings, we further discover two possible potentials of such underlying mechanism of reasoning strength: overthink detection with the predictor and efficient reasoning with activation steering [25].

2 Related Works

2.1 Large Reasoning Models

Large reasoning models (LRMs) [2, 1] have recently emerged as a new paradigm of large language models for complex task solving through step-by-step reasoning [26, 27, 22]. These models conduct explicit reasoning processes between special tokens of <think> and </think> before producing final answers [10]. Recent studies have shown that LRMs can adaptively allocate reasoning strength ( i.e., the number of reasoning tokens) based on problem difficulty-they tend to allocate more reasoning strength to harder questions to improve accuracy [12, 21-23]. Moreover, it is even possible to specify the reasoning strength via prompting a desired number of reasoning tokens, which can be realized through post-training with length-aware objectives [16, 17]. These phenomena suggest that LRMs may possess some underlying mechanisms to plan and control the strength of their reasoning.

2.2 Planning in Language Models

Recent works show that, despite being trained solely on next-token prediction [28], large language models (LLMs) exhibit certain planning capabilities [29-32]. For example, there is evidence that LLMs can anticipate future tokens-such as planning rhyme schemes several lines ahead when composing poems [31]. Moreover, studies have found that models may even pre-plan answer confidence levels or the choices in multiple-choice questions [32]. Despite these findings, the underlying mechanisms behind such planning capabilities remain largely unexplored, and it is still unclear whether similar planning capabilities occur in LRMs. Inspired by these observations, this work presents the first investigation into the reasoning planning capabilities of LRMs, and uncovers the underlying mechanisms that control such planning.

2.3 Activation Steering with Linear Direction

Activation steering is one research line among the representation learning [33-39]. Recent advances in mechanism explainability reveal that there exist linear directions inside the activation space of language models that control specific semantical behaviors [40-42]. These directions are typically derived from activation differences between contrasting semantics, such as refusal versus compliance in responses [42]. Manipulating directions via activation addition or subtraction enables behavior modification of language models during inference. It has been evidenced that response style [25, 43, 44], refusal behaviors [42, 45, 46], and memory extraction capabilities [47] have been encoded in linear directions. Recent studies find evidence that by concatenating question prompts with their corresponding chain-of-thought (CoT) answers and computing activation differences between responses of varying reasoning token numbers, it is possible to identify linear directions that control the length of reasoning [19, 48, 49]. In this work, we take an important step further, by demonstrating that such directions have been pre-allocated by LRMs upon observing the question for reasoning strength control, even before generating the answer.

3 Reasoning Strength in LRMs is Pre-Planned

In this section, we explore the hypothesis that LRM plans the reasoning strength ( e.g., the length of the reasoning process) even before the beginning of the reasoning process [41, 32]. We use linear probing to test this hypothesis [50, 41, 51, 32], predicting the length of reasoning with the activations of the question solely. A good probing result will support our hypothesis [50].

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3.1 Experimental Setup

Linear probing. For each question, we extract the d -dimentional residual stream activation h ( l ) ∈ R d at the position of the start-of-reasoning <think> token, and aim to predict the subsequent reasoning token number y ∈ R using a linear regression model based on h ( l ) at each layer l . We calculate y as the number of tokens between the start-of-reasoning token <think> and the end-of-reasoning token </think> . Formally, given a dataset of n samples, we construct an activation matrix H ( l ) ∈ R n × d where each row corresponds to the activation of one question, and corresponding scalar reasoning token number Y ∈ R n . We then learn a linear regression function ˆ Y = H ( l ) W ( l ) + b ( l ) by minimizing the following regularized loss:

Equation (3) denotes the Lasso regression [52], where W ( l ) ∈ R d and b ( l ) ∈ R are the learnable parameters of this linear regression. A regularization term λ ∥ ∥ W ( l ) ∥ ∥ 1 is introduced for avoiding overfitting, where α is a hyperparameter controlling the regularization strength. To implement this Lasso regression, we use the Python package of scikit-learn [53]. The illustration and details of this probing process can be found in Appendix B.

Datasets. We conduct the linear regression experiments on the MATH [5] dataset, where math questions are divided into five groups according to their difficulty. We randomly split the dataset with a ratio of 9:1 for training and testing.

Models. We conduct experiments on a wide range of open-source LRMs, including the distilled R1 model series [2] and the QwQ model [3]. The models we evaluate span a variety of scales, ranging from 1.5B to 32B parameter sizes.

3.2 Results

Based on the linear regression experiments, we have the following observations:

LRMs plan their reasoning strength even before the generation of the first reasoning token, and this planning capability becomes more evident as the layer depth increases. We visualize the layer-wise prediction results in Figure 2. As shown in this figure, our linear probe can yield high prediction results with correlation coefficients over 0.8 across a range of model sizes and different model kinds, suggesting that the reasoning strength planning is possibly encoded in the model's internal activations before the generation of the first reasoning token. Moreover, as the layer becomes deeper, the prediction results become better. This indicates that the reasoning planning capabilities may be developed in the later layers of these models. The above observations suggest that LRMs may have the capability of planning the reasoning strength in advance. We provide more similar experimental results in the Appendix B.

4 LRMs Encode Reasoning Strength via Pre-allocated Direction Vectors

We investigate the underlying mechanism behind this planning capability, given the observation that LRMs may plan their reasoning strength in advance as revealed above. Specifically, inspired by the emerging phenomenon that linear representations can control specific behaviors in language models [40, 42], we hypothesize that LRMs may modulate their reasoning planning through pre-allocated direction vectors embedded within their activation space. We organize this section as follows: We

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first describe how to find the existence of such pre-allocated direction vectors using the differencein-means approach [54] in Section 4.1. After that, in Section 4.2, we reveal that such pre-allocated direction vectors are indeed used for planning reasoning strengths, through their causal effects with activation steering. Then, in Section 4.3, we point out that such pre-allocated direction vectors can be used for predicting the reasoning strengths with the linear predictors we obtained above. Finally, in Section 4.4, we uncover that the mechanism of length planning is ultimately achieved by adjusting the logits of the end-of-think token </think> with such pre-allocated direction vectors.

4.1 Pre-allocated Direction Vectors Exist for Reasoning Strength Planning

In this section, we test the existence of pre-allocated direction vectors ( i.e., pre-allocation vectors) for reasoning strength control. Motivated by the observation that LRMs automatically allocate longer reasoning strength for more difficult questions, we suspect that LRMs use linear activation directions for this control. Therefore, we find such vectors using the difference-in-means approach between questions of varying difficulties.

Difference in Means [54]. The difference-in-means method [54] effectively extracts activation direction vectors associated with specific model behaviors-such as refusal to answer [42]-by computing the difference between the mean activations associated by two contrasting behaviors of input data pairs ( e.g., refusal and compliance). In our case, we construct contrasting data pairs with questions of different difficulties, since LRMs behave in automatically allocating more reasoning strengths on harder tasks. In this way, we may isolate direction vectors related specifically to reasoning strength control, by applying the difference-in-means method. Specifically, we compute the difference-in-means vector r ( l ) i ← 1 between difficulty the hardest level i and easiest level 1 on the MATH dataset [5] as:

where the first and second terms denote the mean activations at layer l computed over the activation sets D i and D 0 , which correspond to math questions of difficulty level i and 0 , respectively. Here, these activations are also extracted at the start-of-reasoning token <think> position before generation. By varying the target difficulty i from 1 to 5, we can get four such vectors at each layer, namely r ( l ) 5 ← 1 , r ( l ) 4 ← 1 , r ( l ) 3 ← 1 , and r ( l ) 2 ← 1 . These vectors capture the activation shift from a baseline level of difficulty

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1 to increasingly harder questions. These vectors are pre-allocated since we extract them before generation. If the LRM plans the reasoning strength via a shared directional vector, then the four vectors are expected to show a high degree of similarity.

By analyzing these vectors, we have the following findings:

Pre-allocated direction vectors exist for distinguishing questions across different difficulties, since all constructed vectors exhibit consistently high cosine similarities across layers. We visualize the pairwise cosine similarities among the four extracted vectors in Figure 3, which are taken from the layer with the highest averaged similarity. As shown in these figures, the vectors exhibit extremely high directional consistency, with cosine similarities around 0.99. This suggests that LRMs may utilize a single, shared directional vector to distinguish between questions of different difficulty levels. In addition, we present the trend of average cosine similarity across layers in Figure 4. The results show consistently high similarity scores ( i.e., above 0.9), which further increase with layer depth and approach near 1.0 in the final layers.

