Activation-Guided Consensus Merging for Large Language Models
Authors: Yuxuan Yao
Shuqi LIU
Zehua Liu
Qintong Li
Mingyang LIU
Xiongwei Han
Zhijiang Guo
Han Wu
Linqi Song
Venue: NeurIPS 2025 poster ()
Keywords: LLM Reasoning
Model Merging
Long-to-Short
Primary area: applications
TL;DR: We introduce ACM, a framework that enhances model merging by incorporating layer-specific merging coefficients based on activation mutual information.

Abstract: Recent research has increasingly focused on reconciling the reasoning capabilities of System 2 with the efficiency of System 1. While existing training-based and prompt-based approaches face significant challenges in terms of efficiency and stability, model merging emerges as a promising strategy to integrate the diverse capabilities of different Large Language Models (LLMs) into a unified model. However, conventional model merging methods often assume uniform importance across layers, overlooking the functional heterogeneity inherent in neural components. To address this limitation, we propose \textbf{A}ctivation-Guided \textbf{C}onsensus \textbf{M}erging (\textbf{ACM}), a plug-and-play merging framework that determines layer-specific merging coefficients based on mutual information between activations of pre-trained and fine-tuned models. ACM effectively preserves task-specific capabilities without requiring gradient computations or additional training. Extensive experiments on Long-to-Short (L2S) and general merging tasks demonstrate that ACM consistently outperforms all baseline methods. For instance, in the case of Qwen-7B models, TIES-Merging equipped with ACM achieves a \textbf{55.3\%} reduction in response length while simultaneously improving reasoning accuracy by \textbf{1.3} points. We submit the code with the paper for reproducibility, and it will be publicly available.

Activation-Guided Consensus Merging for Large Language Models
Yuxuan Yao Shuqi Liu Zehua Liu Qintong Li', Mingyang Liu Xiongwei Han
Zhijiang G.6 Han Wu Lingi Song!. 1.2f
Department of Computer Science, City University of Hong Kong
City University of Hong Kong Shenzhen Research Institute
Huawei Noah's Ark Lab, Hong Kong SAR
UUiiversity of Hong Kong
Hong Kong University of Science and Technology (Guangzhou)
&oon Kong University of Science and Technology
(yuxuanyao3-c@my 1 linqi. songe))on@@eeeooo cityu. edu. hk wu han1 @huawei. com
Abstract
Recent research has increasingly focused on reconciling the reasoning capabili- ties of System with the efficiency of System 1. While existing trining-bassed and prompt-based approaches face significant challenges in terms of efficiency and stability, model merging emerges promising strategy to integrate the diverse capabilities of different Large Language Models (LLMs) into a unified model. However, conventional model merging methods often assume uniform importance across layers, overlooking the functional heterogeneity inherent neural components. To address this limitation, we propose Activation Guidedd Consensus Merging (ACM), a plug-and-play merging framework that determines layer-specific merging coefficients based on mutual information between activa- tions of pre-trained and fine-tuned models. ACM effectively preserves task-specific capabilities without requiring gradient computations or additional training. Exten- sive experiments on Long-to Mong-to-Short (L2S) and general merging tasks demonstrate that ACM consistently outperforms all bascline methods. For instance, in the case of Qwen-7B models, TIES TIES-Merging equipped with ACM achieves 55.3 % reduction in response length while simultaneously improving reasoning accuracy by 1.3 points, Our code is available at ACM
Introduction
The cognitive evolution of L.MMs has progressed from System System 2 paradigms 16
46
characterized by the emergence advanced reasoning models like OpenAl's o1/33 (2 30), QwQ
31,, and DeepSeek-RI [6]. System 1 implementations [ 71. such GPT-4o 28) LLaMA-3 7
DeepSeck-V3 [5), leverage rapid intuitive processing for immediate responses but struggle with complex reasoning tasks. In contrast, System 2 architectures are fine-tuned with extended thinking chains to promote deliberate analysis through iterative self-assessment, error mitigation, and verifi- cation, albeit facing challenges related redundancy. This system dichotomy motivates the Long-to-Shorr (L2S) framework (37), which seeks to reconcile System 2's analytical depth with System I's operational efficiency. Beyond computationally intensive training- based approaches [O] and instability prone prompting methods (23). promising alternative lies in model merg- ing techniques to seamlessly integrate System models with their counterparts without incurring additional computational overhead 40)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Model merging [I 39 refers to the process of integrating the parameters of tre-trained (PT) model with those of multiple fine-tuned (FT) models to create a single unified model. This approach aims to enhance performance, generalization, and robustness by leveraging the strengths and diverse insights of each individual model. Within the framework of model merging, task vectors [1]] have emerged as essential components for encoding task-specific knowledge representations. Defined as parametric deltas between pre-trained and fine-tuned model weights, these vectors theoretically enable cross-model capability integration through linear arithmetic operations. Current task vector- based techniques 22] 451 predominantly use static coefficient protocols that enforce uniform scaling across all parameters and tasks. This simplification assumes uniform task relevance across all neural weights, regardless of their spyer-icecffic functional criticality. However, layer importance is often heterogeneous. In tasks such L2S, layers critical for specific functions, such the Im. __aad layer for generation length control, may require different weighting coefficients than other layers. To mitigate the problems, recent efforts utilize gradients [9] activations 27 derive layer-specific coefficients for task vectors. Nonetheless, these methods either overlook inter-model relationships by solely focusing PT model's s activations necessitate complex backpropagation.
In this work, we tackle the aforementioned challenges by theoretically analyzing how activation values relate to weight salience, then designing customized layer-specific weighting coefficients to avoid complex gradient calculations. Mutual information (MI) is selected to measure activations, as it can select features that are highly relevant while preserving critical information, quantifying feature redundancy [8] [4]. Specifically, we propose Activation Guided Consensus Merging (ACM), novel and efficient approach based activation MI among models. Different from the previous element-wise activation merging method 277. which concentrates on maintaining the pre-trained model's is capacity, our ACM first computes layer-wise activations for both PT and FT models using shared calibration dataset. Next, ACM measures the mutual information (MJ) between corresponding PT and task-specific FT activations each layer, normalizing these values to obtain layer-specific weighting coefficients. The overall framework is presented at Figure [ Crucially, these coefficients are inversely proportional to the mutual information scores, layers with higher similarity (greater MI) receive lower weights to reduce redundancy, while layers showing significant divergence (lower MI) are assigned higher weights to preserve FT-specific capabilities.
Overall, our contributions include: 1) We analyze the correlation between activation space and weight salience, propose novel merging approach dubbed as ACM, which leverages MI to compute the weight coefficients each layer. 2) Extensive experiments in the L2S merging scenario demonstrate ACM's efficiency in maintaining performance and reducing redundancy compared to both training- based and traditional merging baselines. For instance, in the case of Qwen-7B models, TIES-Merging equipped with ACM achieves 55.3% reduction in response length while simultaneously improving reasoning accuracy by 1.3 points. 3) General merging tasks further validate ACM's 's soundness and efficacy. The results show that ACM serves as plug-and aad--and-pu and-play solution, consistently improving the performance of existing merging methods.
2 Related Work
Long-to-Short Reasoning The paradigm shift in LLM has evolved from rapid, straightforward System 1 reasoning to deliberate, analytical System 2 reasoning frameworks [13] [6] 35]. While System models demonstrate proficiency in generating intuitive responses with low latency, their performance degrades significantly when confronted with complex tasks. In contrast, System 2 models employ recursive self-evaluation mechanisms and error correction protocols to enhance correctness and robustness in multi-step reasoning scenarios. However, this methodological rigor introduces computational inefficiencies, generating excessively verbose responses. Recent advancements in L2S reasoning 337 have emerged as promising direction to address this fundamental trade-off.
Current research prioritizes two complementary strategies for optimizing reasoning efficiency, namely Chain-of ThTThttt (Co'T) compression and task-adaptive computation allocation. The former approach targets semantic distillation of reasoning paths. For example, TokenSkip 41 implements hierarchical token importance scoring followed by strategic omission, while Valve [24] optimizes param- eter space trajectories through madient-guides step size modulation. For computational resource allocation, O1-Pruner 2 integrates reinforcement learning (RL) with curriculum- sampling to prioritize high-complexity tasks, whereas DAST [3] establishes a teneh- difficulty metric to dynamically calibrate reward functions. Parallel efforts explore budget-aware RL frameworks
2

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L. Task-Speciffe Layer- Wise Activation
Calibration Corpus
Calibration
Calibration Corpus
Corpus
layer
layer
Afl
layer
40
layer
layer
Ab
Inyer
Ai
byyer
A
laver
Merged Model
Rase Model 6
01
Model 6n.
8
Jayer
Iayer
Inyer
layer
II. Layer Activation Mutual Information
layer
layer
...
layer_4
layer_k
layer_
III. Merge
6
20
x
[Ay
1-
layer
Figure I: Overall framework of our Activation Detrrttiin-Gideed Consensus Merging Method, which extracts task-specific layer-wiss activation patterns from shared calibration corpus, quantifies their mutual information with the base model, and performs a weighted synthesis of parameters across models.
Despite progress in prompt engineering techniques [23] 33). like few-shot response truncation and conciseness-orientt demonstration design [26). these methods exhibit critical limitations. Their performance demonstrates pronounced sensitivity to different models and prompts, resulting in inconsistent generalization across task domains.
for adaptive reasoning length control [ I0
To alleviate the aforementioned challenges, model merging emerges as a promising strategy to integrate the simplicity of System with the accuracy of System maintaining stable performance without the need for training overhead.
Model Merging Model merging has emerged as a paradigm-shiftinn alternative conventional training- raining-based based approaches, enabling the integration of multiple task-specific models into unified one [43]. This technique demonstrates superiority several scenarios: (1) performance improvement through checkpoints merging 11 42 (2) effective mitigation of catastrophic forgetting via parameter-
space reconciliation 2 and (3) realization of adaptive long-to-short reasoning capabilities 37
Task vectors [T] have recently dominated the field of model merging. These methods can be system- atically classified into three categories, including arithmetic merging operates fine-tuned features as directional task vectors in parameter space [ 39 42 45). These approaches perform algebraic operations (e.g., linear combinations magnitude normalization) to derive consolidated models; 2) low-rank-based based merging leverages singular value decomposition (SVD) to identify latent low-rank structures within task vectors 22 22 Such methods achieve efficient merging through principal component retention while preserving critical task-specinf information, and 3) activation-ban -based merging incorporates input-driven activations [19 (2) and sensitivity-aware balancing mechanisms, thus dynamically adjusting parameter weights based given context. Parallel to these approaches, Mixture-of-Fe -fpeetttttt (MoE) based merging strategies (20 34 constitute distinct research direction. However, their architectural modifications and model size adjustments place them beyond the scope of parameter-space merging techniques discussed in this work.
Notably, recent works 37 40 have revealed the exceptional efficacy of model merging on Long-to- Short reasoning tasks, particularly through activation- based methods. Although these approaches [19 27 demonstrate superior performance across diverse tasks and model scales, they still exhibit sigmificant limitations on the usage of activations, focusing solely on the activations of the pre- pre-trained model, requiring complex gradient calculations, which motivates our further exploration.
3 Methodology
3.1 Preliminaries
Unveiling the Activation-Weige Salience Relation Practically, the salience model parameters is assessed through statistical analysis of activation patterns using calibration dataset [18 27 32

