MergOPT: A Merge-Aware Optimizer for Robust Model Merging
Authors: Enneng Yang
Qun Yang
Peng Wang
Anke Tang
Guibing Guo
Xiaochun Cao
Li Shen
Venue: ICLR 2026 Poster (2026)
Keywords: Model Merging
Fine-tuning
Multi-task Learning
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: This paper proposes a novel merging-aware optimizer (called MergOPT) that injects principled parameter perturbations into the weight update steps so that the fine-tuned model exhibits a more stable loss landscape under subsequent merging operations.

Abstract: Model merging aims to integrate multiple independently fine-tuned expert models into a single model while preserving the knowledge of all experts. However, existing approaches mainly address parameter conflicts at the merging stage and overlook the role of the fine-tuning process, which often leads to significant post-merge performance degradation. To address this limitation, we propose a novel merging-aware optimizer (abbreviated as MergOPT) that injects principled merge-induced parameter shifts into the weight update steps so that the fine-tuned model exhibits a more stable loss landscape under subsequent merging operations. Specifically, we first formulate model merging as a distributionally robust optimization problem in the weight space: the parameters of other experts to be merged are viewed as adversarial merge-offsets, and fine-tuning adapts to the worst-case merging scenario. Building on this formulation, we analyze the distribution of parameter updates and the effects of merging hyperparameters, from which we derive a merging-guided feasible region for weight shifts. Finally, extensive experiments across four large language models (LLMs) and one vision model show that our approach consistently outperforms standard fine-tuning, yielding an average relative gain of 3.5\% and a maximum gain of 9.5\% across four merging strategies when merging seven experts.

Published as a conference paper at ICLR 2026
MERGOPT: A MERGE-AWARE OPTIMIZER FOR Ro- BUST MODEL MERGING
Enneng Yang! Qun Yang", Peng Wang', Anke Tang', Guibing Guo', Xiaochun Cao', Li Shen
Shenzhen Campus of Sun Yat-sen University
Guangdong Laboratory of Artificial Intelligence and Digital Economy (S7.)
8 National University of Defense Technology; 4 Wuhan University; Northeastern University, China ennengyang@gmal com, yangqunEnudt. wdw.uddt.eed........o.oo. edu mathsshenli@gaai com
ABSTRACT
Model merging aims integrate multiple independently fine-tuned expert models into single model while preserving the knowledge of all experts. However, exist- ing approaches mainly address parameter conflicts the merging stage and over- look the role of the fine-tuning process, which often leads to significant post-merge performance degradation. To address this limitation, we propose a novel merging- aware optimizer (abbreviated MergOPT) that injects principled merge-induced parameter shifts into the weight update steps so that the fine-tuned model exhibits more stable loss landscape under subsequent merging operations. Specifically, we first formulate model merging as a distributionally robust optimization problem in the weight space: the parameters of other experts be merged viewed as ad- versarial merge-offsets, and fine-tuning adapts to the worst-case merging scenario. Building on this formulation, we analyze the distribution of parameter updates and the effects of merging hyperparameters, from which we derive merging- guided feasible region for weight shifts. Finally, extensive experiments across four large language models (LLMs) and one vision model show that our approach consistently outperforms standard fine-tuning, yielding an average relative gain of 3.5% and a maximum gain of 9.5% across four merging strategies when merging seven experts.
INTRODUCTION
Multi-task learning is the conventional approach for adapting a foundation model to multiple down- stream tasks, where diverse datasets jointly used to update the model (Zhang & Yang 2021| Chen iet al. 2024). However, this strategy requires centralized access to data, leading to high management costs and privacy concerns. To overcome these limitations, model merging has recently been pro- posed as an alternative paradigm (Yang et al. (024a). In this setting, multiple expert models are first fine-tuned independently on different tasks and then merged into single model at the parameter level, with the goal of inheriting the knowledge of all experts without centralized data sharing. This paradigm has shown promising results various domains, including computer vision (Thharco et al., 2023, Ortiz-Jinm Jimenez et al. 2023 Jin et al. 2024 Gargiulo et al. 2025) and natural language process- ing (Yadav et al. 2023] Wan et al.) 2024a Yu et al. 2024 Akiba et al. 2025). central challenge in model merging lies in effectively mitigating parameter conflicts that arise when integrating multiple expert models, as such conflicts often lead to severe performance degradation.
The most straightforward merging strategy is linear interpolation, where model parameters simply averaged across experts (Wortsman et al. (022). However, due to the highly nonlinear nature of deep neural networks and the complex interdependencies between tasks, this approach typically yields suboptimal results. To overcome these limitations, recent research has explored more sophisticated merging strategies. For instance, task arithmetic (Tharcoo al., 2023) first represents the difference between a fine-tuned model and its pre- trainre counterpart as a task vector, and constructs a unified multi-task model by linearly combining these vectors, thereby partially preserving task-specific knowledge. In addition, adaptive weighting methods dynamically adjust the contribution of each
"Equal contribution Corresponding author

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task according to task characteristics, employing either heuristic approaches such as evolutionary search (Akiba et al.| 20255; Mencattini et al.] (025) or data-driven weight optimization (Matena & Raffel 2022 Vin et al. [023] Yang et 20044b Tang et al. 2024a). Another line of work, subspace
merging methods, a alleviates task interference by projecting parameters into a sparse (Yaday et al.
2023 Yu et al.] 2024 Wang et al.] 2024; Zhuu et al. 2024) or low-rank subspace (Gargiulo et al.
2025 Marczak et al. (225), thereby mitigating performance loss caused by conflicts. Lastly, weight alignment methods exploit the property of linear mode connectivity in deep neural networks, which suggests that multiple equivalent loss landscapes can exist (Garipov et al. [018 Draxler et al. 2018). By parameter permutations or aligning the parameters of expert models such that they lie within the same loss landscape, these approaches aim to reduce potential conflicts during model merging (Jordan) et al. 2023 Ainsworth et al. 2023 Rinaldi et al. 2025). By leveraging fine-grained parameter manipulation, these methods typically achieve better performance than simple averaging.
Even with these advances, most of the existing methods predominantly focus on the merging stage, i.e. designing strategies to reduce conflicts when merging expert models, while largely overlooking the role of the fine-tuning stage. In this work, we contend that the effectiveness of the final merged model crucially depends on both stages: fine-tuning must prepare models in a way that facilitates compatibilityy, while merging must integrate them effectively. To the best of our knowledge, only few model merging works explicitly focus on the fine-tuning stage. For example, tangent-space fine-tuning methods linearize the model and perform optimization in its tangent space to enhance weight disentanglement (Ortiz-Jimenez al. 2023] Jin et al., 2024] Tang al. 2024b), thereby alleviating conflicts during merging. However, inference with such linearized models typically incurs a 3x higher computational cost compared standard models (Ortiz-Jimenez et al. 2023). In
another line of work, SAFT-Merge (Lee et al. (025) is inspired by sharpness- awwae aware minimization (SAM) (Foret et al.] 2021 Kwon al.] 2021) and aims to improve mergeability by encouraging flatter loss landscapes during fine-tuning. Yet SAM-based fine-tuning usually doubles the training time relative to standard fine-tuning. Given that most existing approaches focus primarily on the merging stage and that the few methods targeting fine-tuning often come with substantial training or inference overhead, we argue that there is a strong need for a fine-tuning scheme that is both efficient and effective, while further improving the overall performance of model merging.
To address this limitation, this paper proposes a novel optimization approach for the stage, called Merging-Aware Optimizer (referred to as MergOPT), specifically designed to produce expert models that are more amenable to merging. More specifically, the core idea of Me rerO is to formalize the parameter merging process as a merge-induced parameter offset operation and explicitly construct it during training as a distributionally robust optimization (DRO) (Lin et al. 2022) problem in weight space. In other words, the parameters (or task vectors) from other expert models to be merged can be regarded as merge-induced parameter offsets applied to a target model's s parameters. The training objective is then to optimize against the worst-case merge-induced offset within the feasible region of this space, thereby improving the stability and effectiveness of the model during merging. To this end, we further specify the feasible region over these merge-offset configurations. Specifically, we decompose it into three dimensions: the distribution of task vectors, the range of merging coefficients, and the number of models to be merged. However, when training usually unknown. To solve this problem,
single expert model, these three components conduct an empirical analysis of task vectors. Results across three mainstream LLM architectures and seven real-world tasks demonstrate that each task vector can be well approximated by a Laplacian distribution (Kotz et al.] 2012). For merging coefficients and model numbers, we define discrete feasible regions grounded in empirical observations and prior experience, ensuring both the prac- ticality and interpretability of the resulting merge-offset space. Finally, we evaluate Me G on four LLM architectures of different scales (Llama IB & 3B & 8B, Qwen 1 1.5B) combined with four representative model merging methods, applied to multiple downstream expert models. Experimental results demonstrate that MergOPT delivers substantial performance gains, with average relative improvements of about 3.5% and up to 9.5% when merging seven experts across four strategies, thereby validating its effectiveness in enhancing the robustness and practicality of model merging.
The main contributions of this work are summarized as follows: O We highlight critical yet underexplored aspect of model merging: the fine-tuning stage. We argue that the effectiveness of the merged model depends on both fine-tuning and merging, and emphasize the need for dedicated fine-tuning scheme to improve model compatibility. @ We propose MergOPT, a merging- aware optimizer that formalizes merging as merge-inducee parameter offset in weight space
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and applies distributionally robust optimization to enhance stability and effectiveness. We further define the feasible region of these merge-offset configurations through analysis of task vectors, merging coefficients, and model numbers. ① We perform extensive experiments on four large- scale L.M architectures and one vision model with four representative merging methods across seven downstream tasks. Results show that Me rgoPT consistently outperforms standard fine-tuning, demonstrating its effectiveness in improving the robustness and utility of model merging.
2 RELATED WORK
Methods in the Merging Phase. The most straightforward strategies are weight averaging (Worssman et al. 2022) task arithmetic (Ilharco al., (023), but their performance is often limited due to potential conflicts among models. To address this issue, more advanced merging techniques have been developed, which can be broadly categorized into three families: weighted merging, subspace- based merging, and weight alignment merging. (i) importance- importance-based weighting methods aim to balance the contributions of different models using strategies such as grid search (Ilharco al..
2023 Yadav et al. 2023), evolutionary algorithms (Akiba et al., 2025). or data-driven adaptive weighting (Matena & Raffel 2022, Jin et al.] 2023] Yang et al. 2024b; Tang et al.) (024a). For example, Fisher merging (Matena & Raffel| (022) leverages Fisher information to assign parameter importance, while AdaMerging Yangg et al. 2024b) optimizes merging coefficients with unlabeled test data. (ii) subspace-based methods mitigate conflicts and reduce computational overhead by discarding redundant information and constraining merging to low-rank or sparse subspaces. Such as TeES-Megging (Yadav et al. 2023) and DARE (Yu et al.) 2024), remove large portion of unimportant parameter updates and adjust the remaining ones through sign aligning or rescaling. (iii) Weight alignment methods apply parameter permutations to obtain functionally equivalent solutions that lie in different loss basins (Jordan et al., 2023 Ainsworth et al., 2023 Rinaldi et al., 2025). By adjusting expert models to lie within the same basin, merging can typically be performed more smoothly and effectively.
Methods in the Fine-Tuning Phase. However, while these methods introduce clever designs the merging stage, they still rely on standard optimizers and largely overlook the importance of preparing models to facilitate subsequent merging. To the best of our knowledge, only few works focus on how to train models that are more amenable to merging. OOrtiz-Jimenez et al. (2023) first pointed out that weight disentanglement a key factor for the effectiveness of task-arithmetic-bass model merging. Their method amplifies weight disentanglement by linearizing the model and performing fine-tuning in its tangent space (Jin et al. [024] Tang et al. 20224b Liu et al. 2024). Nevertheless, inference with the linearized model typically takes about two three times longer than with its original nonlinear counterpart (Ortiz-imenezz et al.) 2023). In addition, our experimental results show that such approaches are still inferior in performance to the method proposed in this paper. SAFT-Merge (Lee et al., 2025) enhances mergeability during fine-tuning by applying sharpness- aware minimization. However, its training cost is nearly twice that of standard fine-tuning, making it inefficient for large models or datasets. In contrast, our Merg0P T matches the efficiency of a standard optimizer while explicitly simulating merging via cross-expert merge-offsets, thereby improving stability and overall merging performance. It is worth mentioning that while most existing methods have been evaluated on vision models and image classification tasks, our work is conducted in the context of LLMs and text generation tasks.
