Title: Mitigating Overthinking in Large Reasoning Models via Manifold Steering
Venue: NeurIPS 2025
Accepted: yes
Keywords: Large Reasoning Models

Overthinking

Mechanistic Interpretability

Manifold Steering
Abstract: Recent advances in Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in solving complex tasks such as mathematics and coding. However, these models frequently exhibit a phenomenon known as *overthinking* during inference, characterized by excessive validation loops and redundant deliberation, leading to substantial computational overheads. In this paper, we aim to mitigate overthinking by investigating the underlying mechanisms from the perspective of mechanistic interpretability. We first showcase that the tendency of overthinking can be effectively captured by a single direction in the model's activation space and the issue can be eased by intervening the activations along this direction. However, this efficacy soon reaches a plateau and even deteriorates as the intervention strength increases. We therefore systematically explore the activation space and find that the overthinking phenomenon is actually tied to a low-dimensional manifold, which indicates that the limited effect stems from the noises introduced by the high-dimensional steering direction. Based on this insight, we propose **Manifold Steering**, a novel approach that elegantly projects the steering direction onto the low-dimensional activation manifold given the theoretical approximation of the interference noise. Extensive experiments on DeepSeek-R1 distilled models validate that our method reduces output tokens by up to 71\% while maintaining and even improving the accuracy on several mathematical benchmarks. Our method also exhibits robust cross-domain transferability, delivering consistent token reduction performance in code generation and knowledge-based QA tasks. Code is available at: https://github.com/Aries-iai/Manifold_Steering.

Mitigating Overthinking in Large Reasoning Models via Manifold Steering

Abstract

Recent advances in Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in solving complex tasks such as mathematics and coding. However, these models frequently exhibit a phenomenon known as overthinking during inference, characterized by excessive validation loops and redundant deliberation, leading to substantial computational overheads. In this paper, we aim to mitigate overthinking by investigating the underlying mechanisms from the perspective of mechanistic interpretability. We first showcase that the tendency of overthinking can be effectively captured by a single direction in the model's activation space and the issue can be eased by intervening the activations along this direction. However, this efficacy soon reaches a plateau and even deteriorates as the intervention strength increases. We therefore systematically explore the activation space and find that the overthinking phenomenon is actually tied to a low-dimensional manifold, which indicates that the limited effect stems from the noises introduced by the high-dimensional steering direction. Based on this insight, we propose Manifold Steering , a novel approach that elegantly projects the steering direction onto the low-dimensional activation manifold given the theoretical approximation of the interference noise. Extensive experiments on DeepSeek-R1 distilled models validate that our method reduces output tokens by up to 71% while maintaining and even improving the accuracy on several mathematical benchmarks. Our method also exhibits robust cross-domain transferability, delivering consistent token reduction performance in code generation and knowledge-based QA tasks. Code is available at: https://github.com/Aries-iai/Manifold_Steering.

1 Introduction

Building on the versatility of Large Language Models (LLMs) in text generation, particularly their emergent ability in chain-of-thought (CoT) reasoning [41], the field is now undergoing a transition toward Large Reasoning Models (LRMs). Exemplified by the OpenAI o-series [28] and the DeepSeekR1 series [14], LRMs acquire internal capabilities for long-horizon reasoning through reinforcement learning with verifiable rewards. These models are able to explore diverse solution paths, reflect on potential errors, refine intermediate steps, and validate final outputs, mimicking the process of human problem-solving by scaling inference-time computations [28]. As a result, they excel in domains such as mathematics [1, 23, 39] and coding [27, 43, 44]. This makes them well-suited for tasks that demand deep logical analysis and paves the way for their applications in more complex scenarios, including web search [19] and research assistance [49].

However, despite the remarkable reasoning capabilities, LRMs often suffer from a critical efficiency issue known as overthinking [35], where they generate excessive and unnecessary reasoning steps, even for simple questions. For example, when tasked with a straightforward calculation, like ' 2 + 3 ' [9], an LRM might redundantly validate its approach or explore irrelevant alternatives, significantly increasing the computation overloads. This overthinking not only impacts inference latencies, posing great challenges for time-critical applications, but also risks degrading performance by entangling the model in repetitive verification loops or unproductive reasoning paths [9, 16, 40]. To mitigate such overthinking in LRMs, several approaches [3, 8, 16, 22] have recently been proposed. They often utilize external mechanisms to regulate reasoning and prevent overthinking, which can incur additional computational overhead for probing [16] or be susceptible to performance degradation due to the reliance on external models [22]. While these methods address overthinking from external and behavioral perspectives - relying on human-designed workflows and interventions, the underlying mechanism remains underexplored, posing significant challenges to achieving intrinsic mitigation.

In this paper, we address the overthinking problem of LRMs through mechanistic interpretability [50], based on an in-depth analysis of their internal states. Specifically, we attribute this phenomenon to the distinctive activation patterns in the deeper layers of the model and identify a single, interpretable direction by comparing the differences in the activations between overthinking and concise reasoning. By manipulating the activations along this direction, we can effectively steer the model away from overthinking tendencies. However, this intervention is insufficient to fully resolve the problem. As in Fig. 2(a), the reduction in output tokens does not consistently scale with increasing intervention strength. This suggests that the computed steering direction is not accurate enough and introduces unintended interference noise .

To address this issue, we further analyze the model's activation patterns and find that the overthinking phenomenon is intrinsically tied to a low-dimensional manifold, which can be well approximated by a linear subspace. This result sheds light on why high-dimensional steering directions often introduce noises, as they fail to align with the underlying structure of model activations. To more effectively mitigate overthinking, we introduce a Manifold Steering method to align the steering direction with the reconstructed low-dimensional manifold. We first theoretically derive a linear approximation of the amplitudes of the interference noise and then project the steering direction by nullifying this approximated term. In this way, we can effectively purify the steering direction and better mitigate the overthinking issue with larger intervention strength, as depicted in Fig. 2(a).

Extensive experiments on multiple DeepSeek-R1 distilled models [14] of different sizes verify the effectiveness of our manifold steering method. We first test it on mathematical datasets of varying difficulty, including GSM8K [10], Math500 [20], AMC2023 [24], and AIME2024 [25]. Our method achieves up to 71% tokens reduction while consistently maintaining or improving accuracy. Moreover, it exhibits robust cross-domain transferability, delivering consistent mitigation effects in tasks such as LiveCodeBench [18] (code generation) and Diamond-GPQA [32] (knowledge-based QA), surpassing existing methods in both overthinking mitigation and accuracy preservation.

