Dear Reviewer, We sincerely appreciate your comments and feedback which helps to improve our paper. We reply to all the concerns raised in the weaknesses and questions part.

Weakness-1: A minor limitation is that there are many PeFT methods in the activation space, like RepE, RED, and localized fine-tuning (LoFIT), etc. The paper doesn’t compare their method with those baselines that are related.

Reply to Weakness-1: Thank you for highlighting this important point. We agree that comparing with activation-based parameter-efficient fine-tuning (PeFT) methods such as RepE, RED, and LoFiT would further contextualize the contribution of our method.

As a first step toward this direction, we implemented an activation-based baseline inspired by causal tracing-style full activation vector transfer. Specifically:

1.We extracted MLP activation vectors from several transformer layers of the DeepSeek-R1-Distill-Qwen-7B model for both successful and unsuccessful CoT generations on datasets like AMC23 and GPQA.

2.We computed layer-wise activation deltas (successful − unsuccessful), and patched them into the Qwen2.5-7B base model using forward hooks during inference—similar to how RepE controls latent representations.

3.This method does not require any fine-tuning and simulates a direct activation-space manipulation baseline.

Weakness-2: The effect of the training-free method only works when the model has both the “wait” token inserted and the decaying activation added. Merely amplifying the activations/adding wait tokens doesn’t seem to improve the accuracy (they may even decrease) according to Table 1. It seems that the decaying factor of the activation is very important. Is it possible to disentangle those effects or provide further analysis on why this happens?

Reply to Weakness-2: Indeed, adding the “wait” token influences the generation behavior by encouraging the model to enter a self-reflective mode. However, our findings suggest that while the presence of the token can trigger self-reflection behavior, it does not ensure the quality or correctness of that reflection. The precision and effectiveness of self-reflection are largely governed by the activation values of specific neurons we identify and modulate. This distinction is supported by our ablation results: inserting the “wait” token alone increases the self-reflection rate but has limited effect on accuracy. Conversely, when combined with activation amplification, we observe consistent improvements in both reflection and correctness. This indicates that the interaction between token-level cues and neuron-level control is synergistic.

Weakness-3: It is hard to distinguish between your tuning-free method and your PEFT method from the table at first glance (they are both called EELo-CoT). Is it possible to stress the difference?

Reply to Weakness3: We need to make the following clarifications:

1. The motivation for us to develop the intervention method is to have an easy to implement method with low computational cost where the fixed analytic function only needs to be fitted once with zero training cost.

2. In order to carry the observations we had from the intervention method and have a trainable method to achieve higher performance, we developed a learnable amplification module, as detailed in section4, which requires higher computational cost but with better performance. This design provides a trade-off between efficiency and performance, and users may choose the appropriate version depending on their deployment needs. We will make this distinction clearer in the revised version with a better renaming for the trainable method.

Dear Reviewer, We sincerely appreciate your comments and feedback which helps to improve our paper. We reply to all the concerns raised in the weaknesses and questions part.

Question-1: Why use the number of digits in the last sentence to determine whether to insert the "wait" token?

Reply to Question-1: We use the number of digits in the last generated sentence as a heuristic signal to determine whether to insert the “wait” token because digit-heavy outputs often correspond to arithmetic or numerical reasoning steps, where models are known to be particularly error-prone[Lewkowycz et al., 2022], [Wang et al., 2022], [Rae et al., 2021].

In our observations, errors frequently arise when the model performs arithmetic near the end of reasoning chains—precisely where a self-reflection trigger like “wait” can help.

Thus, we adopt a simple trigger strategy: if the last sentence contains more than a threshold number of digits (e.g., ≥5), we inject a “wait” token before the next sentence, prompting the model to reconsider its previous steps.

We strongly agree this is just one instantiation of a broader reflection-triggering strategy, to simply verify our motivation of activation controlling in eliciting long-cot ability. The mechanism is modular and can be easily adapted to other signals, such as: Frequent use of uncertain terms (e.g., “maybe”, “I think”), High-entropy or low-confidence predictions (e.g., from logits), Specific vocabulary patterns or syntactic cues. We are proposing a new rule and are refining it.

Question-2: Since activations are vectors, how exactly are scalar “activation values” defined in this work? Are they projections onto a direction, an average over selected neurons, or something else?

Reply to Question-2: In the first experiment, we verified that only a small amount of activation values is useful. Therefore, we extracted a small amount of activation positions from the activation vectors. Then, in the intervention procedure, we only focused on the extracted activation positions. At the same time, we approximate the activation patterns by using a function. Then, during inference, we control the activation positions by using the found function.