3 METHOD
In this section, we first introduce the preliminaries and notations used in this paper (Sec. 3.1 Then, we present our proposed method, merge- aware fine-tuning via weight-space robust optimization. which aims to enhance the robustness of model merging (Sec. 3.2
3.1 PRELIMINARIES
Fine- Fine-Tuning from a Pre-Trained Model. Let fu E Rd denote the parameters of a pre-trained base model. We denote the training dataset Dimin {(,,, J where I; is the input and y is the corresponding label for the i-th sample in task (k E (1,2...., K}). The fine-tuned parameters denoted as 0z Rdd The loss function is represented as lg (Ox; (2r, y)), which measures the
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discrepancy between the model's prediction and the true label for given input. The expected empirical risk on the training dataset is defined as:
task ( D
( (Oxs (ar, v))
(I)
Model Merging, Model merging aims to combine multiple fine-tuned models into single merged model merged Given set of fine-tuned models with parameters {0x))=== a common approach to use task arithmetic (Ilharco et al. 2023):
0 mergeed 0o +
AOx.
(2)
where Og is the base model, A0; = 6 Bu denotes the task vector for task k and a >> 0 is a scaling factor. The objective of the merged model is achieve consistently low test loss across all tasks. Formally, the expected test risk of the merged model is defined as:
1 K
Emerge Cotrggo@Omeenn (Omerged: (Di (K=))
E Bop (Omeeeegaet (e))))]
(3)
k=1
where Disst is the test dataset for task k.
Distributionally Robust Optimization (DRO). DRO seeks to optimize model parameters under distributional uncertainty by minimizing the worst-case expected loss over family of probability distributions P that are close to the empirical data distribution (Lin et al. 2022). Formally, the DRO objective can be expressed as:
min sup ((aa)) (4x (Ox: (z, v))] PEP
(4)
Here, P denotes an ambiguity set of candidate distributions around the empirical distribution. P is typically defined by imposing constraints based on a divergence metric (c.g., Wasserstein distance, KL divergence), which controls the proximity between P and the empirical distribution. In this work, unlike conventional DRO that operates in the data space, we extend the DRO framework to the weight space and interpret model merging form of distributional uncertainty model parameters.
3.2 MERGOPT: A MERGE-AWARE OPTIMIZER VIA WEIGHT ROBUST OPTIMIZATION
In this section, we introduce our proposed method, MergOPT, which aims to enhance the robustness of model merging through weight-space robust optimization. More specifically, we treat the merging process as a form of merge offsets in the weight space and apply distributionally robust optimization techniques in the fine-tuning stage train models that are resilient various merging scenarios.
3.2. REFORMULATING MODEL MERGING WEIGHT-SPACE MERGE OFFSETS
Consider fine-tuning on task k where the resulting model parameters can be expressed as 0% 0o A0k, where A is the task vector corresponding task k. When merging K tasks, the merged model parameters mmerged- = Φ(0,, ((a, K, A0)) can be reformulated as:
K ((o,))( Σ ~0,= (0o 20d) -000)-0--11 Σ
A0 =0 ((a-1)A0k +o Σ A03),
((a.K.50)
(5)
where @10;, C(a, K, Ad)) formalizes the process of merging the current task task-specific model (i.e., 0.) with the remaining fine-tuned models. The additional term ((a, K, A0) represents the parameter offset introduced by the merging operation, which depends on the merging coefficient a,, the number of tasks K, and the task vectors Ad, (j E 21,2.... K}) from the other models. It is worth emphasizing that this formulation is consistent with SAFT-Merge (Lee et al. 2025), but our interpretation and solution strategy are fundamentally different. We provide a detailed comparison between the two methods in both the related work section and experiments.
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3.2.2 WEIGHT ROBUST OPTIMIZATION OBJECTIVE
Building on the above interpretation of model merging as merge-induced parameter shifts in weight space, we argue that merge-aware optimizer during fine-tuning should satisfy two key objectives: ! Preservation Objective: Preserve the standard task loss Ltask D&) to ensure strong performance on the current task. @ Robustness Objective: Enhance robustness to diverse merging scenarios by accounting for the worst-case merging parameters ((a,, K, A!) within a feasible set
Formally, we define the weight-space robust optimization (WRO) objective as:
min 2k
sup (B))B
(((,,, K, A())))
(6)
where @f0x. () denotes the merged parameters under merge-induced induced offset Ç. and B is the ambiguity set in the weight space, capturing feasible merging configurations. The feasible set is defined as
B = (o. K, A0): a E A, KE Z,o, K S Kmax, AG E 2 C span A02 A8,...., A0,]]x (7)
which constrains the merging configuration that the induced merge offsets remain within reasonable bounds. Here, A denotes the set of admissible merging coefficients, Kmax specifies the maximum number of tasks allowed for merging, and Z the set of admissible merge-offset vectors, restricted to linear combinations of task-specific parameter differences A0; Throughout, span(-) denotes the linear span of given set of task vectors. Naturally, when Eq. 6 reaches its optimal solution, 0ş inherently satisfies both the previously introduced preservation objective and robustness objective.
To solve the proposed WRO objective Eq. we can employ an alternating optimization strategy. The outer minimization updates the model parameters O₃ using gradient descent, while the inner maximization finds the worst-case merging parameters C(a, K, A0) using projected gradient ascent. Specifically, the optimization proceeds follows: O Inner Maximization: Given the current task parameters 0g, identify the worst-case merging configuration within the feasible set B. The adversarial merging parameters are then obtained by solving the following problem:
(a" K A = Frojn(a', K", A0") = arg max (a' ,A6'' Leaatd (ott C(a', K", AB))); Dc).
(8)
where (r) is a projection operator that projects the x onto the feasible set B. @ Outer Minimization: Update O% to minimize the loss under the adversarially selected merging parameters. This ensures that the model adapts to the worst-case weight-shift introduced by the merging operation:
0% + - 17 Voa (Craal ((a", K" A0
where 17 is the learning rate.
This alternating minimax procedure continues until convergence, effectively ensuring that the fine- tuned model 0% is not only optimized for its own task but also robust to broad range of poten- tial merging scenarios. This alternating optimization strategy follows classical machine learning frameworks like gradient ascent/descent and min-max optimization (Boyd & Vandenberghe (004).. However, for model merging, the objective is impractical due to inaccessible task vectors and costly inner optimization. We tailor this framework to merging with efficient approximations in next setion.
3.2.3 OPTIMIZATION STRATEGY
In this subsection, we discuss the practical challenges associated with optimizing the WRO objective in Eq. Gand propose strategies to address these challenges.
Optimization Challenges. From the optimization problem in Sec. 3.2.2 the ideal worst-case robust optimization faces the following two constraints during practical optimization, rendering inapplicable in real-world scenarios: ① Unknowable Merge-Offset Variables: As derived from Eq. 5 and Eq. 7 the merge-induced parameter shift Ç is primarily determined by three types variables: the merging coefficient the number of merged tasks K, and the task vectors A {AO,... ..... A0x }. However, when fine-tuning the model 0₂ for task (or its corresponding task vector A the task vectors of other models to be merged are often inaccessible- this is because different developers typically fine-tune their respective models independently. Under such circumstances, the merging coefficient and the number of merged tasks that can achieve optimal merging performance
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1200
Distriuttion Laplace Ft
2003
Didribution
2000
D Ditriuution
1000
2003
Lap boo
Laplace Ft
25000
1500
1200
400
1003
500
002
5,005 0.002
-2.053
0.002
-0.302
-2.03
5,002
0.003
0.002
Parameter Change
Parameter
Figure| 1: Distribution of parameter changes (i.e., task vectors) after fine-tuning different large language models: from left to right are Llama-3.2-1B, Qwen2.5-1.5B. and Llama-3.2-3B. The blue curve represents the empirical distribution, while the red curve shows the fitted Laplace distribution. We observe that the Laplace distribution provides close approximation to the empirical distribution.
naturally unascertainable advance. @ Inefficient Inner Optimization: Even though some of the aforementioned variables have been clearly defined, the solution process for the worst-case merge offset described in Eq. rremains highly time-consuming. Specifically, the merging coefficients a, the number of merged tasks K, and the task-vector space 2 together induce feasible set whose size grows exponentially. Performing an explicit worst-case maximization over this space would be computationally intractable, both in theory and in practice.
Feasible Set Approximation. To address the issue of unknowable variables, we propose to effectively approximate the feasible set based on series of prior information. More specifically, we make the following approximations. 1 For lask vectors {0,)/= we conducted analysis across three large language model architectures and seven downstream tasks (detailed in Sec. 4.1). We visualized the distribution of the cumulative task vectors (i.e., Σx= A0;) in the main text and individual task vectors (i.e., { in Appendix [.I.1 As shown Fig. D all task vectors can well-fitted by specific Laplace distribution (Kotz al. 2012), where overwhelming majority of elements are concentrated around O. @ For the optimal merging coefficient a, prior studics on model merging consistently indicate that typically lies in the interval (0, 1). Since fine-grained parameter search is computationally expensive, most works adopt a fixed small value; for example, a = 0.3 is commonly used in Task Arithmetic (Ilharco et al., 2023) and Ties-Merging (Yadav et al.) 2023) To further validate this observation, we evaluated the impact of different a values on merging performance (see Tab. 13 in Appendix D.1.2), which provides a practical discrete candidate set for a. @ For the maximum number of models to be merged, existing evidence shows that performance degrades more severely as more models are merged (Yadav et al. 2024). Consequently, most experiments restrict the number of merged models to fewer than ten. In the context of L.LMs, merging is typically limited to two or three models (Goddard et al., 2024 Wan et al.
2024b Yu et al. 2024 Du et al. 2024 Akiba et al. 2025), and few works explore merging at much larger scales (Wang et al.) 2025)..
Single-Step Merge-Offiet Approximation. To alleviate the computational inefficiency of iterative inner maximization, we approximate Eq. g using single-step sampling strategy over merging configurations. Instead of performing multiple projection gradient-based updates to identify the worst- case merging parameters,
directly sample (a, K, 2) from their respective feasible distributions and construct the merge-offset model in one step. In particular, 2 is drawn from a Laplace distribution fitted to the empirical task vectors, established in the previous analysis. The offsets then given by d(0x. ((a, K, 2)), and Ç(a, x) = (Ka - 1)2 denotes the merge-induced parameter offset induced by merging K tasks with coefficient a. To save sampling time, we note that each task vector is assumed to be z here. This single-step approximation substantially reduces the computational overhead while retaining the essential characteristics of the worst-case merge offsets. Moreover, since the offset 2 is sampled from a Laplace distribution that matches the empirical distribution of task vectors, repeated sampling naturally increases the probability of capturing directions that are close to the true worst-case, or at least adversarially challenging merge offsets. This allows us to achieve substantial robustness improvements even when the combinatorial space extremely large and computing the theoretical optimum is infeasible.
Final Practical Objective. By combining the feasible-set approximation with the single-step merge- offset strategy, we derive a practical optimization objective that can be efficiently implemented during tine-tuning At each training step, we first sample the merging coefficient a from the discrete candidate set A, the number of tasks K from 21,2.... .....Knu Kmax). }. and the offset vector 2 from a Laplace distribution fitted to the empirical task vectors. The merge-offset model parameters are then obtained as (Ok, C(a, K, z)). The task loss is evaluated at these parameters and used to update Og. Formally,

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Table Performance comparison of model merging methods with Llama-3.2 3.2-IB-Insttrue
Task Performance
Method
Avg.
C-STANCE
MeetingBunk
ScienceQA
NumGLUE cm
NumGLUE-ds
20Minuten
Pre Trained
0.3386
0.2581
0.2036
0.5780
0,1220
0.1616
0.3802
0.3061
Standand Fine- Fine-Tuned
0.4980
0.5988
0.5907
0.8524
0.3902
0.5793
0.3830
05254
MezgoFT I Fine Tuned
0.4957
0.6331
0,3158
0.8780
0.4390
0.5305
0.3829
0.525
Weight Averaging
0.4206
0.5040
0.2179
0.7340
02195
0.3171
0.3813
0,3992
Weight As Averuging Merg0FT
0.3825
04422 3911
Task, Anchmetic
0,4219
0,6980
0.2094
0.7370
0,2139
0.3476
0.3805
0,4055
Tiskk Arilhmetic w/ MergopT
0.4203
0.4718
0.2077
0.7530
0.3171
0.3659
0.3797
0 04165
TIES Merging
0.4236
0.4738
0.2145
0.7430
0.2439
0.3537
0.3862
0,4055
TIES- TTES-Merging w/ MergOPT
0.4202
0.4536
0,2093
0.7555
0.2927
0.3720
0.3825
0.4 04125
DARE
0.1195
0.3821
0.3786
DARE Mazgöpt
0.4192
0,4819
0.7485
0,9927
0.3659
0.3843
0
the practical training objective at each step can be expressed as:
min K,, [Crawk (á(0kk: C(ex, =))):: Uniform((1, (1, 1,2,.... Kmax)), z ~ Laplace(14 b),
(10)
s.t. a ~ Uniform(AA,,
where the expectation taken over the sampled merging parameters (a, K). The Laplace dis- tribution is defined as Laplace b) 26 exp
with location parameter and scale pa- rameter b. The model parameters are finally updated using stochastic gradient descent: 0x O2 v/ Crask (6(0s, <); Dz). The optimization procedure summarized in Alg. of Appendix B.3
-لسااا (-
EXPERIMENT
4.1 EXPERIMENTAL SETUP
In this section, we detail the experimental setup used to evaluate the effectiveness of our proposed method. Due space limitations, more experimental details can be found in Appendix B
Datasets and Metrics. We evaluate our proposed method on seven datasets from TraceBench (Wang al. 2023). including C-STANCE (Zhao al. 2023), FOMC (Shah et al. 2023), MeetingBank (Hu et al. 2023), ScienceQA (Lu et al. 2022). NumGLUE-cn (Mishra et al.) (022). NumGLUE- ds (Mishra al. 2022), and 20Minuten (Rios al. 2021). These datasets span variety of tasks, including Nomain-specinfe applications, multilingual understanding. and mathematical reasoning. The evaluation metric for each task as follows: accuracy for C-STANCE, FOMC, ScienceQA, NumGLUE-cn and NumGLUE-ds; ROUGE-L for MeetingBank; and SARI for 20Minuten. For all metrics, the higher the value, the better. We report the average score across all tasks as the overall performance metric. The statisties of these datasets are summarized in Table 6 in the Appendix.