The magnitudes of these pre-allocated vectors highly correlate with the required reasoning token number, showing implicit connections. Given that the extracted four vectors exhibit nearly identical directions, their magnitudes ( i.e., the L2 norm) become the key factor in distinguishing questions of varying difficulty. We plot the magnitudes of these four vectors across different layers in Figure 5. As shown, the vector magnitude increases with question difficulty, and is approximately proportional to the average additional reasoning token number required to solve the question (See more details in Appendix C). This suggests a strong positive correlation between the pre-allocated vector magnitudes and the reasoning strengths allocated by the model.

4.2 Pre-allocation Vectors Causally Affect the Reasoning Strengths

To further examine whether these direction vectors are used for reasoning strength planning, we test their causal effect on reasoning strengths via intervention of activation steering [25]. The key idea of activation steering is to inject direction vectors on the activation of language models, to test whether such direction vectors can causally affect the model behaviors [25, 42]. We conduct such activation steering experiments with the average vector r ( l ) of our extracted four vectors ( i.e.,

where h ( l ) and h ( l ) ′ are the original and post-steered activations at layer l , and λ is a hyperparameter controlling the strength of steering. More implementation details can be found in Appendix A. By varying the steering strength λ , we have following observations (See more results in Appendix C.2):

Such pre-allocated vectors are indeed responsible for the reasoning strength planning, since steering with extracted vectors will causally affect the reasoning token number. We visualize in Figure 6 the change in model response length under different steering strengths from -0.2 to 0.2, with an interval of 0.05. As shown, increasing the negative steering strength progressively decreases the model's reasoning token numbers, while the length of the final answer (i.e., the number of tokens after the </think> token) remains unaffected. This indicates that the pre-allocated vector causally controls the planning of the reasoning token number, rather than the answer token number.

Controlling reasoning strengths with this pre-allocation vector causally affects the performance [27, 10, 16]. As shown in Figure 6, reducing the model's reasoning token number generally leads to a drop in performance. This demonstrates that steering with the pre-allocated vector enables a simple yet effective test-time scaling mechanism. Furthermore, applying a positive steering

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strength can even improve model performance. As shown in Table 1, moderate positive steering shows potential in enhancing performance across multiple math datasets, including MATH500 [5], AIME [55], and OlympiadBench [56]. However, increasing the steering strength beyond a certain point does not lead to further gains, and may even degrade performance. We attribute this to the possible intelligence upper bound of such LRMs. More results are in the Appendix C.2.

4.3 Pre-allocation Vectors Yield Positive Reasoning Token Number Prediction

In this section, we discuss the connection between the reasoning token number predictor and these pre-allocated vectors we obtained. We reveal that these vectors tend to generate positive reasoning token number predictions, further proving their role in the reasoning strength control. Specifically, we can estimate the effect of these vectors with the linear predictor we obtained in Section 3 as follows:

The pre-allocation vectors yield positive reasoning token number predictions in most cases. We visualize the predicted reasoning token number across layers when applying the steering vector with a multiplier of 0.2 in Figure 7. The average prediction ( i.e., ˆ y ( l ) ) shows a consistent positive trend, indicating that the steering vector reliably adjusts the reasoning length. Moreover, ˆ y ( l ) aligns well with the actual causal changes shown in Figure 6, highlighting a strong link between regression predictions and the steering-induced effects, thus reinforcing the vector's role in reasoning strength planning. More similar results are in Appendix C.3.

4.4 Pre-allocation Vectors Control Reasoning Strengths by Modifying Logits of </think>

To study how such pre-allocated vectors affect the reasoning strength, we take one possible perspective: the impact on the logits of the end-of-reasoning token </think> . We have the following findings:

These pre-allocation vectors control the reasoning strength by modifying the logits of the endof-reasoning token </think> . We visualize the distribution of logits for the </think> token under different steering strengths in Figure 8. As shown, applying a negative steering strength results in an overall increase in the logits of the </think> token, indicating a higher likelihood of its occurrence, which leads to fewer reasoning tokens. Conversely, positive steering strength decreases the logits of the </think> token, reducing the likelihood of generating this token, which leads to more reasoning

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token numbers. We also compare the impact on the logits with the eos token 
 and randomly selected tokens. As shown in Figure 8b, the impact on the end-of-reasoning token is significantly higher than random tokens and the eos token |endoftext| . These observations suggest that the pre-allocated vectors primarily modulate reasoning strength by adjusting the logits of the end-of-reasoning token. More similar results are in Appendix C.4. We also reveal that the steering mechanism also affects reasoning-related token logits within the reasoning process in Appendix C.5

5 Potentials of Our Findings

We aim to investigate whether our findings have potential in more diverse domains, despite our current analysis mainly focusing on mathematical problems. Specifically, we discuss two possible generalized potentials of our findings: overthink detection and efficient inference. It is important to highlight that we merely outline the potential application directions, and more efforts are required to make such potential applicable in real-world practice.

5.1 Overthink Detection before Model Generation

In this section, we demonstrate how to detect potential overthink behavior before the generation of LRMs. LRMs exhibit risks in overthink unexpectedly, generating unnecessarily long reasoning traces. Such overthink phenomena can cause significant real-world deployment consequences, not only significantly increasing the computational cost for model providers, but also unnecessarily prolonging the waiting time for users [57, 58, 13]. If we can detect overthink in advance ( i.e., before generation), we may reduce both computation and latency by, for example, switching to a lighter model for serving [58]. We argue that we can effectively identify the occurrence of possible overthink, by using our trained predictors to estimate the reasoning strength in advance. We test the predictions differences on data pairs of non-overthink questions and overthink questions. These overthink questions are constructed by forcing LRMs to overthink on vanilla questions by adopting overthink attacks [57], where these vanilla questions are sampled from the AlpacaEval dataset. More details can be found in Appendix D.1. We visualize our prediction results in Figure 9. We can find that our predictor yields significantly longer reasoning lengths on overthink questions than on the vanilla

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non-overthink questions. This indicates that we can detect possible overthink phenomena before the generation, which is based on our findings that LRMs plan their reasoning strengths.

5.2 Efficient Inference

In this section, we present how to leverage our findings to achieve more efficient inference, avoiding overthinking on simple questions [13]. To test this potential, we conduct activation steering experiments on two kinds of questions that LRMs tend to overthink: general language understanding dataset MMLU[60] and Level 1 questions on MATH500 [5]. We reduce the number of reasoning tokens by applying activation steering with a proper negative steering strength λ . We report the performance under such steering experiments in Figure 10. As shown in this figure, we can significantly reduce the number of reasoning tokens on such questions, indicating that LRMs may wrongly allocate reasoning strengths on these easy tasks, which induces their overthinking. While reducing the number of reasoning tokens on these tasks can still maintain the performance of LRMs. This result suggests the potential of using activation steering for efficient reasoning, and also reveals the underlying overthink mechanism of LRMs on easy questions.

6 Limitations

This work has several limitations. First, we only use a linear probe and do not explore whether more complex architectures, such as MLPs, could yield better performance in predicting reasoning length. In addition, our experiments focus primarily on the Qwen model series [61], and it remains unexplored whether these findings hold for reasoning models based on other backbones [62].

7 Conclusion

This paper investigated whether and how large reasoning models (LRMs) plan reasoning strength ( i.e., the number of reasoning tokens) before generating answers. Using linear probing, we showed that the reasoning token number can be predicted merely using the activations of the question, suggesting implicit reasoning strength planning capabilities before generation. We found the existence of preallocated direction vectors in LRMs, whose magnitude causally affects the number of reasoning tokens. We further revealed that these vectors may affect the logits of the end-of-thinking token </think> to achieve reasoning strength control. Finally, we discussed two potential applications of our findings: overthink detection before generation and efficient inference. Our paper studied the underlying mechanism of the reasoning strength planning in LRMs from the model activation perspective, which can help the community better understand LRMs 2 .

