Response To Reviewer wt9t

We greatly appreciate the insightful comments and suggestions from the reviewer. Below, we will provide point-by-point responses to each of your questions and recommendations.

Response To Weakness #1

We appreciate the reviewer's insightful feedback.

Knowledge Tree Granularity and Node Organization: The knowledge tree is constructed with three layers. It originates from a [Root] node, branching into distinct Main, Secondary, and Sub-level domains. You can visualize its specific structure in Figure 7 of our appendix within the supplementary materials.

New Node Creation: During each meditation phase, starting from the root, our Thompson Sampling (TS) algorithm samples child nodes from existing ones. When a sampled child node is unk (e.g., sampling unk from the Mathematics node), it signifies that the corresponding parent node (Mathematics) requires new sub-node expansion. At this point, a Sprout operation is executed, prompting the source model to propose new domains to be added as sub-domains under Mathematics. For more specific operational details, please refer to the algorithm pseudocode in Appendix B.4.

Node Category Determination: The resulting node tree is stored as a dictionary, which clearly defines the hierarchical relationships. During the meditation phase, after a path of nodes (Main → Secondary → Sub) is sampled, we perform a Harvest operation in parallel for each path to generate data corresponding to that path. For instance, if data A is sampled along the path Mathematics (Root) → Algebra (Secondary) → Linear Algebra (Sub), it will be stored in the list corresponding to the innermost key (Linear Algebra) of that path in the dictionary. This allows for clear querying of its associated Main, Secondary, and and Sub domains.

The unk Arm: Simply put, the unk arm represents the need for "current parent node expansion." Each node, upon creation, is automatically assigned an initialized unk arm, and these unk arms are independent across nodes. When the unk arm is sampled from node 'a', a Sprout operation is executed to generate new child nodes for node 'a'. You can find clear details regarding the specific execution of this operation in the algorithm pseudocode in Appendix B.4.

Response To Weakness #2

We deeply value the reviewer's insightful comments. Through a series of comprehensive experiments, we have compellingly demonstrated the consistency and stability of Bohdi's performance.

In the comparative experiments, we conducted a thorough evaluation of all methods across four target models with different architectures and parameter sizes: Llama3.2-3B-Instruct, Qwen2.5-7B-Instruct, Gemma2-9B-IT, and Llama3.1-8B-Instruct. As shown in Table 1 of the main text and Table 2 in the appendix, Bohdi consistently outperforms other baseline methods across different target models.

In the ablation experiments, we further explored Bohdi's performance under different source model configurations. When using more parameter-efficient source models (Llama3.2-3B-Instruct, Qwen2.5-3B-Instruct, and Gemma2-2B-IT) and fusing them with the relatively larger Gemma2-9B-IT as the target model, the results still indicate that the target model fused by Bohdi can effectively absorb the advantages of the source models. This is particularly evident in tasks where Gemma2-9B-IT originally performed weaker than the source models, such as GPQA and TheoremQA.

Regarding the organization of generated domains, as visually illustrated in Appendix Figure 7, when Llama3.2-3B-Instruct serves as the target model, the domains generated by Bohdi consistently include the vast majority of domains from scenarios with fewer source models as the number of source models increases. This indicates that Bohdi maintains stability in terms of domain expansion.

Furthermore, throughout the evaluation process, we uniformly adopted greedy sampling to minimize the impact of autoregressive generation randomness on the evaluation results, ensuring the rigor of the assessment, as elaborated in Appendix C.

The consistent improvements observed across these diverse evaluations and experimental results fully validate Bohdi's remarkable stability under various conditions. In light of your valuable feedback, we will incorporate these analyses and findings into the main text as much as possible in the final version, enabling readers to more intuitively grasp these significant improvements. We deeply appreciate your valuable input.

Response To Weakness #3

We deeply value the reviewer's valuable feedback. Bohdi is designed to evaluate feedback by randomly selecting a Leader Model from among the source models, rather than relying on an external reward model. The primary motivation for including an ablation study with an external reward model is to validate the effectiveness of the random Leader Model selection scheme. Following the reviewer's suggestion, we conducted an additional set of experiments comparing the current approach of randomly selecting a Leader Model with fixing each of the three source models as the Leader Model, using Llama3.2-3B-Instruct as the target model. The results, presented in the table below, demonstrate that random selection of the Leader Model yields more consistent average performance improvements. This is because each model inherently possesses judgment biases that could lead to performance imbalances, and random Leader selection better mitigates the negative impacts of such biases. We have incorporated this experiment into our revised version. Your valuable input is crucial to enhancing the quality of our work.

Response To Weakness #4

We deeply value the reviewer's valuable suggestions. In Table 3 of the appendix to our paper, we present statistics on the actual total runtime (in minutes) of each baseline method and Bohdi on each target model when using 8 A100 GPUs, allowing for a fair comparison of the practical costs of each method. Across all target models, Bohdi's actual runtime consistently remains shorter than that of other baselines. This result effectively demonstrates Bohdi's practical efficiency advantages over other baselines. In the final version of the paper, we will also move this result into the main text to more clearly present Bohdi's efficiency advantages to readers. Your valuable suggestions are greatly appreciated.

Response To Question #1

We deeply value the reviewer‘s insightful questions.