Question-3: Is the “amplification factor” in Section 2 equivalent to the constant intervention method used in Table 1? If so, why do the two yield such different results (positive trends in Figures 2 & 3, mostly negative results in Table 1)? If not, how do they differ operationally, and why is it not reported in Section 3 alongside other decoding strategies?

Reply to Question-3: Section 2 (Figures 2 & 3): The amplification factor study is conducted as a controlled experiment, where we isolate the effect of activation scaling by keeping all other variables fixed (e.g., no wait token insertion, no adaptive scheduling). The goal is to analyze how increasing the amplification factor affects accuracy and self-reflection in isolation. These plots show trends, not benchmark-level performance.

Table 1 (Constant Intervention row): this row evaluates constant amplification on full benchmarks, where the model must solve a wide variety of problems. Unlike the controlled setting in Section 2, Table 1 includes additional factors such as: A fixed set of 150 activation positions, selected via contrastive analysis. No use of analytic scheduling (unlike in Section 3's EELo-CoT method). As a result, the constant amplification may be misaligned with the reasoning context in some cases—leading to unstable or degraded performance on certain examples.

Section 3 introduces the full EELo-CoT framework, which improves over constant intervention by: Dynamically modulating activation values based on token position (via f(t)). Triggering amplification only after wait tokens. Avoiding excessive or context-insensitive intervention. We treat constant intervention as a baseline rather than a decoding strategy, which is why it is presented in Table 1 but not included as part of Section 3’s framework.

Question-4: Table 3 is not referenced in the main text. Also, it appears that the average reasoning length does not significantly increase, which seems at odds with the intervention’s stated goal.

Reply to Question-4: Thank you for pointing this out. We acknowledge the omission and will explicitly reference Table 3 in the revised version of the main text. This was an oversight during formatting and editing.

Regarding the second part of your question: while it's true that reasoning length (measured by word count) does not increase dramatically under our intervention, our goal is not merely to extend the output length. Instead, we aim to elicit meaningful long chain-of-thought reasoning, which includes self-reflective behavior, logical error correction, and more accurate intermediate step analysis.

To clarify this distinction, we added a comparison table below including a no-finetuning baseline and other methods for reference. We emphasize two key takeaways:

1.Performance improvements: Despite not fully fine-tuning, our method brings strong gains over the no-FT baseline and competitive results compared to LoRA.

2.Length & reflection tradeoff: Although reasoning length increases moderately, it is accompanied by increased self-reflection behavior and better answer accuracy—demonstrating that the quality and deliberativeness of reasoning improves, not just verbosity.

We appreciate your suggestion and will make both the Table 3 reference and this nuanced explanation clearer in the final revision.

Question-5: Since activations are determined by inputs, have the authors examined whether specific textual patterns naturally induce high reflection activations? This might suggest alternative, more interpretable control signals.

Reply to Question-5: Yes, we have examined how specific textual patterns influence activation dynamics, and this motivated our use of the "wait" token as a reflection trigger. As shown in Figure 4, the presence of the “wait” token causes a sharp spike in activation values in certain long-CoT-related neurons, while common tokens like “the” or digit tokens like “1” produce little to no activation in the same positions. This suggests that the model has internally learned to associate “wait” with a mode switch into more reflective or cautious reasoning.

This observation led us to select "wait" as an interpretable, symbolic trigger for activating the long-CoT pathway. Unlike learned neuron triggers, this approach is transparent, easily controllable, and portable across models.

Dear Reviewer

Following your suggestion, we have extended our analysis to test on other potential triggering patterns. Specifically, we replaced the "wait" token by the "however" token. The result is shown as below:

Inserting trigger tokens significantly improves the reasoning behavior of the Qwen2.5 7B base model. Specifically, inserting the "wait" token yields the highest gains — increasing accuracy from 30.30% to 35.86% and self-reflection rate from 4.04% to 68.18%. The "however" token also improves performance over the base.

We fully agree with your points, and we are already undertaking substantial changes to the paper in response.

Here is an outline of the major revisions we are making:

1. Integration of amplification factor experiments We will restructure the content in Figures 2 & 3, merging the results into the main results section (Table 1), and revise Section 2 to focus solely on the neuron selection methodology. This should reduce redundancy and improve clarity.

2. Adding a no-trigger baseline We will add a new row in Table 1 to include the decay-based adaptive scheduling without the “wait” trigger, helping isolate the effect of dynamic modulation from the heuristic.

3. Unifying naming and presentation across figures We will revise figure captions and legends (particularly Figure 7) to ensure all methods are consistently named and labeled (e.g., “Constant”, “Adaptive”, “Forcing”, “EELo-CoT”), with a legend added to improve readability.

Unfortunately, NeurIPS does not allow uploading a revised manuscript during the rebuttal phase, but we have already begun these revisions.

Thank you again for your valuable input — your comments were sharp, constructive, and very much aligned with our goals for improving the clarity and generality of this work.