Base Models and Optimizers. We conduct experiments on four base models: Llama-3, 3.2-- Instruct (Meta 2024). Qwen2.5-1.5B -nntttruesB-I (Qwen et al.) (025). Llama-3.2-3B-Imm Instructt (Metal 2024), and
(Meta 2024). In this work, we adopt AdamW (Loshchilov & Hutter 2017) the default base optimizer for both the standard fine-tuning baseline and our merge- aware fine-tuning; implementation details are provided in Appendix B.2 We further verify optimizer agnosticism by instantiating our method with SGD and by comparing against the SAM optimizer; the corresponding results are reported in Appendix D.2
Merging Methods. Since our method operates during the fine-tuning stage, remains independent of the specific choice of merging algorithms. To verify its effectiveness, we employ four representative
merging strategies, including Weight Averaging (Wortsman et al. 2022). Task Arithmetic (Ilhareo et al. 2023). TIES TIES-Merging (Yadav et al. (023)), and DARE Yu et al. 2024), applied to models
obtained from both standard fine-tunne Lne-tuning and our proposed Me MergOPt GPPT fine-tuning approach.
4.2 PERFORMANCE COMPARISON AND ANALYSIS
This section presents the main results and analysis of our experiments, demonstrating the effectiveness of MergOPT T in enhancing merging performance. More experimental results and analyses can be found in Appendix Cad Appendix
Robustness Across Architectures and Downstream Tasks. Tables I and 2 we evaluate ro- bustness under the challenging setting of merging seven independently fine-tuned expert models,
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Table 2: Performance comparison of model merging methods with Llama-
Task Performance
Method
Avg.
C-STANCE
FOMC
MeetingBunk
ScienceQA
NumGLUE cm
NumGLUUEds
20Minuten
Pre- Trained
0,4082
0.3528
0.2054
0,8962
0.1707
0.2195
0.3857
0.370
Standard Fine- Tan-Tened
0.5415
0.6835
0.4317
0.9335
0.6098
0.6463
0.3898
0.0057
MezgoFT I Fine Tuned
0,5545
0.6653
0.2896
0.9360
0,5122
0.6341
0.3886
0.5836
Weight Averaging
0.4617
0.5065
0.2213
0.9140
0.4290
0.4146
0.3891
0,4866
Weight As Averuging w/ Merg0FT
0,4790
0,4390
0,4085
0.3876
Task, Anchmetic
0,4685
0.5605
0.2186
0.9100
0.4634
0,1024
0.3862
0,4871
Tiskk Arilhmetic w/ MergoPr
0.4755
0.5948
0,2167
0.9110
0.4878
0.4573
0. 0,3883
1.5045,. Soit
TIES Merging
0.4670
0,5705
0.2211
0.9130
0.4634
0.4024
0.3900
0.4898
TIES- TTES-Merging w/ MergoPT
0.4770
0,8028
0.2142
0.9175
0.5123
0:4573
0.3878
0.50%8
DARE
0.4630
0.5867
0.9055
0.4634
0.3871
0.4906
DARE MazgOpp
0.4690
0.6129
0.9140
0.4878
0:4451
0.3851
0,504% 0,504% (2009
Table 3: Performance of different merging methods on 4-task groups (Ilama-3.22 1-a--3..-21--ntruuue Instructt..
Mathol
Group
Grop
FOMC
MestigBark
NunCLLUE-As
20Minuase
Avg. (1)
C.STANCE
FOMC
Seienc:OA
Nun
Avg. (1)
Taok Ariihmetic
0.4003
6.3412
0.4512
0.3816
0.308
0,430
0.4633
0.7210
0.3171
0.4959
Yaok Arilhmatic ot Mergopt
0,4758
6:2320
044122
0.3814
0.383
0.4300
0:4597
0.7945
0.3690
0.5130
THiS Merging
0,5922
0.2412
0.6573
0.1846
0.5706
0.4255
0.2714
0.779
0.3115
0,5022
TIES MirgiiMgggngg W/Meego
0.4637
0.3352
04312
0.3643
0.364),
0.4244
0.4698
0.7985
0.3699
0.9154, 1309
comparing the performance of different merging strategies using Llama-3.2-11 and Llama-3.2-3B as the base models, respectively. We assess robustness by applying four representative merging strategies (Weight Averaging, Task Arithmetic, TIES- Mergnng and DARE) to models fine-tuned either with the standard procedure or with Mer Across all model scales, incorporating MergOPT consistently improves the merged performance. For example, in Table [ Weight Averaging combined with MergOPT achieves an average score of 0.4123, outperforming plain Weight Averaging (0.3992). The same trend is observed for Task Arithmetic (0.4165 vs. 0.4055) and DARE (0.4147 vs. 0.3786). Then, on the larger J.ama-3.2-3B (Table the merged models with MergOPT still show consistent improvements, e.g.. Task Arithmetic increases from 0.4871 to 0.5045 (+3.6%) and TIES-Merging from 0.4898 to 0.5098 (+4.1%). On average, these enhancements correspond to about 3.5% relative improvement across 8 cases, with the largest observed gain reaching 9.5% (i.e., DARE Llama-3.2. IB). Tables 7 and g in the appendix further demonstrate that we have validated the effectiveness of consistent across
our method on Qwen2.5-1.5B and LLama-8B. In word, the improvements model scales and merging methods, highlighting the generality and practicality of our approach.
Robustness to the Number of Tasks. Tables 2 report results when merging all seven expert models. To further evaluate the effectiveness of our method under varying numbers of tasks, we also conduct experiments on smaller groups of experts, specifically 2-task, 4-task, and 6-task settings. Due to space constraints, 3 presents results on 4-task groups, while the results for 2-task and 6-task groups are deferred to the Appendix (Tables 20 and 21). Concretely, we randomly sample two groups of four tasks from the full set of seven, merge the corresponding fine-tuned models within each group, and then evaluate the merged models. As shown in Table Task Arithmetic w/ Me Mer achieves an average score of 0.3851 in Group I, compared to 0.3708 without MergOPT yielding 3.86% relative improvement. Similarly, in Group 2 the average score improves from 0.4959 to 0.5130 (+3.45%). Comparable gains are also observed for IIES-Merging, highlighting that our method consistently enhances merging robustness and generality across diffcrent task configurations.
Robustness to Merging Coefficients. In this part, visualize the joint loss landscapes of models fine-tuned with the standard Adam optimizer and with our proposed Me MergOPT method, in order to illustrate the robustness of approach under varying merging coefficients. Specifically, randomly selected four pairs of tasks (e.g.. C-STANCE & MeetingBank, MeetingBank & ScienceQA). and plotted contour maps of the joint-task loss as a function of the merging coefficients. As shown in Figure 2 each pixel in the heatmap corresponds to the joint loss value of a merged model defined by mmerged = 0g + ar A0 + A62, where the joint loss is given by [feerggd:: D1) + (6 D2). The horizontal and vertical axes represent the merging coefficients (a1,a.)) while the color intensity indicates the magnitude of the loss. Across the four task pairs, we observe the following: (i) AdamW W fine-tuning (left column): the low-loss regions are relatively narrow, and the loss increases sharply as the merging coefficients deviate from the optimum. This indicates sensitivity to merging shifts and weaker robustness. (ii) Our method (right column): the low-loss regions are substantially larger, and the contours around the optimum are flatter. This suggests that models fine-tuned with our optimizer exhibit greater stability under merging shifts, allowing them to better tolerate diverse coefficient configurations. These visualizations provide intuitive evidence that our method leads to more favorable loss landscapes for model merging.
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Figure 2: Visualization of the joint loss landscape for two task-specific models across two downstream tasks. The left panel shows AdamW-fine-tunee models, the right shows models fine-tuned with our MergOPT; darker colors indicate lower loss.
4.3 COMPARE WITH OTHER FINE-TUNING METHODS
Compare with SAM-based Fine-Tuning SAFT-Merge (Lee et al. 2025) employs SAM-based optimizers (Foret et al., 2021 Kwon et al. 2021) during the fine-tuning stage to improve model mergeability. We compare SAFT-Merge and Me gOPT from two perspectives: (i) As shown in Table 4 (a), under the same number of training epochs, SAFT-Merge and MergOPT each exhibit distinet advantages. For instance, under Weight Averaging and DARE, Merg outperforms SAFT-Merge (SAM) by 2.59% and 5.20%, respectively. In contrast, under Task Arithmetic and TIES-Merging, Mer3OPT falls behind by 2.23% and 1.29%. However, SAM-based optimization requires 2.04 x the cost of AdamW, whereas MergOPT incurs only 1.17x cost. (ii) Furthermore, Table 4 (b) demonstrates that when training time is comparable, Me T consistently surpasses SAFT-Merge. More specifically, Merg0PT T achieves improvements of 4.08%, 0. 0.70%, 0.95%, and 3.99% over SAFT-Merge across the four merging strategies. In addition, comparing SAFT-Merge (SAM) and SAFT-Merge (ASAM), observe that ASAM is generally superior when trained for the same number of epochs, whereas SAM becomes slightly better under comparable training cost. Under the same configuration, the two methods exhibit similar training time.
Table 4: Performance comparison of MergOPT T and SAFT-Merge (based on SAM and ASAM) under (a) equal training epochs (b) close to the training duration Llama-3.2-11 1.B--II-IIInttrucc
Method
Weight Averaging
Task Arithmetic
TIES- MergMnggg
DARE
Time
(a) SAFT-Merge (SAM)
0.3980
0.4260
0.4177
0.3942
2.04x
(a) SAFT-Merge (ASAM)
0.4047
0.4119
0.4226(-1.199)
0.4101
2.06x
(a) MergOPT
0.4083 2.59%)
0.4165, (22165 (2239)
0.4123 1.29%)
0.4147,.5..00g
1.17x
(b) Merge (SAM)
0,3923
0.4136
0.4084
0.3988
1.04x
(b) SAFT-Merge (ASAM)
L.48))
(.4.81
0. ...08)
0.3943
1.04x
(b) MergOPT
0,4083
0.4165 7003)
0.4123 (4.055)
0,4147
1.17x
Compare with Tangent Space Fine-Tuning Ortiz-Jimenez et al. (2023) proposes fine-tuning models in the tangent space to enhance their mergeability. In Table 5 we compare standard fine- tuning, tangent-space fine-tuning, and MergöPT fine-tuning. We observe that: (i) under Task Arithmetic, TeEg-Merging, and DARE, tangent-space fine-tuning improves over standard fine-tuning by 3.14%, 3.95%, and 2.54%, respectively, but drops by 8.01 % under Weight Averaging: (ii) MergOPT improves over standard fine-tuning by 2.37%, 3.44%, 4. 4.10% and 3.58% under Weight Averaging, Task Arithmetic, Merging,g and DARE, respectively, and yields larger gains than tangent-space fine-tuning, Note that the inference cost of linear models obtained via tangent-space fine-tuning typically 2-3x that of standard models, leading to efficiency issues.
Table 5: Performance comparison of MergOPT and Tangent Space fine-tuning on ViT-B/32.
Method
Weight Averaging
Task Arithmetic
TIES FrES-Merging
DARE
WUDI Merr-nggging
Standard
54.9
66.9
65.8
67.0
83.2
Tangent
8,019)
69.0(+3.44)
68.4
68.7 (-.7
77.197399)
MergoPT (Ours)
56.2 +2 (2.59)) 578)
69.2,-14498
68.5 1095)
...4...588)
84.3
Summary. These results indicate that MergOPT is both more efficient and more effective than SAM-based and tangent-space fine-tuning methods.