Acknowledgments

This research/project is supported by the National Research Foundation, Singapore under its National Large Language Models Funding Initiative (AISG Award No: AISG-NMLP-2024-002). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore

References

Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, Alex Iftimie, Alex Karpenko, Alex Tachard Passos, Alexander Neitz, Alexander Prokofiev, Alexander Wei, Allison Tam, Ally Bennett, Ananya Kumar, Andre Saraiva, Andrea Vallone, Andrew Duberstein, Andrew Kondrich, Andrey Mishchenko, Andy Applebaum, Angela Jiang, Ashvin Nair, Barret Zoph, Behrooz Ghorbani, Ben Rossen, Benjamin Sokolowsky, Boaz Barak, Bob McGrew, Borys Minaiev, Botao Hao, Bowen Baker, Brandon Houghton, Brandon McKinzie, Brydon Eastman, Camillo Lugaresi, Cary Bassin, Cary Hudson, Chak Ming Li, Charles de Bourcy, Chelsea Voss, Chen Shen, Chong Zhang, Chris Koch, Chris Orsinger, Christopher Hesse, Claudia Fischer, Clive Chan, Dan Roberts, Daniel Kappler, Daniel Levy, Daniel Selsam, David Dohan, David Farhi, David Mely, David Robinson, Dimitris Tsipras, Doug Li, Dragos Oprica, Eben Freeman, Eddie Zhang, Edmund Wong, Elizabeth Proehl, Enoch Cheung, Eric Mitchell, Eric Wallace, Erik Ritter, Evan Mays, Fan Wang, Felipe Petroski Such, Filippo Raso, Florencia Leoni, Foivos Tsimpourlas, Francis Song, Fred von Lohmann, Freddie Sulit, Geoff Salmon, Giambattista Parascandolo, Gildas Chabot, Grace Zhao, Greg Brockman, Guillaume Leclerc, Hadi Salman, Haiming Bao, Hao Sheng, Hart Andrin, Hessam Bagherinezhad, Hongyu Ren, Hunter Lightman, Hyung Won Chung, Ian Kivlichan, Ian O'Connell, Ian Osband, Ignasi Clavera Gilaberte, and Ilge Akkaya. Openai o1 system card. CoRR , abs/2412.16720, 2024.

DeepSeek-AI, Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, Xiaokang Zhang, Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, Damai Dai, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangbo Hao, Guanting Chen, Guowei Li, H. Zhang, Han Bao, Hanwei Xu, Haocheng Wang, Honghui Ding, Huajian Xin, Huazuo Gao, Hui Qu, Hui Li, Jianzhong Guo, Jiashi Li, Jiawei Wang, Jingchang Chen, Jingyang Yuan, Junjie Qiu, Junlong Li, J. L. Cai, Jiaqi Ni, Jian Liang, Jin Chen, Kai Dong, Kai Hu, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Liang Zhao, Litong Wang, Liyue Zhang, Lei Xu, Leyi Xia, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Meng Li, Miaojun Wang, Mingming Li, Ning Tian, Panpan Huang, Peng Zhang, Qiancheng Wang, Qinyu Chen, Qiushi Du, Ruiqi Ge, Ruisong Zhang, Ruizhe Pan, Runji Wang, R. J. Chen, R. L. Jin, Ruyi Chen, Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shengfeng Ye, Shiyu Wang, Shuiping Yu, Shunfeng Zhou, Shuting Pan, and S. S. Li. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. CoRR , abs/2501.12948, 2025.

Qwen Team. Qwq-32b: Embracing the power of reinforcement learning, March 2025. URL https://qwenlm.github.io/blog/qwq-32b/ .

Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. Training verifiers to solve math word problems. CoRR , abs/2110.14168, 2021.

Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the MATH dataset. In NeurIPS Datasets and Benchmarks , 2021.

Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. In ICLR . OpenReview.net, 2024.

Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Pondé de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela Mishkin, Brooke Chan, Scott Gray, Nick Ryder, Mikhail Pavlov, Alethea Power, Lukasz Kaiser, Mohammad Bavarian, Clemens Winter, Philippe Tillet, Felipe Petroski Such, Dave Cummings, Matthias Plappert, Fotios Chantzis, Elizabeth Barnes, Ariel Herbert-Voss, William Hebgen Guss, Alex Nichol, Alex Paino, Nikolas Tezak, Jie Tang, Igor Babuschkin, Suchir Balaji, Shantanu Jain, William Saunders, Christopher Hesse, Andrew N. Carr, Jan Leike, Joshua Achiam, Vedant

Misra, Evan Morikawa, Alec Radford, Matthew Knight, Miles Brundage, Mira Murati, Katie Mayer, Peter Welinder, Bob McGrew, Dario Amodei, Sam McCandlish, Ilya Sutskever, and Wojciech Zaremba. Evaluating large language models trained on code. CoRR , abs/2107.03374, 2021.

Jacob Austin, Augustus Odena, Maxwell I. Nye, Maarten Bosma, Henryk Michalewski, David Dohan, Ellen Jiang, Carrie J. Cai, Michael Terry, Quoc V. Le, and Charles Sutton. Program synthesis with large language models. CoRR , abs/2108.07732, 2021.

David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R. Bowman. GPQA: A graduate-level googleproof q&a benchmark. In First Conference on Language Modeling , 2024. URL https: //openreview.net/forum?id=Ti67584b98 .

Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettlemoyer, Percy Liang, Emmanuel Candès, and Tatsunori Hashimoto. s1: Simple test-time scaling. arXiv preprint arXiv:2501.19393 , 2025.

Yue Wang, Qiuzhi Liu, Jiahao Xu, Tian Liang, Xingyu Chen, Zhiwei He, Linfeng Song, Dian Yu, Juntao Li, Zhuosheng Zhang, Rui Wang, Zhaopeng Tu, Haitao Mi, and Dong Yu. Thoughts are all over the place: On the underthinking of o1-like llms. CoRR , abs/2501.18585, 2025.

Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, Rui Wang, Zhaopeng Tu, Haitao Mi, and Dong Yu. Do NOT think that much for 2+3=? on the overthinking of o1-like llms. CoRR , abs/2412.21187, 2024.

Alejandro Cuadron, Dacheng Li, Wenjie Ma, Xingyao Wang, Yichuan Wang, Siyuan Zhuang, Shu Liu, Luis Gaspar Schroeder, Tian Xia, Huanzhi Mao, Nicholas Thumiger, Aditya Desai, Ion Stoica, Ana Klimovic, Graham Neubig, and Joseph E. Gonzalez. The danger of overthinking: Examining the reasoning-action dilemma in agentic tasks. CoRR , abs/2502.08235, 2025.

Xiaoye Qu, Yafu Li, Zhaochen Su, Weigao Sun, Jianhao Yan, Dongrui Liu, Ganqu Cui, Daizong Liu, Shuxian Liang, Junxian He, et al. A survey of efficient reasoning for large reasoning models: Language, multimodality, and beyond. arXiv preprint arXiv:2503.21614 , 2025.

Haotian Luo, Li Shen, Haiying He, Yibo Wang, Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning. CoRR , abs/2501.12570, 2025.

Pranjal Aggarwal and Sean Welleck. L1: Controlling how long a reasoning model thinks with reinforcement learning. arXiv preprint arXiv:2503.04697 , 2025.

Weizhe Yuan, Ilia Kulikov, Ping Yu, Kyunghyun Cho, Sainbayar Sukhbaatar, Jason Weston, and Jing Xu. Following length constraints in instructions. arXiv preprint arXiv:2406.17744 , 2024.

Bradley Butcher, Michael O'Keefe, and James Titchener. Precise length control for large language models. Natural Language Processing Journal , page 100143, 2025.

Chung-En Sun, Ge Yan, and Tsui-Wei Weng. Thinkedit: Interpretable weight editing to mitigate overly short thinking in reasoning models. arXiv preprint arXiv:2503.22048 , 2025.

David D Baek and Max Tegmark. Towards understanding distilled reasoning models: A representational approach. arXiv preprint arXiv:2503.03730 , 2025.

Yi Shen, Jian Zhang, Jieyun Huang, Shuming Shi, Wenjing Zhang, Jiangze Yan, Ning Wang, Kai Wang, and Shiguo Lian. DAST: difficulty-adaptive slow-thinking for large reasoning models. CoRR , abs/2503.04472, 2025.

Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling LLM test-time compute optimally can be more effective than scaling model parameters. CoRR , abs/2408.03314, 2024.

Zhiyuan Zeng, Qinyuan Cheng, Zhangyue Yin, Yunhua Zhou, and Xipeng Qiu. Revisiting the test-time scaling of o1-like models: Do they truly possess test-time scaling capabilities? CoRR , abs/2502.12215, 2025.

Weixiang Zhao, Xingyu Sui, Jiahe Guo, Yulin Hu, Yang Deng, Yanyan Zhao, Bing Qin, Wanxiang Che, Tat-Seng Chua, and Ting Liu. Trade-offs in large reasoning models: An empirical analysis of deliberative and adaptive reasoning over foundational capabilities. CoRR , abs/2503.17979, 2025.