Sincerely, Authors

Dear Reviewer, We sincerely appreciate your comments and feedback which helps to improve our paper. We reply to all the concerns raised in the weaknesses and questions part.

Weakness-1: One evident weakness is that while the paper identifies that amplifying a small set of activations in the last few layers elicits long CoT, it does not provide a deep mechanistic explanation of why these activations govern such reasoning. The approach is largely empirical, and the mapping between specific neurons and reasoning behaviors remains mostly correlative, not causal. It would be really interesting to see why this is happening.

Reply to Weakness-1: We appreciate this insightful comment. Indeed, providing a full mechanistic and causal explanation for complex behaviors such as long chain-of-thought (CoT) reasoning remains an open challenge in interpretability research. Existing literature has theoretically discussed it from different perspectives[1,2,3]. Concretely, recent theoretical analyses have begun to formalise and critique CoT reasoning. For instance, Ton et al. (2024) treat each CoT step as an information-gain operation, revealing when apparent reasoning is vacuous; Barez et al. (2025) demonstrate that verbalised chains are often unfaithful and call for activation-level causal validation; Chi et al. (2025) diagnose the limits of current causal reasoning and provide new evaluation benchmarks. These works collectively motivate our focus on minimal, causally-validated activation interventions rather than exhaustive symbolic explanations.

[1] Ton, Jean-Francois, Muhammad Faaiz Taufiq, and Yang Liu. "Understanding chain-of-thought in llms through information theory, 2024." URL https://arxiv. org/abs/2411.11984.

[2] Barez, Fazl, et al. "Chain-of-thought is not explainability." Preprint, alphaXiv (2025): v2.

[3] Chi, Haoang, et al. "Unveiling causal reasoning in large language models: Reality or mirage?." Advances in Neural Information Processing Systems 37 (2024): 96640-96670.

However, given the vast number of parameters and nonlinear dynamics in large language models (LLMs), it is hard to propose a completely accurate mechanistic or causal explanation for this phenomena. Thus, our primary goal in this paper is to identify a minimal and actionable set of activation patterns that are sufficient to elicit this behavior reliably, not to exhaustively explain why certain neurons govern reasoning. The strength of our approach lies in its efficiency and effectiveness—we demonstrate that amplifying a sparse set of MLP activations in the final transformer layers leads to meaningful improvements in accuracy, CoT length, and self-reflection rates. While our method is empirical, it offers useful causal evidence through targeted interventions, suggesting that these neurons are functionally significant, not merely correlated. Our findings will provide a useful basis for future studies aiming to formally characterize the causal pathways underlying high-level reasoning in LLMs.

Weakness-2: The intervention is heavily dependent on the presence and timing of special tokens like "wait." If the model does not generate or respond to these tokens as expected, the intervention may not activate, leading to inconsistent results.

Reply to Weakness-2: We strongly agree that the presence and timing of the “wait” token matters in our method. The “wait” token acts as a behavioral trigger and then high-activation regions of long chain-of-thought (CoT) neurons can better guide the LLM to generate accurate results. Without our wait token insert strategy, models do not always generate such tokens at the right moments, leading to unexpected low self-reflection rate. Thus, our approach explicitly inserts the “wait” token at strategic points in the generation process. This is not a reliance on random chance, but rather a controlled intervention designed to nudge the model toward reflection behavior when necessary. In the following table, we show a pair of comparison examples with and without using wait token. Without the wait token, the model confidently settles on an incorrect answer With the wait token and activation modulation, the model pauses, reevaluates its reasoning steps (Step 7 → Step 8 → Step 9), and ultimately arrives at the correct answer. This illustrates that our designed wait-token-insert strategy can lead to better timing and presence to enable recovery from errors by engaging deeper reasoning.

Weakness-3: After looking at the supplement materials, the code relies on manually selected hyperparameters (e.g., amplification factors, number of neurons, t_max, cooldown windows). These are tuned for specific models and datasets, and there is no robust procedure for adapting them to new settings. Small changes in these values led to instability or even degraded performance.

Reply to Weakness-3: Our training-free method (Section 3) involves a set of manually selected hyperparameters, such as amplification factor, number of neurons, and cooldown window. Since this approach applies direct interventions without gradient-based optimization, some sensitivity to these hyperparameters is indeed expected—this is a known trade-off for training-free interpretability methods [4,5].

[4] Bansal, Naman; Agarwal, Chirag; Nguyen, Anh. “SAM: The Sensitivity of Attribution Methods to Hyperparameters.” arXiv preprint arXiv:2003.08754 (2020).