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For given layer characterized by a weight matrix W' E RVX,, we amalyze its parameter sensitivity by introducing a perturbation matrix AW RNNM resulting perturbed weights defined as W" = W + AW. For an input vector æ E R.,, the transformation of the perturbed layer can be expressed as y' =W' =W + rAW.
Let us examine the differential output resulting from weight refinement, defined as Ay := y y (W"x) - <W)). By applying Taylor's expansion the activation function o, we derive:
Ay xW"x) (W
o(Wx) (Vo(Wa) 2), W' Wx) +O[I|W'> Wxll3) oWWz)
(Vo(W))) AWw)) + O(IAAW]))
= (Vo(W)),AWa))
where the higher-order term [[] [W]))) is negligible due to the sufficiently small magnitude of the weight perturbation.
Based on this approximation, we formally define the weight salience S(W) with respect to calibration input as follows:
+(W; == (o() S(W) = sup s(W;
[|
In the specific case where o is the activation function, we observe that Vo E {0, 1}. Consequently, the weight salience for the activation function is bounded by S(W) //p||=|[=1 (1, (1, x) < |W]]-
The derived weight salience S(W) reflects activation function sensitivity via gradient-perturbatin interactions, revealing how parameter importance emerges from the interplay between weight changes and activation responses.
Mutual Information Mutual Information (MI) is statistical measure that quantifies the depen- dency between two random variables, defined as:
p(z,y) p(z)p(y)
I(x;)) ZEX ZEX
p(a, u) v) log Σ
This measure indicates how much knowledge of one variable reduces the uncertainty of the other. In feature space, MI assists in selecting features that are highly relevant to the target task, ensuring the preservation of critical information enabling the optimization of objective functions to minimize this redundancy [8 48). The essence of
50] Additionally, MI quantifies feature redundancy.
model merging is to integrate complementary information from various models or features, and
can assist in enhancing merging effectiveness.
In our preliminary attempts, we also considered Kullback- divergence and cosine similarity to measure model relationships.
KL divergence is asymmetrie; for instance, with P 00.9, 0.1] and Q [0.5. 0.5). we found (K || Q) xs 0.368 and DKL(Q P) z
0.511, leading us to exclude this metric.
Cosine similarity exhibits substantial variability across layers, approximately ranging from 0.25 to 0.8, which negatively impact performance, as prior studies emphasized that weight coefficient fluctuations should be minimall 19]. Furthermore, the range of cosine similarity is (-1, 1), complicating the interpretation of negative values.
Therefore, We chose MI as a robust tool for examining model relationships.
3.2 Activation Consensus Merging
Consider the merging of N specific models with parameters 01, 02...., ......,,... Bx. all derived from
common PT backbone 0g The goal of the merged model O is to effectively handle multiple tasks simultaneously. Each fine-tuned model's capabilities are encapsulated by task vectors [II), defined as the difference between the task-tuned parameters and the backbone: 5, 0; 00-00. Oo. for {1, (I....,N7 NN. Based on the vector, single, static merged model is formulated as:

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N N i=1
0 mergged 80
6
As previously noted, due the differing importance and characteristics of each layer, it is essential to employ distinct weight coefficients rather than a uniform coefficient for all layers. Given a task- agnostic representative calibration corpus D, we can feed the calibration data into the models to obtain activations. We denote the layer-wise activations of model as A A ....... . A where indicates layer index. Subsequently, we can derive the mutual information between the PT and FT models of each layer across the calibration dataset as:
1, = I A
kEK
The mutual information values can be relatively large, whereas the range of the weight coefficients typically constrained between and 22 45). To ensure consistency, employ the sigmoid function for normalization, as described below:
1 1
where is the hyperparameter, practically ranging from -1 and X represents the layer-specific importance of each task vector. A lower coefficient indicates higher mutual information, suggesting significant overlap between the two models. In the context of L.2S tasks, this overlap may correlate with shared fundamental generative capabilities, thereby justifying smaller weight coefficients. Conversely, higher weight coefficient may signify that those particular weights play a more critical role in enhancing reflective capabilities.
Overall, the merged layer is for the model Imerged is expressed as:
N N
Othenged 0
ot, KEK
We perform the above operations each layer to obtain the merged model. The overall framework can be found Figure [1] We would like to highlight that our method is plug-and-play aiming to identify the optimal weight coefficients X/. These coefficients can be seamlessly integrated into various existing task-vector-bard based merging methods, such as TA and - (42
4 Experiments
We evaluate our method on both Long-to-Short merging tasks and general model merging tasks. The results show that our approach consistently outperforms existing merging strategies across diverse benchmarks, demonstrating stronger cross-task adaptability and knowledge integration capabilities.
4.1 Long-to-Short Merging
Models and Datasets
Long-to-Short Merging aims to combine the strengths of fast (System
1) and slow-thinking (System 2) models, achieving high accuracy with reduced redundancy. To evaluate, we conducted experiments across various model sizes and tasks, utilizing Qwen2.5-Math
(1.5B, 7B), Qwen2.5 ( (14B, 32B), and their corresponding DeepSeck-RR distilled series models (6]. Model performance assessed established reasoning datasets, including GSM8K (4) MATH500
17]. Minerva Math [5). Olympiadbench (9. College Math (36). and AIME 2024 To ensure reproduuibiility, employed the public evaluation toolkit provided by QwenLM 2 adhering their
recommended versions of dependencies. Code generation capabilities are measured on HumanEval-
Pro 47 and LiveCodeBench [12). Following DeepSeek-Al al. (6. fast-thinking models
evaluated in few-shot context, while slow-thinking models are in a zero-shot framework.
5

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Table 1: Evaluations of different model merging methods Qwen-7B models. The number in indicates the average response length the dataset. Length reduction comparisons are conducted with RI, the superior results of the merging methods on each benchmark are highlighted in bold.
Bench
Minerva Math
Olympiad Bench
College Math
GSM8K
MATII500
AIME24
Avg.
Method
88.9
52.2
12.1
17.5
22.6
Dwen2.5-Math-78
32.8
(130.2)
(526.2)
(956.7)
(1259.2)
(794.8)
(1528.0)
89.3
87.4
36.4
39.8
23.3
DeepSeck-R1-7B
54.5
(1062.0)
(2825.9)
(3055.9)
(5793.8)
(2461.6)
(8675.4)
33.8
39.7
56.7
DPO
(983.6)
(2587.1)
(2304.9)
(4932.3)
(2073.5)
(7029.5)
(-15.0%)
Aritlmetic Merging Methods
81.6
78.2
30.9
37.9
36.1
26.7
48.6
Average Merging
(636.4)
(1416.7)
(2277.4)
(3202.2)
(2065.7)
(5964.8)
(-34.6%)
90.5
83.4
41.9
45.0
40.3
20.0
53.5
Task Arithmetic
(617.5)
(1617.4)
(1416.2)
(2650.6)
(1443.9)
(3594.6)
(-48.7%)
90.6
81.8
38.2
43.0
41.9
33.3
54.8
TIES-Merging
(552.2)
(1492.9)
(1349.2)
(2473.7)
(1287.8)
(3302.1)
(-53.0%)
84.0
75.4
29.4
35.7
36.2
23.3
47,3
DARE
(815.6)
(2237.1)
(2317.8)
(3266.3)
(2072.1)
(3803.1)
(-30.6%)
87.9
84.0
29.4
41.6
38.3
26.7
51.3
DARE-TA
(600.4)
(1703.9)
(1567.2)
(2774.8)
(1533.9)
(3454.2)
(-47.0%)
89.6
82.4
37.5
41.3
40,2
23.3
52.4
DARE-TIES
(584.3)
(1589.4)
(1307.4)
(2655.5)
(1378.5)
(3579.9)
(-50.4%)
Activation--eae Merging Methods
90.8
83.0
40.8
46.4
42.3
26.7
55.0
AIM
(540.6)
(1374.5)
(1229.8)
(2323.8)
(1249.6)
(3265.9)
(-55.3%)
91.2
83.4
41.5
43.9
40.2
30.0
55.0
Sens-Merging
(604.2)
(1613.3)
(1402.1)
(2673.0)
(1454.0)
(3355.8)
(-49.4%)
90.6
83.8
38.6
40.1
$5.5 (+1.0)
ACM-TA
(652.4)
(1636.1) 1)
(1514.1)
(2706.2)
(1494.5)
(3409.9)
(-47.4%)
92,2
38.6
46.4
40.3
55.8(+1.3)
ACM-TIES
(538.3)
(1450.1)
(1153.1)
(2356.8)
(1284.6)
(3076.4)
(-55.3%%
For activation-basee merging, the s1K dataset 25 is used the calibration data, which provides aligned short- and long-CoT answers for each question. The dataset containing about 1000 pieces of data is first clustered by the K-means algorithm into 20 categories, followed by an even sampling of 10% of the total data. To enhance numerical stability, we perform a translation transformation by subtracting the maximum MI obtained from different data pieces. The maximum sequence lengths for quick and slow-thinking models are set to 8K and 10K, respectively. All models are uploaded and evaluated with the BF16 data type. We report the average scores across five runs with different random seeds.
Baselines We evaluate the effectiveness of our ACM by comparing it with individual task-specific models and established model- mmegingg techniques, including Average Merging, Task Arithmetic (TA) M.I. TIES-Merging 42 DARE 45), AIM (27), and Sens-Merging [19]. TA enhances the merging process by introducing task vectors, demonstrating that simple arithmetic operations on these vectors effectively generate merged output. DARE and TIES utilize pruning-thes teatingggtt----cnnnggg methods to merge these vectors, based on the premise that not all parameters contribute equally to overall performance. AIM and Bens-Merging integrate seamlessly with the existing methods by assigning layers with different importance weights. AIM computes only the PT model's activations, overlooking the FT model's task characteristics. Sens-Merging requires complex backpropagation to calculate sensitivity.
designed to be plug-and- and-play, allowing them to
Hyperparameters Both the baseline methods and our ACM-enhanced methods use the same range of weight coefficients for fair comparison. When applying Task Arithmetie, we utilize scaling coefficient of X 0.7 by default. This choice ensures that the task vector's original magnitude