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5 CONCLUSION AND FUTURE WORK
This paper introduced a novel fine-tuning optimizer (MergOPT) designed to enhance the robustness of expert models during model merging. By reformulating fine-tuning robust optimization problem in the weight space, our method guides models to converge toward minima that are more amenable to merging and more resilient the parameter changes introduced at the merging stage. Extensive experiments demonstrate that Mer Merg consistently improves the performance of merged models. Several promising avenues for future research remain: First, developing more accurate approximation techniques to simulate key merging factors during fine-tuning could further enhance the model's s adaptability to merging. Second, combining Me MerOPP with other robustness-oriente training techniques may further strengthen merging stability. Third, integrating the models trained via our MerTOPT method into various more advanced merging schemes is also feasible and valuable.
ACKNOWLEDGMENTS
This research is supported by the National Natural Science Foundation of China (Grant Nos. 62576364, 62576083, 6241 1540034, U2541229), the Shenzhen Basic Research Key Project (Natural Science Foundation) (No. JCYJ202412022 124430041), the China Postdoctoral Science Foundation un- der Grant Number 2025M781 the Open Research Fund from Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) (NO. GMI--KF-24-23, and Ningho Science and Technology Innovation 2025 Major Project (20252027).
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Appendix Contents. The appendix is structured into several sections, each presenting supplementary information and detailed explanations to support the main text.
A LLM Usage Statement
15
Experimental Details
15
B. Dataset Statistics
16
B.2 Implementation Details
16
B.3 Algorithm
17
Additional Experimental Results
17
Applications in Other LLM Architecture
17
Applications in Large-Scale LLM Architecture
17
Applications in Visual Architecture and Tasks
18
D
Additional Experimental Analysis
19
D.I
Analysis of the Feasible Region of Hyperparameters)
19
D.I.1 Analysis on Task Vectors A0
19
D.1.2
Analysis Scale Parameter b of Laplace Distribution
21
D.1.3
Analysis Location Parameter y of Laplace Distribution
21
D.1.4
Analysis on Merging Coefficient
21
D.2
Comparison with Different Optimizers
21
D.2.1
Comparison with SAM Optimizer
21
D.2.2
Combined with Other Base Optimizer
22
D.2.3
Comparative Analysis of Model Merging via Different Optimization Methods
23
D.3
Ablation Study on Number of Tasks to Merge
23
D.4
Hyperparameter Sensitivity Analysis
24
D.4.1
Different Task Vector Distributions
24
D.4.2
Batch Sizes
24
D.4.3
Learning Rates
24
A LLM USAGE STATEMENT
This paper makes use of a large language model (ChatGPT) exclusively for language polishing, spelling correction, and grammar checking. The LLM was not involved in literature retrieval or the development of specific ideas. Following the polishing process, the authors carefully reviewed and revised the content as necessary and assume full responsibility for the final published version.
B EXPERIMENTAL DETAILS
In this section, we provide detailed statistics of the datasets used in our experiments (Sec. B.1 and elaborate the implementation details of our proposed Me MergOPT method (Sec. B.2
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Table 6: An overview of dataset statistics in experiments. 'Source' indicates the origin of the context. 'Avg. Len.' denotes the average length in words for English, German, and code datasets, and in characters for Chinese. 'SARI' is a metric specific simplification. For all metrics, the larger the corresponding value, the better.
Dataset
Source
Language
Avg. Len.
Metric
Domain-specific
ScienceQA (Lu et al. 2022
Science
English English English
210
Accuracy Accuracy ROUGE-L
FOMC (Shah et al. 2023)
Finance Meeting
MeetingBank (Hu el al. 2023
2,853
Multi-lingun lunti-lingul
C-STANCE Zhao ct al. 2023
Social media
Chinese Germany
127
Accuracy SARI
20Minuten (Rios et al. 2021)
News
382
Muthematicul reasoning
NumGLUE-cn (Mishra et al.
2022
Math Math
English English
32
Accuracy
NumGLUB-de (Mishra et al.
2022
Accuracy
B. DATASET STATISTICS
This section provides detailed statistics of the datasets used in our experiments, as summarized in Table 6 The datasets in TraceBench (Wang et al. (023) are constructed based on the following principles: (i) they are sufficiently novel such that most LLMs have not been trained on them; (ii) they are designed to pose meaningful level of challenge L.LMs; and (iii) they cover diverse range of tasks to provide a comprehensive evaluation of model capabilities. A detailed description of the seven datasets is provided below.
Domain-specific Applications. ScienceQA (Lu et al. 2022) is a multi-hop question answering dataset built upon elementary and high school science curricula. It exhibits rich domain diversity, covering natural sciences, social sciences, and language sciences. FOMC (Shah et al. 2023) is a novel financial-done -omaan classification task focused on hawkish-dovin categorization. The dataset consists of three subsets: meeting minutes, press conference transcripts, and speeches, each capturing different aspects of monetary policy communication. MeetingBank (Hu et al.) (023) is a new benchmark dataset for summarization of city council meetings. It requires a comprehensive understanding of lengthy background materials, making it particularly challenging.
Multilingual Understanding Tasks. C-STANCE (Zhao al. 2023) is a zero-shot stance detec- tion dataset collected from Sina Weibo, one of the most popular social media platforms in China. It serves benchmark for evaluating models' ability to understand and analyze Chinese text. 20Minuten (Rios et al. 202T) is a text simplification dataset consisting of full-length articles paired with shorter, simplified summaries from Swiss news magazine. It provides a benchmark for assessing models' capability in generating German text, particularly for simplification tasks.
Mathematical Reasoning Tasks. NumGLUE (Mishra al. 2022) is designed to evaluate the mathematical reasoning ability of AI systems, with a core focus on understanding and performing basic arithmetic. In our experiments, we adopt two subsets: NumGLUE-cm (Commonsense)) which involves simple arithmetic computations based on mathematical facts, and NumGLUE-ds (Domain Specific), which extends arithmetic reasoning by requiring additional Nomain-specine knowledge.
B.2 IMPLEMENTATION DETAILS
The main experiments in this work focus on L.MM architectures and language tasks, while the details More specifically, we build our experiments
for vision tasks are provided separately in Section C3
on the HuggingFace Transformers (Wolf et al.] 2020) library for loading pre-trained models and
conducting task-specific fine-tuning. The pre-traine trained models include Llama-3.2 2- B- Instrucct (Meta) 1.iee-..-----ttuuuue (Meta 2024). and Llama- (Meta 2024). Unless otherwise specified, adopt AdamW (Loshchilov & Hutter 2017) as the default base optimizer during fine-tuming Following the TraceBench ( (Wang et al. (023) protocol, we fine-tune the models C-STANCE, FOMC, MeetingBank, ScienceQA, NumGL. UK-cm,
2024). Qwen2.5-1 1.5B In-ntruutt (Qwen et al. 2025).
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Algorithm I MergOPT: A Merge-Aware Optimizer for Robust Model Merging
Require: Pretrained model feu task dataset Dx. candidate merging coefficient set A, maximum number of merged tasks maxx Laplace distribution parameters (μ,, b). base optimizer (e.g., SGD or Adam Ensure: Fine-tuned parameters 0z.
I: Initialize 02 f- 0
2: for each training step do
Sample mini-batch B& <- ((r, Bi) [5 ~ DE
4: Sample merging parameters: a ~ Uniform(A), K ~ Uniform((1. (1, Kmax 2 Laplace(Ju, b)
5: Construct merge-offiet parameters: 0%
K, K,))) 0s (Ka 1)2
Compute task and gradient 84: g t- Liask (0/; Ba)
7: Update parameters using the base optimizer: 0s + Optimizer(On.
8: end for
9:
return 0x
NumGLUE-ds, and 20Minuten for 3, 3, and epochs, respectively. The learning rate is set to 2e-5, the batch size to 8, and the weight decay to 0.001.
For our proposed MergOPT method, we set the default parameters of the Laplace distribution to (n, b) (0. 0.0005). We further evaluate different values of b. including 0.05, 0.001, and 0.0005 in Table II and observe consistently strong robustness across these settings. For the feasible set A of merging coefficients, we adopt default configuration of A [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]. Additionally, we report results in Table B for coefficient values ranging from 0.1 to 1.0 with an increment of 0.1. The maximum number of tasks Kmax considered for merging is set to 7 by default.
All experiments are conducted on a machine with an Intel(R) (eon(R) Gold 6459C CPU (12 cores), NVIDIA RTX 4090 GPUs (48 GB memory), and 90 GB of RAM. The software environment consists of Python 3.8 and PyTorch 2.1.2.
B.3 ALGORITHM
The pseudocode of the proposed MergOPT algorithm is presented in Algorithm I Given the input hyperparameters, for each task (k) initialize the model with the pretrained parameters (Line 1).
At each optimization step, we first sample a mini-batch of data (Line 3), then sample the merging coefficients, the number of tasks, and the task vectors from predefined feasible region (Line 4). Next, we construct a merged parameter offset (Line 5), and finally compute the gradients (Line 6) and update the parameters (Line 7).
C ADDITIONAL EXPERIMENTAL RESULTS
In this section, we validate the effectiveness of the proposed method on other architectures, including two LLMs 1-....2.--1.BBIntrruu and Llama3. 1emaa..--B-BA I-S--Insttt and vision model (ViT-B/32).
C. APPLICATIONS OTHER LLM ARCHITECTURE
Beyond the mainstream Llama (e.g., Tables and I 2 architecture, we also validate the effectiveness of our proposed method on the Qwen architecture by merging seven -wen2.5-11.B-Innstie each fine-tuned separately improves performance over standard tnn-ttning by 2.34%, 5.51 %, 4.45%, and 1.56% under Weight Averaging, Task Arithmetic, TIES-M Merging, and DARE, respectively. These results demonstrate that our method exhibits robust cross-architecture generalization.
models, single task. As shown in Table 7 our Tbased fine-tuning
C.2 APPLICATIONS IN BAAGGE-SCALL LLM ARCHITECTURE
In the main text, we primarily conduct experiments on Llama- 1B/3B and Qwen2.5-1.5B To further validate the effectiveness of our approach on larger-scale architectures, in this section additionally present results on Llama-8B Specifically, we merge expert models fine-tuned on C-STANCE, FOMC, ScienceQA, and NumGLUE-en and apply proposed method four representative model
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Table 7: Performance comparison of model merging methods with Qwen2.5511.B-IIsttuee
Method
Tisk Performance
Avg.
MeetingBank
ScienceQA
NumGLUE
Num6LUE-ch
Trained Fine-Tuned Tuned
0.4700
0.3569
0.1895
0.7182
0.0976
0,2195
0.3885
0.3456
Standard Fine-
0.5385
0.6230
0.1190
0.8439
0,3902
0.1695
0.3956
0.4974
HezgOFT Fine- Tuned
0.5250
0.6351
0.3459
0.8775
0,5122
0.4390
0.3977
0.5336
Weight
0.4880
0.4012
0.1967
0.7500
0.4390
0.3841
0.3920
0.4359
Weight Averaging MergOFT
0.4461.e
Task. Anchmetic
0.5055
0.6677
0.1889
0.7560
0.1146
0.3902
0.3890
0,4454
Tisk Arilhmetic w/ Mergopr
0.5220
0.5121
0.2205
0.7625
0,5122
0. 0.3963
0.3839
04473
TIES- Merging
0.5160
0.4597
0,2253
0.7475
0.4900
0,4024
0.3875
0,4539
TIES Merr-iggging w/ MergoPT
0.5260
0.5081
0.2210
0.7680
0.5122
0.3963
0.3890
0,4741
DARE
0.5035
0,4390
0,4491
DARE Nergopr
0.3100
0.5161
0.7710
0.4390
0.35V8
0.3794
0.456)
merging techniques: Weight Averaging, Task Arithmetic, TIES-Merging, and DARE. As shown in T MerqOPT yields average performance improvements of 1.08%, 1.40%, 0.46% and 0.51% for Weight Averaging, Task Arithmetic, "TFS-Merging and DARE, respectively. These results provide strong evidence that our method remains effective at larger parameter scales.
Table 8: Performance Comparison of Model Merging Methods Llama3.1 1--BB Instruct
Task Performance
(f)
Method
Avg.
C-STANCE
FOMC ScienceQA
NumGLUB-cm
Traiire
0,4197
0.3085
0.9075
0.2927
0.4821
Standard Fine-Tuned
0.5712
0.7234
0.9418
0.6721
0.7271
MergoPT Fine-Tuned
0.5637
0.7335
0.9403
0.6234
0.7152
Weight Averaging
0.4982
0.6489
0.9293
0.7319
0.7021
Weight Averaging w/ MPr
0,5071
0.6627
0,9307
0.7384
0.7097
Task Arithmetic
0,5268
0.6731
0.9218
0.6833
0.7012
Task Arithmetic w/MergOPT
0.5318
0.6803
0.9251
0.7069
0.7110
TIES- MES-Merging
0.5193
0.6792
0.9212
0.7074
0.7068
TIES-ME -IE--Merging w/ MergOPT
0.5236
0.6824
0,9237
0.7106
0.7101 46%)
DARE
0.5227
0.6696
0.9168
0.7071
0.7041
DARE w/ MergOPT
0.5259
0.6765
0.9192
0.7092
0.7077
C.3 APPLICATIONS IN VISUAL ARCHITECTURE AND TASKS
Beyond language tasks, vision tasks are also a major application area for model merging methods. To evaluate the effectiveness of approach across different domains, further conduct experiments in the vision setting.