Nina Rimsky, Nick Gabrieli, Julian Schulz, Meg Tong, Evan Hubinger, and Alexander Matt Turner. Steering llama 2 via contrastive activation addition. In ACL , 2024.

Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Jie Wang, Xiuyi Chen, Yingying Zhang, Fei Yin, Jiahua Dong, Zhijiang Guo, Le Song, and Cheng-Lin Liu. From system 1 to system 2: A survey of reasoning large language models. CoRR , abs/2502.17419, 2025.

Qiyuan Zhang, Fuyuan Lyu, Zexu Sun, Lei Wang, Weixu Zhang, Zhihan Guo, Yufei Wang, Irwin King, Xue Liu, and Chen Ma. What, how, where, and how well? A survey on test-time scaling in large language models. CoRR , abs/2503.24235, 2025.

Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. Language models are few-shot learners. In NeurIPS , 2020.

Wilson Wu, John X Morris, and Lionel Levine. Do language models plan ahead for future tokens? In COLM , 2024.

Tianyi Men, Pengfei Cao, Zhuoran Jin, Yubo Chen, Kang Liu, and Jun Zhao. Unlocking the future: Exploring look-ahead planning mechanistic interpretability in large language models. In EMNLP , pages 7713-7724. Association for Computational Linguistics, 2024.

Anthropic. On the biology of a large language model, March 2025. URL https:// transformer-circuits.pub/2025/attribution-graphs/biology.html .

Zhichen Dong, Zhanhui Zhou, Zhixuan Liu, Chao Yang, and Chaochao Lu. Emergent response planning in LLM. CoRR , abs/2502.06258, 2025.

Leheng Sheng, Changshuo Shen, Weixiang Zhao, Junfeng Fang, Xiaohao Liu, Zhenkai Liang, Xiang Wang, An Zhang, and Tat-Seng Chua. Alphasteer: Learning refusal steering with principled null-space constraint. arXiv preprint arXiv:2506.07022 , 2025.

Leheng Sheng, An Zhang, Yi Zhang, Yuxin Chen, Xiang Wang, and Tat-Seng Chua. Language representations can be what recommenders need: Findings and potentials. In ICLR , 2025.

Xiaohao Liu, Xiaobo Xia, Jiaheng Wei, Shuo Yang, Xiu Su, See-Kiong Ng, and Tat-Seng Chua. Calibrated multimodal representation learning with missing modalities. arXiv preprint arXiv:2511.12034 , 2025.

Yi Zhang, An Zhang, XiuYu Zhang, Leheng Sheng, Yuxin Chen, Zhenkai Liang, and Xiang Wang. Alphaalign: Incentivizing safety alignment with extremely simplified reinforcement learning. CoRR , abs/2507.14987, 2025.

Xiaohao Liu, Xiaobo Xia, See-Kiong Ng, and Tat-Seng Chua. Principled multimodal representation learning. arXiv preprint arXiv:2507.17343 , 2025.

Yuxin Chen, Yiran Zhao, Yang Zhang, An Zhang, Kenji Kawaguchi, Shafiq Joty, Junnan Li, Tat-Seng Chua, Michael Qizhe Shieh, and Wenxuan Zhang. The emergence of abstract thought in large language models beyond any language. CoRR , abs/2506.09890, 2025.

Xiaohao Liu, Xiaobo Xia, See-Kiong Ng, and Tat-Seng Chua. Continual multimodal contrastive learning. NeurIPS , 2025.

Kiho Park, Yo Joong Choe, and Victor Veitch. The linear representation hypothesis and the geometry of large language models. In ICML , 2024.

Guillaume Alain and Yoshua Bengio. Understanding intermediate layers using linear classifier probes. In ICLR (Workshop) , 2017.

Andy Arditi, Oscar Obeso, Aaquib Syed, Daniel Paleka, Nina Panickssery, Wes Gurnee, and Neel Nanda. Refusal in language models is mediated by a single direction. In NeurIPS , 2024.

Weixiang Zhao, Jiahe Guo, Yang Deng, Xingyu Sui, Yulin Hu, Yanyan Zhao, Wanxiang Che, Bing Qin, Tat-Seng Chua, and Ting Liu. Exploring and exploiting the inherent efficiency within large reasoning models for self-guided efficiency enhancement. CoRR , abs/2506.15647, 2025.

Tom Lieberum, Senthooran Rajamanoharan, Arthur Conmy, Lewis Smith, Nicolas Sonnerat, Vikrant Varma, János Kramár, Anca D. Dragan, Rohin Shah, and Neel Nanda. Gemma scope: Open sparse autoencoders everywhere all at once on gemma 2. CoRR , abs/2408.05147, 2024.

Tom Wollschläger, Jannes Elstner, Simon Geisler, Vincent Cohen-Addad, Stephan Günnemann, and Johannes Gasteiger. The geometry of refusal in large language models: Concept cones and representational independence. CoRR , abs/2502.17420, 2025.

Chenlu Ding, Jiancan Wu, Leheng Sheng, Fan Zhang, Yancheng Yuan, Xiang Wang, and Xiangnan He. Mllmeraser: Achieving test-time unlearning in multimodal large language models through activation steering. CoRR , abs/2510.04217, 2025.

Yihuai Hong, Dian Zhou, Meng Cao, Lei Yu, and Zhijing Jin. The reasoning-memorization interplay in language models is mediated by a single direction. arXiv preprint arXiv:2503.23084 , 2025.

Xinyu Tang, Xiaolei Wang, Zhihao Lv, Yingqian Min, Wayne Xin Zhao, Binbin Hu, Ziqi Liu, and Zhiqiang Zhang. Unlocking general long chain-of-thought reasoning capabilities of large language models via representation engineering. CoRR , abs/2503.11314, 2025.

Runjin Chen, Zhenyu Zhang, Junyuan Hong, Souvik Kundu, and Zhangyang Wang. Seal: Steerable reasoning calibration of large language models for free. arXiv preprint arXiv:2504.07986 , 2025.

Wes Gurnee and Max Tegmark. Language models represent space and time. CoRR , abs/2310.02207, 2023.

Kenneth Li, Aspen K. Hopkins, David Bau, Fernanda B. Viégas, Hanspeter Pfister, and Martin Wattenberg. Emergent world representations: Exploring a sequence model trained on a synthetic task. In ICLR , 2023.

Jonas Ranstam and Jonathan A Cook. Lasso regression. Journal of British Surgery , 105(10): 1348-1348, 2018.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research , 12:2825-2830, 2011.

Sam Marks and Max Tegmark. Diff-in-means concept editing is worst-case optimal, May 2024. URL https://blog.eleuther.ai/diff-in-means/ .

Mathematical Association of America. American invitational mathematics examination (aime), February 2024. URL https://maa.org/math-competitions/ american-invitational-mathematics-examination-aime .

Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, Jie Liu, Lei Qi, Zhiyuan Liu, and Maosong Sun. Olympiadbench: A challenging benchmark for promoting AGI with olympiad-level bilingual multimodal scientific problems. In ACL (1) , pages 3828-3850. Association for Computational Linguistics, 2024.

Abhinav Kumar, Jaechul Roh, Ali Naseh, Marzena Karpinska, Mohit Iyyer, Amir Houmansadr, and Eugene Bagdasarian. Overthink: Slowdown attacks on reasoning llms. CoRR , abs/2502.02542, 2025.

Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Hanjie Chen, Xia Hu, et al. Stop overthinking: A survey on efficient reasoning for large language models. arXiv preprint arXiv:2503.16419 , 2025.

Yann Dubois, Balázs Galambosi, Percy Liang, and Tatsunori B. Hashimoto. Length-controlled alpacaeval: A simple way to debias automatic evaluators. CoRR , abs/2404.04475, 2024.

Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. Measuring massive multitask language understanding. In ICLR . OpenReview.net, 2021.

An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu. Qwen2.5 technical report. CoRR , abs/2412.15115, 2024.

Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, Anirudh Goyal, Anthony Hartshorn, Aobo Yang, Archi Mitra, Archie Sravankumar, Artem Korenev, Arthur Hinsvark, Arun Rao, Aston Zhang, Aurélien Rodriguez, Austen Gregerson, Ava Spataru, Baptiste Rozière, Bethany Biron, Binh Tang, Bobbie Chern, Charlotte Caucheteux, Chaya Nayak, Chloe Bi, Chris Marra, Chris McConnell, Christian Keller, Christophe Touret, Chunyang Wu, Corinne Wong, Cristian Canton Ferrer, Cyrus Nikolaidis, Damien Allonsius, Daniel Song, Danielle Pintz, Danny Livshits, David Esiobu, Dhruv Choudhary, Dhruv Mahajan, Diego Garcia-Olano, Diego Perino, Dieuwke Hupkes, Egor Lakomkin, Ehab AlBadawy, Elina Lobanova, Emily Dinan, Eric Michael Smith, Filip Radenovic, Frank Zhang, Gabriel Synnaeve, Gabrielle Lee, Georgia Lewis Anderson, Graeme Nail, Grégoire Mialon, Guan Pang, Guillem Cucurell, Hailey Nguyen, Hannah Korevaar, Hu Xu, Hugo Touvron, Iliyan Zarov, Imanol Arrieta Ibarra, Isabel M. Kloumann, Ishan Misra, Ivan Evtimov, Jade Copet, Jaewon Lee, Jan Geffert, Jana Vranes, Jason Park, Jay Mahadeokar, Jeet Shah, Jelmer van der Linde, Jennifer Billock, Jenny Hong, Jenya Lee, Jeremy Fu, Jianfeng Chi, Jianyu Huang, Jiawen Liu, Jie Wang, Jiecao Yu, Joanna Bitton, Joe Spisak, Jongsoo Park, Joseph Rocca, Joshua Johnstun, Joshua Saxe, Junteng Jia, Kalyan Vasuden Alwala, Kartikeya Upasani, Kate Plawiak, Ke Li, Kenneth Heafield, Kevin Stone, and et al. The llama 3 herd of models. CoRR , abs/2407.21783, 2024.

Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph E. Gonzalez, Hao Zhang, and Ion Stoica. Efficient memory management for large language model serving with pagedattention. In Proceedings of the ACM SIGOPS 29th Symposium on Operating Systems Principles , 2023.

Naman Jain, King Han, Alex Gu, Wen-Ding Li, Fanjia Yan, Tianjun Zhang, Sida Wang, Armando Solar-Lezama, Koushik Sen, and Ion Stoica. Livecodebench: Holistic and contamination free evaluation of large language models for code. In ICLR . OpenReview.net, 2025.

A Implementation Details

We implement all the experiments on 8 NVIDIA A100 GPUs. The whole computational resource cost of this research is about 80 A100 GPU days, which is mainly spent on the answer generation.

For the answer generation, we use the vLLM [63] framework for acceleration. Following the suggestions of DeepSeek 3 , we set the temperature as 0.6 to prevent endless repetitions, set the maximum new generation length as 16,384, and set the rollout number as 8. We take the average accuracy of all 8 rollouts as the accuracy of one question, and report the final accuracy by taking the average accuracy of each question.

We use the following template for generation:

PROMPT:

Please reason step by step, and put your final answer within \boxed{}. This is the problem: {problem}

Here, the {problem} will be replaced by a real question. After we finish generation, we extract the answer inside the \boxed{} for evaluation.

B Reasoning Strength in LRMs is Pre-Planned

B.1 Experimental Details

We visualize the linear probing process in Figure 12. We first extract the activation of LRMs h ( l ) at the last token position. Then we train a linear regression for predicting the subsequent reasoning token number y , which is calculated through the tokenizer. For reducing the overfitting, we set the regularization term α in Equation 1 as 10.

Last token

h(l)

Linear

y

Reasoningtoken

activation

Predictor

number

LM

Tokenizer

Generation

Tokenizer

Compute:$1-2+3-4+5-\\dots+99-100$.<Think>

First,I'll..Next,..the sumbecomes50*(-1)=-50</Think>

B.2 Layer-wise Regression Results

We visualize the layer-wise regression results on R1-Distill-Qwen-14B and R1-Distill-Qwen-32B in Figure 13. On these two models, the linear regression exhibits the same pattern of an increasing trend as the model depth increases. Similarly, the correlation coefficient reaches over 0.8, indicating that the reasoning strength can be predicted before the model generation.

R

0.80

Spearman

0.75

0.70

0.65

S

0.60

5

1015202530354045

LayerIndex

0.85

0.80

0.75

0.70

0.65

0.60

0

51015202530354045505560

LayerIndex

(a) R1-Distill-Qwen-14B

(b) R1-Distill-Qwen-32B

C LRMs Encode Reasoning Strength via a Pre-allocated Direction Vector

C.1 Existence of Pre-allocated Direction Vectors for Reasoning Strength Control

We visualize the cosine similarity matrix of the four extracted vectors from R1-Distill-Qwen-14B and R1-Distill-Qwen-32B in Figure 14. We have a similar observation that all these vectors exhibit extremely high cosine similarities near 1.0. This indicates that LRMs actually use a single direction vector for distinguishing questions of different difficulty levels.

1.00

r2←1

1.00

0.99

0.98

0.95

0.75

0.50

r3+1

0.99

1.00

1.00

0.97

0.25

0.00

r4 1

0.98

1.00

1.00

0.99

0.25

0.50

r51

0.95

0.97

0.99

1.00

0.75

-1.00

(a) R1-Distill-Qwen-14B

1.00

r2←1

1.00

0.99

86'0

0.95

0.75

0.50

r31

0.99

1.00

1.00

86'0

0.25

0.00

r41

86'0

1.00

1.00

0.99

0.25

0.50

r5 -1

0.95

86'0

0.99

1.00

0.75

-1.00

(b) R1-Distill-Qwen-32B

We visualize the layer-wise mean cosine similarities between four extracted vectors from R1-DistillQwen-14B and R1-Distill-Qwen-32B in Figure 15. We observe that these vectors exhibit consistently high cosine similarities, with an increasing trend as the layer depth increases. Finally, the mean cosine similarity reaches around 1.0, indicating these vectors become a single direction vector in the later layers.

Similarity

1.0

0.8

0.6

0.4

MeanS

0.2

0.0

0

5

10152025 30354045

LayerIndex

(a) R1-Distill-Qwen-14B

(b) R1-Distill-Qwen-32B

MeanSimilarity

1.0

0.8

0.6

0.4

0.2

0.0

0

51015202530354045505560

LayerIndex

We visualize the L2 norm of these extracted four vectors from R1-Distill-Qwen-14B and R1-DistillQwen-32B in Figure 16. We observe that the norm of these vectors becomes bigger as the difficulty increases. Moreover, this trend is also similar to the increased reasoning token number as the difficulty increases, as shown in Figure 17. This indicates that LRMs use the magnitude of these direction vectors for handling different question difficulties.

(a) R1-Distill-Qwen-14B

160.0

48

45

140.0

40 3530252015

120.0

Index

Norm

100.0

80.0

Layer

2

60.0

40.0

10

20.0

5

0.0

0

r2←1

r3←1

r4 ←1

r5 ←1

(b) R1-Distill-Qwen-32B

300.0

40550545315205050

64

250.0

LayerIndex

Norm

200.0

150.0

2

100.0

50.0

0.0

r2←1

r3 ←1

r4 1

r5 +1

(a) R1-Distill-Qwen-14B

(b) R1-Distill-Qwen-32B

000S

Average Token Number

4000

3000

2000

1000

Level 1

Level 2

Level 3

Level 4

Level 5

5000

Average Token Number

0000

3000

2000

1000

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Level 2

Level 3

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Level 5

C.2 Pre-allocated Vectors Causally Affect the Reasoning Strengths

We apply the activation steering at each layer and each position of LRMs. We provide more results when steering with the pre-allocation vector r ( l ) , in Figure 18, Figure 19, and Figure 20. We have similar observations to those in Section 4.2. When steering with negative λ , we observe a consistent decreasing trend in the reasoning token number and the decreased performance. When steering with positive λ , we observe a consistent increasing trend in the reasoning token number. However, despite appropriate positive λ can improve the performance, this is not consistent as the λ increases. We attribute this to the capability upper bound of these LRMs. Moreover, the steering only affects the reasoning token number, while maintaining the answer token number largely unchanged. This indicates that the pre-allocated direction vector is mainly responsible for the reasoning token number.

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C.3 Pre-allocation Vectors Yield Positive Reasoning Token Number Prediction

We provide more results in predicting the reasoning token number directly using the pre-allocation vectors in Figure 21. As shown in this figure, in most cases, the pre-allocation vectors yield positive predictions, indicating the close correlation of such vectors with our obtained predictors. This suggests that LRMs are indeed using such pre-allocated vectors for planning their reasoning strength, and the predication also largely relies on these vectors.