[5] Novello, Paul; Poëtte, Gaël; Lugato, David; Congedo, Pietro Marco. “Goal‑Oriented Sensitivity Analysis of Hyperparameters in Deep Learning.” arXiv preprint arXiv:2207.06216 (2022).

To address this limitation, we proposed a parameter-efficient trainable method in Section 4, which allows the model to automatically learn context-dependent amplification behavior. Specifically: We introduce a lightweight Activation Amplification Module that learns to scale neuron activations based on the input context. This module is applied only to a small subset of identified long-CoT neurons in the last layer. We combine it with LoRA layers in earlier layers to enable broader representation adaptation, while keeping most model parameters frozen. Despite updating only 1.51% of the total parameters, our trainable method achieves strong performance across benchmarks: on Math500, accuracy improves to 90.2%, close to full fine tuning (91.6%), while reducing token length. On AMC23, we achieve 88.75% accuracy, outperforming LoRA (85.0%). On GPQA, our method attains 70.02% accuracy, outperforming both LoRA (66.17%) and full finetuning (69.19%). This result shows that our trainable method can learn the appropriate intervention dynamics in a robust and data-driven way, avoiding manual tuning while maintaining efficiency.

Weakness-4: The answer extraction and equivalence checking rely on regex and symbolic math parsing, which can fail or produce false positives/negatives for non-standard output formats. This can inflate or deflate reported accuracies.

Reply to Weakness-4: Indeed, symbolic math parsing and regex-based methods can occasionally fail, especially for non-standard or free-form outputs. To minimize this issue, we adopted a state-of-the-art answer extraction and equivalence checking approach from recent works [6]. While no extraction method is perfect, this approach ensures high coverage and low false-positive/negative rates in practice. More importantly, we apply the same extraction pipeline across all baselines and ablation settings, ensuring experimental fairness and comparability when comparing the improvement of our methods with baselines.

[6] Yang, An, et al. "Qwen2. 5-math technical report: Toward mathematical expert model via self-improvement." arXiv preprint arXiv:2409.12122 (2024).

Weakness-5: The method uses R1-distilled models to identify "long-CoT" activations, then applies these to base models, potentially introducing bias toward the specific distillation approach used.

Reply to Weakness-5: We would like to clarify that our method does not rely on R1-distilled models to extract or apply long-CoT activations. In Figure5, we analyzed that the activation patterns on the R1-distilled models are highly similar to the base model, particularly in the sparsity and dynamics. Based on this, we can just do experiments on the base model to extract or apply long-CoT activations.

Question-1: The core evaluation metric for "self-reflection" in your code and experiments is the presence of certain keywords (e.g., "wait", "let me double check") in the output, and your main accuracy improvements are modest (often within a few percentage points). Given that your intervention logic (as implemented in intervene_functions.py and model.py) forcibly injects these tokens and amplifies activations based on brittle, rule-based triggers (such as digit counts or sentence boundaries), how can you rule out that your method is not simply gaming the metric—producing longer, more reflective-sounding outputs—without any substantive improvement in actual multi-step reasoning or problem-solving ability? Have you validated that the reasoning chains are more logically coherent or correct, beyond just being longer or containing more "reflection" phrases?

Reply to Question-1: Through looking at many examples, we discovered that the accuracy of intermediate steps indeed improves a lot, especially after the self-reflection operation. But accurately evaluating the intermediate steps within the chain of thought is still an open question, so we have not found a usable qualified metric. Here, we give some examples for demonstration. We can see that after self-reflection, our method successfully elicits the LLM to check and revise the intermediate reasoning results, leading to accurate final answers.

Question-2: Author's method assumes that amplifying a small, empirically selected set of "long-CoT-related" activations in the last layers is sufficient to elicit genuine long chain-of-thought reasoning. However, your selection process uses a fixed threshold on activation differences from just 160 contrastive pairs and does not account for the vast combinatorial space of possible reasoning patterns or tasks. How do authors justify that this sparse, static intervention—based on such a limited and potentially unrepresentative sample—captures the true causal mechanisms of reasoning in large language models, rather than merely inducing superficial verbosity or keyword repetition?

Reply to Question-2: In this work, we select 160 contrastive pairs for reducing the data construction cost and meanwhile efficiently testing the proof-of-concept of our motivation. Our goal in this work is not to claim a complete or exhaustive characterization of the causal mechanisms behind long chain-of-thought (CoT) reasoning, but rather to provide an efficient and practical method to elicit this ability using sparse, interpretable interventions. Therefore, we hope the entire method is low cost. For example, using a small dataset (160 pairs), a model's own generated result (from base model), a small number of activation values (40), and a simple intervention (non-parameteric function). Therefore, we let the readers know that this pathway is workable and enlighten the future works.