Architecture and Datasets. We follow standard configurations used in prior work vision model merging [Ilaacco et al.) (2023). adopting as the base model and fine-tuning into expert models on ten downstream tasks: SUN397 (iia et al. 2016). Cars (Krause et al. 2013), RESISC45 (Cheng et al. 2017), EuroSAT (Helber et al. 2019). SVHN (Yuval GTSRB (Stallkamp al. (011)). MNIST (LeCun) 1998). DTD (Cimpoi et al. 2014), Flowers 102 (Nilsback & Zisserman 2008), and PCAM (Veeling et al. 2018). As all tasks are classification tasks, we adopt Top-1 classification accuracy as the unified evaluation metric and report the average value across all tasks.
(Dosovitskiy et al. [021] Radford et al. 202
Fine-tuning Methods. We use Adam W the standard fine-tuning baseline, with hyperparameters following previous work. In addition, consider fine-tuning in the tangent space (Ortiz-Jimenez ct al. 2023) as well as our proposed MergOPT-basee fine-tuning scheme.
Merging Methods. Consistent with our LLM experiments, compare four representative model merging approaches: Weight Averaging (Wortsman et al. 2022). Task Arithmetic (Iharcoo et al. 2023), TIES-Merging (Yadav et al. 2023), and DARE YYu al.) 2024). Moreover, include WUDi-Merging (Cheng et al. 2025), a recent optimization-bant data-free merging method that has been shown to significantly outperform several typical model merging baselines.
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Performance Comparison. As shown in Table 2 make the following observations: (i) Com- pared with standard fine-tuning, the proposed MerqOPT significantly improves performance when merging 10 tasks. For example, under five representative merging methods- Averaging, Task Arithmetic, 2.36%, 3.43%, 4. 4.10%, 4.05%, and 1.32%, respectively. (ii) Fine-tuning in the tangent space allows better decoupling between the input space and the weight space, thereby reducing interference during merging (Ortiz-Jimenez et al. 2023 We observe that, in most cases, tangent-space fine-tuning indeed improves performance over standard fine-tuning: under Task Arithmetic, TIES- Merging, and DARE, it brings gains of 3. 3.,3,, 3. 3.95% and 3. 3.00%, respectively, although these improvements are still lower than those achieved by MergOPT in the corresponding settings. However, under Weight Averaging and WUDI-Merging, the merged models exhibit some performance degradation; we leave a deeper investigation of this phenomenon to future work. (iii) WUDI-Merging shows consistently stronger performance than other merging basclines, as it constructs a data-fice optimization objective and explicitly optimizes the merged model parameters. Overall, these results provide consistent evidence that our proposed method is broadly applicable across diverse domains.
DARE, and BUUDD-Merging-Mergree
yields average gains of
Table 9: Performance Comparison of Model Merging Methods on Visual Tasks with CLIP-ViT-BI
Method
SUN397
Cars
RESISC15
EuroSAT
SVIIN
GTSRB
MNIST
DTD
Flowers
PCAM
Avg. (f)
Averaging (Standard)
54.9
Weight Averaging (Tangent)
53.7
36.4
26.3
29.8
58.2
80.3
50.5,
Weight Averaging (MargOPT)
60.8
56.6
59.7
36.9
32.9
35.5
66.9
42.5
71.5
92.3
56,2.
Task Arithmetic (Standard)
62.1
$2.0
72.0
77.7
64.5
59.0
91.4
46.3
68.6
20.5
66.9
Tisk Arithmetic (Tangent)
62.7
64.1
77.8
89.3
54.7
55.9
84.5
52.7
72.5
76.0
69.0 69.0...191
Task Arithanctic (HergOPP)
70.0
76.6
80.0
Merging (Standard)
70.6
74.7
62.8
92.0
65.7
TIES- Merging (Tangent)
63.8
65.0
78.
90.1
54.0
55.9
85.0
50.5
70.6
71.5
TIFS-Morging (NergoPP)
56.2
58.1
70.0
66.7
78.0
73.0
96.7
45.2
64.7
75.8
68% 5
DARE (Sumlaadd
61.1
$6.9
71.5
78.5
65.6
56.7
92.1
45.2
67.6
71.6
66.7
DARE (Tangent)
62.7
64.5
77.1
90.1
51.3
56.7
85.2
51.5
72.5
76.1
6-.7.-
(MergOeT)
74.8
78.4
WUDI Merging (Slandard)
67.5
72.6
84.0
93.8
89.4
95.8
99.2
61.2
77.5
91.2
83.2
WUDD Merging (langent)
66.8
67.0
$1.9
92.1
96.3
79.7
94.4
61.2
80.4
71.2
WLDI DUDL-Merging Merging (Merg
70.2
69.9
86.5
92.9
90.7
97.3
99.0
63.8
79.4
93.0
84.3
D ADDITIONAL EXPERIMENTAL ANALYSIS
In this section, we provide a comprehensive analysis of the feasible region of hyperparameters: in our proposed MergOPT T method (Sec. D.I) and compare its performance with different optimizers (Sec. D.2). Next, we present additional experimental results on various task combinations (Sec. D.3) Finally, in Appendix D.4 we discussed the sensitivity of the proposed method to the hyperparameters.
D.1 ANALYSIS OF THE FEASIBLE REGION OF HYPERPARAMETERS
D.1.1 ANALYSIS ON TASK VECTORS AO
Our MergOPT approach requires treating task vectors from other expert models as merge-induced parameter shifts during single-task fine-tuning. in order to simulate potential merging disturbances. However, in practice, such task vectors from other experts are typically inaccessible. To address this, conduct a detailed analysis of the distributional properties of task vectors. Interestingly, we find that these vectors can be well approximated by Laplace distribution Laplace(p, 6). where denotes the location parameter corresponding to the mean of the task vectors, and b represents the scale parameter that characterizes their dispersion around the mean.
To validate this, we visualize the distribution of task vectors { (A01, AB2..... A0k H obtained from fine-tuning Llama-3.2. 3.2- 1B- Instruct on the six (i.e., ScienceQA, FOMC, MeetingBank, C-STANCE,
'It is important to note that the inference cost of linear models obtained via tangent-space fine-tuning is typically 2 - 3x higher than that of standard fine-tuning, For details, please refer to the Computational complexity section in Appendix B of the original paper (Ortiz-limenez et al. 2023). In contrast, our method does not incur additional inference costs for the model.
"Since the dimensionality of task vectors matches that of model parameters, direct visualization of the complete task vector distribution is infeasible. To address this, randomly sampled one million parameters from the entire task vector for visualization purposes.
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Porameter Digg bution for bosk Sciene04
Porometer Diprrbuttion for Tisk: FOMC
Porameter button Took HockingBank
17500
15000
Loptaco
115500
30200
Distribution
Laploco
24420
5020
Distriiztiion
10003
10500
9220
7983
7500
2050
2500
0.0015
0000
g00s
COOL
2011
8000
0,00
8000
0222
2011
2.001
0.002
Parameter Change
Parameter Change
Parameter Change
Permmnter Eistrbuttion Text: C-STACC
Parameter Derristion for Task: 20Minstee
Parameter stribed for Thil: M.maal
1500
strribuu on
9020
Distribution
17500
Distribution
1000
Lafisce
Laplace Fit
Lagisce
2-2500
Za500
D12560
E2000 22000
1500
8 2000
3020
10300
7300
3200
1820
4 10W0
2,0000
4 Paramattr Change
0006
Paramiter Change
Parameter Change
Figure 3: Distribution of task vectors for different tasks. The histograms show the empirical distributions of task vectors (blue), along with the fitted Laplace distributions (red).
20Minuten, and NumGL.UF-cm) tasks, as shown in Figure 3 The histograms illustrate that the empir- ical distributions (blue color) of these task vectors closely aligr with the fitted Laplace distributions (red color), confirming our assumption. Based on this observation, we set the location parameter μ to O (the mean of the task vectors) and treat the scale parameter as a tunable hyperparameter in our method. Table 11 further explores the impact of different b values on merging performance.
Moreover, as shown in Figure 1 we also observe that the accumulated task vectors (i.e., Σ AO)) closely follow a Laplace distribution. This finding holds consistently across three mainstream architectures, namely Llama-3.2- 3.2-IBBIInstruct Llama-3.2-3--nsttruu,, and Qwen2.5-1.55 -.5--tuett- This property enables us to approximate real merging scenarios during expert fine-tuning by sampling from the corresponding Laplace distribution, thereby effectively simulating the parameter changes induced by accumulated task vectors.
The above analysis is primarily based on visual inspection and empirical fitting of the task-vector distributions. To provide a more rigorous statistical validation, we additionally randomly sample three tasks and, for each, compute the Kolmogorov-Smimon (K-S) distance and the average log- liglliieldoodd to quantify the goodness-of-fi of the Laplace distribution. As shown in Table [0] the K-S distances for the three tasks are 0.101, 0.1, and 0. 106, all around 101 indicating a reasonably close match between the Laplace distribution and the empirical distributions in terms of overall shape. Meanwhile, the corresponding average log-likes liglliies are 5.76, 5.87, and 6.54, which are relatively high and stable, further suggesting that the Laplace distribution provides good approximation to the main mass of the task-vector distributions.
It is important emphasize that MergOPT does not rely the Laplace distribution perfectly capture the full, true distribution of task vectors. Instead, Laplace is adopted as a structurally simple and easily sampled approximation to potential worst-case merge offiset,, enabling a distributionally robust optimization objective in weight space.
Table 10: K-S Distance and Average Log Likelihood for Each Task Vector.
Task
K-S Distance
Avg. Log Likelihood
C-STANCE
0.101
5.76
MectingBank
0.106
5.87
ScienceQA
0.106
6.54
'It is worth emphasizing that the empirical distribution in the figure does not perfectly fit a Laplace distribu- tion; there are noticeable deviations, especially a slight underestimation of the tail mass. In practice, optimization in deep learning is highly complex, and the distribution of parameter updates induced by optimization is difficult capture exactly with any simple explicit distribution.
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D.1.2 ANALYSIS ON SCALE PARAMETER b LAPLACE DISTRIBUTION
Table [ presents the performance of Task Arithmetic merging on seven models using Llama- 3.2- 1221IB-nnstruct under different values of the Laplace scale parameter b. We observe that our proposed Merg0FT method consistently enhances merging performance across a range values, demonstrating its robustness to this hyperparameter. Notably, setting b 0.0005 yields the best average score of 0.4164, representing a +2.68% relative improvement over the task arithmetic baseline (average score of 0.4055). This indicates that approach effectively simulates merging shifts during fine-tuning, leading to more robust merged models.
D.1.3 ANALYSIS ON LOCATION PARAMETER OF LAPLACE DISTRIBUTION
Based the results in Figures T and empirically observe that the task vectors approximately follow a Laplace(p, (u, b) distribution with concentrated around O. Therefore, in our main experiments, we set μ 0 by default. In this section, we further analyze the impact of shifting the mean μ in the Laplace distribution on performance. As shown in Table 12 under both Task Arithmetic and TIES-Merging, performance consistently degrades when μ deviates from 0. For example, when merging two models with Task Arithmetic, the average scores with = 0.1 and = -0.1 are 0.4878 and 0.4877, both lower than 0.4902 obtained with μ = O. Similarly, for TIES-Merging, the scores with μ = 0.1 and results indicate that setting = a well well-justified default choice that better matches the empirical distribution of task vectors.
-..1 are 0.4910 and 0,4912, compared to 0.4929 when μ 0. These
Table 11: Task Arithmetic Merging Results on Llama-3.2-1 B-2-1B-IIsstuuu with Varying Laplace Scale b.
Task Performance
Avg. (t)
C-STANCE
FOMC
MeetingBank
SciencoQA
NumGLUE-cm
NumGLUE-ds
20Minuten
(base)
0,4219
0.4980
0.2094
0.7370
0.2439
0.3476
0.3805
0.0005 (Default)
0.3995
0.5101
0.2039
0.7499
0.2683
0.4024
0.3808
0.4164
0.001
0.3991
0,5040
0.2060
0,7479
0.2439
0.4024
0,3801
0.4119
0.3991
0.2014
0.7365
0.2683
0.4024
Table 12: Task Arithmetic Merging Results on 3.-......BB-nttttrrct with Varying Location
Method
= 0.1
p= (Default)
p=0.1
CTTANCE
FOMC
Avg. (*)
C-STANCE
POMC
Avg.
C-STANCE
FOMC
Aug.