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C.4 Pre-allocated Vectors Control Reasoning Strengths by Modifying Logits of </think>

We provide more results about how these pre-allocated direction vectors control the reasoning strength by modifying the logits of the end-of-reasoning token </think> .

We conduct the same activation steering as we do in Section 4.2, varying the steering strength λ from -0.2 to 0.2. Then, we directly extract the logits of each token at the last token position ( i.e., the start-of-reasoning <think> ). We visualize the results in Figure 22. We can observe that, as the steering strength λ increases from -0.2 to 0.2, the logits of the end-of-reasoning token </think> decrease. This indicates that LRMs are less likely to generate such tokens, thereby leading to more reasoning tokens. Moreover, as shown in Figure 22b, this steering mainly has more impact on the logits of </think> than randomly selected tokens and the EOS token <endoftext> . Here, the random token logits denote the average logits of 500 randomly selected tokens. This indicates that the steering mainly focuses on adjusting the reasoning strength by manipulating the </think> .

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Figure 22: The effect on the end thinking token </think> when steering with different strengths on R1-Distill-Qwen-7B. (8a) The pre-allocated vectors control the reasoning strength by causally affecting the logits of end-of-reasoning token </think> . (8a) The impact of logits on </think> is significantly higher than other tokens.

C.5 Pre-allocated Vectors Control Reasoning-related Token Logits

We further test the changes in the logits of reasoning-related tokens. We find that with a positive steering strength, the logits of complex reasoning-related tokens also increase, beyond merely decreased logits of the end-of-reasoning token </think> .

We report the changes in the logits for these reasoning-related tokens as follows in Table 2. These tokens are usually regarded as reflection patterns in the R1-style response. Increasing the logits of

Averagey()

these tokens increases the probabilities of reflection and increases of reasoning token numbers, and decreasing them has the opposite effect. As shown in Table 2, positive steering strengths increase the logits of these tokens while negative steering strengths decrease them. This indicates the reasoning strength control is not superficial.

Additionally, to further test whether simply changing the logits of the end-of-reasoning token can achieve the same performance, we conduct experiments by multiplying the logits of the end-ofreasoning token with a factor γ ( i.e., , logit new = γ ∗ logit old ). We report the results on MATH500 in Table 3. We find that naively changing the logits will lead to unstable manners, either leading to overly increased answer token number ( i.e., γ = 2 on R1-Distill-Qwen-7B) or easily leading to decoding errors ( i.e., γ = 0.8).

These results further suggest that the changes in the logits of the end-of-reasoning token are the result of planning, rather than the cause of planning.

D Potentials of Our Findings

D.1 Overthink Detection before Model Generation

In this section, we discuss whether our findings can help us detect the potential overthinking phenomenon even before the generation. To study this, we sample 100 questions from the AlpacaEval [59] dataset as the vanilla questions. We then generate one overthink question for each vanilla question, with the overthink attack [57], which proves to be effective in inducing overthink while maintaining the accuracy on vanilla questions. In this way, we can test whether our predictor can detect the overthink phenomenon in advance, by checking whether the predicted token number on overthink questions is much more than that on vanilla questions. Results in Section 5.1 show that our predictor shows potential in overthink detection.

D.2 Efficient Inference

D.2.1 Details

For evaluation efficiency, we sample 100 questions from MMLU [60] and transform them into single-choice questions for LRMs to answer. We adopt the same setting as in lm-evaluation-harness 4 for evaluation.

E Discussion

E.1 Generalization on More Domains

We discussed the generalization capabilities of our findings on other general domains beyond MATH, such as AlpacaEval and MMLU in Section 5, where our findings of reasoning strength prediction and strength control also hold on these two datasets. We also add one more experiment on the complex logic reasoning tasks such as GPQA diamond [9] and LiveCodeBench [64] to better demonstrate the generalization capabilities. As shown in Table 4 and Table 5, the number of reasoning tokens generally exhibits a similar pattern with the λ , indicating the generalization of this pre-allocation vector to other domains. Additionally, proper positive steering can also bring performance improvements. Since we found it hard to extract the generated code in a correct format for evaluation for code generation tasks when varying the response lengths, we just report the effect on the reasoning token numbers. There is only one exception on R1-Distill-Qwen-1.5B, where reducing the reasoning token number even brings the performance gain. We carefully analyze this model and find that when generating overlong responses, it tends to forget to follow the original instruction, and sometimes the results get cut off. Therefore, reducing the reasoning token number helps it avoid such bad issues like cut off, and increasing it will have the opposite effect.

E.2 Generalization on More Model Backbones

We add experiments on another kind of LRM DeepSeek-R1-Distill-Llama-8B [2]. All of our findings also hold on this model, and we will add more results in our paper. We illustrate some datapoints of our main observations on DeepSeek-R1-Distill-Llama-8B [2]. We report the linear probing results in Table 7, Table 8, and Table 9. We also report the activation steering results in Table 10. Interestingly, DeepSeek-R1-Distill-Llama-8B is more sensitive to the steering strength λ .

E.2.1 Case Study

Question:

Compute:

1

-

2 + 3

-

4 + 5

-···

+99

-

100

.

w/o Steering: <think> Okay, so I have this problem to compute the sum: 1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100. Hmm, that looks like an alternating series where the signs alternate between positive and negative. Let me try to figure this out step by step. First, let me write out the series to understand the pattern better: 1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100. I notice that this series alternates between adding an odd number and subtracting the next even number. So, each pair of terms is like (1 - 2), (3 - 4), (5 - 6), and so on. Maybe I can group them into these pairs and see what each pair adds up to. Let me compute a few pairs: 1 - 2 = -1, 3 - 4 = -1, 5 - 6 = -1, 7 - 8 = -1, ... It seems like each pair of terms adds up to -1. That's interesting. So, if I can figure out how many such pairs there are, I can multiply that number by -1 to get the total sum. Since the series starts at 1 and ends at 100, that's a total of 100 numbers. If I'm pairing them two by two, the number of pairs should be 100 divided by 2, which is 50. So, there are 50 pairs.

· · ·

That is, for each term, if n is odd, we add it, and if n is even, we subtract it. So, the general term

is

(

-

1)

(

n

+1)

∗

n

. Maybe I can use a formula for such alternating series. I remember that the

sum of an alternating series can sometimes be calculated using arithmetic series formulas or by

grouping terms. Wait, another approach: Maybe I can separate the series into two separate sums:

the sum of the odd terms and the sum of the even terms. Let's see: The series is 1 + 3 + 5 + ...

+ 99 minus (2 + 4 + 6 + ... + 100). So, if I can compute both of these sums separately, I can

subtract them to get the result. First, the sum of the odd numbers from 1 to 99. How many terms

are there? Since we're going up to 99, which is the 50th odd number (since 99 = 2*50 - 1). So,

the number of terms is 50.

· · ·

Wait, another way: Let's think about the series as telescoping. But I don't think it's telescoping because there's no cancellation beyond the immediate pairs. Each term cancels only part of the next term, but in this case, each pair is independent. Alternatively, maybe writing the series as: (1 - 2) + (3 - 4) + ... + (99 - 100). Each parenthesis is -1, and there are 50 of them. So, 50*(-1) = -50. Yep, same result. I think I've approached this problem in multiple ways: pairing terms, separating into odd and even sums, using the formula for alternating series, and each time I get -50. So, it seems pretty solid. Just to recap all the methods: 1. Pairing: Each pair (1-2), (3-4), etc., is -1, 50 pairs total, sum is -50. 2. Separating into odds and evens: Sum of odds is 2500, sum of evens is 2550, difference is -50. 3. Using the formula for the sum of an alternating series of consecutive integers with even terms: -n/2, which gives -50. All methods lead to the same conclusion, so I think it's safe to say the answer is -50. **Final Answer** The value of the series is \boxed{-50} </think> . (2253 tokens)

w Steering: <think> First, I observe that the sequence alternates between addition and subtraction of consecutive integers. To simplify the calculation, I can group the terms in pairs: (1 - 2), (3 - 4), (5 - 6), and so on, up to (99 - 100). Each pair results in -1. Since there are 100 numbers in total, there are 50 such pairs. Multiplying the number of pairs by each result gives 50 times -1, which equals -50. </think> (113 tokens)

Question:

What is the correct answer to this question:

Kant's humanity formulation of the

categorical imperative makes it impermissible for us to, he argues, Choices: (A) sell one of our

teeth. (B) engage in prostitution. (C) both A and B (D) Neither A nor B Only put the option

letter in the box, e.g.

boxedA. There is only one correct answer, .

w/o

Steering:

<think>

Okay, so I need to figure out what Kant's humanity formulation

says about selling one of our teeth or engaging in prostitution. Let me start by recalling what

the humanity formulation is. From what I remember, Kant's categorical imperative has several

formulations, and one of them is the humanity formulation. The key idea here is that we should

treat humanity, whether in oneself or in others, always as an end and never merely as a means

to an end. So, the question is asking which actions Kant would consider impermissible under

this principle.