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Table 2: Evaluations of various model merging methods on Qwen-1.5B models.
Bench
Minerva Math
Olympaid Bench
College Math
GSM8K
MATTI500
AIME24
Avg.
Method
Qwen2.5-Math
75.9
36.2
11.4
22.8
5.6
0.0
25.3
(118.1)
(411.0)
(1036.8)
(607.7)
(864.9)
(864.9)
DeepSeck-R1
76.6
69.6
15.1
30.4
34.2
20.0
41.0
1.58
(2743.3)
(4508.2)
(6374.2)
(7389.3)
(4058.1)
(8952.3)
26.6
12.2
7.4
5.6
0.0
9.5
Average Merging
(3248.7)
(3890.6)
(3706.0)
(3928.6)
(3853.4)
(3977.3)
(-24.11%)
74.5
62.6
21.0
28.6
10.0
37.6
Task Arithmetic
(549.7)
(1619.4)
(1671.0)
(2588.6)
(1321.7)
(3395.3)
(68.7%)
75.7
66.2
22.1
30.8
29.6
10.0
39.1
TIES-Merging
(414.0)
(1038.5)
(1066.8)
(1963.7)
(876.7)
(2901.0)
(-75.5 %)
38.7
35.4
11.4
22.8
5.6
16.7
21.8
AIM
(1084.9)
(2034.7)
(2510.9)
(3301.9)
(1464.6)
(2105.1)
(-61.9%)
71.3
63.8
24.8
28.9
30.5
13.3
38.8
Sens-Merging
(720.0)
(1611.3)
(1774.1)
(2683.8)
(1394.7)
(3546.7)
(-66.7%)
76.8
68.8
25.3
31.1
29.6
16.7
41.4(+0.4)
ACM-TA
(438.0)
(1309.6)
(1214.7)
(2291.6)
(1067.3)
(3240.9)
(-73.7%%
78.4
71.4
28.7
33.8
37,9
10.0
43.3(+2.3)
ACM-TIES
(962.1)
(1235.6)
(1350.5)
(1849.6)
(848.5)
(2688.5)
(-73.5%)
maintained when integrated with the pretrained backbone. In contrast, the DARE technique is more susceptible to changes in both the scaling coefficient, X, and the drop rate, Consequently. to obtain stable performance with DARE, we configure its scaling coefficient to 0.7 and its default drop rate to 0.3. For AIM, we utilize MTES-Merging, we consistently follow settings reported by previous work [40] for different models. For our ACM, set t 0.7.
0.4 as recommended. As for Sens-Merging and
Main Results As presented in Tables | and we provide the results for the 1.5B and 7B models. For comprehensive results regarding the code benchmark and experimental details for the 14B and 32B models, please refer to Appendix A
The following observations can be derived:
(1) ACM exhibits substantial improvements in accuracy across various model scales. For the 7B model (Table [J, ACM-TA and ACM-TIES achieve average accuracies of 55.5% and 55.8% respectively, outperforming both task vector merging methods (e.g.. Task Arithmetic at 53.5%) and activation-based approaches like AIM (55.0%). With the 1.5B model (Table 2 ACM-TA and ACM-TIES attain accuracies of 41.4% and 43.3% %, significantly surpassing TiES-Merging Merging (39.1%) and Sens-Merging (38.8%) Experiments on larger models (14B and 32B) further confirm ACM's effecttiveness, with integrated TA and TIES strategies consistently enhancing performance. These results underscore the necessity of establishing appropriate layer-specific weight coefficients. ACM systematically derives these coefficients for each layer by analyzing the mutual information relationships among the models, thereby enhancing performance.
(2) ACM significantly mitigates redundant outputs while enhancing inference efficiency in smaller-seale models. Figure demonstrates that ACM-TA and ACM-TIES achieve sequence lengths of approximately 1,000 tokens in the 1.5B code generation task, significantly shorter than the 6,000+ tokens required by the DeepSeek counterpart. Similar trends are observed for the 14B code task (Table 8). In mathematical reasoning tasks, ACM-TIES reduces sequence length by 55.3% % for the 7B model (Table and 73.5% for the 1.5B model (Table 2). highlighting ACM's efficiency in compressing outputs without compromising performance.
Specifically, consistent with previous findings [40, we observed that response length positively correlates with question difficulty. Furthermore, as shown in the appendix AA.3 the merged model retains reflective capabilities; however, reflection frequency has decreased due to the PT fast-thinking model. According to our careful case study, while the merged model maintains favorable reasoning ability, it avoids redundant reflection on simpler mathematical problems, such as those in GSM8K, thereby reducing response length.
7

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inpect Mooght donts
Weth Model Layer wise Sootheient
Lorgl
Code Lavenatio Conticurt
6008
Figure 2: The impact of weight coefficients of the task vector-based merging on Qwen- 14B models. As weight coefficients increase, accu- racy improves while response length grows.
Figure 3: Layer-wise coefficients across different task-specific models, with the Top-5 coefficients highlighted in red.
Table 3:
Evaluation of various methods integrating three LLaMA series models. Our ACM demon- strates an improvement combined with other approaches. Comparisons conducted with baseline merging methods, the superior results among them on each benchmark are highlighted in bold.
Bench
GSM8K
HellaSwag
MRPP-Pro
Avg.
Method
Llama-2-7b-bf
16.60
69.01
3.17
29.59
MammoMATH
46.45
67.09
11.10
41.55
codellama-7b
17.13
30.18
29.10
25.47
23.58
69.05
6.61
33.08
TIES
22.90
68.98
8.99
33.62
ACM-TA
23.68 (+1.0)
69.27 (+0.22)
6.55 (-0.06)
33.18 (+0.1)
ACM-TIES
22.82 (-0.08)
69.16 (+0.18)
9.11 (+0.12)
33.70(+0.08)
(3) ACM highlights the necessity of layer-specific coefficients in model merging. As depicted in Figure the weight coefficients between the im _eehhad layer and the embed layer in the L2S task are considerably lower than those of the intermediate layers, with the mutual information in the former being around 4, whereas the mutual information in the intermediate layers is approximately 2.5. This discrepancy may stem from the knowledge distillation process between the slow- and fast-thinking models: shared pretrained semantic representations at these layers necessitate only minimal parameter adjustments during aligmment. Notably, this pattern persists consistently across models varying scales, underscoring the robustness of the observed behavior.
(4) Balancing accuracy improvement and length reduction in larger-scale models proves chal- lenging. Experiments show that in large models like the 14B and 32B, setting the task vector coefficient around 0.7 improves accuracy difficulty achieving notable length reduction as smaller models, sometimes even exceeding that of the slow-thinking model, aligning with the findings in Wu et al. [40]. Moreover, Figure exploors that higher weight coefficients enhance slow-thinking features, resulting in longer outputs and improved accuracy. Smaller models, however, can gain accuracy while maintaining shorter lengths. This discrepancy arises from the significant parameter redundancy in large models, which enables the coexistence of both fast and slow- slow-thinking modes, complicating the process of length reduction.
Further analysis highlights that task characteristics affect the accuracy-length trade-off. As shown in Table the 14B model compresses output length while enhancing accuracy coding tasks, due to strict syntactic constraints and clear logical goals. This enables effective elimination of redundancy while ensuring semantic correctness. In contrast, reasoning tasks are more prone to conflicts between accuracy and length due to lack of structural constraints.
4.2 General Model Merging
Models and Datasets We further validate our ACM approach on general model merging tasks, ensuring that the merged model retains the capabilities of the baseline models. In addition to Qwen, we also apply our ACM to the LLaMA architecture by merging multiple LLaMA -based FT models and compare against strong baselines, including Llama-2-7b-hh (38, MammoMATH fine-tuned

---

Effect Hyperparameterr
0.90
(-05
Comparison RL-based
t-0.7
0.80
b-0.8
1-09
Weigee Crefticen
0.75
40
Reductio Roto
0.70
0.45
20
Deesceek RL Math 1.38
0.35
Li-Max
0.50
25
Figure 4: Ablation study of hyperparameter I 7B L.2 task. "-1" layer corresponds to the embed layer, "-2" layer represents the model.norm layer, and "-3" layer implies the Im Im_head layer.
Figure 5: Comparison with training-base based methods regarding the trade-off between re- sponse length and accuracy.
version for mathematical reasoning, and Codellama-77-hh a code-specialized model designed for general code synthesis and understanding. We assess performance on GSM8K, a dataset of grade school math word problems; HellaSwag [49], a commonsense reasoning benchmark; and MBPP-Pro [47] dataset of Python code generation problems.
Main Results To ensure the merged model retains the capabilities of all individual models, we set the hyperparameter for the TA method to 0.2, while the TIES method uses coefficients of 0.7 and 0.2, respectively. Accordingly, the hyperparameter t for our ACM method is set to -1.8. Table 3 illustrates the effectiveness of the ACM method when integrated with existing approaches to enhance the performance of LLaMA -bbseedd models across three benchmark tasks. The baseline models exhibit distinct performance characteristies on these benchmarks. When combined with the TA and TIES methods, the ACM method demonstrates varying degrees of improvement. Notably, the merging methods yield limited performance on the MBPP-Pro and GSM8K tasks compared the baseline, likely due to the low TA coefficient and the relatively inferior performance of two of the three models. In contrast, both ACM-TA and ACM-TIES achieve more consistent improvements on HellaSwag, where the baseline models align more closely. The incorporation of ACM enhances robustness and generalization capabilities, particularly in scenarios with limited model diversity and strategically optimized weight allocation. These findings highlight ACM's feasibility strategy for synergistically combining multiple large language models across various domains.
versatile and effective
Additionally, Figure 3 also demonstrates that different models and tasks require distinct layer-wist wise coefficients for optimal performance. The uneven distribution of coefficients across layers, along with the task- specifie focus certain layers, emphasizes the necessity for adaptive weighting strategies.
5 Further Analyses
Ablation Study on Hyperparameter To investigate the sensitivity of our model merging frame- work to the hyperparameter we conducted an ablation study analyzing its impact on layer- weight coefficients, as shown in Figure 4 The results demonstrate that varying /. within the range [0.5, 0.9] induces only minor fluctuations in the learned weights across all layers. This highlights the robustness of our adaptive weighting mechanism to hyperparameter choices. Moreover, our findings indicate that across experiments involving models ranging from 1.5B to 32B, the ACM method consistently yielded favorable outcomes with fixed hyperparameter 0.7. In contrast, the Sens-Merging method displayed significant variability, with its temperature coefficient fluctuating between and 6, while the scaling coefficient varied from 0.4 0.8. A similar trend observed in the TIES Mer-ingg method. Collectively, these results suggest that the ACM method exhibits superior robustness, both in terms of the number of hyperparameters and the breadth of parameter adjustments.

---

Table 4: Effect of the number of calibration data.
Table 5: Effect of different random seeds.
Pleces
20
50
100
200
300
seed a
seed b
seed c
Acc.
91.4
90.8
92.2
91.8
92.1
Acc.
91.9
91.7
92.4
Length
623.63
624.17
538.3
585.65
603.0
Length
$58.33
553.58
541.41
Table 6: Effect of different clusters.
Table 7: Performance on IFEval.
Clusters
random
10
20
30
prompt-level
instruction-level
Acc.
88.6
91.1
91.8
91.6
TIES
18.48
30.58
Length
643.4
602.2
538.3
586.7
ACM-TIES 20.15 (+1.67)
31.06 (+0.488
Ablation Study on Calibration Dataset We evaluate the robustness of ACM from multiple dimensions, including the number of sampled calibration data pieces, the number of clusters employed prior to sampling. the choice of random seeds, and the use of distinct calibration datasets. The Experiments are conducted on Sween.5--Mth-11-5 model series. Tabel 4 indicates that once the number of calibration data points reaches 100, accuracy remains high while length remains short. We also analyzed the weight coefficients at this threshold. When the number of data is below 100, the distribution of weight coefficients fluctuates significantly, with the top five layers showing considerable variation. Conversely, when the count exceeds 100, these characteristics stabilize. This trend is similar across models such as 1.5B and 14B. Thus, we advocate for 10% sampling rate in our experimental design. We also present the results of the 7B model using different sampling seeds in Table evident that our clustering and sampling methods are both reasonable and robust. Additionally. ly, we investigated the effects of varying the number of clusters. Table demonstrats that random clustering results in suboptimal performance, indicating possible imbalance the dataset's distribution. Notably, with and beyond 20 clusters, we observed improved accuracy and reduced length, suggesting that clustering then sampling effectively mitigates data imbalance. We further validate the effectiveness of ACM using calibration datasets other than S1K; detailed experimental results are provided in the Appendix A.4
benchmark for instruction Broader Task We additionally selected the IFEval dataset 51
following- to evaluate our method. For simplicity, we use 1.5B Owen model and choose TIES as our baseline. The experimental results are shown in Table 7 We find that on the enstruction-follvvint dataset, ACM can further enhance the model merging performance of TIES, thereby further validating the effectiveness of our ACM approach.
Comparison with RL-based Methods Figure presents a comparative analysis of our proposed method (ACM-TA) against both the bascline model and RL-based training methods in terms of aceuracy-length trade-off. Our approach demonstrates three key advantages: 1) not only improves Deepseek-RI R1's accuracy by approximately 1.2%, but also achieves about 51 % length reduction rate; 2) Despite requiring no training cost, ACM-TA matches the length compression efficiency of
training-intensive methods like LI-Max I1 (about 52%) and ThinkPrune (about 50%) [10] though the accuracy improvement is relatively limited compared to training-based methods; 3) Compared to its non-training counterpart Task Arithmetic (TA), ACM-TA turn TA's 10% accuracy drop at 40% compression to slight performance improvement at 50% compression. This highlights our method's unique ability to simultancously enhance model accuracy and efficiency through adaptive merging. Besides, our training-free free ACM method requires only tens of seconds to one or two minutes (depending on model size), exhibiting extremely low time overhead and high efficiency.
Conclusion
We propose ACM, a novel and efficient activation based model merging method, which analyzes the MI of activations between models to calculate appropriate weight coefficients. Experimentas on L2S reasoning tasks and general merging tasks demonstrate the effectiveness of ACM. Further comparison with RL-based approaches indicates that our method can achieve comparable length reduction on the L2S task without training. We believe our work can inspire future research in this field.
10