2 Related Work

Mechanistic Interpretability. Mechanistic interpretability [5, 11, 26, 29, 31, 34, 37, 50] seeks to reverse-engineer the internal computations of LLMs to uncover the causal mechanisms underlying their behavior, offering fine-grained insights into learned representations and decision processes. A key technique within this framework involves identifying steering directions [29, 34, 37]-linear vectors in the activation space that correspond to specific model behaviors. By manipulating these directions during inference, researchers can precisely control outputs, such as ablating refusal behaviors in safety-critical scenarios [2, 45]. Similarly, Cao et al. [7] proposed Bi-directional Preference Optimization (BiPO), leveraging steering vectors derived from contrasting human preference pairs to customize attributes like truthfulness and hallucination. These approaches highlight the versatility of steering directions in manipulating models' behaviors. Additionally, some efforts have explored dimensionality reduction in activation spaces: [6] use SVD-based spectral filtering to suppress noise in residual streams, while others derive steering directions from probabilistic classification of user history for multi-preference alignment [33]. Our work extends this paradigm to address overthinking in LLMs [9, 16, 35], a phenomenon characterized by redundant or divergent reasoning trajectories. By analyzing the latent space, we identify a steering direction that encapsulates overthinking and

further propose manifold steering , a novel method that projects this direction onto a low-dimensional manifold to mitigate interference noise, thereby improving its performance.

Overthinking Mitigation. Efforts [3, 8, 16, 22, 30, 42] to mitigate overthinking in LRMs have gained traction as a means to enhance inference efficiency and output quality. Among them, the training-based method [30] tend to modify the reward function for length control in reinforcement learning. However, these incur significant computational costs and are orthogonal to inference-time interventions like ours, thus warranting no direct comparison in this work. Existing training-free methods mainly rely on external mechanisms to regulate reasoning. For instance, Dynasor [16] employs periodic monitoring to detect and halt redundant reasoning, incurring computational overhead, while Thought Manipulation [22] uses auxiliary models to guide inference, limited by the external model's performance. These shortcomings suggest that a more fundamental solution lies in understanding and modifying the model's internal reasoning processes. Though some concurrent works [3, 8] have tried to leverage mechanistic interpretability for achieving it, they only partially reduce overthinking, quickly encountering bottlenecks due to interference noise in high-dimensional steering directions. In contrast, we propose manifold steering to project the steering direction onto a low-dimensional manifold, effectively eliminates interference noise, achieving superior overthinking mitigation and substantial token reductions across diverse tasks, as demonstrated in Sec. 5.2.

3 Mechanistic Analysis of Overthinking

In this section, we investigate the phenomenon of overthinking within the activation space of Large Reasoning Models (LRMs) and identify a general mechanism by which ablating a single direction in the activation space can reduce redundant reasoning steps to some extent.

3.1 Background

Transformers. Decoder-only transformer language models [21, 38] map an input token sequence x = [ x 1 , . . . , x T ] to a probability distribution over the vocabulary for next-token prediction. Each token x i is associated with a sequence of residual stream activations h ( l ) ( x i ) ∈ R d across L layers, initialized by the token embedding h (0) ( x i ) = Embed ( x i ) . At each layer l ∈ { 1 , . . . , L } , the residual stream h ( l ) ( x i ) is updated by combining the previous layer's activation h ( l -1) ( x i ) with two components: (i) a multi-head self-attention mechanism, which computes a ( l ) ( x 1: i ) by attending to prior tokens { x j : j ≤ i } using a causal mask to enforce autoregressive context flow; and (ii) a multi-layer perceptron (MLP), which applies non-linear transformations to the post-attention state h ( l -1) ( x i ) + a ( l ) ( x 1: i ) and produces m ( l ) ( x i ) . The whole update is expressed as follows:

Through autoregressive aggregation, each h ( l ) ( x i ) aggregates context from prior tokens, with the final token's residual stream h ( l ) ( x ) : → h ( l ) ( x T ) encapsulating the entire input's context.

Large Reasoning Models. LRMsare tailored for complex problem-solving and instruction-following, which leverage structured templates to handle user inputs:

where the content following <think>\n comprises the model's reasoning process and final answer, separated by </think> . Despite the excellent reasoning capabilities of these models, they often exhibit the overthinking phenomenon [9, 12] during the reasoning process, characterized by repetitive validation or redundant deliberation. As a high-level cognitive phenomenon, overthinking may manifest in the model's residual stream activations, similar to other abstract concepts such as safety [5] and honesty [50], as widely studied from the perspective of mechanistic interpretability. This suggests that overthinking and concise reasoning exhibit distinct activation patterns. In the next section, we systematically examine this hypothesis and investigate whether these activation differences are sufficient to identify a specific direction that characterizes overthinking - one that, if isolated, could be ablated to improve reasoning efficiency.

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3.2 Extracting and Ablating an Overthinking Direction

Before extracting an overthinking direction, we first investigate whether the residual stream activations corresponding to redundant and concise reasoning are separable in the model's activation space, as this is a necessary condition for identifying a meaningful and controllable direction. Drawing on [16], we also focus on mathematical problems, where the overthinking phenomenon is particularly pronounced. To construct representative data, we first randomly sample questions from the OpenMathInstruct-2 training set [36]. For each model, five responses per question are independently generated. Based on these responses, we construct two model-specific datasets 2 as follows:

Redundant set D redundant: consists of questions for which all five responses exceed 16k tokens and contain hesitation keywords (e.g., ' wait ', ' alternatively ', etc.) surpassing a specified number.

Concise set D concise: consists of questions for which all five responses are under 1k tokens and contain none of the hesitation keywords.

As demonstrated in Fig. 1, we visualize the distribution of residual stream activations h ( l ) ( x ) for both D redundant and D concise across different layers of R1-7B. We observe that, while early layers exhibit substantial overlap between the two distributions, the middle-to-late layers display clear separation. This separation indicates that the overthinking phenomenon is more prominent in specific layers and provides empirical support for identifying a meaningful overthinking direction.

We use the difference-in-means technique [4] for extracting the steering direction, which computes the mean difference in residual stream activations between the redundant and concise data for each layer l . The overthinking direction r ( l ) is then defined as:

where h ( l ) ( x ) denotes the residual stream activation of the final token of input x at layer l , with x being the prompt concatenated with the response for x ∈ D redundant but only the prompt for x ∈ D concise. The direction r ( l ) is normalized to unit length, i.e., r ( l ) = r ( l ) / ∥ r ( l ) ∥ 2 . Following [2], we also select the single most effective direction r ( l ∗ ) and apply it for intervention across all layers.