Weakness-6: I am curious and was unable to find which aspects of the intervention (activation amplification vs. wait token insertion) contribute most to improvements. hence, claims about "any LLMs and any datasets" are not sufficiently supported by the limited experimental validation and the paper conflates correlation between activations and long-CoT behavior with causal relationships

Reply to Weakness-6: In our experiments (Table 1),

we conduct detailed ablations, to study the contribution of activation amplification and wait token insertion. (1) Using only wait token insertion significantly increases the self-reflection rate, but has limited and inconsistent effects on accuracy. (2) Using only activation amplification improves accuracy, but does not reliably induce self-reflective behavior. (3) Combining both leads to the most robust and consistent gains in both accuracy and self-reflection across all benchmarks. These results suggest that each component contributes independently to a different aspect of long-CoT behavior, and their combination yields the strongest effect. Regarding causality, we demonstrate functional causality—i.e., manipulating specific neurons produces reliable changes in model behavior. Such a way is more useful for us to devise the efficient and effective long CoT ability eliciting methods, including the training-free and parameter-efficient fine-tuning approaches. For the words about any LLMs and any datasets, we agree that more validation across more domains and architectures are necessary to support the claim. We will remove the overclaim words and conduct more experiments for validating the generality.

Dear Reviewer,

Thank you again for your initial review and positive feedback. We have carefully addressed your concerns in our rebuttal and provided detailed explanations along with additional experimental results to support our claims.

We would greatly appreciate it if you could review our response and share your feedback. If there are any remaining concerns that require further clarification, we would be more than happy to provide more details and have a further discussion.

Best regards, The authors

Question-3: Why did authors not include comparisons to other interpretability-based intervention techniques? For example, would random neuron amplification or attention head interventions yield similar effects? I am curious if you also took a look at these papers and methods to analyze the attention [1], [2]

Reply to Question-3: Thank you for the thoughtful suggestion and for referencing relevant interpretability-based works. Following the suggestion, we compare our method against two intervention techniques, including:

(1) Full Activation Vector Transfer (Causal Tracing Style): we extracted MLP activation vectors from multiple layers of DeepSeek-R1-Distill-Qwen-7B for positive and negative pairs, and computed layer-wise activation differences and patched them into a base model Qwen2.5-7B during inference. (2) Random Neuron Amplification (with wait token): we randomly selected neurons to amplify, and follow the same other used settings in EELo-CoT.

The result on GPQA dataset is shown in the table below. We can see that both variations perform not better than our methods. The reason is that our EELo-CoT can better capture the fine-grained main factors for the long CoT ability, i.e., few activation values. Such a sparse intervention way reduces the influence of other confounders and also guarantees the strength of controlling.

Question-4: Have authors tested their approach on tasks requiring different types of reasoning (e.g., commonsense, logical, or open-domain QA)? If not, how can you be sure the intervention generalizes?

Reply to Question-4: Thank you for raising this important point regarding generalizability across reasoning types. To evaluate the broader applicability of our method beyond arithmetic and factual tasks, we conducted additional experiments on the commonsense reasoning benchmark: CommonSenseQA. We applied our EELo-CoT method to the Qwen2.5-7B base model and compared performance against the non-intervened baseline. These results show that our intervention can lead to improvement, but not as significant as in complex reasoning tasks. The reason is that the commonsense reasoning task is relatively easier and originally has higher accuracy, hence the long-CoT reasoning ability will not lead to great gain.

Dataset: common-sense-qa

Dear Reviewer,

We sincerely thank you for your detailed and constructive comments. We have carefully addressed all the identified weaknesses and questions in our previous responses, including:

1.The causality vs correlation concern in activation amplification, 2.Evaluation of trigger sensitivity and generalization across tasks, 3.Comparison to interpretability-based baselines (including random interventions), 4.Clarification on static intervention design and reasoning diversity, 5.Supplementing the "self-reflection" evaluation with more detailed metrics and examples

Since the rebuttal phase ends very soon, we would greatly appreciate any final feedback or confirmation that our responses addressed your concerns.

Your input would be invaluable in helping us improve the clarity and rigor of the paper.

Best regards, The Authors

Dear Reviewer

We sincerely thank the reviewer for his or her thoughtful engagement throughout the rebuttal phase. We greatly appreciate your careful consideration of both our responses and the broader conversation. As suggested, we will incorporate the relevant results and clarifications from the discussion into the final version of the manuscript to ensure completeness and clarity.

Sincerely, Authors

Dear Reviewer,

We sincerely appreciate your comments and feedback which helps to improve our paper. We reply to all the concerns raised in the weaknesses and questions part.

Weakness-1: Limited definitions and clarifications: lacks clear definitions and clarifications for several key concepts. For example, the terms “(key) activation values,” “activation value difference,” “positive and negative samples” (Line 86), and “self-reflection rate” (Line 120) are not rigorously defined.