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Acknowledgments
This work was supported in part by the Research Grants Council of the Hong Kong SAR under Grant Collaborative Research Fund C1042-23GF and GRF 11217823, the National Natural Science Foundation of China under Grant 62371411, InnoHK initiative, the Government of the HKSAR, Laboratory for Al-Powered Financial Technologies.
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Table Evaluations of various model merging methods on Qwen- 14B models.
Bench
HuamnEval Pro
GSM8K
MATH500
AIME24
Avg.
Method
90.8
47.2
3.3
51.8
Qwen2.5-14B
48.3
(138.5)
(522.9)
(1493.8)
(101.4)
91.9
89.0
50.0
61.0
DeepScck-R1-14B
73.0
(558.8)
(2314.1)
(7724.8)
(229.5)
91.5
88.2
46.7
63.4
72.5
Average Merging
(642.8)
(2925.1)
(7922.7)
(158.0)
(+3.2%)
94.1
85.4
33.3
63.4
69.1
Task Arithmetic
(565.9)
(2191.4)
(6873.6)
(160.1)
(-11.3%)
93.4
84.6
26.7
62.8
66.9
TIES-Merging
(503.1)
(2169.7)
(6953.7)
(92.0)
(-21.55%)
94.8
86.2
46.7
63.4
72.8
Sens-Merging
(641.0)
(2697.5)
(7155.4)
(132.8)
(-4.58%)
94.2
87.8
46.7
64.6
73.3 (+0.3)
ACM-TA
(608.9)
(2650.4)
(7376.6)
(159.1)
(-2.93%)
92.6
88.6
50.0
64.1
73.8(+0.8)
ACM-Average
(591.4)
(2981.4)
(7971.8)
(160.4)
(+1.92%)
A Technical Appendices and Supplementary Material
A.1 Code Evaluation on 1.5B Models
The experimental results in Figure demonstrate the effectiveness of our ACM-based methods (ACM-TA and ACM-TIES) on the LiveCode benchmark. Compared to the baseline TA method, ACM-TA achieves a 0.7% accuracy improvement while reducing average response length by 12%. Similarly, ACM-TIES outperforms the TIES method by 0.2% accuracy and 9% shorter response length. showcasing the benefits of integrating activation- aware calibration into existing frameworks. These gains highlight ACM's ability to enhance model performance without sacrificing computational efficiency, particularly in long-context code generation tasks.
Code Bench Performance Analysis on 1.58 Models
15.0
12.5
10.0
1.000
1Q.7
2.000
25
1,00
0.
Dem-Mati-1.p 58
Deedbren e1 aisa Lte
Marging
Acdesa
Figure 6: Performance comparison of different methods on LiveCode Benchmark
A.2 Experiments on Larger-scale Models
The results in Table g demonstrate the superiority of ACM-based methods across multiple bench- marks. ACM-TA achieves a 4.2% higher average accuracy than Task Arithmetic while maintaining comparable efficiency, as indicated by similar computational costs (e.g., GSM8K: 608.9 vs. 565.9). Similarly, ACM-Average outperforms Average Merging by 1.3% with slightly increased resource
22

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Table Evaluations of various model merging methods on Qwen-32B models.
Bench
GSM8K
MATH500
AIME24
Avg.
Method
92.3
55.4
6.7
51.5
Qwen2.5-32B
(130.3)
(497.2)
(1127.9)
95.7
89.2
60.0
81.6
DeepSeck-FR 11-32B
(822.6)
(2621.8)
(7194.2)
95.1
88.8
46.7
76.9
Task Arithmetic
(586.7)
(2171.2)
(6752.3)
(-17.3%)
95.4
87.8
43.3
73.5
TIES- Migg-Mggging
(516.9)
(1898.7)
(5823.3)
(-27.9%)
46.7
77.4 (-4.2)
ACM-TA
(544.8)
(2124.4)
(6735.3)
(-19.7%)
usage. Notably, ACM methods consistently achieve top-tier performance on challenging benchmarks like HumanEval Pro (64.6%) and AIME24 (46.7%), surpassing all other merging strategies.
Likewise, the experimental results in Table also demonstrate the superiority the ACM-TA method on Qwen-32B models. Compared Task Arithmetic, ACM-TA achieves 0.5% higher average accuracy (77.4% vs. 76.9%) while maintaining comparable computational efficiency, as evidenced by similar sequence length reductions (e.g.. -11.7% -10.7%).
A.3
Reflection Statistics
Table 10 and 11 present the number of reflections using different merging methods across models of varying scales different benchmarks. We determine whether reflection has occurred based on the presence of keywords, including: "wait, re-examine, recap, double-check, let me (just) check, and let (just) verify".
Table 10: Number of responses containing reflective content across various datasets on 1.5B models.
Minerva Math
Olympiad Bench
College
Bench
GSM8K
MATHS00
AIME24
Math
Avg.
Method
(1319)
(500)
(272)
(675)
(2818)
(30)
Qwen2.5-1.5B
0
0
0
DeepSeck-R1-1 R1-1.55
1315
499
234
668
2769
30
914.2
Average Merging
774
306
173
369
1892
16
588.3
Task Arithmetic
151
187
295
818
21
259.0
-erging
22
45
13
85
118
3
47.7
Sens-Merging
211
205
304
909
288.5
ACM-TA
63
107
33
175
353
13
124.0
ACM-TIES
137
166
280
722
18
230.5
A.4 Different Calibration Dataset
We have also chosen the recently released LIMO FF1 dataset as the calibration dataset for our experiments. LIMO challenges conventional wisdom in mathematical reasoning by showing that models can achieve superior performance with significantly less, yet higher quality, training data. In line with the settings applied in s1K, conducted experiments using LIMO on GSM8K and Minerva Math, and results are presented in Table [2] Our method demonstrates good adaptability to the new calibration dataset and exhibits robustness.
A.5 Case Study of ACM
23

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Table 11: Number of responses containing reflective content across various datasets on 14B models.
Bench
GSM8K
MATI1500
AIME24
Avg.
Method
(1319)
(500)
(30)
Qwen2.5-14B
2
0
0.7
DecpSeck-R1-ee
678
473
30
393.7
Average Merging
372
457
30
286.3
Task Arithmetic
861
572
29
487.3
TIES TTES-Megging
991
455
29
491.7
AIM
568
462
30
353.3
Sens-Merging
714
483
29
408.7
ACM-TA
717
481
27
408.3
ACM-Average
329
451
29
269.7
Table 12: Effect of Different Calibration Dataset
GSM8K: Acc. (Length)
Minerva Math: Acc. (Length)
Qwen-Math- Math- I.5B
75.9 (118.1)
11.4 (I036.8)
DeepSeek-RI-1.5
76.6 (2743.3)
15.1 (6374.2)
Task Arithmetic
74.5 (549.7)
21.0 (1671.0)
ACM ACM-TA-sIK TA-sIK
76.8 (438.0)
25.3 (1214.7)
ACM-TA-LIMO
76.9 (604.9)
22.3 (1549.7)
Table 13:
Case study of ACM and other merging methods GSM8K
Garrett popping popcorn for snack. As the pan of kemelss beats the kernels start popping faster. Twenty pop in the first 30 seconds of zooking, then three times amount in the next secends. kernels increase four times initial popping rate
Question
thirty seconds.
but in the (inal 30 seconds, the pupping slows down hall the rate the pust 30 seconds.
After Garrett takes the pan off the beat.
quarter of the number of kernels that popped in the tinal 30 seconds of cooking also pop from the residual heat. How many pieces of popcorn does Garrell have to cut?
Gold Answer
210
Let's think step by step. seconds, 20 kemels pop. 30 scconds,
that amount pop. * Ieernels pop.
In the 30 seconds, times the initial popping rate
20 80 kernlls pop.
In the final 30 seconds, the popping slows down half the rate the past 30 seconds, so 60 30 kemels pop.
Qwen2.5
In the final seconds, quarter of the number of kernels that popped the final kemels pop.
30 seconds also pop from residual heat, 30 Since have half kemel.
round down kernels popping from the residual heat. In total, Garrett has 20 60 + 80 30 7 207 pieces of popcorn eat.
24

---

Okay, let's to ligure how many of popcoen Garrett
So, he's popping popcorn in four different 30-sccond intervals, and the popping rate changes cach time.
Then, after taking the pan off the heat, some more kermels pop from the residual beat. complicated, but break down step by step.
Hmm, sounds information given:
First, let's list
1. In the first 30 seconds. 20 kernels pop.
2. In the next 30 seconds, three times that amount So, that's 20 60 kerneks.
3. In the next 30 scconds, the popping rate increases to four times the initial rate.
The initial rate was 20 kernels per 30 seconds. so times would
In the final 30 seconds, the popping slows down to half the
previous interval.
The previous interval was 80 kernels, so half of that is 40 kernels.
5. After taking the pan off the heat, quarter of the numher of kemeess that
popped in the final seconds also pop from the residual heat.
So, that's is quarter of 40, which is kemnels.
Alright, let's add up these numbers
total number of kernels popped
during cooking and then add the that popped from residual heat.
First interval: 20 kernels.
Second interval: 60 kernels.
Third interval: 80 kernels.
Fourth interval: 40 kermels.
Residual
So, total kernels popped during cnoking: 60 80
Lei calculate that: 20 60 80, plus is 160, plus 40 200. Then, residual heat adds another 10 kernels.
So, total kernels: 200 10 210.
Wait, but let me double-check to make sure I didn't miss anything.
secunds;
Next 30 seconds: times 20 So, 20
80.
Next 30 seconds: times the initial rate. which 20,
80. So, 80 160.
Final 30 seconds: half the previous rale, which was 80, so half is 40. So, 160 40 200. Then, residual heat: a quaster of the final 30 seconds.
which was 40, so 40/
So, 200 + 10= 110210.
Wait, seems consistent. So, make sure interpreted "Twenty pop in the first 30 seconds of cooking.
popcorn
correctly. The problem says:
DeepSeek-RI
then three times that amount in the next 30 seconds.
The kernels incresse to four times the initial popping rate in the oext thirty scconds,
but in the final 30 seconds, the popping slows down to half the rate as the past 30 seconds."
initial rate per seconds.
Next interval: times that,
Next interval: times the initial rate, which is 20 80.
Final interval: half the rate of the past 30 seconds, which was 80, so half 40.
Yes, that scems right.
Then, residual heat: a quaster of the final seconds.
So, total 20 60
10 210.
think that's correct. So, the answer should be 210.
*Final Answerte
Garrett has to cat Vhoxed(2100 pieces of popcorn.
<Athink>
Gamrett popping popcorn four different 30 30-second intervals,
with the popping changing each time.
After taking the pan off the heat, some additional kernels from the residual beat.
Here is the breakdown of the popping rates and the total numher of kemels:
1. In the first 30 seconds, 20 kernels pop.
In the next seconds, three times that amount pop: (3 times 20 60) kemels. the initial rate:
next seconds, the popping increases
(4 times 20 80) kernels.
4. In the final 30 seconds.
the popping slows down to half the rate of the previous interval: (Mrac(800 (2) 40) kernels.
5. After taking the pan off heat, a quarter of the number of kernels
that poppod in final seconds also pop from the residual heat: [ffacc40][4] kernels.
Adding up these numbers:
First interval: 20 kemeess
Second interval: 60 kernels
Third interval: 80 kernels
Fourth interval: 40 kernels
Residual beat: 10 kemelss
Total kernels popped during cooking-(20
200)
Adding the residual heat kemels:: (200 10 210)
Thus, the total mumber of pieces popcorn Garrett has to eat (bboxed) 210 )).
25