Finally, to further explore the role of the overthinking direction r ( l ∗ ) in the model's computations, we ablate the component aligned with r ( l ∗ ) each residual stream activation h . Specifically, the modified activation h ′ is computed as:

where α controls the intervention strength. We apply this ablation to every activation h ( l ) ( x i ) , across all layers l and token positions i . The parameter α allows adapting the extent of overthinking mitigation, balancing the reduction of redundant reasoning with the problem-solving accuracy.

4 Manifold Steering for Robust Intervention

Following our mechanistic analysis in Sec. 3, which identifies a single direction capturing overthinking in the model's activation space, we proceed to explore whether increasing the intervention strength α further reduces redundant reasoning, as expected.

4.1 Low-Dimensional Manifold Analysis

To rigorously evaluate the effect of increasing intervention strength α for the direction r ( l ∗ ) , derived via Eq. (2), we test R1-7B's performance on the Math500 dataset [20], a diverse mathematical test set, different from the anchor dataset used in Sec. 3.2.

Formulation of Interference Noise. As illustrated in Fig. 2(a), increasing the intervention strength α initially reduces the token count. However, beyond a certain threshold, the token count ceases to decrease, and as α continues to increase beyond 1 . 5 , it rebounds, even nearly returning to levels observed without intervention. This suggests that the intervention direction r ( l ∗ ) may be imprecise and introduces unintended noise in the model's activation space, which is defined as interference noise . Meanwhile, we confirm the model collapse caused by interference noise, as below:

Instruction: What power of 4 is equal to 8? Express your Response: 10000000000000000000000 · · ·

answer.

Thus, we can hypothesize that the r ( l ∗ ) , computed via the difference-in-means method in R d , comprises both the overthinking direction r overthinking and an orthogonal 3 interference component r other , such that r ( l ∗ ) = r overthinking + r other . The Eq. (3) actually modifies the activation as follows:

The r other term perturbs h ′ ( l ) ( x i ) , potentially disrupting unrelated capabilities such as normal expression, especially for large α . This interference explains the token count rebound beyond α = 1 . 5 , as the intervention affects dimensions irrelevant to overthinking.

Linear Low-Dimensional Manifold Verification. As shown above, the direct computation of difference in high-dimensional activation space leads to noisy estimation due to the existence of the interference part r other . A straightforward solution is to estimate the amplitude of r other and remove its influence from the steering direction r ( l ∗ ) . However, it is orthogonal to the overthinking direction r overthinking and is decided by the space of r overthinking . Inspired by prior work [15] that the activations in LLMs reside on a low-dimensional manifold M⊂ R d , it is reasonable to assume that r overthinking , representing the shift between activations of redundant and concise reasoning paths, also falls into this manifold. To verify this, we employ a simple linear method - Principal Component Analysis (PCA), on the activations from the complete reasoning dataset D reasoning = D redundant ⋃ D concise at layer l . Let A ( l ) = [ h ( l ) ( x 1 ) , . . . , h ( l ) ( x N )] ∈ R d × N denote the matrix of activation vectors h ( l ) ( x i ) ∈ R d for inputs x i ∈ D reasoning. We compute the covariance matrix and its eigendecomposition as:

where ¯ A ( l ) = 1 N ∑ N i =1 h ( l ) ( x i ) , U ( l ) ∈ R d × d contains the principal components, Λ ( l ) = diag ( λ ( l ) 1 , . . . , λ ( l ) d ) , and VR ( k ) = ∑ k i =1 λ ( l ) i ∑ d i =1 λ ( l ) i is the variance ratio. As Fig. 2(b) shows, the top k = 10

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Figure 2: (a) Performance of R1-7B with varying α for direct and manifold steering on Math500. (b) Cumulative variance ratio of R1-7B's activation space on D redundant across different hidden layers.

components account for over 70% of the variance, indicating that the effective dimension of M , denoted d eff, is significantly smaller than the ambient dimension d . This confirms the low-dimensional structure of M . This also suggests that the linear manifold composed by the orthogonal basis effectively captures the activations of reasoning trajectories and therefore overthinking direction r overthinking

can be estimated using simple linear dimensionality reduction in this subspace. Eventually, this finding supports our earlier hypothesis (Eq. (2)) that the steering direction r ( l ∗ ) = r overthinking + r other includes an orthogonal interference component r other , which falls into M ⊥ .

4.2 Theoretical Analysis of Interference Noise

As discussed in Sec. 4.1, the overthinking phenomenon is tied to the low-dimensional manifold structure of the activation space. The overthinking direction r ( l ∗ ) , computed via Eq. (2), introduces an orthogonal interference component r other due to computation in high-dimensional spaces. When the activation dimension d far exceeds the sample size N ( d ≫ N ), interference noise even accumulates in M ⊥ , inflating r other and disrupting the model's other normal abilities. To further clarify the potential effects, we quantify this interference noise in the following theorem.

Theorem 4.1. (Proof in Appendix B) Let P M = U ( l ) [: , 1 : k ]( U ( l ) [: , 1 : k ]) ⊤ be the projection matrix onto the low-dimensional manifold M , where U ( l ) [: , 1 : k ] contains topk principal components of the activation covariance C ( l ) for D redundant and D concise . As the sample sizes grow sufficiently large, the expected noise norm of r other is:

The trace is significant, indicating that the interference noise is substantial and is greatly likely to disrupt the model's normal abilities.

The significant noise norm of r other , as established in Theorem 4.1, suggests that interventions using r ( l ∗ ) introduce considerable perturbations in M ⊥ . Moreover, these perturbations can propagate through layers, amplified by attention mechanisms, non-linear activations, and residual connections, leading to more substantial shifts in the activation distribution. To understand this, we further analyze the mean activation shift and its layer-wise amplification in the following theorem.

Theorem 4.2. (Proof in Appendix B) Let r ( l ∗ ) and r other be as in Theorem 4.1, and let the intervention be applied as in Eq. (4) . The mean activation shift at layer l and its amplification through layers are:

where α is the intervention strength, h ( l ) ( x i ) is the activation at layer l , W ( l +1) denotes the combined MLP and attention weights, γ attn and γ σ are the minimum amplification factors of the attention softmax and GeLU non-linearities, σ min ( W ( l +1) ) is the minimum singular value of the weights, and γ > 1 is the layer-wise amplification factor.

The shift in M ⊥ is significant and grows through layer-wise propagation, driven by attention and non-linear transformations, severely disrupting the model's other normal abilities.