Tusk Arithmetic MargoPT
0.4417
0.5339
0.4878
0.4440
0.5363
0.4902
0.4423
0.5331
0.4877
TIES-Merging w/ MergOFT
0.4396
0,5423
0.4910
0.4414
0.5444
0.4929
0.4408
0.5416
0,4912
D.1.4 ANALYSIS ON MERGING COEFFICIENT &
Table 13 reports the performance of Task Arithmetic merging on the 1.0maa332--BBInnstrree model under different merging coefficients a. We observe that smaller merging coefficients (i.e., a in Eq. 2 generally yield better results. For example, when ranges from 0.1 to 0.6, the merged models consistently achieve scores above 0.34, with the best performance 0.4055 attained at = 0.2. In contrast, larger coefficients cause severe performance degradation, with results those of the pretrained model (e.g., 0.3064). In particular, when a = 1.0, the merged model drops to 0.2194, which is approximately half of the best score. These findings suggest that optimal merging coefficients are typically small. Accordingly, we adopt the range [0.1, 0.6] as the feasible set (i.e., A) of coefficients throughout this work.
falling below
D.2 COMPARISON WITH DIFFERENT OPTIMIZERS
D.2.1
COMPARISON WITH SAM OPTIMIZER
2025 is robust model merging approach that employs the Sharpness-Aware SAFT-Merge (Lee et al.
Minimization (SAM) (Foret et al., 202T or Adaptive SAM (ASAM) (Kwon et al., (202T) optimizer during fine-tuning to seek flatter minima, thereby reducing performance degradation at the merging
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Table 13: Task Arithmetic Merging Results on Jlama-3.2-IB-Instrne with Varying Merging Coeffi- cient.
Task Performance
Avg. (1)
C-STANCE
FOMC
MeetingBank
ScienceQA
NumGL.UB-cm
NumGLUUE-ds
20Minuten
Pre-Trained
0,3386
0.2581
0.2036
0.6780
0.1220
0.1646
0.3802
0,3064
0.1
0.4098
0.4456
0.2094
0.7125
0.1951
0.2927
0.3878
0,3790
0.2
0,4220
0,4980
0,2094
0.7370
0.2439
0.3476
0,3805
0,4055
0.3
0,4120
0,4718
0,2274
0,7355
0,1951
0,3902
0.3809
0,4019
0.4
0.4104
0.4355
0.2336
0.7170
0.2439
0.3963
0.3772
0.4020
0.5
0.3931
0.4476
0.2242
0.6735
0.1707
0.3902
0.3790
0.3826
0.6
0,3517
0.4395
0.1758
0.6264
0.0976
0.3598
0.3783
0.3470
0.7
0.3503
0.1231
0.5615
0,0976
0.3354
0.3718
0.3193
0.8
0.3090
0,3690
0.0949
0.4667
0,0000
0.3171
0.3687
0.2750
0.9 0.2998
0.2621
0.0895
0.4094
0.0488
0.2500
0.3665
0,2466
1.0 0.3138
0.2823
0.0848
0.3611
0.0000
0.1280
0.3658
0.2194
stage. In this section, we compare our proposed Me MergOPT with SAFT-Merge from two perspectives: equal training epochs and comparable fine-tuning time.
Equal Training Epochs. As shown in Table 14 when all optimizers are trained for the same number of parameter updates, the results exhibit the following trends: Under Weight Averaging and DARE, our method surpasses SAFT-Merge (SAM) by 2.59% and 5.20%, respectively. In contrast, SAFT-Merge (SAM) slightly outperforms MerT under Task Arithmetic and TIES- TIES-Merging, with relative gains of 2.24% and 1. 1.29%. Furthermore, when comparing SAFT-Merge (SAM) and SAFT-Merge (ASAM), observe that ASAM is generally more effective: under Weight Averaging, TIES-Merging, and DARE, achieves improvements of 1.68%, 1.17%, and 4.03%, respectively, This advantage may stem from the adaptive perturbation radius used in ASAM, as opposed to that in SAM. However, as shown in Table T5] SAFT-Merge (SAM) and SAFT-Merge (ASAM) require an average runtime that is 2.04x and 2. 2,06x AdamW, while Mer only ineurs 1.17x AdamW overhead. SAFT-Merge (SAM) and SAFT-Merge (ASAM) are computationally expensive because they require one gradient ascent step compute the perturbation direction at each parameter update step, followed by one gradient descent step for parameter updates. Consequently, each update step involves two full forward-backwe backward propagation passes. leading a computational cost roughly twice that of standard fine-tuning. In contrast, our MergCPT method directly samples the perturbation direction, resulting in computational cost much closer to that of standard fine-tuning. This highlights that MerT offers better efficiency while still delivering competitive robustness.
Comparable Fine-tuning Time. To ensure a fair comparison, we further align the computational cost of SAM (ASAM) and T (1.04x and 1.17x AdamW, respectively, see Table As shown in Table 16 in this setting, the performance improvements become more consistent: With Weight Averaging. Task Arithmetic. TIES- MEES-Merging, and DARE, MergOPT achieves relative gains of 4.08%, 0.70%. 0.95%, and 3.98% over SAFT-Merge (SAM), respectively. Compared with SAFT-Merge (SAM), SAFT-Merge (ASAM) shows only limited gains under Weight Averaging, Task Arithmetic, and TTES-Merging This may be because, when restricted to a training budget comparable to Adam the optimizations performed by ASAM and SAM are less thorough than those of AdamW, which in turn limits their performance. These results demonstrate that at comparable computational cost, MergOPT consistently outperforms SAFT-Merge (SAM) and SAFT-Merge (ASAM), striking a better balance between efficiency and robustness.
D.2.2 COMBINED WITH OTHER BASE OPTIMIZER
While AdamW is our default base optimizer, MergOPT is optimizer-agnosti and can be combined with any standard optimizer. To assess this generality, we also instantiate MergCPT with SGD. Table 18 reports results on -.ama-3.2-IB-Insttae when SGD is used as the base optimizer.
Relative to the naive SGD fine-tuning, MergOPT yields more robust post-merge performance for most merging procedures: Task Arithmetic improves from 0.3286 to 0.3566 (+8.52%). TIES- Mergingg from 0.3225 to 0.3552 (+10.14%) and DARE from 0.2313 to 0.2471 (+6.83%), while Weight Averaging decreases slightly from 0.3634 to 0.3468 (-4.56%). We also note that both Mer and standard SGD achieve relatively low absolute scores under DARE (0.2471 vs. 0.2313). A plausible
22

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Published as a conference paper at ICLR 2026
Table 14: Performance comparison of MergOPT and SAFT-Merge (based on SAM and ASAM) under equal training epochs on Llama-3.2- Instruuuc.. Notably, SAM incurs x.04x the optimization cost of standard AdamW, whereas ours incurs only 1.17x.
Medhod
Task Performance
STANCE
FOMC
MeetingBank
ScienceQAA
NamGLUB
NumGLUE de
20Minuien
Tuned w/ SAFT-Mrrg (SAM)
0.4820
0.5927
0.2354
0.5122
0.5428
0.3338
UL5325
Pine Tuned w/ SAFT (ASAM)
0.4867
0,6005
0.2287
0.4878
0.5215
0.3814
0.5245
Mergor
0.4300
0.3829
Weight Avaraging SAFT-Merg (SAM)
04320
0:4355
0.2108
0,3075
0.2027
0.3781
0,5000
Weight Averaging W/
(ASAM)
Weight Averaging MorgoP?
0.2927
Artthnetic SAFT-Merge (SAM)
0.2051
0.39012
0.3861
U.4200
Artthmetic SAFT-Meng (ASAM)
0.4280
0.3415
0.3526
0.4199 13991
Thek Arithmetic MareCPP
0,2013
0.3077
0.7530
0.3171
0.3797
TIES Merging w/ Serg--Mrre (SAM)
044395
0,4698
0,2063
0.7232
0.3415
0.3598
0.3836
0.4177
TIES Merging w/ Serg- (ASAM)
0.4423
0,4752
0.2089
0.7268
0.3561
0.3648
0.3843
'IEE-Mergling w/ Nazgore
0.4202
0.4336
0.2043
0.7555
0.2927
0.3720
0.3825
0,4123 12R1
DARE SALT Merge (SAM)
0.4280
0.4234
0.2079
0.6895
0.2927
0.3415
0,3907
0.3922
DARE SAFT-Megg (ASAM)
0.4318
0.4615
0.2057
0.7142
0.5268
0.3512
0.3815
0.410)
DARE w/ MezgdP?
0.4192
0:4819
0.3107
0,7485
0.2927
0,3689
0,3843
0.4147
Table 15: Average fine-tuning time (seconds) of AdamW, SAFT-Merge (based on SAM and ASAM), and MergOPT under equal training epochs.
Optimizer
Task Tine Oinettnnng Time (6)
Avg. (1)
C-STANCE
FOMC
MeetingBank
ScienceQA
NamGLUE-<tn
NumGLUE-ds
20Minuten
AdamW
1927.74
1155.33
2688.37
1156,57
1923,30
1921. 97
2684.57
1922.55
MArg-Merge (SAM)
3933.49
2360.41
5497,92
2363.90
3927.65
3927.04
$488.63
3928.43 04:2
SAFT-Merge (ASAM)
3968.43
2377.58
5531.46
2378.92
3958.27
3953.68
$527.37
3956.54
MergOPT
2347.64
1348.34
3147.20
1349.36
2241.04
2240.76
3141.03
2245.05g 15:0
explanation is that DARE's stochastic masking of task-vector coordinates can inadvertently suppress salient parameters, leading to nontrivial information loss during merging.
D.2.3 COMPARATIVE ANALYSIS OF MODEL MERGING VIA DIFFERENT OPTIMIZATION METHODS
In our main experiments, we assume that all models are fine-tuned either with standard AdamW or with the proposed Mer A natural question can models fine-tuned with standard AdamW and with MergOPT be merged together effectively? To investigate this, we conduct experiments on Llama3.2- 1---2-1---nnttuccc Specifically, we randomly select two tasks, NumGLUE-cn and NumGLUE-dds, and fine-tune models on each task using both AdamW and MergOPT. We then evaluate the following three merging settings: (i) Adam W Adam W: merging two models fine-tuned with standard AdamW: (ii) Adam O+MergOPT. merging one AdamW fine-tuned model with one MergOPT fine-tuned model; and (iii) MergOPT+MergOPT. merging two models mne-tuned with MergOPT.
As shown in Table 19 observe that even when only one of the two models (AdamW+MergOPe) fine-tuned with MergOPT, the merged model already achieves noticeably better performance than merging two standard AdamW models (AdamW+Adae W+dddmW). For example, under Task Arithmetic, AdamW+Mergon MerrgOPP attains an average score of 0.4116, compared to 0.3994 for AdamW+Adam When both models are fine-tuned with MergOPT, the performance further improves. These re- sults indicate that MergOPT is compatible with and beneficial for merging models obtained from heterogeneous fine-tuning strategies.
D.3 ABLATION STUDY ON NUMBER OF TASKS TO MERGE
In Tf the main text, we have already reported the results for the 4-task merging scenario. To further examine the effecttiveness of our approach under different task scales, this section extends the study to 2-task and 6-task merging. Specifically, we randomly sampled subsets from the full set of seven tasks, with each subset containing either 2 or 6 tasks. We then merged the expert models fine-tuned with the standard Adam W optimizer, as well as those fine-tuned with our proposed Mer MergOPT, , and evaluated their performance.
The results are presented in Tables 20 and 2T Overall, we observe the following: (i) 2-task merging, shown in Table 20 For both Task Arithmetic and Teriine, incorporating Me rgOPT
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Published as a conference paper at ICLR 2026
Table 16: Performance comparison of MergOPT and SAFT-Merge (based on SAM and ASAM) under comparable fine-tuning cost on Llama-3.2-1
Method
Taak Petformance
Arg. (7)
C-STANCE
FOMC
Mortingant
SciennrQA
NumCil Ui-emm
Numti../Fxch
20Minuten
Fine-Tum TuneT w/ SAFT-Merge (SAM)
0.494
0.5746
0.3615
0.8305
0,4390
0.5671
0.3850
0.5217
Pine Tuned w/ Merge (ASAM)
0.8829
0,5874
0.2725
0.3452
0.4634
0.5942
0,3897
0.5322
Reegcet Fine-Tinal
04957
D.6311
0.3158
0.8780
0.4990
0.5305
0.3820
0.5250
Weight Avoraging w/ SAFF-Meryy (SAM)
0-245
0,4115
0.3149
0.6930
0. 1.3683
0.3293
A33866
D. 1.9033
Waight Avezaging w/ SAFF-Meree (ASAM)
04196
0.4267
0.2127
0.6822
0.2631
0.3214
0.3821
0.3673
Weight Averaging MorgoP?