---

Okay, let's break down this problem step step.
It's about popcorn popping over time, and we noed to figure out the total number of pieces Garrett has to cat.
Firtt let's list out information given:
seconds, kernels pop.
scconds, three times that So, 3 20 60 kernels.
In the
pop.
3. In the following. 30 seconds, the popping rate increases to four times the initial rate.
The initial rate was 20 per 30 seconds.
so four times that
kemnlss.
the final seconds, popping
of previous 30 scconds. The previous
scconds,
so half that 40 kemnlls.
5. After taking the pan off the heat, quarter of
the number of kemels that popped in the final 30 seconds
also pop from the residual heat.
quarter
kemels.
Now, let's calculate the total number popped kemels in each time interval:
First 30 seconds: 20 kemelss
Sens-Merging
2. Next 30 seconds: 60 kernlk
3. Following 30 seconds: kemels
Final secomds: 40 kemells
Residual
To find the total number of kemelss popped,
add all these logether:
20 + 60 + 80 40 + 10 = 210 kernels
So, Garrett has to eat 210 pieces popcorn.
To determine the total number of pieces of popcorn Garrett has to eal, down problem step by step:
#erirst seconds: 20 kernels pop.
4* Next 30 seconds:**
times the initial rate, (3 times 20 6) kernels pup.
3. **Following 30 seconds:** ** 4 times the initial rate, so (4 times 20 80) kernels pop. **Final 30 **comds:** Hall the rate of the previous 30 seconds.
(Mirac (2))
pop.
**Residual beat quarter the final scconds' popping rate.
so( (r))
kernels pop.
Now, let's add all the popped kernels:
[20 - 60 80 + 10 + 10 210]
Therefore, the total number of picces of popcorn Garrett bas is:eee 210
26

---

To solve this problem, need calculate the number of popcorn kernels that each 30-second interval and then account for the additional popping from the residual heat.
Let's break down the problem step-by-step:
the
kernels pop.
In the
scconds,
the initial popping
times kernlls pop.
In the next 30 seconds,
times the initial popping rate, (4 times 20 80) kernels In the final 30 scconds, half the rate of the previous 30 seconds. so (Mrrac80))2) (2) = 40) kernels pop. pan
off
quarter the number kemells that popped in the final scconds also pop from the residual beat.
So, (Mrrac 40] [4) 10) additional kernels from the residual heat. The toral number of kernels that pop is the sum
of the kermels that pop ench interval plus the additional
pop from residual
Let's calculate this using Python code.
AIM
Python
Initial popping rate initial_rate 20
Popping each 30-aecond interval
first_interval initial_rate
second_interval 3 initial_rate _rat
third_interval initial_rata
fourth_interval (4 initisl_rate) //
Additional popping residual heat residual_popppng interval //
Total number of kernels that pop potal_popped - first_interval second_interval. + ibiervinteeral Fourth_interva rocidual_popping
(ritaltooll
The total number of pieces popcorn that Garrett has to cat (bboxed
27

---

Okay, let's break down this problem step step.
It's about popcorn popping over time, and we noed to figure out the total number of pieces Garrett has to cat. First, let's list out the information given:
the
seconds, kernels pop.
In the next seconds, three times that amount pop. 3 20 kemnlss.
In the following seconds, four times the initial popping rate.
The initial rate was 20 per 30 seconds, so 4 * 20 80 kernels. In the final 30 scconds, the popping rate half of the previous 30 seconds.
The provious rate was 80 per seconds, half of that 40 kernels.
After taking the pan
quarter the number kernels that popped in the final scconds also
pop from the residual heat.
So, quarter of 40 is 10 more kernels.
Now, let's add up all the popped kornels:
-First 30 seconds; 20
seconds:
ACM
Following 30 seconds:
Final 30 seconds: 40
Residual heat: 10
Toral popped kernels m 20 60 80 + 40 10 210
So, the total mumber of pieces of popcorn Garrett has to eal 210.
To
number pieces popcorn Garrett to eat, we'll break down the problem step by step:
1. **First 30 seconds:** ** 20 kernels pop.
2. **Next 30 secomds:* times the initial rate,
sa (3 times 60) kernels pop.
".*Following seconds:** times the initial rate, so (4 times 20 80) kernels pop. +*Fiinal 30 secomds:* Half the
previous 30 seconds.
(Mirac (2)) 40) kemels pop-
**Residual beat** A quarter of the linal 30 seconds' pops.
(Mrrac[40) (4) = 10) additional kereels
Adding all these together:
[20 60 + 80 + 40 + 10 = 210]
Therefore, the total numher of pieces of popcorn is (boxed 210
Table 13 presents the specific cases of ACM and other merging approaches on GSM8K dataset, showcasing the reasoning efficiency of our method. The comsumed tokens for each methods are 151 (Qwen, wrong answer), 737 (R1, correct answer), 356 (Sens-Merging, correct answer), 236 (AIM, wrong answer), 325 (ACM, correct answer) accordingly.
A.6 Limitations
We acknowledge the potential limitations of our work. First, due to constrained computational resources, we did not conduct evaluations on extremely large-scale models, such as LLaMA-3.1-1 3.B..... Furthermore, all the models we tested are dense models, leaving evaluations on Mixture-of- ox-erts (MoE) models unexplored. From the perspective of model merging, our work focuses exclusively on merging models within the same architecture, without addressing heterogeneous model merging.
A.7 Broader Impacts
Positive Societal Impacts By improving the efficiency and performance of LLMs in complex reasoning tasks while controlling output length, this research has the potential for significant positive societal impacts. More efficient and capable reasoning LLMs can accelerate scientific discovery, improve complex problem-solye and enhance educational tools by providing more nuanced and detailed explanations. The ability to generate concise yet accurate summaries of long reasoning chains through the L2S framework, as improved by ACM, could make advanced LLM capabilities more accessible and less computationally expensive, broadening their application in resource-constraines environments. This could lead to wider adoption of sophisticated AI assistants, potentially increasing productivity and innovation across industries and making advanced Al tools available to a broader range of users.
in various domains (e.g., medical diagnosis, engineering design).
28

---

Negative Societal Impacts Despite the potential benefits, the advancements presented also carry potential negative societal impacts. Improved reasoning and efficiency in LLMs, particularly the ability to condense complex information, could be leveraged for malicious purposes, such gener- ating highly convincing disinformation, crafting sophisticated phishing attacks, or automating the creation of deceptive content at scale. The enhanced ability to process and condense information might also raise privacy concerns applied to sensitive data without robust safeguards. Furthermore, while the paper focuses technical merging, the resulting models' deployment could exacerbate existing societal biases present in the training data or the models being merged, potentially leading to unfair or discriminatory outcomes in prciisoonmmkinng processes where these models applied. The increased efficiency might also contribute to the concentration of power in the hands of those with access to and control over such advanced AI technologies. Mitigation strategies, such promoting responsible development and deployment guidelines, developing methods for detecting malicious Al outputs, and addressing fairness and bias, crucial to address these risks.
29