4.3 Manifold Steering

The interference direction r other , quantified in Theorem 4.1, causes activation shifts that amplify through transformer layers and disrupt reasoning (Theorem 4.2). To eliminate this interference, a simple but effective approach is to set Eq. (6) to 0 . Based on this insight, we propose Manifold Steering , which projects the direction r ( l ∗ ) onto M to mitigate r other .

Formally, let U ( l ) eff ∈ R d × k denote the topk principal components of the activation covariance in Eq. (5), spanning M . The manifold direction is obtained by:

where P M = U ( l ) eff ( U ( l ) eff ) ⊤ is the projection matrix onto M . The reason why the interference norm E [ ∥ r other ∥ 2 2 ] = tr ( ( I -P M ) Σ ( l ) noise ) = 0 holds is because Σ ( l ) noise is now primarily supported in M ,

GSM8k

MATH500

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1035 (-49%)

77.2 (+0.8)

3694 (-22%)

72.5 (+2.5)

6505 (-8%)

26.7 (+0.0)

10564 (-7%)

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1076 (-47%)

77.8 (+1.4)

3721 (-22%)

70.0 (+0.0)

6418 (-10%)

26.7 (+0.0)

10437 (-8%)

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593 (-71%)

78.6 (+2.2)

3458 (-27%)

72.5 (+2.5)

6236 (-12%)

30.0 (+3.3)

10134 (-11%)

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1143

88.2

3824

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5871

50.0

10784

Dynasor

87.6 (+0.1)

732 (-36%)

88.2 (+0.0)

2723 (-29%)

85.0 (-2.5)

5121 (-13%)

46.7 (-3.3)

9864 (-9%)

SEAL

87.7 (+0.2)

829 (-32%)

87.8 (-0.4)

2651 (-34%)

85.0 (-0.0)

4750 (-19%)

46.7 (-3.3)

9394 (-13%)

R1-7B

Ours

87.6 (+0.1)

440 (-62%)

88.4 (+0.2)

2239 (-42%)

87.5 (+0.0)

4440 (-24%)

53.3 (+3.3)

8457 (-22%)

Vanilla

82.7

1217

87.8

4009

85.0

5723

33.3

11278

Dynasor

82.9 (+0.2)

826 (-32%)

88.0 (+0.2)

3171 (-21%)

82.5 (-2.5)

5019 (-12%)

46.7 (+13.4)

9901 (-12%)

SEAL

82.7 (+0.0)

749 (-38%)

87.4 (-0.4)

3091 (-23%)

85.0 (+0.0)

4731 (-17%)

46.7 (+13.4)

9789 (-13%)

R1-8B

Ours

82.8 (+0.1)

542 (-55%)

88.0 (+0.2)

2873 (-29%)

85.0 (+0.0)

4400 (-23%)

50.0 (+16.7)

9457 (-16%)

Vanilla

93.2

742

92.8

3496

90.0

5484

66.7

9986

Dynasor

93.4 (+0.2)

596 (-20%)

92.6 (-0.2)

3233 (-8%)

92.5 (+2.5)

4817 (-12%)

63.3 (-3.4)

8941 (-11%)

SEAL

93.6 (+0.2)

583 (-21%)

92.8 (+)

3139 (-10%)

87.5 (-2.5)

4470 (-18%)

60.0 (-6.7)

8563 (-14%)

R1-14B

Ours

93.6 (+0.4)

438 (-41%)

92.8 (+0.0)

2074 (-41%)

90.0 (+0.0)

4061 (-26%)

63.3 (-3.4)

8132 (-19%)

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resulting in zero components under I -P M , i.e. , M ⊥ , successfully eliminating perturbations.

The performance of manifold steering is shown in Fig. 2(b) and Sec. 5.2, where we find that, unlike the original paradigm, our manifold steering enables a sustained reduction in token count.

5 Experiments

5.1 Experimental Setups

We begin by briefly outlining the baseline methods, target LRMs, evaluation datasets, and metrics. For more detailed descriptions of the experimental settings, please refer to Appendix A.

Baseline Methods. We compare our manifold steering with two latest baselines, including Dynasor [16] and SEAL [8], both chosen for their ability to maintain the model's original accuracy. For their settings, we both adopt its official setting. To be aware, Dynasor's early stopping often omits the problem-solving process in the final answer, which is impractical for real-world applications. Thus, we require the model to provide a complete solution upon stopping.

Target LRMs. For a comprehensive evaluation, we select the DeepSeek-R1-Distilled series [14], comprising models of varying scales and architectures: DeepSeek-R1-Distill-Qwen (R1-1.5B, R17B, R1-14B) and DeepSeek-R1-Distill-Llama-8B (R1-8B). All models use recommended settings: temperature of 0.6, top-p of 0.95, and a maximum token limit of 16,384.

Evaluation Datasets & Metrics. To evaluate the effectiveness of Manifold Steering, we include mathematical datasets of varying difficulty: GSM8K [10], MATH500 [20], AMC2023 [24], and AIME2024 [25]. To further verify the transferability, we use LiveCodeBench [18] for code generation and GPQA-Diamond [32] for expert-level disciplinary knowledge. All datasets are evaluated using Pass@1 as the task-solving metric and the average token count ( #Tokens ) for overthinking mitigation.

Implementation Details. The data for computing steering directions is filtered using the method outlined in Sec. 3 on the OpenMathInstruct2 dataset [36]. For each model, we specify the layer

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,

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Tokens: 501

used to compute the steering direction and the intervention strength α as follows: R1-1.5B (layer 27, α = 0 . 7 ), R1-7B (layer 27, α = 0 . 3 ), R1-8B (layer 31, α = 0 . 5 ), and R1-14B (layer 47, α = 0 . 3 ). During inference, this direction is applied to all layers as stated in Eq. (3).

5.2 Performance of Manifold Steering in Overthinking Mitigation

We conduct experiments on four mathematical datasets of varying difficulty using four LRMs with different parameter sizes and architectures. Table 1 presents the results, where models are evaluated for accuracy and redundancy reduction. Based on Table 1, we draw the following observations:

Manifold steering achieves the best performance across all models and datasets. Our method consistently outperforms baselines on four out-of-distribution mathematical datasets, with particularly strong results on GSM8K, where it achieves token reduction of 41% ∼ 71% while preserving accuracy. This is reasonable, as unlike Dynasor, which relies on external monitoring of the model's certainty, our method modifies model outputs at the more fundamental feature level to mitigate overthinking behavior. Moreover, Dynasor's reliance on external monitoring brings extra computational overhead. We include a comparison of average time cost to demonstrate this drawback in Appendix E, while our method incurs nearly no latency. Compared to SEAL, our manifold steering effectively reduces interference noise, yielding a more precise direction. Additionally, we observe that the overthinking phenomenon diminishes to some extent as model parameter size increases, which is expected, as some overthinking stems from models' inability to solve complex problems.