Reply to Weakness-1: Due to the page limitation, we were unable to define all terms rigorously in the initial submission. In the revision, we plan to include a concise term-definition table to clarify all technical concepts. Below we provide definitions for the specific terms mentioned:

Key activation values: Activation values refer to hidden states in the MLP activation (act_fn) layers of the model. The key activation values are the ones with larger values in a certain layer, which generally indicate that important knowledge or ability is invoked during LLM inference[1,2].

[1] Shafran, Or; Geiger, Atticus; Geva, Mor. “Decomposing MLP Activations into Interpretable Features via Semi‑Nonnegative Matrix Factorization.” arXiv preprint arXiv:2506.10920 (2025).

[2] Garde, Albert; Kran, Esben; Barez, Fazl. “DeepDecipher: Accessing and Investigating Neuron Activation in Large Language Models.” arXiv preprint arXiv:2310.01870 (2023).

Activation value difference: This is the difference in average activation values between positive and negative samples. For a given MLP layer, we compute the mean activation over all positive outputs and over all negative outputs separately, and then compute the difference as: Δ = mean_positive − mean_negative. This allows us to identify neurons that are significantly more active in high-quality (e.g., accurate or reflective) generations.

Positive and negative samples: As described in Section 2.1, we select contrastive examples from model outputs to help identify key activation values. Specifically: Positive samples are CoT responses that are accurate, long (length > 1000 tokens), and contain self-reflection cues such as "wait", "let me double check", etc. Negative samples are responses that are inaccurate, shorter, and lack reflective phrases.

Self-reflection rate: This metric is to measure the percentage of self-reflection outputs generated by the model. If the output contains at least one predefined self-reflective phrase, such as "wait", "let me double check", or "let’s verify", we classify it as positive one, and otherwise negative. This is a binary classification per sample and we average it over each dataset to compute the metric. We will include a term description table in the revised version to improve the understanding of all the terms.

Weakness-2: Finding-3 could be better justified. The “significant improvement” in accuracy in Figure 2 is not clearly visible, and the increase in self-reflection rate might simply result from adding a “wait” token rather than the activation amplification itself. Have the authors tried adding the “wait” token alone in Figures 2 and 3? This would help isolate the effect of the proposed activation manipulation.

Reply to Weakness-2: Our intention in Figures 2 and 3 was to evaluate whether combining activation amplification with the insertion of the “wait” token yields greater improvements than using activation amplification alone. This week, we followed the suggestion of the reviewer and test the wait-token-only method performance in the following table. The results show that while inserting the wait token alone does increase the self-reflection rate, its effect on accuracy is limited. In contrast, the combination of activation amplification and wait token insertion leads to a more substantial and consistent improvement in both accuracy and self-reflection. This supports our claim that the two components are complementary.

To better show the comparison of the two methods, we randomly select one example as follows. We can see that although wait-token-only enforces the LLM to perform “self-reflection”, but the generated contents are just repeating the question. It is just like an imitation of reflection without thinking. In comparison, with the activation control strategy, the LLM starts to think deeply and check the correction of the answer in the self-reflection parts.

Inference on GPQA benchmark

Weakness-3: The paper would benefit from more careful discussion about potential confounding factors. For example, how does adding tokens interact with the model’s natural decoding dynamics?

Reply to Weakness-3: We appreciate the reviewer’s concern about potential confounding factors, particularly regarding how adding tokens like "wait" may affect the model’s natural decoding dynamics. In our previous experiments, we found that adding the “wait” token influences the generation behavior by encouraging the model to imitate the self-reflective behavior. However, our findings suggest that while the presence of the token can trigger self-reflection behavior, it does not ensure the quality or correctness of that reflection. The precision and effectiveness of self-reflection are largely governed by the activation values of specific neurons we identify and modulate. (See the case study above) This distinction is supported by our ablation results: inserting the “wait” token alone increases the self-reflection rate but has limited effect on accuracy. Conversely, when combined with activation amplification, we observe consistent improvements in both reflection and correctness. This indicates that the interaction between token-level cues and neuron-level control is synergistic. (See the experiment results above)

In addition, we also consider the following potential variables in our methods, and add the ablation studies in the following table. Concretely, we conducted two additional studies:

1.Random Neuron Amplification (with wait token): We randomly selected activations to amplify using the same decay schedule as EELo-CoT. The results (on AMC23) are shown below:

These results confirm that simply amplifying arbitrary neurons—despite increasing reflection-like behavior—fails to improve accuracy, emphasizing the importance of targeted neuron selection.