Reviews:
[{"review_id": "RvdJVZ6kOa", "reviewer": "Reviewer_7bwQ", "summary": "The paper proposes Activation-Guided Consensus Merging (ACM) to improve the integration of multiple LLMs through model merging. Existing merging techniques often assume uniform importance across model layers, ignoring the diverse functional roles of different layers. ACM addresses this by using mutual information (MI) between layer-wise activations of pre-trained and fine-tuned models to assign layer-specific merging coefficients, giving more weight to divergent task-specific layers and less to redundant ones. This approach is plug-and-play, requiring no gradient computations or retraining.", "questions": "Do you assume that the fine-tuning data for all models is available? \n* If so, why would one apply model merging instead of simply fine-tuning on all the data, given that fine-tuning is usually not considered costly? \n* If not, can you provide an example of an application scenario where the datasets are not available, but the fine-tuned weights are?", "limitations": "I don't see obvious negative societal impact of this work.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n* The paper writing is overall clear and easy to follow.\n* The proposed model merging technique is well-motivated and reasonably principled.\n* The experimental performance is well acceptable, even compared with strong baselines such as Deepseek r1 and Qwen-2.5.\n\n**Weakness**\nI don't see significant weakness.", "was_revised": true, "final_justification": "The authors addressed my concerns in their rebuttal, and I have increased my score from 4 to 5.", "rebuttal": "We greatly appreciate the reviewer’s helpful feedback and recognition of our contributions. We would like to address your concerns as follows:\n\n---\n\n**R1Q1:** Availability of fine-tuning data\n\n**R1A1:** We address the reviewers' considerations as follows:\n\n* **Data Acquisition Challenges:** For fine-tuned models, the associated fine-tuning data is often inaccessible due to concerns regarding data privacy, ownership, and compliance with regulatory policies. For instance, while the HuggingFace platform hosts a large number of open-weights models, such as Qwen series and DeepSeek R1 series, the corresponding fine-tuning datasets are frequently unavailable or undisclosed.\n* **Orthogonality of Model Merging and Fine-Tuning:** Model merging and fine-tuning are orthogonal processes. After fine-tuning, model merging can still be performed. For example, we can merge models that have been fine-tuned in specific domains, such as fast-thinking models (Qwen series) and slow-thinking models (R1-Distill series), thereby integrating their capabilities, obtain a model that possesses long-chain reasoning capability while maintaining concise overall responses.\n* **Comparative Time Efficiency:** Fine-tuning is comparatively more time-intensive than model merging. In our experiments, merging a 1.5B model on  **CPU** required approximately **40 seconds**, whereas fine-tuning the DeepSeek-R1-1.5B model (optimized for slow thinking) with COT data (optimized for fast thinking) from s1K took around **10 minutes** for **three epochs on GPU**. The experimental results are presented below:\n\n |                | MATH: Accuracy(Length) | GSM8K: Accuracy(Length)| Time Consumption |\n| ------------------- | ------------------------ | ------------------------- | ----------------- |\n| Qwen2.5-Math-1.5B | 36.2 (411.0)          | 75.9 (118.1)           | NA               |\n| DeepSeek-R1-1.5B  | 69.6 (4508.2)         | 76.6 (2743.3)          |       NA         |\n| Qwen2.5-SFT       | 70.6 (4372.5)         | 77.5 (2536.3)          | 10 minutes      |\n| ACM(ours)       | 71.4 (1235.6)         | 78.4 (962.1)           | 40 seconds      |\n  \n   It can be observed that the model merging approach is more efficient, with higher performance and shorter length. Additionally, we reported the performance of DPO on the 7B model in *Section 4, Table 1*, finding that model merging is a resource-efficient yet highly effective method.\n\nOnce again, we greatly appreciate the reviewer’s valuable feedback and constructive suggestions."}, {"review_id": "5Y15DWhI7s", "reviewer": "Reviewer_fHAX", "summary": "The paper studies model merging over LLMs, with particular focus on the Long-to-Short task aiming to reduce the “reasoning trace” of reasoning models without waiving accuracy. To do so, they leverage task vectors, differences between finetuned models and their pretrained counterpart. The novelty of the paper stems in finding layer-specific merging coefficients that are a function of the mutual information between the activations of the task-specific model and the pretrained one.  The approach is extensively evaluated on long-to-short over Qwen2.5, Qwen2.5-Math and corresponding DeepSeek-R1 versions over GSM8K, MATH500, Minerva Math, Olympiadbench, College Math and AIME 2024. While LLama2-7B, MammoMath and CodeLlama-7b-hf over GSM8K, HellaSwag, MBPP-Pro are considered for general merging.", "questions": "- L100 says “arithmetic merging operates fine-tuned features as directional task vectors in parameter space”. What does this mean? I suggest rephrasing\n- Is there a way to assess to what degree does the result depend on the quality/size of the calibration dataset?\n- How significant are the gains? being somewhat marginal, are these expected to be consistent across different seeds and setups?\n\nOverall, given the added requirements with respect to standard baselines, the method needs to yield convincingly better results while ensuring the significance of these ones.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths\n\n- The paper is fairly clearly written, with clear methodology and detailed experimental setup. The code  is also provided for reproducibility and expected to be released upon acceptance.\n- The empirical evaluation is extensive, covering a diverse set of both reasoning and standard tasks for several different open state-of-the-art LLMs. The set of baselines is comprehensive enough.\n- The paper tackles an interesting and felt problem, as reducing the reasoning trace without waiving accuracy has immediate impactful applications, saving both computation and time.\n\n### Weaknesses\n\n- The gains seem marginal. When compared with AIM, the method obtains the same length reduction and an increase of 0.8% in accuracy. What is most striking, however, is that ACM-TIES with respect to standard TIES only results in +1% accuracy and +2.3% length on QWEN-1.5B and +0.08% accuracy on Lllama, despite requiring calibration data and added complexity.\n- The proposed approach seems to be incremental with respect to Sens-Merging [1], with the main difference stemming from a different way to compute the sensitivity of the parameters, as the proposed approach uses mutual information and Sens-merging using gradients. The paper only motivates the benefit of the approach with respect to Sens-merging as not requiring “complex gradient calculation”; I am not sure what complex here might mean. is it computationally expensive? error-prone?\n- Unconvincing motivation. I did not fully grasp why the mutual information between the activations of the pretrained model and those of the task-specific models is a meaningful quantity to be considered. Some additional explaination or theoretical/quantitative analysis might help understanding why this is a good idea in the first place.\n- Some minor inconsistencies.\n    - the paper claims: “In the specific case sigma is the activation function, the gradient is {0, 1}”; this is only true for some activation functions, e.g. ReLU, and does not hold in general.\n    - There are often inconsistenc spaces before/after equatons. I suggest removing all empty lines surrounding equation blocks in the source code.\n\n[1] Liu, Shuqi, et al. \"Sens-Merging: Sensitivity-Guided Parameter Balancing for Merging Large Language Models.\" *arXiv preprint arXiv:2502.12420* (2025).", "was_revised": true, "final_justification": "The paper presents a novel model merging approach mainly aiming to reduce the length of the models' output while preserving their accuracy. I raised the following concerns: minimal gains with respect to existing data-free baselines, incrementality of the approach and unconvincing motivations, along with some typos and inconsistencies. The rebuttal partially addressed some of these concerns, but I still feel the first and most important one to hold true: while ACM shows ~4% improvement over TIES in some cases, gains are marginal for LLaMA and TIES remains highly competitive for the stated goal of length reduction. The need for task-specific calibration data limits applicability, and the main stated reason of qualitative difference between the proposed method and prior work (not necessitating complex gradient computation) offers only modest practical benefit given merging’s one-off cost. Overall, the improvements do not, in my view, justify the added complexity and requirements. I maintain my borderline reject score.", "rebuttal": "We sincerely thank the reviewer for the constructive suggestions. We would like to address your concerns as follows:\n\n---\n\n**R2W1&Q3-a&Q4:** Analysis and Explanations of Gains on ACM\n\n**R2A1:** In the L2S task, we would kindly clarify that ACM improves on TIES and R1  by **4.2%** and **2.3%** respectively, not 1% as the reviewer stated. Our Table 2 in the manuscript shows ACM significantly outperforms AIM on the 1.5B model, with a supplementary 14B AIM experiment yielding\n75.5% accuracy compared to ACM's 77.1% (a 1.6% increase). We will incorporate the  AIM results into Appendix A.2.\n\n|    | GSM8K | MATH500 | AIME | Avg. |\n| ----- | ------- | --------- | ------ | ------ |\n| AIM | 46,7  | 88.2    | 46.7 | 75.5 |\n| ACM | 92.6  | 88.6    | 50.0 | 77.1 |\n\nMeanwhile, we would like to remind that as clarified in section 2, *L2S task prioritizes length reduction while maintaining accuracy[2,3]*. It is expected that responses are slightly longer on the L2S task due to the integration of long CoT model, compared to short CoT model. ACM achieves a **73.5%** length reduction relative to R1 on the 1.5B model with minimal resources.\n\nAs for resource consumption, as outlined in Section 4.1 Table 1, we employed merely 10% of the calibration data. In our experiments, merging a 1.5B model on a **CPU** required approximately **40 seconds**, whereas fine-tuning the R1-1.5B model (optimized for slow thinking) with COT data (optimized for fast thinking)  from S1K took around  **10 minutes** for three epochs on **GPU**.\n\n|                  | MATH  Accuracy(Length) | GSM8K Accuracy(Length) |\n| ------------------- | ------------------------ | ------------------------- |\n| Qwen2.5-Math-1.5B | 36.2 (411.0)          | 75.9 (118.1)           |\n| DeepSeek-R1-1.5B  | 69.6 (4508.2)         | 76.6 (2743.3)          |\n| Qwen2.5-SFT       | 70.6 (4372.5)         | 77.5 (2536.3)          |\n| ACM     | 71.4 (1235.6)         | 78.4 (962.1)           |\n\nThe model merging approach proves to be more efficient, delivering higher performance with reduced length. In Section 4, we highlighted the DPO performance on the 7B model, demonstrating that model merging is both resource-efficient and effective. Section 5 compares our method to popular RL L2S approaches. Despite the higher training costs of RL, our method achieves a similar reduction in length. We report average scores across **five** runs with different random seeds.\n\nIn general tasks, smaller gains align with UniTE[1]'s recommendation that model accuracy differences should be less than 15%, as the performance disparity among models in the pool is substantial, resulting in limited improvements.\n\n[1] Determine-Then-Ensemble: Necessity of Top-k Union for Large Language Model Ensembling. ICLR 2025\n\n[2] O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning.  Arxiv 2025/01\n\n[3] L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning. Arxiv 2025/03\n\n**R2W2:** Difference compared to Sens-Merging\n\n**R2A2:**  ACM and Sens-Merging are fundamentally distinct in methodology and design. **1)**  ACM leverages activation information—commonly used in model quantization [4]—and requires only forward propagation, whereas Sens-Merging depends on gradient computation, necessitating both forward and backward passes. This results in higher computational overhead for Sens-Merging. **2)**  ACM assesses model information correlation through mutual information, whereas Sens-Merging requires multiple task-specific and cross-task scaling hyperparameters, adding complexity and sensitivity. In contrast, ACM depends on a single hyperparameter, demonstrating robustness and simplicity. **3)** Experimental results demonstrate that ACM consistently outperforms Sens-Merging, validating its effectiveness.\nDue to space constraints, we focused on ACM principles in the manuscript but will incorporate more details on baseline methods like Sens-Merging in the final version. \n\n[4] AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration. MLSys 2024\n\n**R2W3:** Usage of Mutual Information\n\n**R2A3:** We present our rationale for utilizing mutual information from the following perspectives:\n\n**1) Definition and Application:** Mutual information(MI) quantifies the interdependence between two variables, reflecting the extent to which knowledge of one reduces uncertainty about the other. It is extensively employed in representation learning [5]. In model merging, as outlined in Section 3.1, MI assesses the relationship between the weights of the FT and PT models. High MI indicates redundancy (e.g., both models excel at similar tasks or response styles), resulting in limited performance improvements and potential noise introduction. Conversely, low MI suggests orthogonal knowledge, facilitating the effective integration of complementary capabilities and enhancing generalization.