Overthinking is more pronounced in simpler problems. As presented in Table 1, all methods exhibit more effective overthinking mitigation on simpler datasets, with GSM8K and MATH500 ( ∼ 40%) showing greater token reduction compared to the more complex AMC2023 and AIME2024 datasets ( ∼ 20%). This suggests that overthinking is more pronounced in simpler problems, which is reasonable, as complex problems inherently require larger token budgets and may exceed the models' internal capabilities, thereby constraining mitigation effectiveness.

5.3 Cross-Domain Transferability for Overthinking Mitigation

To further investigate the transferability of manifold steering for overthinking mitigation, we assess its performance across two distinct domains: code generation and discipline-specific knowledge, both separate from the mathematical domain used for steering direction extraction. We utilize two representative datasets: 1) LiveCodeBench [18], a benchmark of coding challenges that probe algorithmic and programming expertise, and 2) GPQA-Diamond [32], a carefully curated dataset of challenging multiple-choice questions targeting expert-level disciplinary knowledge across various

fields. As shown in Fig. 3, our manifold steering achieves token reduction of 12% ∼ 27% across both datasets while maintaining accuracy, demonstrating the generalizability of manifold steering to diverse domains. This cross-domain effectiveness offers multiple benefits: it incurs no additional computational overhead, adapts seamlessly to varied problem structures, and effectively mitigates overthinking without requiring domain-specific fine-tuning.

5.4 Directional Analysis and Hyperparameter Tuning

In this section, we first explore the precise impact of the direction computed by manifold steering on model outputs through case studies, analyzing how steering and its reversal affect response characteristics to better understand directionality's role. Then, we conduct hyperparameter tuning.

Directional Analysis. As shown in Fig. 4, applying the steering direction for overthinking mitigation leads to model outputs that are significantly more concise and confident. Specifically, overthinking behaviors, such as hesitant phrases (e.g., 'wait'), frequent shifts in reasoning (e.g., 'alternatively'), and repetitive self-checking, are largely eliminated. The model generates streamlined responses with clear, focused reasoning, delivering direct outputs. This effect strengthens as the intervention strength increases to 0 . 5 . In contrast, when reverse steering is applied, the model becomes markedly more hesitant, often repeatedly checking. This leads to verbose outputs filled with excessive caution. Thus, it is crucial to underscore the role of directionality for overthinking.

Hyperparameter Tuning. We use R1-7B model on MATH500 for this analysis, with results for other models in Appendix C. As shown in Fig. 5, our manifold steering direction demonstrates efficacy at a much lower strength of α = 0 . 1 . As α increases, token counts continue to decrease, with a remarkable 77.1% reduction observed at α = 0 . 5 . This substantial token reduction highlights the purity and effectiveness of our steering direction in mitigating overthinking. However, excessively rapid reasoning, induced by intervention strengths, can hinder the model's ability to thoroughly address complex problems, a phenomenon also observed in human cognition, leading to a decline in accuracy. To balance the trade-

88.2

89.4

88.4

71.0

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off between overthinking mitigation and maintaining accuracy, we select an intervention strength of α = 0 . 3 as the optimal value for robust performance.

5.5 Cross-Task Transferability of Manifold Steering

In this section, we investigate the applicability of manifold steering to tasks beyond overthinking mitigation, such as refusal feature ablation, to assess its cross-task transferability. Prior studies [2, 45] demonstrate that while steering directions can suppress refusal features in models, some instances persist unless intervention strength is increased, which risks model collapse. Here, we apply our manifold steering method using the Qwen2.5-7B-Instruct as the target LLM, computing the steering direction with the same data as in [2]. As shown in Fig. 6, our method achieves a 100% jailbreak success rate (JSR) on AdvBench [51] while the baseline [2] obtains a JSR of 74% ( α = 2 . 0 ), with all responses verified as valid through manual

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check, which further validates the robust transferability of manifold steering across diverse tasks and underscores the urgent need for enhanced safety efforts [13, 17, 46, 47, 48] to ensure responsible AI.

6 Discussion and Limitations

Our proposed manifold steering method has demonstrated robust effectiveness in mitigating overthinking, as evidenced by significant token reductions across varying LRMs. However, its applicability to multi-modal large language models remains unexplored. Additionally, while our approach excels in controlling overthinking with minimal accuracy trade-offs, its interaction with highly specialized tasks, such as domain-specific reasoning, e.g., legal or medical analysis, warrants further investiga-

tion. Moreover, the sensitivity of our method to varying intervention strengths suggests potential for optimizing dynamic steering strategies, where the strength adapts to task complexity in real-time.

7 Conclusion

In this work, we propose manifold steering, a novel method to address overthinking in LRMs while preserving task performance without additional computational cost. Specifically, by aligning the steering direction with the low-dimensional activation manifold, our approach effectively eliminates the interference noise based on theoretical analysis. Extensive experiments across diverse models and datasets confirm substantial token reductions and robust cross-task transferability. These findings underscore the potential of manifold steering to enhance model efficiency and adaptability, opening new avenues for improving LRMs.

Acknowledgments and Disclosure of Funding

This work was supported by NSFC Projects (62576020, 62276149) and was also supported by the Fundamental Research Funds for the Central Universities.

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A Implement Details

In this section, we will introduce the implementation details of our approach, focusing on the data selection process for computing the steering direction to mitigate overthinking in each model and the specific configurations of the baseline methods used for comparison.

A.1 Data Selection for Direction Computation

To construct representative datasets for computing the steering direction to mitigate overthinking, we begin by randomly sampling 20k questions from the OpenMathInstruct-2 training set [36]. For each model, we generate five independent responses per question using the official sampling configuration: a temperature of 0.6, top-p of 0.95, and a maximum length of 16k tokens. These responses form the basis for constructing two model-specific datasets, the Redundant set ( D redundant) and the Concise set ( D concise), as described below:

Redundant set ( D redundant ): This dataset includes questions where all five responses exceed 16k tokens without terminating and contain more than 20 times of hesitation keywords (e.g., 'wait', 'alternatively', etc.). To capture meaningful overthinking behavior, we process the responses using the following template, truncating the response at the occurrence of the hesitation keyword:



{instruction}
<think>\n {partial_response}{hesitation keyword}

The truncation at a hesitation keyword is reasonable because overthinking typically emerges after a certain point in the response, rather than immediately upon encountering the question. Moreover, through activation visualization, we observe no significant differences in the activation patterns of different hesitation keywords. Thus we choose 'wait' as a consistent marker here.