The options are selling one's tooth, prostitution, both, or neither.

First, let me

break down each option. Selling a tooth: that's essentially selling part of your body. Now, in the

context of Kant's ethics, using oneself as a means to an end might be problematic.

· · ·

Wait, but what about the actual examples? I remember that Kant specifically mentions prostitution

in his works, right? He considered it immoral because it treats the person as an object for sexual

use, which is a means to an end. Similarly, selling body parts might be similar. But selling a

tooth is a physical part, whereas prostitution is an action. However, in both cases, the person

is using their body for monetary gain, possibly reducing themselves to a means. But maybe

Kant would say that selling a tooth is permissible if it's for a good reason, like saving a life, but

not sure. Wait, the formulation is about treating humanity as an end. So any action that uses

a person (including oneself) merely as a means would be wrong. So selling your tooth would

involve using your body as a means to get money, but does that mean you're treating yourself as

a mere means? Maybe. Because you're using your body as a commodity, rather than valuing

it as an end in itself. Alternatively, maybe Kant would distinguish between selling a tooth (a

part) and selling services (like prostitution). But I think both involve commodifying the body.

So perhaps both are impermissible. Thus, the answer would be (C) both A and B.

· · ·

Alternatively, maybe he only opposes prostitution, but I think both. Let me think again. Another

angle: the humanity formulation requires that in any action, you never use a person merely as a

means. So if you sell your tooth, you are using yourself as a means (to get money), but you're

also an end. However, if you are selling a tooth, maybe you are treating yourself as an end in

some way. Wait, perhaps the distinction is whether you are using your body as a mere means.

If you sell a tooth, you are using that part of your body as a tool, but does that mean you are

treating your humanity as a means? The humanity is your rational nature. So maybe selling a

tooth doesn't directly violate that, as it's a physical part. Alternatively, Kant might argue that the

body is part of what makes a person, so using it as a commodity reduces oneself. So perhaps

both are wrong. Since I'm a bit torn here, but I think the standard interpretation is that Kant

would say both are impermissible. Hence, answer (C).

</think>

. (1610 tokens)

w

Steering:

<think>

"Okay, so I need to figure out what the answer is here. The question

is about Kant's humanity formulation of the categorical imperative and what he says is imper-

missible. The options are selling a tooth, prostitution, both, or neither. First, I remember that

Kant's categorical imperative has different formulations.

· · ·

So both selling a tooth (if it's your own) and prostitution would be impermissible because both

involve treating humanity (either your own or someone else's) as a means. So the answer should

be C, both A and B? But wait, maybe selling a tooth isn't considered the same as prostitution?

Like, a tooth is part of your body but maybe it's not using humanity as an end? Hmm, but Kant

might say that even your own body shouldn't be treated merely as a resource to exploit for gain.

So selling a tooth could still be wrong because you're using your own body as a means to an end

(making money) rather than respecting your own humanity as an end in itself. So both A and B

are impermissible. Therefore, the answer should be C. "

</think>

(418 tokens)

F Broader Impacts

This paper aims to investigate whether LRMs pre-plan their reasoning strength within their activation space, and how such planning is encoded with pre-allocated direction vectors. Our study contributes to a deeper understanding of LRMs within the LLM research community.