\n\n**2) Evaluation of Alternative Metrics:** In our preliminary experiments, we considered KL divergence and cosine similarity to measure model relationships.\n\n* **KL divergence** is asymmetric; for instance, with P=[0.9,0.1] and Q=[0.5,0.5], we found $D_{KL}(P∥Q)≈0.368$ and $D_{KL}​(Q∥P)≈0.511$, leading us to exclude this metric.\n* **Cosine similarity**  exhibits substantial variability across layers, approximately ranging from 0.25 to 0.8, which can negatively impact performance, as prior studies emphasized that weight coefficient fluctuations should be minimal [6]. Furthermore, the range of cosine similarity is (-1, 1), complicating the interpretation of negative values.\n\nWe chose MI as a robust tool for examining model relationships. Due to space limitations, we emphasized its relevance in model merging and our further experiments validate its effectiveness. We appreciate the reviewers' advice and will incorporate preliminary observations in the final version.\n\n[5] A Mutual Information Maximization Perspective of Language Representation Learning. ICLR 2020\n\n[6] Sens-Merging: Sensitivity-Guided Parameter Balancing for Merging Large Language Models. ACL 2024\n\n**R2W4:** Activation Theoretical Analysis\n\n**R2A4:** We sincerely thank the reviewer for this insightful comment. Our intention was to use ReLU as an illustrative example to clearly present the core mechanism of our proposed method.  In our analysis, the central quantity of interest is $S(W) := sup_x sup_∇ ⟨∇, Δ W x⟩$, where the supremum is taken over the set of all possible gradients ∇ of the activation function. For this quantity to be well-defined and serve as a meaningful bound, the essential requirement is that the set of gradients must be **bounded.**\n\n* In the specific case of ReLU, the set of gradients is simply {0, 1}, making the characterization of $S(W)$ very straightforward. We used this case to build intuition.\n* For more general activation functions, such as GELU and SwiGELU, the gradient ∇ is not binary but belongs to a continuous, bounded interval (approximately [-0.17, 1.17]). Because this set is bounded, the sup_∇ operation is still well-defined, and our formulation of $S(W)$ remains valid and finite.\n\nTherefore, our core argument does not rely on the gradient being binary, but on the fact that for almost all modern activation functions, the gradient is bounded. This ensures that $S(W)$  is a meaningful quantity that can be analyzed.\n\nWe appreciate the reviewer's feedback and will revise this section to introduce the quantity $S(W)$ and a bounded gradient. We will adjust space format as well.\n\n**R2Q1:** Explanation of L100\n\n**R2A5:** The task vector is defined as  $δ_i = θ_i − θ_0$, $θ_i$ usually refers to the weights of fine-tuned models, and $θ_0$ is that of the pretrained model. Task vectors highlight fine-tuned features. Arithmetic merging, including average or weighted averaging (TA), directly operates on these task vectors.\n\n**R2Q2&Q3-b:** Calibration dataset\n\n**R2A6:** In Section 4 “Models and Datasets”, we mentioned that we cluster the data in s1K and uniformly sample 10% (100 pieces) of the data for multiple experiments. This approach is intended to mitigate potential biases arising from uneven sampling. Additionally, in earlier experiments, we sampled varying sizes of data for analysis, and the test results for GSM8K on the 7B model are presented below:\n\n| Data Pieces | 20     | 50     | 100   | 200    | 300   |\n| ------------- | -------- | -------- | ------- | -------- | ------- |\n| Accuracy| 91.4   | 90.8  | 92.2 | 91.8  | 92.1  |\n| Length      | 623.63 | 624.17 | 538.3 | 585.65 | 603.0 |\n\nOur results show that accuracy stabilizes and response length remains short once calibration data reaches 100 samples. We analyzed the weight coefficients at this threshold. Below 100 data points, the distribution fluctuates significantly, particularly in the top five layers. However, when the count exceeds 100, these characteristics stabilize. This trend holds across 1.5B and 14B models, supporting our use of a 10% sampling rate. For larger models (e.g., >100B), more data may be needed, though resource constraints limited further study. We posit that activation-based methods necessitate fewer data and computational resources compared to SFT or RL.\n\nWe also present the results of the 7B model using different seeds as follows:\n\n|         | seed a | seed b | seed c |\n| ---------- | -------- | -------- | -------- |\n| Accuracy | 91.9 | 91.7  | 92.4   |\n| Length   | 558.33 | 553.58 | 541.41 |\n\nIt is evident that our clustering and sampling methods are both reasonable and robust. We sincerely appreciate the reviewers' suggestions and will incorporate these experiments into the appendix.\n\nAgain, we sincerely appreciate the valuable suggestions provided by the reviewers. If our explanations can assist the reviewers in better understanding our paper, we would be delighted. Should the reviewers have any further questions, we welcome further discussion."}, {"review_id": "H9IXfWfeI9", "reviewer": "Reviewer_Dbaq", "summary": "This paper proposes Activation-Guided Consensus Merging (ACM), a plug-and-play method for merging large language models (LLMs) using layer-wise weighting based on mutual information (MI) between activations. Motivated by the observation that different layers contribute unequally to downstream task performance, ACM computes per-layer MI between the pre-trained and fine-tuned models and uses this to derive adaptive coefficients for merging. Unlike previous methods that require gradient computation or rely solely on activations from a single model, ACM introduces a symmetric MI-based strategy that balances parameter reuse and task-specific adaptation. Extensive experiments on Long-to-Short (L2S) reasoning and general merging tasks across various model scales (1.5B to 32B) demonstrate that ACM consistently improves accuracy while reducing redundancy, outperforming existing merging baselines.", "questions": "I list my concerns and questions in the \"weaknesses\" section. \n\nAside from those, I have one additional point of interest:\n- Given that the method computes MI over shared inputs, how well does it handle merging models trained on different tasks or exhibiting divergent behaviors? It would be helpful to discuss whether MI remains a meaningful signal in such heterogeneous scenarios.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n- The paper presents a well-motivated solution to the limitations of uniform merging strategies, introducing a mutual information (MI)-based method for assigning layer-wise coefficients in a principled way.\n\n- The proposed approach is training-free and computationally efficient, which is particularly appealing for real-world settings where retraining is impractical.\n\n- The experimental setup is comprehensive, covering a range of model sizes, architectures (e.g., Qwen, LLaMA), and task types including math, commonsense reasoning, and code generation. The method demonstrates consistent gains across these settings.\n\n- The use of MI as a signal for balancing redundancy and task specificity is conceptually clear and supported by both theoretical rationale and empirical evidence.\n\n- The method is compatible with existing merging frameworks such as TA and TIES, and appears to further enhance their performance, particularly in managing accuracy and response length trade-offs.\n\nWeaknesses:\n\n- The computation of MI-based merging coefficients relies on a calibration dataset and its clustering, which may introduce some sensitivity to the choice of data and its representativeness. A more detailed discussion of this point would be helpful.\n\n- While the method is designed to be plug-and-play, the requirement to extract activations from both the pre-trained and fine-tuned models introduces added complexity compared to simpler, static baselines.\n\n- The evaluation primarily focuses on long-to-short reasoning and mathematical tasks. Additional results on open-ended generation or instruction-following could help better understand the method’s generalization across a wider range of use cases.", "was_revised": true, "final_justification": "Thanks for the detailed responses. All my concerns are addressed.", "rebuttal": "We sincerely appreciate the valuable advice from the reviewer. And we would like to address your concerns as follows:\n\n---\n\n**R3W1:** Calibration dataset\n\n**R3A1:** In Section 4 “Models and Datasets”, we mentioned that we cluster the data in s1K and uniformly sample 10% (1000 \\* 10% = 100 pieces) of the data for multiple experiments. This approach is intended to mitigate potential biases arising from uneven sampling. Additionally, in earlier experiments, we sampled varying sizes of calibration datasets for analysis, and the test results for GSM8K on the 7B model are presented below:\n\n| Data Pieces | 20     | 50     | 100   | 200    | 300   |\n| ------------- | -------- | -------- | ------- | -------- | ------- |\n| Accuracy  | 91.4   | 90.8  | 92.2 | 91.8  | 92.1  |\n| Length      | 623.63 | 624.17 | 538.3 | 585.65 | 603.0 |\n\nOur observations indicate that once the number of calibration data points reaches 100, accuracy remains high while length remains short. We also analyzed the weight coefficients at this threshold. When the number of data is below 100, the distribution of weight coefficients fluctuates significantly, with the top five layers showing considerable variation. Conversely, when the count exceeds 100, these characteristics stabilize. This trend is similar across models such as 1.5B and 14B. Thus, we advocate for a 10% sampling rate in our experimental design. For larger models (e.g., those exceeding 100B), additional calibration data may be required; however, resource limitations prevented us from further experimentation. We posit that activation-based methods necessitate fewer data and computational resources compared to supervised fine-tuning or reinforcement learning.\n\nWe also present the results of the 7B model using different sampling seeds as follows:\n\n|         | seed a | seed b | seed c |\n| ---------- | -------- | -------- | -------- |\n| Accuracy | 91.9 | 91.7  | 92.4   |\n| Length   | 558.33 | 553.58 | 541.41 |\n\nIt is evident that our clustering and sampling methods are both reasonable and robust.  \n\nAdditionally, we investigated the effects of varying the number of clusters. Our results demonstrate that random clustering results in suboptimal performance, indicating possible imbalance in the dataset's distribution. Notably, with and beyond 20 clusters, we observed improved accuracy and reduced length, suggesting that clustering then sampling effectively mitigates data imbalance.\n\n| Clusters | random | 10    | 20    | 30    |\n| ---------- | -------- | ------- | ------- | ------- |\n| Accuracy | 88.6   | 91.1 | 91.8  | 91.6 |\n| Length   | 643.4  | 602.2 | 538.3 | 586.7 |\n\nWe sincerely appreciate the reviewers' suggestions and will incorporate these experiments into the appendix.\n\n**R3W2:** Computational overhead as a plug-and-play approach\n\n**R3A2:**  According to our analysis, the ACM method demonstrates exceptional computational efficiency on the experimental equipment mentioned in the paper: the 1.5B model experiment requires only about **40 seconds** on **CPU**, while the 7B and 14B models need only about **1-1.5 minutes**. Considering the significant accuracy improvement brought by ACM (such as **2.3%** improvement over R1 for the 1.5B model) and the substantial length reduction (**73.5%** reduction compared to R1), the required computational overhead is negligible. Furthermore, some baseline methods, such as Sens-Merging and AIM, also require additional calibration calculations. As analyzed in section 5, Figure 5, compared to resource-intensive training methods, ACM can easily achieve significant length reduction effects at extremely low cost.\n\nWe further supplement the results with fine-tuning of the DeepSeek-R1-1.5B model (optimized for slow thinking) on s1K's COT data (optimized for fast thinking), which took approximately **10 minutes** for three epochs on a **GPU**. The experimental results are presented below:\n  \n |                | MATH: Accuracy(Length) | GSM8K: Accuracy(Length)| Time Consumption |\n| ------------------- | ------------------------ | ------------------------- | ----------------- |\n| Qwen2.5-Math-1.5B | 36.2 (411.0)          | 75.9 (118.1)           | NA               |\n| DeepSeek-R1-1.5B  | 69.6 (4508.2)         | 76.6 (2743.3)          |       NA         |\n| Qwen2.5-SFT       | 70.6 (4372.5)         | 77.5 (2536.3)          | **10 minutes**     |\n| ACM(ours)       | 71.4 (1235.6)         | 78.4 (962.1)           | **40 seconds**      |\n  \nIt can be observed that our model merging approach ACM is more efficient, with higher performance and lower length. \n\n**R3W3:** Extension Experiments\n\n**R3A3:** For a fair comparison, we followed the task selection of the baseline methods and conducted experiments on the L2S tasks (including both simple and complex reasoning tasks, code generation tasks), as well as general model merging tasks (math and code model merging tasks). We appreciate the reviewer's suggestion; due to limitations in API resources, we selected the IFEval dataset [2]—a benchmark for instruction following—to evaluate our method. The experimental results are as follows:\n\n|        | prompt-level   | instruction-level |\n| ---------- | ---------------- | ------------------- |\n| TIES     | 18.48          | 30.58             |\n| ACM-TIES | 20.15 (+1.67) | 31.06 (+0.48)    |\n\nWe find that on the instruction-following dataset, ACM can further enhance the model merging performance of TIES, thereby further validating the effectiveness of our ACM approach.