Concise set ( D concise ): This dataset includes questions where all five responses are under 1k tokens and contain none of the hesitation keywords. The template for these responses includes only the instruction without the response, as they inherently represent concise and focused outputs:

These selection criteria ensure that D redundant captures responses exhibiting excessive verbosity and hesitation, while D concise represents efficient and direct responses, providing a clear contrast for computing the steering direction representing overthinking. To ensure high-quality data, we retain only 500 samples for each dataset after applying the selection criteria and double checking. For computing the steering direction, we follow [50] to sample 100 samples from each dataset and employ the IsolationForest algorithm to filter out outliers. For manifold subspace estimation, we utilize the entire set of 500 samples from each dataset to capture the full representational structure.

A.2 Baseline Methods

As stated in Sec. 5.1, we select two latest baselines, Dynasor [16] and SEAL [8], for their ability to preserve the original accuracy in reasoning tasks. Below, we detail the specific settings for them:

General Setting. All large reasoning models adopt the official recommended settings with a temperature of 0.6, top-p of 0.95, and a maximum length of 16k tokens.

Dynasor. We adopt the official settings for Dynasor. The configuration probes the model every 32 tokens with a 'Probe-In-The-Middle' technique and injects a 'Final Answer' prompt at each iteration to ensure complete solutions upon early termination. Generation stops when the Certaindex metric ( ˜ H ) exceeds a predefined confidence threshold. To be aware, Dynasor's early stopping often omits the problem-solving process in the final answer, which is impractical for real-world applications. Thus, we require the model to provide a complete solution in the final answer upon stopping.

SEAL. We adopt the official settings for SEAL [8], using 1k training samples from the Math dataset [20] to extract the reasoning steering vector. Reasoning processes are segmented into thoughts using '\n\n' delimiters, classified as execution, reflection, or transition via keyword-based rules

(e.g., 'Alternatively' for transition, 'Wait' for reflection). The steering vector is computed at layer 20 as S = ¯ H E -¯ H RT , where ¯ H E and ¯ H RT are average representations of execution and reflection/transition thoughts, respectively. During greedy decoding, hidden states of '\n\n' tokens at layer 20 are adjusted as ˜ H = H +1 . 0 · S .

B Proofs

B.1 Proof of Theorem 4.1

Proof. We derive the expected noise norm of the interference component r other , the part of the overthinking direction r ( l ∗ ) in the orthogonal complement M ⊥ of the low-dimensional manifold M . The theorem states:

where P M = U ( l ) [: , 1 : k ]( U ( l ) [: , 1 : k ]) ⊤ , and U ( l ) [: , 1 : k ] are the topk principal components of the activation covariance C ( l ) . We build on prior findings that M is low-dimensional, identified via PCA on D reasoning = D redundant ∪ D concise, with k = 10 capturing over 70% of the variance, validating the linear manifold assumption.

Step 1: Define the overthinking direction r ( l ∗ ) . Per Eq. (2), r ( l ∗ ) = r overthinking + r other , where r overthinking ∈ M captures the shift between redundant and concise reasoning, and r other ∈ M ⊥ is interference. We model:

Assume activations h ( l ) ( x i ) ∼ N ( µ set , C ( l ) ) , with µ redundant or µ concise for each dataset, and C ( l ) estimated over D reasoning. The covariance is:

Step 2: Define M and derive I -P M . The manifold M is spanned by the topk eigenvectors of C ( l ) = 1 N -1 A ( l ) ( A ( l ) -¯ A ( l ) ) ⊤ , where A ( l ) = [ h ( l ) ( x 1 ) , . . . , h ( l ) ( x N )] , and ¯ A ( l ) = 1 N ∑ N i =1 h ( l ) ( x i ) . The eigendecomposition C ( l ) = U ( l ) Λ ( l ) ( U ( l ) ) ⊤ yields U ( l ) [: , 1 : k ] , and:

The projection onto M ⊥ is I -P M , as it removes the M -component. Since U ( l ) [: , 1 : k ] is orthonormal, P M is idempotent and symmetric, so:

PCA's linear basis ensures M ⊥ captures the d -k dimensions of noise, critical when d ≫ k .

Step 3: Define r other . Since r overthinking ∈ M , the interference is:

This isolates noise in M ⊥ , which disrupts normal abilities due to high-dimensional computation.

Step 4: Compute the squared norm. Calculate:

using the idempotence of I -P .

Step 5: Take the expectation. Compute:

Substitute:

Thus:

B.2 Proof of Theorem 4.2

Proof. We derive the mean activation shift ∆ µ ( l ) at layer l due to the intervention (applied as in Eq. (4).) along the overthinking direction r ( l ∗ ) , showing its norm is proportional to α ∥ r other ∥ 2 , and establish the layer-wise amplification of the shift at layer l +1 . The theorem builds on Theorem 4.1. Step 1: Derive the mean activation shift. The intervention at layer l is:

with α > 0 . The mean activation before intervention is:

and post-intervention:

Compute:

The mean shift is:

matching the first part of Eq. (7).

Step 2: Decompose the shift and isolate r other contribution. Since r ( l ∗ ) = r M + r other with r M ⊥ r other , we can decompose:

Thus:

Let:

Then:

Since r M ⊥ r other :

Let s = s M + s other . Then:

By Theorem 4.1, when the error component r other is present (i.e., ∥ r other ∥ 2 > 0 ), it contributes to the total norm. The dominant term depends on the relative magnitudes of ∥ r M ∥ 2 and ∥ r other ∥ 2 . Assuming h ( l ) ( x i ) ∼ N ( µ set , C ( l ) ) and | s | is a positive constant, we obtain:

when ∥ r other ∥ 2 dominates, completing Eq. (7).

Step 3: Derive the layer-wise amplification from r other . For layer l +1 , the activation is:

where W ( l +1) combines MLP and attention weights, Attn is the attention mechanism, and σ is GeLU. The mean shift is:

To isolate the r other contribution, decompose the single-input shift at layer l :

The norm is:

The component from r other can be isolated by considering its contribution:

when the r other term is significant. Propagate to layer l +1 :

where Attn ′ and σ ′ are the Jacobians of attention and GeLU. The attention softmax and GeLU have minimum amplification factors γ attn , γ σ > 0 , and the linear transformation by W ( l +1) satisfies:

Thus:

Focusing on the r other contribution:

The mean shift norm is:

Assume the layer-wise propagation amplifies the previous shift by γ > 1 , reflecting attention and non-linear effects across layers. Combining the amplification of the existing shift and the new r other contribution:

matching Eq. (8). This shows that the r other component causes layer-wise amplification through both the accumulated shift (first term) and the direct contribution at each layer (second term).