However, our findings may also pose potential risks. For instance, malicious methods could exploit the discovered property that reasoning length can be manipulated through the model's internal activations to implant backdoor attacks. Such attacks might trigger excessively long chains of thought under specific conditions, thereby significantly slowing down model execution.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper uses techniques from mechanistic interpretation to identify a directional vector which corresponds to the number of thinking tokens used by Qwen reasoning models prior to reaching a final answer. They show that this direction vector exists prior to the beginning of token generation, and that changing it effects the number of tokens generated. They also show improvements in performance on math olympiad benchmarks simply by increasing the activation of this vector a small amount.\n\nSTRENGTHS AND WEAKNESSES:\n**Quality:**\n\n*Strengths:* The results seem to be technically sound, and the methods are logical. The finding that a single dimension largely controls the length of LLM generations is likely to be true given the evidence provided.\n\n*Weaknesses:* As the authors acknowledge, the paper is narrow in focus, testing only Qwen models and evaluating performance only on math olympiad benchmarks (with a bit of physics). This raises the important question: are the results a training artefact from how the Qwen models were trained for math olympiad puzzles? I do think this is a serious concern, particularly when the claims made refer to \"planning\" which may just be a recognizing of a certain type of problem from pre-training. I would strongly encourage showing results on another type of reasoning benchmark. \n\nTwo other methodological concerns: \n\n- The results on L222 about \"moderate\" steering seem difficult to use in practice. How would we predict how much steering is beneficial versus harmful? Without a principled reason to use this amount of steering, the results in Table 1 are an  unfair comparison.\n\n- The paper consistently claims that allocating more or less tokens is a planning strategy related to reasoning strength. However, I am not convinced by the connection made between \"length\" and \"strength\". Other works have found that models can overthink (e.g. https://arxiv.org/abs/2502.07266) and have lower performance with more tokens. \n\n**Clarity:** \n\n*Strengths:* The submission is generally well-organized. The text is clearly written. \n\n*Weaknesses:* The organization of the sections is a bit confusing. There are a number of sections which jump back and forth between methods and results, but only one section called results. The placement of the figures is also annoyingly far from the references in the text, though less of this blame falls on the authors.\n\n**Significance/Originality:** \n\n*Strengths:* The paper makes a useful contribution to controlling the behavior of reasoning LLMs. The work is original to my knowledge and could be useful for improving training methods in future models.\n\n*Weaknesses:* The methods themselves are not original, but this is not the intention of the paper.\n\nQUESTIONS:\n1. How do we know that these results are not an artefact of training Qwen to solve math olympiad problems? I would strongly encourage you to show results on another reasoning benchmark, since the three shown are fundamentally the same domain. A logical reasoning benchmark without mathematics would be ideal. Including another model would be nice, but less important.\n\n2. Can you get a similar effect simply by prompting the model to use more thinking tokens? Does doing so change the activations in this vector?\n\n3. Under what conditions does more reasoning lead to better responses? Can you tell when using this vector would be helpful versus harmful?\n\nLIMITATIONS:\nYes, though I think some of the weaknesses should be addressed in more detail as described above.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper investigates the underlying mechanisms of reasoning strength planning in Large Reasoning Models (LRMs) and reveals that these models pre-allocate reasoning strength before generation. The authors employ linear probing and activation steering techniques to demonstrate that: (1) LRMs can predict the required reasoning token count solely from question activations before generation; (2) LRMs encode reasoning strength through pre-allocated directional vectors in activation space, where vector magnitude modulates reasoning strength; and (3) these vectors causally control reasoning by affecting the logits of the end-of-reasoning token. At the same time, it put forwards two important applications of this finding on solving overthinking and improving reasoning efficiency. Overall, this paper is well structured and presents novel insights that advance our understanding of how LRMs manage computational resources during reasoning tasks. The findings have both theoretical significance and practical implications for optimizing reasoning performance in large language models.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n\n•\tThis paper fills the gap that provide the first systematic investigation into the internal mechanisms of reasoning strength planning in LRMs, addressing an important gap in understanding how these models automatically allocate computational resources. The findings are well presented and the experimental designs are clearly articulated.\n\n•\tThis paper applies solid analysis approach through the combination of linear probing and activation steering, which provides compelling evidence for the existence of pre-allocated reasoning strength vectors. In addition, the causal intervention experiments using activation steering effectively demonstrate the functional role of these vectors.\n\n•\tThis paper provides comprehensive analysis including compariing the actiavtion directions and magnitudes across different difficulty levels and invetiagting on the effect of activation magnitude steering and enhancement to the reasoning token length. \n\n•\tThis paper provides insights of concrete applications including overthinking detection and efficient inference, showing the potential real-world value of these findings.\n\nWeakness:\n\n•\tFirstly, domain limitation, the analysis is predominantly conducted on mathematical reasoning tasks. While as stated in introduction, coding generation tasks also require reasoning, the author may consider adding experiments in section 4 with coding generation dataset. At the same time, the author may consider adding experiments with reasoning VLMs to test on different scenarios other than LLMs.\n\n•\tSecondly, insufficient analysis of counter cases, the paper doesn’t thoroughly analyze the cases where the model doesn’t follow the founded relationships between reasoning token lengths and activation magnitude. For example, as noted in the introduction, post-training methods such as SFT and RL can affect reasoning strength. The authors should consider incorporating counter-case analyses, such as comparative experiments between pre-trained and post-trained models, to strengthen their claims.\n\n•\tThirdly, limited baseline comparisons and evaluation. The author may consider comparing with alternative methods for reasoning length control while maintaining accuracy. Moreover, in section 5.2, the authors should expand their evaluation beyond easy tasks to include harder tasks, examining whether activation steering causes significant degradation in accuracy performance on harder tasks.\n\nQUESTIONS:\n1. For results shown in figure 7, the predicted token length $y ̂^{(l)}$ exhibit high volatility across different layers, with some predictions even showing negative values. Why This appears inconsistent with the findings in Figure 2, where deeper layers theoretically should yield more accurate and stable predictions. For example, in figure 7(a), layers 20-25 demonstrate high Spearman correlation coefficients in Figure 2(a), yet the predicted token lengths in these deeper layers are relatively small and sometimes negative. This discrepancy warrants further explanation regarding why high correlation does not translate to more reasonable absolute predictions.\n\n2. For figure 8, why not include results from larger models 32B? Cause Based on previous findings, larger models appear to better align with the hypothesis. For instance, in Figure 2, the Spearman correlation coefficients for the 32B model are consistently high across most layers, and in Figure 5, the L2 norm changes are more pronounced for the 32B model.\n\n3. Regarding the results in Figure 10 using the MATH dataset, QwQ-32B shows significantly less reduction in token length after steering compared to R1-Distill-Qwen-32B. Is this difference due to the use of a different negative steering strength $λ$, or are there other factors?\n\n4. In section 5.2, for the experiments shown in figure 10, how to define the \"proper negative steering strength $λ$ \"?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-27"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies LLMs' internal representations related to their output CoT lengths. It finds that representations right after the question encodes the CoT length to some degree using a linear probe. Further, it finds a vector direction that correlates with the length. Finally, it is shown that altering internal representation using this vector does change the resulting CoT lengths.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper looks into an interesting topic of CoT length. Its finding about internal representations corresponding to CoT lengths is intriguing, especially because it is measured before the CoT begins. There is also a practical application of this finding to change output CoT lengths. However, I have several concerns:\n\n- As the authors discuss, it is possible that this internal vector might be controlling the output probability of </thought> token. Such a superficial control would be less interesting because one can directly control that token probability instead. So this can be another baseline where one simply controls this token probability by manually increasing it or decreasing it.\n\n- Another question I have is about the strength of this correlation. How strong is spearman R 0.84? If one makes a prediction using it, what would be the average error in percentage? Knowing this will help one to get intuitive feeling about the accuracy. Another possible analysis to compare two random CoTs from the same question. How strongly they will correlate? Multiple responses sampled will have differing lengths for the same question.\n\n- About the practical application, it seems only small performance gain can be achieved with this method. As the CoT length increase, the performance actually drops as shown in fig6. This of course limits the application of this work.\n\nQUESTIONS:\n- it is not clear which layer's representation is chosen in the experiments. For example, how is it chosen for fig6? Does each lambda value use a different layer, or it is shared?\n- similar to above, how is lambda chosen for tab1 results? what are the actual values? (can be written in the table) Also the same questions for fig10.\n- why fig2c has x=0 point but not the others?\n- about sec5.1, does the overthink questions actually do have longer responses? how much longer in average?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper investigates the internal mechanisms behind how Large Reasoning Models (LRMs) adjust their reasoning strength (i.e., the number of reasoning tokens generated) based on task difficulty. The authors propose that LRMs encode a pre-allocated directional vector in the activation space before generating any reasoning tokens. This vector’s magnitude correlates with the difficulty of the task and modulates reasoning length. Through linear probing and activation steering, the paper shows: 1) Reasoning length is predictable from pre-generation activations. 2) A consistent direction in activation space correlates with task difficulty. 3) Manipulating this vector causally affects reasoning length and performance. 4) The vector modifies the logits of the end-of-reasoning token </think>. Two applications are demonstrated: predicting overthinking before generation and reducing unnecessary reasoning on simple tasks for efficiency.\n\nSTRENGTHS AND WEAKNESSES:\n## Strength \n\n- Addresses an important mechanistic question about reasoning strength in LRMs with practical applications for overthinking detection and efficient inference\n- Clear research questions and logical progression from hypothesis to validation. \n- Well-designed experimental framework using linear probing to test the pre-planning hypothesis.\n- The authors provide validation across multiple model sizes and datasets. The results are promising, e.g., moderating positive steering shows potential in enhancing performance across other math datasets, including MATH500, AIME, and OlympiadBench. \n\n\n## Weaknesses \n\n\n1. Scope & Generalizability:\n- Experiments focus primarily on mathematical reasoning (MATH). Unclear if findings generalize to other reasoning domains (logical reasoning, coding, etc.). Given the current results, authors might consider revising the scope to acknowledge this as a focused study on mathematical reasoning, rather than general claims about reasoning mechanisms in LRMs. \n- Heavy reliance on Qwen-based models with limited validation on other model families (e.g., LLaMA, Mistral, GPT-based models)\n\n2. Methodological/Experimental Design Justification:\n- For linear probing, the choice of residual stream activations at each layer lacks justification. Why not use input embeddings at each layer or other activation representations?\n- Equation 1 presents a regularized loss with hyperparameter $\\alpha$  without discussion of how this hyperparameter $\\alpha$ is selected. Additionally, the rationale for choosing Lasso (L1) regression (e.g., over L2 regularization) is not provided.\n- For activation steering (Section 4.2), it's unclear whether steering applies to every transformer layer $l$ or only specific layers\n- Table 1 doesn't specify how the steering strength $\\lambda$ is selected across different benchmarks. Are values consistent across tasks or require task-specific tuning?\n\n3. Analysis: \n- Section 3.2: The linear predictor is both trained and tested on MATH. It's unclear whether separate predictors are trained for each difficulty level or if a single joint predictor handles all difficulties. Can this predictor accurately predict token lengths for other mathematical reasoning tasks beyond MATH?\n\n- Figure 2 reports only correlation coefficients without accuracy metrics. For practical understanding, concrete examples would be helpful: given an actual token length y for question x, what is the predicted length y' and the absolute error?\n\n- While Section 3.2 observes that deeper layers yield better predictions, but it lacks explanation for why reasoning planning capabilities develop in later layers.\n\n- Figure 7 appears inconsistent with Figures 2/4: while later layers show better prediction accuracy in Figure 2, Figure 7 shows seemingly random results across layers without clear layer-specific accuracy patterns.\n\n4. Baseline and Comparison Issues:\n- Figure 3 and lines 181-182 claim high cosine similarity between vectors, but without proper baselines, these absolute similarity values lack context. A baseline comparing difference-in-mean vectors from randomly sampled question pairs might strengthen the argument.\n\n- Figures 6 and 7 should be presented together for direct comparison between actual and predicted token lengths. The predicted token lengths in Figure 7 (≈4000, 3500, 2000) don't align well with actual lengths from the models (≈5000, 4000, 8000 under λ=0.2), suggesting prediction limitations that need addressing.\n\n\n5. Application Practicality\n-  Section 5.1's overthinking detection is interesting, but how should practitioners determine token length thresholds for detecting attacks? The current approach compares predictions before/after attacks, but real-world scenarios require determining if a single question represents vanilla or attack conditions without prior knowledge. \n\n\n\n\n6. Related work:\n- The probing analysis would benefit from discussing related work on reasoning interpretability in language models, such as [1] \n\n7. Minor: \n- Typo \"b\" in line 107\n- Inconsistent difficulty level numbering: line 176 mentions difficulty 0, while Equation 2 and line 178 refer to easiest difficulty level as 1.\n\n\n \nReference \n\n- [1] Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process. ICLR 2025\n\nQUESTIONS:\nsee the Weaknesses part\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-07"}