\n\n**R3Q1:** Mutual information on heterogeneous scenarios\n\n**R3A4:** Mutual information quantifies the interdependence between two random variables, reflecting the extent to which knowledge of one reduces uncertainty about the other. It is extensively employed in representation learning [1]. In the context of model merging, as outlined in Section 3.1, mutual information assesses the relationship between the weights of the FT and PT models. High mutual information indicates redundancy (e.g., both models excel at similar tasks), resulting in limited performance improvements and potential noise introduction. Conversely, low mutual information suggests orthogonal knowledge (e.g., code and math tasks), facilitating the effective integration of complementary capabilities and enhancing generalization.\n\nTherefore, in the design of our ACM framework, when merging models with substantially different response patterns—such as in L2S tasks—or across heterogeneous tasks like code generation and mathematical reasoning, we assign relatively lower merging weights when the mutual information between corresponding layers is high, and higher weights when the mutual information is low. This adaptive weighting scheme effectively emphasizes task-specific (non-shared) features while preserving shared knowledge, thereby enhancing the model's ability to generalize across diverse task domains.\n\nWe sincerely thank the reviewer for the insightful and constructive feedback. We hope our responses could adequately addressed the reviewer's concerns.\n\nReferences:\n\n[1] A Mutual Information Maximization Perspective of Language Representation Learning. ICLR 2020\n\n[2] Instruction-Following Evaluation for Large Language Models.  Arxiv 2023.11"}, {"review_id": "Imedt2aB4b", "reviewer": "Reviewer_W7BU", "summary": "The paper proposes Activation-Guided Consensus Merging (ACM), a novel method for merging Large Language Models (LLMs) by dynamically weighting layer contributions based on mutual information (MI) between activations of pre-trained and fine-tuned models. Unlike traditional merging techniques that assume uniform layer importance, ACM identifies task-specific critical layers, reducing redundancy while preserving performance. Experiments on Long-to-Short (L2S) reasoning and general merging tasks demonstrate that ACM improves reasoning accuracy (e.g., +1.3 points on Qwen-7B) while significantly shortening responses (e.g., -55.3% length). The method is plug-and-play, requiring no additional training or gradients, and outperforms baselines like TIES-Merging and DARE.", "questions": "1. Why use mutual information instead of other similarity metrics? The paper argues MI captures redundancy, but alternatives (e.g., cosine similarity, KL divergence) might offer different trade-offs in efficiency or interpretability.\n\n2. How does ACM handle conflicting tasks in multi-task merging? The experiments focus on L2S and single-task merging. Can ACM resolve conflicts when merging models fine-tuned for opposing objectives (e.g., conciseness vs. verbosity)?\n\n3. Is the improvement statistically significant? Accuracy gains (e.g., +1.3 points) are modest. Were significance tests conducted to rule out random variation?", "limitations": "While the hyperparameter t is claimed to be robust, its optimal value may vary across tasks (e.g., coding vs. math reasoning). No adaptive tuning strategy is proposed.\n\nResults for 32B models show diminishing returns in length reduction. The paper does not address whether ACM’s benefits hold for trillion-parameter models or on-device LLMs.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "1. Evaluated primarily on Qwen and LLaMA families; unclear how ACM performs on architectures with significantly different layer structures (e.g., MoE models).\n\n2. Relies on a curated dataset (s1K) for activation alignment. Performance may degrade with poorly representative or biased calibration data.\n\n3. How does the system 1/2 discussion related to this work \"Visual agents as fast and slow thinkers\" ICLR? Both work has similar motivation.", "was_revised": true, "final_justification": "This is an interesting work that introduces a novel technique. Given its value, I would like to see it made visible to the broader community.", "rebuttal": "We sincerely appreciate the time and effort you put into reviewing our paper. We appreciate the insightful feedback and address your concerns as follows:\n\n---\n\n**R4W1:** MoE architecture\n\n**R4A1:** We would kindly clarify that as we stated in the end of section 2, Mixture-of-Experts (MoE) merging strategies require fundamental architectural modifications, including the incorporation of expert routing mechanisms and gating networks, which extend beyond the scope of parameter-space merging techniques addressed in this work [1]. While MoE represents a related research direction, its dynamic expert selection mechanism and architectural adaptations fundamentally distinguish it from the static parameter merging approaches investigated herein. We would like to note that the baseline methods compared in this paper didn‘t consider MoE merging either.\n\n[1] Branch-Train-MiX: Mixing Expert LLMs into a Mixture-of-Experts LLM. COLM 2024\n\n**R4W2:** Other calibration dataset\n\n**R4A2:** To alleviate the reviewers' concerns, we have also chosen the recently released LIMO[2] dataset as the calibration dataset for our experiments. LIMO challenges conventional wisdom in mathematical reasoning by showing that models can achieve superior performance with significantly less, yet higher quality, training data. In line with the settings applied in s1K, we conducted experiments using LIMO on GSM8K and Minerva Math, and the results are presented below:\n\n|                | GSM8K: Accuracy (Length) | Minerva Math: Accuracy (Length) |\n| ------------------ | -------------------------- | --------------------------------- |\n| Qwen-Math-1.5B   | 75.9 (118.1)             | 11.4 (1036.8)                   |\n| DeepSeek-R1-1.5B | 76.6 (2743.3)            | 15.1 (6374.2)                   |\n| Task Arithmetic  | 74.5 (549.7)             | 21.0 (1671.0)                   |\n| ACM-TA-s1K       | 76.8 (438.0)             | 25.3 (1214.7)                   |\n| ACM-TA-LIMO      | 76.9 (604.9)             | 22.3 (1549.7)                   |\n\nOur method demonstrates good adaptability to the new calibration dataset and exhibits robustness.\n\n[2] LIMO: Less is More for Reasoning. COLM 2025\n\n**R4W3:** Comparison of system 1/2 discussion to previous work\n\n**R4A3:** System 2 architectures are fine-tuned with extended thinking chains to promote deliberate analysis through iterative self-assessment, error mitigation, and verification, albeit facing challenges related to redundancy. In our work, the concept of System 2 follows [3,4,5], which is consistent with the notion that \"System 2 delineates a cognitive mode distinguished by deliberate, analytical, and consciously reasoned processes\" mentioned in \"Visual agents as fast and slow thinkers.\" Furthermore, these works also align in their definition of System 1. We appreciate the reviewer's reminder, providing us with a visual perspective on system 1/2. We will cite this paper in our related works section in the final version.\n\n[3] OpenAI. Openai o3-mini: Pushing the frontier of cost-effective reasoning. Arxiv 2025.01\n\n[4] Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. Arxiv 2025.01\n\n[5] From system 1 to system 2: A survey of reasoning large language models. Arxiv 2025.02\n\n**R4Q1&Q2-a:** Usage of Mutual Information\n\n**R4A4:** We present our rationale for utilizing mutual information from the following perspectives:\n**1) Definition and Application:** Mutual information quantifies the interdependence between two variables, reflecting the extent to which knowledge of one reduces uncertainty about the other. It is extensively employed in representation learning [6]. In the context of model merging, as outlined in Section 3.1, mutual information assesses the relationship between the weights of the FT and PT models. High mutual information indicates redundancy (e.g., both models excel at similar tasks), resulting in limited performance improvements and potential noise introduction. Conversely, low mutual information suggests orthogonal knowledge, facilitating the effective integration of complementary capabilities and enhancing generalization.\n**2) Evaluation of Alternative Metrics:** In our preliminary experiments, we considered KL divergence and cosine similarity to measure model relationships.\n\n* **KL divergence** is asymmetric; for instance, with P=[0.9,0.1] and Q=[0.5,0.5], we found $D_{KL}(P∥Q)≈0.368$ and $D_{KL}​(Q∥P)≈0.511$, leading us to exclude this metric.\n* **Cosine similarity**  exhibits substantial variability across layers, approximately ranging from 0.25 to 0.8, which can negatively impact performance, as prior studies emphasized that weight coefficient fluctuations should be minimal [7]. Furthermore, the range of cosine similarity is (-1, 1), complicating the interpretation of negative values.\n\nIn summary, we selected mutual information as a robust tool for examining model relationships. Due to space limitations, we emphasized its relevance in model merging and our further experiments validate its effectiveness. We appreciate the reviewers' suggestions and will incorporate preliminary observations in the final version.\n\n[6] A Mutual Information Maximization Perspective of Language Representation Learning. ICLR 2020\n\n[7] Sens-Merging: Sensitivity-Guided Parameter Balancing for Merging Large Language Models. ACL 2024\n\n**R4Q2-b:** Illustration of ACM on “conciseness vs. verbosity”\n\n**R4A5:** In the design of our ACM framework, when merging models with substantially different response patterns—such as in L2S tasks—or across heterogeneous tasks like code generation and mathematical reasoning, we assign relatively lower merging weights when the mutual information between corresponding layers is high, and higher weights when the mutual information is low. This adaptive weighting scheme effectively emphasizes task-specific (non-shared) features while preserving shared knowledge, thereby enhancing the model's ability to generalize across diverse task domains.\nWe would kindly clarify that, as we mentioned in section 4.1 “Main Results”，we observed that response length positively correlates with question difficulty. Furthermore, as shown in the Appendix A.3, the merged model retains reflective capabilities; however, reflection frequency has decreased due to the PT fast-thinking model. According to our careful case study, while the merged model maintains favorable reasoning ability, it avoids redundant reflection on simpler mathematical problems, such as those in GSM8K, thereby reducing response length.\n\n**R4Q3:** Analysis and Explanations of Gains on ACM\n\n**R4A6:** In the L2S task, for instance, we would kindly clarify that ACM improves on TIES and R1 by **4.2%** and **2.3%**, respectively. Our manuscript shows ACM significantly outperforms AIM on the 1.5B model, with a supplementary 14B AIM experiment yielding 75.5% accuracy compared to ACM's 77.1% (a **1.6%** increase). We will incorporate the  AIM results into Appendix A.2..\n\n|   | GSM8K | MATH500 | AIME | Avg. |\n| ----- | ------- | --------- | ------ | ------ |\n| AIM | 46,7  | 88.2    | 46.7 | 75.5 |\n| ACM | 92.6  | 88.6    | 50.0 | 77.1 |\n\nMeanwhile, we would like to remind that as clarified in section 2, L2S task prioritizes length reduction while maintaining accuracy [8,9]; ACM achieves a **73.5%** length reduction relative to R1 on the 1.5B model with minimal resources.\n  \nIt can be observed that our model merging approach ACM is more efficient, with higher performance and lower length. \n\nWe report the average scores across **five runs** with different random seeds. In Section 5, a comparison is made between our method and reinforcement learning (RL) approaches. Despite the considerably higher training costs associated with RL, our method attains a comparable reduction in length.\n\n[8] O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning.  Arxiv 2025/01\n\n[9] L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning. Arxiv 2025/03\n\n**R4Q4:** Hyperparameter and model size limitations\n\n**R4A7:** In comparison to alternative approaches, our method requires searching only **one** hyperparameter, whereas other baseline methods typically necessitate multiple hyperparameter searches. Due to resource constraints, we were unable to conduct experiments on 100B-scale models; however, we have successfully performed experiments on 32B (mentioned section 4.1 and Appendix Table 5) and 1.5B (Page 7, Table 2) models as reported. \n\nWe would like to reiterate our sincere appreciation for the reviewer’s helpful and thoughtful comments."}]

Author rebuttal:

Meta-review: This paper proposes a plug-and-play merging framework that determines layer-specific merging coefficients based on mutual information between activations of pre-trained and fine-tuned models. The proposed method, called activation-guided consensus merging (ACM), preserves task-specific capabilities without requiring gradient computations or additional training. The experimental evaluation on Long-to-Short (L2S) and general merging tasks demonstrates that ACM outperforms baseline methods.

This paper is generally well-written and easy to follow. The design principle and experimental evaluation are reasonable. The proposed ACM is compatible with existing merging methods. However, some weaknesses were pointed out by the reviewer, such as a marginal performance gain and unconvincing motivation.

The authors' rebuttal made the contribution of the paper clear to most reviewers. Compiling the reviewers' comments and discussion, I think that the strengths of this paper outweigh its weaknesses. Therefore, I recommend accepting this paper.

I would encourage the authors to include the explanations and experiments added in the rebuttal and discussion phase in the revised paper, and clarify the advantages and motivation of the presented method.
Decision: Accept (poster)