Step 4: Analyze the amplification mechanism. The amplification factors γ > 1 , γ attn , γ σ > 0 , and non-zero σ min ( W ( l +1) ) ensure that perturbations from r other grow across layers. The first term γ ∥ ∆ µ ( l ) ∥ 2 represents the propagation of accumulated shift, while the second term represents the fresh perturbation introduced at layer l +1 due to r other . This dual mechanism ensures the shift grows across layers, disrupting the model's normal abilities.

and post-intervention:

C Hyperparameter Tuning

In this section, we present the results of tuning the intervention strength α across four models: DeepSeek-R1-Distill-Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B, DeepSeek-R1-Distill-Llama-8B, and DeepSeek-R1-Distill-Qwen-14B on MATH500 [20]. As shown in Fig. 7, to achieve an optimal balance between efficiency and accuracy, we ultimately select α = 0 . 7 for R1-1.5B, α = 0 . 3 for R1-7B, α = 0 . 5 for R1-8B, and α = 0 . 3 for R1-14B.

Accuracy (%)

Tokens

88.2

89.4

88.4

71

66.4

66.4

3824

3276

2239

876

858

835

0

1000

2000

3000

4000

5000

0

20

40

60

80

100

0

0.1

0.3

0.5

0.7

0.9

Tokens

Accuracy (%)

Tokens

Accuracy (%)

Tokens

92.8

93.2

92.8

80.2

72

71.8

3496

2930

2074

1670

961

913

0

1000

2000

3000

4000

5000

0

20

40

60

80

100

0

0.1

0.3

0.5

0.7

0.9

Tokens

87.8

88.2

87.8

88

73.6

71.2

4008

3764

3428

2873

1761 1465

0

1000

2000

3000

4000

5000

0

20

40

60

80

100

0

0.1

0.3

0.5

0.7

0.9

Tokens

Accuracy (%)

Tokens

R1-1.5B

R1-7B

R1-8B

R1-14B

76.4

79.8

79.2

78.8

78.6

70.4

4762

4320

4276

3834

3458

2736

0

1000

2000

3000

4000

5000

0

20

40

60

80

100

0

0.1

0.3

0.5

0.7

0.9

Tokens

D Layer Selection for Manifold Steering

The selection of intervention layers is critical for the effectiveness of Manifold Steering. We conduct a layer-wise analysis across multiple model sizes to determine the optimal intervention points. As shown in the tables below, we evaluate the performance across different layers by measuring accuracy and tokens on the MATH500. The results demonstrate that later layers consistently achieve better performance: Layer 27 for R1-1.5B and R1-7B, Layer 31 for R1-8B, and Layer 47 for R1-14B.

E Time Latency Analysis

In this section, we analyze the time latency for the DeepSeek-R1-Distill-Qwen-7B model on the Math500 dataset [20], comparing our approach with Dynasor [16] and SEAL [8]. All experiments are conducted on an Ubuntu 22.04 system with A800 GPUs. We find that Dynasor exhibits the

significantly longest time latency, which is reasonable due to its frequent probing of intermediate states and its unsuitability for parallel processing of large reasoning models. For SEAL, although both SEAL and our method introduce negligible additional computational cost, SEAL's token reduction is less effective than ours, resulting in higher time latency.