2.Token-Level Activation Comparison: We also analyzed how different tokens affect the activations of long-CoT-related neurons. The table below reports the average activation magnitude and the percentage of neurons exceeding a threshold (e.g., >4.0) for each token:

As shown, the “wait” token activates the target neurons more strongly and more frequently than neutral tokens. This provides quantitative evidence that certain tokens (e.g., “wait”) function as interpretable triggers for switching the model into a more reflective mode.

To be honest, we acknowledge the existence of additional factors that may influence decoding dynamics (e.g., context length, token distribution). But it is hard to consider all potential confounders in this work. From the goal of proposing an efficient and effective approach, our main focus is to identify and validate the two dominant contributors: (1) token-based triggering and (2) activation-based control, for eliciting the long chain-of-thought ability. Then, based on that, we can devise our rather efficient training-free and parameter-efficient fine-tuning methods. (See Section 3 and 4).

Question-1: In different figures, the scale of activation values varies widely (e.g., up to 1000 in Figure 1 but close to zero in Figures 4–6). What accounts for this discrepancy? Are the scales normalized or comparable?

Reply to Question-1: We sincerely thank the reviewer for your careful reading, and will revise this part to make the description more clear. Actually, the y-axis in Figure 1 and Figures 4–6 represent the count and magnitudes of activation values, respectively. Concretely, Figure 1 reports the number of activation values greater than 4 in each layer. It is a count of significantly activated values. In contrast, Figures 4–6 plot the actual activation values of selected neurons over the sequence or relative to specific tokens (e.g., “wait”). Figure 1 illustrates the distribution of high-activation neurons across layers, while Figures 4–6 aim to visualize the temporal dynamics and sparsity of key activation trajectories during generation. As shown in these figures, we can see that (1) Long-CoT Activations Mainly Exist in Last Few Layers; (2) Base and Long-CoT Models Exhibit Similar Sparse Activation Dynamics; (3) Activations around Wait Token Have Predictable Pattern. All the above findings motivate us to design our rather efficient training-free and fine-tuning methods.

Question-2: In Eq. (1), how are the parameters a,b and c determined? Are they specific to each model or layer, or are they fixed? Could they be made trainable for better results?

Reply to Question-2: To determine the parameters a,b, and c in Equation (1), we first collect activation trajectories from the identified long-CoT-related neurons, particularly focusing on their behavior around the “wait” token. We then fit the analytic function f(t)=a−b⋅log(t+c) to the empirical activation curves using standard curve fitting techniques. These parameters are derived from contrastive example pairs (Section 3) and are fixed during inference for the training-free method. In our training-free method, we use a rather simple way that applies the same fitted function globally, across layers and across models. This allows for a simple and easy-to-follow implementation, while still yielding strong performance, as shown in the following table.

Inference on GPQA benchmark

The observation that many long-CoT-related activations follow similar decay trends enables this shared approximation. We strongly agree with the reviewer that the optimal parameters may vary across different neurons or models. Therefore, in Section 4, we extend this idea into a trainable setting by designing an activation amplification module. Instead of fitting a single fixed function, this module learns context-dependent scaling factors for a selected subset of neurons, allowing the amplification behavior to be learned directly from data. This learnable approach results in even better performance, as shown in the following table.

GPQA

To summarize:

1.Section 3 (training-free): fixed analytic function fitted once, efficient, zero training cost.

2.Section 4 (trainable): learnable amplification module, parameter-efficient training, better performance.

This design provides a trade-off between efficiency and performance, and users may choose the appropriate version depending on their deployment needs. We will make this distinction clearer in the revised version.

Question-3: What exactly is the relative distance in Eqs. (1) and (2)? How is it computed in practice?

Reply to Question-3: In Equations (1) and (2), the variable t represents the relative distance (in tokens) from a designated trigger token—typically the "wait" token—to another token in the same sentence. Concretely, during generation, whenever a "wait" token is inserted, we define it as the reference point (i.e., t=0). For each subsequent token in the same sentence, t is incremented by 1 per token until the sentence ends (e.g., at a period, newline, or EOS). The amplification function f(t) is then applied to adjust the activations of selected neurons based on their position relative to this "wait" token. This design reflects our empirical observation that activation values tend to spike immediately after the "wait" token and then decay over the following tokens. The function f(t)=a−b⋅log(t+c) captures this behavior, allowing us to dynamically modulate neuron activations during generation.

Dear Reviewer,

Thank you again for your initial review. We have carefully addressed your concerns in our rebuttal and provided detailed explanations along with additional experimental results to support our claims.

We would greatly appreciate it if you could review our response and share your feedback. If there are any remaining concerns that require further clarification, we would be more than happy to provide more details and have a further discussion.

Best regards, The authors

Dear Reviewer

We sincerely appreciate your comments and feedback which helps to improve our paper. We reply to all the concerns raised in the weaknesses and questions part.