0:1130
0:4819
021533
0.7530
0.2927
0.317
0.3850
0 0.40%
Tack Anthmetic Merge (SAM)
0-2255
0.4919
0.2015
0.6840
0.3415
0.3598
0. 0.3822
0.41 36
Task Arithmetic w/ Merge (ASAM)
0.4316
0,4967
0,2098
0
0.3456
0.3651
0,3837
Tisk Arithmncii MergOpt
0,2213
0.4718
0.3677
0.7530
0.3671
B.3655
0.3797
0,415
TIES-Merging Merging SArg-Mogee (SAM)
0,2255
D.4758
0.3075
0,0230
0.3171
0.5537
0.3826
0.4084
TIES Merging Serr-Mere (ASAM)
04255]
0,4698
0.2043
0.6837
0.3109
0.3472
0.3798
0,6030.1770
TTES- w/ Mergop?
0/4022
0.4536
0.3093
0,7355
0:2927
0:3720
0,3825
0,123
SAFT Merge ISAM)
0.4335
0.4355
0.2134
0.3171
0.3776
0,2988
SAFT-Merg
0.4298
0.2108
0.6548
0.3127
MacgdP?
0.4192
0.2107
0.2927
0,3843
Table 17: Average fine-tuning time (seconds) of AdamW, SAFT-Merge (based SAM and ASAM),
and MergOPT under comparable fine-tuning cost settings.
Optimizer
Task Fine-tuning Time (6)
Avg. (L)
C-STANCE
FOMC
MeetingBank
ScienceQA
NumGLUE-cm
NumGLUE-ds
20Minuten
Adam
1927.74
1155.33
2688.37
1156.57
1923,30
1921.97
2684.57
1922.55
MArT- (SAM)
1994.25
1196.54
2788.16
1197,83
1990.55
1994.05
2782.05
1991.92
SAPT-Merge (ASAM)
1153.39
1254.05
2018.30
2020.72
2782.95
1990.71, (..07)
MergOPT
2347.64
1348.34
3147.20
1349.36
2241.04
2240.76
3141.03
2245.05
consistently improves the average performance of the merged models, with the maximum gain exceeding 8%. (ii) 6-task merging, as shown in Table [1] Compared to standard fine-tuning, MergOPT also provides stable improvements across different task groups, with relative performance gains ranging from 2.57% to 6.78%. These findings indicate that MergOPT remains robust across both small- and large-scale merging scenarios, further validating its generality and reliability.
D.4 HYPERPARAMETER SENSITIVITY ANALYSIS
D.4.1 DIFFERENT TASK VECTOR DISTRIBUTIONS
In this work, our analysis suggests that the Laplace distribution provides a better fit to the empirical task-vector distribution. Accordingly, in MergOPT we sample perturbation vector from this Laplace distribution at each optimization step to simulate merge-induced parameter offsets. To further assess the sensitivity to the choice of distribution, we additionally experiment with sampling task vectors from Gaussian distribution, i.c., at each step we draw perturbations from Gaussian instead of a Laplace. As shown in Table 22 both choices lead to consistent gains over standard fine-tuning. For example, under T'ES-Merging the average performance of MergOPT T w/ Gaussian and Mer w/ Laplace when merging two tasks is 0.4912 and 0.4929, respectively, both higher than the baseline value of 0.4854. This indicates that Gaussian sampling can also serve reasonable approximation for task vectors, even though it is slightly weaker than the better nettivemotivated Laplace- based approximation.
D.4.2 BATCH SIZES
In this part, analyze the sensitivity of the proposed method the batch size. In main experiments, we use a default batch size of 8, and here we additionally evaluate batch sizes of 4 and 16. As shown in Table 23 MergOPT improves over standard fine-tuning by 6.60% and 1.53% when the batch size is 4 and 8, respectively. When the batch size is increased to 16, we observe slight decrease of 1.04%. Overall, across a reasonable range of batch sizes, MergOPT remains competitive and often yields clear gains over the standard fine-tuning baseline.
D.4.3 LEARNING RATES
In this part, we analyze the sensitivity of the proposed method to the choice of learning rate. In the main experiments, default learning rate of 2 x 10-5 Here, additionally consider two
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Published as a conference paper at ICLR 2026
Table 18: Performance Comparison Model Merging Methods on Llama-3.2- 1n--tuctttt (SGD as
base optimizer).
Method
Task Performance
Avg. (1)
C-STANCE
FOMC
MeetingBunk
ScienceQA
NumGLUE-cm
NumGLUE-ds
20Minuten
Truined
0.3386
0.2581
0.2036
0.6780
0.1220
0.1646
0.3802
0.3064
SGD Fine-Tuned
Mazg0FT
Weight. Averaging
0.4023
0.3407
0.1700
0.6668
0.3699
0.2622
0.3962
0.3634
Weight Averaging w/ MergOPT
0.3912
0.3185
0,1535
0.6351
0.2439
0.3049
0,3804
0,3468
Tack Artthmetic
0.4068
0.2782
0.1382
0.5983
(1.349
0.2561
0.3788
0. 0.3286
Task Arithmetic MaxgOP?
0.1219
0.3293
0.3783
0.356
Merging
TIES-Merging w/ Mergoer
0.3712
0.4176
0.1286
0.5791
0,2139
0.335d
0,3808
0.3552
DARE
0.3393
0.2449
0.0938
0.3073
0,0976
0.1585
0.3779
0.2313
DARE w/ HargOPT
0.3164
0.2883
0.0906
0.4131
0.0732
0.1768
0.3710
0.247
Table 19: Performance Comparison of Merged Models Trained with Different Fine-Tuning Methods on Llama-3.2- 3.2-1IB-Instruee B-Instruct.
Method
NumGI.
NumGLUFEdds
Avg. (t)
Task Arithmetic (Adam AAdam)
0.3659
0,4329
0,3994
Task Arithmetic A.dam-+MerrgPP))
0.3659
0.4573
0.4116,43.055)
Task Arithmetic (MergOPT+MMergOP)
0,3659
0.4817
0.4238
TIES- MES-Merging (AdamW+Addaml)
0.3415
0.4390
0.3903
TIES-Merging (AdanW*MerrOOPT)
0.3659
0.4450
0,4055
TIES-Merging (MergOPT-MergOPT)
0.3659
0.4817
0.4238
variants by halving and doubling the learning rate to 1 x 10-5 and 4 x 10-5, respectively. As shown Table MergOPT consistently outperforms standard fine-tuning under all three learning-rate rate settings. For example, when the learning rate is set to 1 x 10 2 10-5, and 4 x 10 Mer yields relative improvements 2.92%, 1.53%, and 0.32%, respectively, over the Task Arithmetic baseline. These results suggest that our method is robust reasonable variations in the learning rate.
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Published as a conference paper at ICLR 2026
Table 20: Performance of different merging methods on 2-task groups 1lama-3.--B-IInsrruu
Group
Group 2
Method
C-STANCE
FOMC
Avg. (1)
NunGLUE-cm
NumGLUE-ds
Avg. (1)
Task Arithmetic
0.4475
0,5181
0.4828
0.3659
0.4329
0,3994
Task Arithmetic MergOPT
0.4440
0,5363
(.490
0.3659
0.4817
0.4238 (299
TIES-Merging
0,4445
0.5262
0.4854
0.3415
0,4390
0,3902
TIES- w/ MergOPT
0.4414
0,5444
(,4929
0.3659
0.4817
0.4238
Table 21: Performance of different merging methods on 6-task groups (L.lmm-3.22-1 121-----eet)
Group
Method
C-STANCE
FOMC
MoetingBank
ScienecQA
NamGLUB-<cm
NumGLUE-ds
Avg. (f)
Task Arithmetic
0,4244
0.5101
0.2136
0.7380
0.2439
0.3537
0,4146
Task Arillmetic MergOPT
0.4237
0.5101
0,21155
0.7785
0,3415
0.3537
0,4365
Merging
0.2195
0.3598
TIES- Merging w/ MexgOPT
0.4199
0.5121
0.2099
0.7695
0.3415
0.3598
0.4354,-.791
Group 2
Method
C-STANCE
POMC
Meetinglankk
NumGLUEE.cm
NumGLUE-t
20Minulen
Arg. (1)
Task Arithmetic
0.4242
0.5363
0.2177
0,2683
0.3476
0.3811
0.3625
Task Aritlumetic MergOPT
0.4221
0.5363
0.2199
0.3171
0.3537
0.3877
0.3718
Mer-Mngginng
0.4242
0.5181
0.2171
0,2439
0,3476
0.3789
0.3550
Merg.M MaxgOPT
0.3707
Table 22: Performance Comparison of Different Task Vector Sampling Methods for 2-Task Groups
on Llama-3.2-1 1--.2-1B-Inntruue
Method
C-STANCE
FOMC
Avg. (t)
Task Arithmetic
0.4475
0.5181
0.4828
Task Arithmetic (MergOPT w/ Gaussian)
0.4440
0.5363
0.4901(
Task Arithmetic (MergOPT w/ Laplace)
0.4485
0.5320
0,4903
TIES- MerrMMg
0,4445
0.5262
0.4854
-eEg-ng (MergOPT w/ Gaussian)
0.4452
0.5372
0.4912(+.118)
TeES-Merging (MergOPT w/ Laplace)
0.4414
0.5444
(14929
Table 23: The Effect of Different Batch Sizes on MergOPT Performance on 3.2--BBIInstttuuc
Method
Batch Sizcef
Batch Sizee8 (Delault)
Batch Size=16
C-STANCE
FOMC
Avg.
C-STANCE
FOMC
Avg:
C-STANCE
FOMC
Avg. (f)
Tusk Arithmetic
0.4570
0.4879
0.4725
0.4475
0,5181
0.4828
0.4530
0.5222
0.4876
Arithmetic Mergoer
0.5037.4608)
0.1902.-1199)
0.1825
Table 24: The Effect of Different Learning Rates on MergOPT Performance on Alama-3.2-1 Instruct.
Mechol
Ir- le-S
Ir 26-5 (Defaal)
Ir Ir-
C-STANCE
FOMC
Arg. (f)
C-STANCE
FOME
Avg. (1)
C.STANEE
FOMC
Avg. (?)