Table 6: Average Time Latency on Math500 for different overthinking-mitigation methods in R1-7B.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper aims to mitigate overthinking in large reasoning models (LRM) by adjusting their internal activations. Based on the assumption that activations corresponding to overthinking reasoning traces can be distinguished from concise ones, the paper introduces a correction term derived from the difference-in-means from overthinking (redundant) and concise reasoning traces (in math). However, the paper finds that such a correction doesn’t always guarantee redundancy reduction. As a remedy, the paper introduces manifold steering, where the correction term is projected to a low-dimensional space (manifold). Experimental results on math (in-domain), code generation, and disciplinary knowledge (out-of-domain) demonstrate a reduction of reasoning trace lengths while achieving the same or better accuracy.\n\nSTRENGTHS AND WEAKNESSES:\n*Strength* \nThe paper addresses an important issue in LRMs. Indeed, empirical results show that the proposed method can mitigate overthinking in R1-based models. \n\n*Weakness*\nI see the main weakness in the major flaws of the formal derivations of the paper, which might impact the actual results of the paper. In that regard, the paper needs major rewriting. \n- Paragraph “Linear Low-Dimensional Manifold Verification” states that the steering direction is composed of an overthinking ($r_{overthinking}$) and an error ($r_{other}$) term by performing a PCA on joint redundant and concise reasoning traces. However, I don’t see how a PCA shows orthogonality between the two by doing a joint PCA. The PCA just shows the concentration of the variance in the first k=10 dimensions (of the PCA), no separation between different traces. \n- Moreover, the comparison between the magnitudes of $r_{M}$ and $r_{other}$ are confusing. Step 2 in the proof of Theorem 4.2 states that the magnitude of the error term is much larger than the $r_{M}$. However, $r_{M}$ contains 70\\% of the eigenvalues, hence it has a larger norm!\n- Theorems 4.1 and 4.2 are based on empirical evidence; hence, they cannot be stated as formal theorems. When being framed as a formal theorem, all assumptions have to be stated inside the theorem. \n- Step 1 in the proof of Theorem 4.1 shows equality between an expectation and an empirical estimation of the covariance matrix. \n- Eq. (4) is missing the cross terms $r_{overthinking}^T h^{l}(x_i) r_{other}$ and $r_{other}^T h^{l}(x_i) r_{overthinking}$\n- The covariance matrix in Eq. (5) is missing the average on the LHS: $\\frac{1}{N-1}(A^{l}-\\overline{A}^{l}) (A^{l}-\\overline{A}^{l})^T\n\nApart from the formal flaws, the paper only focuses on DeepSeek-R1-based reasoning traces. It is not given that the finding will also hold for other families of LRMs.\n\nQUESTIONS:\n- I would appreciate it if the formal flaws could be addressed in a revised version.\n- Moreover, experiments on another family of reasoning models (e.g., Qwen 3) might be interesting. \n- Line 150 states that the intervention is applied across all layers. However, Lines 264-265 mention only single layers to be adjusted. Please clarify.\n\nLIMITATIONS:\nLimitations are provided in the paper (Section 6).", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-16"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents Manifold Steering, an Inference Time Intervention (ITI) strategy to mitigate overthinking in Large Reasoning Models (LRMs). The authors first sample \"redundant\" and \"concise\" responses to derive a steering vector that assocates with the overthinking direction. Given that, the authors perform ITI on LRMs at various intensities，and observe that the steer contains noisy components that interfere with reasoning. Through PCA on the activations, they reveal that these distruptive components reside in a subspace spanned by residuals. By removing the redudance via a simple linear transformation, Manifold Steering(MS) achieves effective and robust overthinking mitigation than simple ITI.\n\nThe authors conduct comprehensive experiments to demonstrate MS: \n\n(1) consistently reduce generation tokens while maintaining reasoning performance, and\n\n(2) demonstrates strong cross-domain generalization.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The discovery of the \"low-dimensional manifold\" within a steer vector is interesting.\nThe interpretability tool introduced to identify such a subspace is both intutive and easy to grasp.\nIt resonates with me, as residual components that preserve core language abilities can indeed hinder precise reasoning. Overall, I find these operations and insights valuable.\n2. The experiments are fairly comprehensive and effectively address concerns about the robustness of the ITI method in cross-domain transferability. The experimental results also confirm the method’s effectiveness in token reduction.\n3. This paper is mostly well-written and easy to follow.\n\n\nWeakness\n\n1. The font size used in the figures is too small to read\n\n2. Decomposing activations or parameters and performing steering using selected low-dimensional components has been extensively studied in prior works, for example [1, 2]. However, the discussion of these related studies is insufficient.\n\n3. See Questions.\n\n[1] Spectral Filters, Dark Signals, and Attention Sinks\n\n[2] Effectively Steer LLM To Follow Preference via Building Confident Directions\n\nQUESTIONS:\nQ1: The Implementation Details section (Lines 264–265) specifies the layers used to implement Manifold Steering. However, it lacks an explanation for why these particular layers were chosen or a discussion on the sensitivity of layer selection. Could you provide some insight or illustration to justify your choice?\n\nQ2: You manually select the values of $\\alpha$ for different models based on test performance and generation length. This is a form of data leakage and gives your method an unfair advantage over the baselines. I remain unconvinced by the experimental fairness unless a method for selecting $\\alpha$ that is independent of test accuracy is proposed.\n\nQ3: Could the underlying mechanism by which your method reduces overthinking be the simple suppression of transitional tokens such as \"wait\" or \"alternatively\"? Figure 4 shows that as α decreases, the token \"wait\" appears more frequently. [1] noted that such tokens tend to carry high entropy. They may share significant features on a low-dimensional manifold—which may coincide with the one your method identifies. Or, could you report the performance of a model that simply removes \"wait\" and \"alternatively\" from the vocabulary? Would it be comparable to your method?\n\nUpdate: Today I came across a new paper [2], which explicitly removes \"wait\" from the vocabulary, leading to shorter generations and improved performance. I’m not suggesting that your work should be compared with this paper, especially since your submission predates it. Rather, I mention it to support my hypothesis raised in Q3.\n\n[1] Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning\n\n[2] Wait, We Don’t Need to “Wait”! Removing Thinking Tokens Improves Reasoning Efficiency\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-18"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces **Manifold Steering**, a novel method to mitigate \"overthinking\" in Large Reasoning Models (LRMs). The authors begin by identifying a single \"overthinking direction\" in the model's activation space but find that steering along it introduces interference noise that limits its effectiveness. They further discover that the overthinking-related activations reside on a low-dimensional manifold. Manifold Steering leverages this by projecting the initial steering vector onto this manifold to remove the noise. This technique leads to token reductions of up to 71% on math benchmarks, maintains or improves accuracy, and demonstrates strong transferability to other domains.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- The paper's proposed approach efficiently addresses LRM overthinking from the perspective of mechanistic interpretability, offering a new perspective on the \"overthinking\" problem.\n- The proposed method achieves impressive experiment results, consistently reducing token counts while maintaining or even improving accuracy across evaluated math benchmarks.\n- The paper is well-written and logically organized, presenting a sound derivation and theoretical justification for the proposed method.\n\nWeaknesses\n- The evaluation is limited to the DeepSeek-R1-Distilled model family, which raises questions regarding the generalizability of the proposed method.\n- The method intervention strength is sensitive to real-time task complexity, which might limit the practicality of the method.\n\nQUESTIONS:\n- Do you plan to test this method on non-DeepSeek-distilled models?\n- In section 3.2, the steering is applied to all model layers. However, in section 5.1, model steering is only applied to a single specific layer, why? How do you choose this layer, does it involve expensive hyper-parameter search?\n- Table 1 shows that Manifold Steering can sometimes improve the accuracy on challenging math benchmarks like AIME24, could you share some insights behind this phenomenon?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposed a novel method to mitigate overthinking in large reasoning models (LRMs) while maintaining the performance. First, by using the OpenMathInstruct-2 training dataset, the authors obtain a difference vector that represents the direction of the difference between concise and redundant responses. While directly steering the model along this direction too much might even increase the length of the response, the authors utilize a low-dimensional manifold obtained by principal component analysis (PCA) to effectively mitigate overthinking. They conducted extensive experiments across different models and different datasets, corroborating the effectiveness of the manifold steering method. They also showed that the manifold steering method can be effectively transferred to other tasks such as jailbreaking.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. The problem of Mitigating Overthinking is important.\n\n2. The authors propose a simple yet effective method to solve the problem.\n\n3. The proposed method is applicable to various tasks.\n\n**Weaknesses:**\n\n\nThere is no obvious weakness of this paper. There might be some minor issues in the theoretical derivation (see the question section).\n\nQUESTIONS:\n1. In (2), does $x$ refer to “prompt + response” or only “prompt”? Also, is (3) applied to each decoding step or only at the first decoding step?\n2. In (5), why $C = 1/(N-1) A(A-\\bar A)\\^T$ instead of $C = 1/(N-1) (A-\\bar A)(A-\\bar A)\\^T$, as the latter one is the definition of the covariance matrix.\n3. In Theorem 4.1, it states $C\\^{(\\ell)}$ is for the redundant dataset, but in line (195) it says $A\\^{(\\ell)}$ is calculated using all reasoning data. Which one is correct?\n4. In Line 240, $P = UU\\^T$ where $U \\in \\mathbb{R}\\^{d\\times k}$ and $k << d$, then how could $P = I$ (it cannot be full-rank)?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-29"}