Weakness-1: The observation that most activations differ in the last few layers may be closely related to the fact that these layers contribute heavily to the logits of final tokens. Since the positive and negative pairs are constructed from SFT and instruct models, the activation differences in the final layers could be attributed to the different token patterns between SFT-ed and instruct models. An alternative approach would be to construct positive-negative pairs using RL-trained models and the base models, which I wonder whether it might lead to more insights.

Reply to Weakness-1: We sincerely appreciate the reviewer’s insightful observation. To explore this concern, we followed the reviewer’s suggestion and conducted the experiments that re-construct the positive-negative pairs using the generated outputs from RL-trained models and base models, respectively. Concretely, we use the same sampled data, follow the same rule to select the positive and negative samples, but from R1-distilled Qwen-7B and Qwen-7B respectively. We identified key long-CoT neurons via activation difference analysis (Δ-activation) in Qwen 2.5 7b base, and conducted the experiments on reasoning benchmarks using our training-free method. The result is as follows. It can be seen that using positive and negative pairs from R1 generated examples will also bring improvements to the model, which is a similar observation as we had in the paper. It indicates that the activation control is not just following the token pattern, but the actual long-cot reasoning paradigm.

Weakness-2: While the intervention methods offer some interpretability insights, their effectiveness may not match that of actual fine-tuning approaches. The parameter-efficient fine-tuning method trades some efficacy for some efficiency gains. The evaluation is conducted on LIMO (~800 examples), it is not sure whether using larger datasets would see a wider performance gap between full fine-tuning and the proposed method.

Reply to Weakness-2: We first need to make the following clarifications:

1. We develop the intervention method to have an easy-to-use method with low computational cost, as the proof-of-concept of our motivation.

2. Then, we follow this motivation and devise a trainable method to achieve better performance. As it can train the parameters using more data, it is promising to perform much better. This design provides a trade-off between efficiency and performance, and users may choose the appropriate version depending on their deployment needs.

To address the reviewer’s concern about generalization to larger datasets, we extended our evaluation beyond LIMO by training our method on the Bespoke-Stratos-17k dataset (https://huggingface.co/datasets/bespokelabs/Bespoke-Stratos-17k) and evaluated on MATH500 and GPQA datasets. These results show that our trainable method achieves comparable or even better performance than LoRA-based finetuning, indicating the effectiveness of our approach.

Weakness-3: The experiment contains one model family (Qwen). It is unsure how the results could generalize across different model families like Llama.

Reply to Weakness-3: Thank you for the suggestion. We strongly agree that testing the generalizability on other models is important. To address this, we included an additional evaluation using the LLaMA-3.1 model in the Appendix of the original submission. Specifically, we applied our intervention method and evaluated it on Math500, a challenging benchmark requiring multi-step mathematical reasoning. This result has shown that our method can also lead to significant improvement in accuracy and self-reflection rate, indicating its effectiveness in eliciting the long chain-of-thought reasoning ability of LLMs.

Weakness-4: For Table 2 can you provide distilled models’ performance as references as well? It is not directly comparable but it sets a reference for the strength of intervention method

Reply to Weakness-4: Thank you for the suggestion. We follow it by adding the results of R1-distilled Qwen 7B, and also applied our intervention method to it. We report the results on GPQA dataset, and we can also see a significant improvement on the distilled model. It further indicates the effectiveness of our approach. Despite the improvement on accuracy, our intervention further improves the reasoning length and self-reflection rate, demonstrating its effect on long cot ability controlling.

Weakness-5: While figure 4 shows some clear qualitative trends for a few examples, it might be beneficial to show some quantitative results as well for measuring this behavior.

Reply to Weakness-5: Thank you for the valuable suggestion. Figure 4 is to qualitatively illustrate the contrast in activation values between reflective triggers (e.g., “wait”) and neutral tokens (e.g., “the”, digits). To show more quantitative results for measuring the behavior, we add new quantitative metrics to support the evidence. Concretely, we report (1) the average activation magnitude of long-CoT-related neurons when each token appears; (2) the proportion of selected neurons that exceed a threshold (e.g., activation > 4) for each token type. As shown in the following table, the “wait” token reliably elicits higher average activation and activates a greater fraction of long-CoT neurons compared to neutral tokens like “the” or mathematical operators like “equals”. This provides quantitative confirmation that certain tokens (e.g., “wait”) serve as interpretable triggers for switching the model into a reflective reasoning mode.

Dear Reviewer,

Thank you again for your initial review. We have carefully addressed your concerns in our rebuttal and provided detailed explanations along with additional experimental results to support our claims.

We would greatly appreciate it if you could review our response and share your feedback. If there are any remaining concerns that require further clarification, we would be more than happy to provide more details and have a further discussion.

Best regards, The authors