Tusk Arithmetic
0,4270
0.5020
0.4645
0.4475 0.440
0.5181 0.5363
0.4828 0.4002,.13399
0.4805
0.5900
0.5203
Task Arithmetic MazgOPT
0,4781,220N4
0.4790
0.5650
0.5220l.a
26


Reviews:
[{"review_id": "jBd5Iv0k5J", "reviewer": "Reviewer_yTnV", "summary": "The paper considers the problem of model merging with LLMs. The key idea to propose a new optimization method is that, usually, despite a good merging procedure, fine-tuning processes don't address parameter conflicts between models in a robust way, which decreases performance severely. To solve this problem, the work introduces a merging-aware optimizer inspired by the recent *distributional robust optimization* (DRO) method (Lin et al. 2022), which sets an objective based on training data coming from a perturbed distribution around a divergence constraint (let's say these distributions are perturbed versions of the empirical data density). The authors adapt this idea for the weight-space, where perturbations are now caused by the addition of new models to the merging objective. Despite computational and privacy issues, the paper proposed a manageable objective and tested it on several LLM-oriented datasets.", "questions": "- Results are very confusing without explaining what the performance metrics are, not bold numbers and not having insights on its properties (what is better, being higher or lower). Leaving all this little effort to the reader is not the best idea for communicating precisely the empirical results.\n- How many times and how is the Laplace distribution fitted to the empirical changes? is the empirical distribution computed per-model or taking into account all K models together?\n- Could the authors add some info on the computational/combinatorial cost of the methodology?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The manuscript is in good shape, and I can see the research quality of the work at first sight. The paper is excellently written, extremely clear, does a very good review of the needed background and SOTA methods, and derives the solution in a thorough way. One of the key points I enjoyed more while reading is the clarity and transparency on the challenges and how these are addressed (i.e. basically the approach and discussion introduced in section 3.2.3).\n- The DRO techniques are quite interesting, and it makes sense to me that authors develop their solution in this direction. Although I missed a bit of an extra teaser-figure or empirical evidence in pp.4 on how DRO works (for the sake of being a self-contained work or better comprehension), the way it works is well explained and connected to the solution.\n- The way the method is proposed, with the perturbation-based approach and later the Laplace-fit and sampling, is very proximal to some probabilistic merging approaches which have been mostly ignored due to they have not yet been applied to LLMs, etc. I don't think this is precisely a big weakness, but I just wanted to mention it. The way objectives are presented and discussed is insightful.", "weaknesses": "To me, the paper doesn't have very big critical weaknesses that make it difficult to communicate a scientific contribution. However, what I detect are several big gaps of information, derivations, avoidance of certain clarity on tricky issues and some details that should be corrected:\n\n- I can guess how the last terms in Eq. 5 are obtained, but I would like to have/see the entire derivation of it. Where is the baseline/initial parameter set $\\theta_{0}$?\n- The paper abuses a bit of the word \"perturbation\". In some way it confuses the reader, as what we have is different arithmetic combinations of parameters. Someone this naming and recursive mentioning decouples the line-of-explanations from the usual model merging clarity and intuition.\n- Not a lot of references to the maximum number of K models to merge or the size. These two are key limitations, and I think they should be present in the discussion and development since the beginning of the manuscript.\n- The *alternating optimization strategy* mentioned in pp.5 looks a lot like something we have already considered in the optimization literature with focus on ML/AI (i.e. coordinate ascent/descent, min/max or expectation-maximization). I am sure the authors can find and add some extra details in that direction, so it provides more insights to the reader.\n- Already in section 3.2 the combinatorial problem of having a lot of different perturbations as K increases (without even considering the size of models), can be deduced easily. This is somehow mentioned lated in section 3.2.3 in a way that is not very precise for this reviewer. Having a combinatorial problem of this sort is a big problem, despite doing sampling later solves it a bit.\n- The comments on the innacessibility of models and tasks in pp. 5 should have been considered from the beginning as a big assumption. What about alignment of logits/labels? what are the main features of the models we are considering?\n- First paragraph in pp.6: the empirical distribution of weight perturbations doesn't seem like a good fit to a Laplace distribution, but more of an approximation which underestimates a lot the probability mass on the tails.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4y8kQ21Bq6", "reviewer": "Reviewer_5xzh", "summary": "The paper proposes MergOPT, a merge-aware optimizer designed to improve model robustness to parameter perturbations during model merging. The key idea is to introduce merge-aware regularization during fine-tuning, formulated under a distributionally robust optimization (DRO) framework. By injecting Laplace-distributed weight perturbations during training, the model becomes more resilient to merging-induced parameter shifts. Experiments on multiple large language models (Llama3, Qwen2.5, etc.) and merging baselines (Weight Averaging, Task Arithmetic, TIES, DARE) show consistent performance gains — typically around +3.5% average and up to +9.5% on certain benchmarks.", "questions": "1. Have the authors tested combining MergOPT with evolutionary or gradient-based merging recipe optimizers?\n2. When merging more than 10 models, does the Laplace noise assumption still approximate the merge perturbation distribution well?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Novel training perspective: The work is among the first to explicitly incorporate merge robustness into the optimization objective, shifting the focus from “how to merge” to “how to train for merging.”\n2. Theoretical motivation: The DRO-based formulation provides a principled justification for the merge-aware objective.\n3. Empirical breadth: The experiments cover several LLM architectures and multiple merging algorithms, showing consistent performance improvements.", "weaknesses": "1. Insufficient Baseline Comparisons: The paper does not compare against optimization-driven merging methods, such as [1] and later variants using evolutionary or gradient-based recipe search. This omission weakens the claim of superiority.\n2. Scalability and Efficiency Concerns: While MergOPT is shown to be more efficient than SAM, it still adds a non-trivial 17% computational overhead to the fine-tuning process (Table 9). This cost is incurred for every single expert model that is fine-tuned. The paper does not adequately discuss the scalability of this approach in a real-world scenario where dozens of expert models might need to be trained before merging.\n3. Scalability is not verified: Experiments focus on 1B–3B models; results for larger (≥7B) or multimodal models are missing, leaving questions about scalability.\n\n[1] Akiba T, Shing M, Tang Y, et al. Evolutionary optimization of model merging recipes[J]. Nature Machine Intelligence, 2025, 7(2): 195-204.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "K7uFWz4QhL", "reviewer": "Reviewer_wjmi", "summary": "The paper proposes MergOPT, a fine-tuning-time optimizer that models downstream parameter-level merging as weight-space perturbations and trains each expert to be robust to those perturbations. Experiments on three LLM bases (Llama-3.2-1B/3B, Qwen-2.5-1.5B) and four merging schemes (WA, Task Arithmetic, TIES, DARE) show consistent average gains when merging seven experts, visualizations suggest flatter joint-loss landscapes.", "questions": "Refer to the weakness", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Shifts attention from *merging-time* heuristics to *fine-tuning-time* preparation, the weight-space DRO view is intuitive and connects to robustness.\n2. The single-step perturbation keeps cost close to standard fine-tuning and is optimizer-agnostic. \n3. Tables 1–3 show improvements for WA/TA/TIES/DARE; 3.5% average, up to 9.5% in a seven-expert setting. \n4. Heatmaps indicate flatter, wider low-loss regions after MergOPT, supporting the robustness claim.", "weaknesses": "1. While Figure 1 and Figure 3 empirically show \"reasonable\",  Laplace fits for task vectors, the choice is ultimately justified mostly visually and via mean/scale parameter tuning. There is no mathematical analysis or statistical test quantifying goodness-of-fit (e.g., K–S distance, log-likelihood comparison to alternatives), nor discussion of the method’s sensitivity to non-Laplacian deviations, skew, or multi-modal effects. As this modeling choice affects the entire robust optimization, more rigor is needed.\n2. The practical DRO surrogate in Algorithm 1 replaces the inner maximization over merging perturbations with a simple Monte Carlo sampling from the approximated feasible region. There is little analysis of the gap between this heuristic and true minimax-optimality, particularly for non-Laplacian/real-world merging scenarios. How often does the sampled perturbation land in truly adversarial directions (i.e., the “tails”)? Is there a risk of systematically missing impactful merging failures?\n3. The choice of the Laplace distribution, the settings $\\mu=0$, $b$ values, and the discrete set $\\mathcal{A}$ for $\\alpha$ are justified by empirical distributions and prior work, but ablation results (see Table 6, Table 7) could be improved with more diagnostic measures: e.g., what happens if a different parametric family is used (Gaussian, mixture, etc.)? How robust are improvements if empirical task vector statistics deviate (e.g., outlier tasks, long tails, multi-modal structure)?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pci1sFhqgT", "reviewer": "Reviewer_VdQC", "summary": "The paper tackles model merging, particularly during the fine-tuning stage, similar to few previous works. The paper takes a similar perspective with a previous work that views merging process as parameter perturbation process. From this perspective, the paper proposes a new optimizer, named MergOPT that employs a distributionally robust optimization (DRO). The experiments on three LLM demonstrate the effectiveness of the proposed method, in comparison to using standard fine-tuning in terms of the performance of merged model.", "questions": "- The datasets used in the experiment seem to be different from standard datasets used in the field of model merging. What's the justification for such setting? How does the performance compare against previous works on fine-tuning methods on standard datasets?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The proposed method is simple yet practical, avoiding the double-forward/backward passes required by SAM and thereby achieving the efficiency.\n- The proposed method demonstrates strong performance, validated on three LLM models.\n- The paper is well-organized and easy to follow.\n- The paper shows that a task vector can be well-approximated by a Laplacian distribution, which provides a new insight.", "weaknesses": "- The paper claims that one of core ideas of the proposed method is viewing merging process as perturbations. However, to the best of the reviewer's knowledge, the view of seeing other experts as adversarial perturbation seems to be similar to the view introduced by SAFT-Merge, a work mentioned in the paper. The mathematical formulation in Eq. (5) seems to be similar to the one in SAFT-Merge as well. However, the paper does not provide credit to the previous work for the perspective and formulation.\n- The introduction section lacks discussions on previous works that also focus on fine-tuning stage for merging, including but not limited to SAFT-Merge and [A,B,C].\n- The related work section lacks discussions on similar previous works [A,B,C].\n- The experimental results lack comprehensive comparisons against previous works [A,B,C].\n- The experiments are mainly performed only on seven language tasks, in contrast to previous model merging works that also show experiments on vision tasks to demonstrate the applicability and generalizability .\n\n[A] Tang et al., Parameter Efficient Multi-task Model Fusion with Partial Linearization. ICLR 2024.  \n[B] Ortiz-Jimenez et al.,Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models. NeurIPS 2023.  \n[C] Jin et al., Fine-Tuning Attention Modules Only: Enhancing Weight Disentanglement in Task Arithmetic. ICLR 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "r8r4ZwbpZY", "reviewer": "Reviewer_emci", "summary": "This paper proposes MergOPT, a merge-aware optimization method that enhances the compatibility and robustness of fine-tuned models for subsequent model merging. The method reformulates fine-tuning as a distributionally robust optimization problem in the weight space, where parameters from other expert models are regarded as adversarial perturbations. By introducing controlled perturbations during the fine-tuning stage, MergOPT guides models toward flatter and more stable loss landscapes, thereby improving their adaptability under potential merging operations. In particular, the article designs a fine-tuning optimization method that enables the fine-tuned model to remain more compatible with potential future model-merging operations, thereby achieving better performance when merging occurs. Overall, this work aims to establish a more merge-friendly fine-tuning ecosystem for future model merging, providing a feasible approach to improve merge performance through enhanced finetuned model compatibility.", "questions": "Q1. The Laplace distribution used for perturbation sampling is fitted from a specific set of task vectors. How should this distribution be re-estimated or adapted for new domains, modalities, or highly conflicting task collections? Is there any online or adaptive estimation strategy?\nQ2. In real-world collaboration, contributors may fine-tune their models with different strategies. Must all participants adopt MergOPT to benefit from improved mergeability, or can MergOPT-trained and standard fine-tuned models be merged effectively?\nQ3. Beyond the parameters explicitly discussed in the paper, does MergOPT exhibit sensitivity to factors such as batch size, learning-rate schedule, or training steps, similar to the SAM?\nQ4. What specific experimental device or environment were the results reported in the paper based on? This is crucial for promoting reproducibility.\nQ5. What are the significant differences in the experimental settings between Tables 8-9 and Tables 10-11 in the appendix? Why is the latter considered a fairer comparison? Did Tables 10-11 adjust the hyperparameters of SAM to align with those of MergOPT in order to match the computational costs?\nQ6. As shown in Tables 8-11 in the appendix, MergOPT and the SAM method actually have their own advantages and disadvantages in terms of performance when combined with different merging methods and in terms of runtime under different configurations.What are the significant differences between these two optimization methods in terms of optimization objectives and perturbation modeling? What inspirations did MergOPT draw from SAM?\"", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The paper introduces a new perspective by shifting the focus of model merging from a post-merging adjustment problem to a fine-tuning optimization problem. This ''merge-aware fine-tunin`` view is conceptually novel and provides a promising new direction for improving model compatibility before merging.\n\n2. The article aims to build a more friendly model ecosystem for future parameter-level merging, allowing users to obtain more compatible expert models during the fine-tuning stage. It is essentially an infrastructure method for constructing a merge-friendly ecosystem, establishing the foundation for future collaborative fine-tuning and model merging workflows.\n\n3. The paper includes extensive analysis on perturbation parameters (e.g., Laplace scale, number of tasks, and merge coefficient) and provides insights into how these factors influence the merge robustness and final model quality.\n\n4. The study demonstrates strong generality, showing that merge-aware fine-tuning can benefit multiple architectures and merging algorithms.\"", "weaknesses": "1. The method assumes that robustness to future, unseen tasks can be achieved by simulating “potential merging perturbations” using only data from single-task fine-tuning. This assumption is overly strong because it depends on the empirical task-vector distribution estimated from the current benchmark and may not generalize to unseen tasks. The diversity of real-world merging scenarios can far exceed what a single parameter distribution can approximate. Moreover, the Laplace assumption mainly captures sparsity or concentration in parameter differences but fails to represent semantic conflicts or gradient-direction contradictions between tasks. Consequently, the assumed perturbation distribution may deviate substantially in cases of stronger conflicting or different modal tasks.\n\n2. Although Eq. (6) defines a robustness objective against worst-case perturbations, the implementation (Eq. 10) adopts the single-step approximation. This procedure perturbs only within a local noise neighborhood instead of solving the true inner maximization. Hence, the method effectively behaves as a heuristic regularization rather than a strict distributionally robust optimization. No theoretical justification or upper/lower bounds are provided to show that the sampled perturbation covers the genuine worst-case scenario. The robustness may thus fail when the future merging tasks deviate from the training-time task-vector distribution.\n\n3. Since MergOPT requires access to fine-tuning data, its applicability in privacy-restricted or cross-organizational settings remains unclear. For example, if user A fine-tunes a model using MergOPT but user B fine-tunes without it, how would the merging behave? Does the method require all participants to adopt MergOPT to realize its benefits?\n\n4. The paper cites recent works such as AdaMerging but does not experimentally compare with them. Including comparisons with newer or optimization-driven merging strategies such as WUDI Merging or RegMean would make the evaluation more convincing.\n\n5. All experiments were conducted on text-based tasks. Extending the evaluation to other modalities, such as vision, would better demonstrate the generality and impact of the proposed method across different modalities.\n\n6. It is recommended that the “Related Work” and “Introduction” sections include more discussion on current fine-tuning methods. For example, an analysis of why previous fine-tuning methods result in poor compatibility during model merging would be valuable. Furthermore, it would be beneficial to review any existing work that is similar to the proposed method and to detail their approaches. This would better align with the positioning of this research.\n\n7. Although SAM results are reported, the discussion could be more prominently integrated into the main text rather than deferred to the appendix, as SAM represents the most closely related optimization paradigm to MergOPT.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)