Bohdi's response generation takes place within the Harvest operation. In fact, we adopt the approach you described: the Leader Model (including the reward model in the ablation study) is used to select the superior answer from the responses of the three source models, rather than leveraging all source model responses collectively for training.

The role of HMAB here is not targeted at the problem itself, but constructed at the granularity of problem domains. When sampling training data, a batch of paths is sampled via the TS algorithm, and data generated during the meditation phase under each corresponding path is drawn to construct the training set. Further details of this process can be found in the description of the Sprout and Harvest operations in Appendix B, as well as the pseudocode in Appendix B4.

Response To Question #2

We deeply value the reviewer's valuable suggestions.

Regarding the issue of limited domain coverage: This constraint is addressed through the self-construction of the knowledge tree in HMAB. By enabling autonomous construction of a structured knowledge tree among models, comprehensive and systematic organization of problem domains is achieved automatically, ensuring the breadth of domain knowledge. Meanwhile, the Harvest operation allows for data synthesis tailored to each domain path, thereby resolving the issue of missing open-source data in fine-grained domains.

Regarding the problem of fixed data allocation: This limitation is overcome through dynamic adjustment of the posterior distribution of reward distribution parameters for each arm in HMAB. Based on the performance evaluation of the target model and source models across different domains, the alpha and beta parameters of these arms are dynamically adjusted. This facilitates a shift in data allocation toward domains where the target model performs weaker relative to the source models, enabling more rational distribution.

We will elaborate on these two points in greater detail in the main text of the final version. Your valuable suggestions are crucial for enhancing the clarity of our work.

Response To Reviewer 3FuQ

We appreciate the reviewer's valuable comments and suggestions. We will provide point-by-point responses to each of your questions below.

Response To Cons #1

We appreciate the reviewer's valuable suggestions.

Regarding the performance improvements of our method, it is evident from the experiments on all four target models (results in Table 1 of the main text and Table 2 of the appendix) that Bohdi achieves the optimal performance improvement on average. Moreover, it accomplishes this with significantly less data than other baselines and without relying on any real external data, which is no easy feat under such conditions.

Even setting these prerequisites aside, the performance improvements brought by Bohdi are still prominent. For instance, compared to explicit fusion baselines like FuseChat, Bohdi delivers remarkably significant performance gains in single domains. For example, on TheoremQA, Bohdi brings a 72.09% relative improvement to the target model Gemma2-9B-IT compared to the original model, while FuseChat only achieves a 6.40% relative improvement. When compared to other implicit fusion baselines such as FuseChat3.0, Bohdi's advantages remain evident, mainly reflected in more balanced performance improvements across tasks and better average performance. For example, when the target model is Llama3.2-3B-Instruct, the model fused with Bohdi shows performance gains in every domain, and in most cases, achieves the optimal improvement—particularly a 9.07% relative improvement on GPQA. In contrast, FuseChat3.0 exhibits significant performance declines on GPQA, TheoremQA, and BBH, with a 20.01% decline specifically on GPQA.

Thus, the performance improvements brought by our method are relatively significant, especially considering the prerequisites that it does not rely on any real data and uses far more data-efficiently than baseline methods.

Regarding the stability of the evaluation, we have strongly demonstrated the consistency and stability of Bohdi's performance through multiple comprehensive experiments. For example, in the comparative experiment dimension, we compared all methods on four target models with different structures and parameter sizes: Llama3.2-3B-Instruct, Qwen2.5-7B-Instruct, Gemma2-9B-IT, and Llama3.1-8B-Instruct. The results reported in Table 1 of the main text and Table 2 of the appendix show that Bohdi stably outperforms other baselines across different target models. In the ablation experiments, we also tried using several more compact source models (Llama3.2-3B-Instruct, Qwen2.5-3B-Instruct, and Gemma2-2B-IT) and conducted fusion experiments with the larger Gemma2-9B-IT as the target model. The results indicate that the target model fused with Bohdi can still effectively absorb the advantages of the source models, particularly evident in tasks where Gemma2-9B-IT itself performs weakly, such as GPQA and TheoremQA. Additionally, in Figure 7 of the appendix, we visualized the generated domain structure organization when Llama3.2-3B is used as the target model. As the number of source models increases, the generated domains still include most of the domains observed when there are fewer source models, which strongly illustrates the stability of Bohdi in domain expansion. The consistent improvements across these diverse evaluations and experimental results fully demonstrate Bohdi's stability under different conditions. Furthermore, during the evaluation, we used greedy sampling to minimize the impact of randomness in autoregressive generation, as described in Appendix C. Following your suggestion, in the final version, we will incorporate these analyses and results into the main text as much as possible to help readers understand these improvements more intuitively.

We again appreciate your valuable suggestions, which have been very helpful in enhancing the clarity of our paper.

Response To Cons #2

We appreciate the reviewer’s insightful comments.

Regarding Condor and FuseChat3.0, only FuseChat3.0 relies on a reward model, whereas Condor does not [1]. In our comparison, we retained FuseChat3.0’s reward model exactly as prescribed in the original paper, as stated in our experimental setup. Bohdi itself is designed to operate without any additional reward model.

Concerning the two baselines you mentioned, we are unsure if the SuperMario you referred to refers to the DARE method in [2]. This is a homogeneous model fusion scheme, which only applies to scenarios where the models involved in fusion have identical structures and parameter sizes. It is not applicable to the heterogeneous model fusion setting we are researching.

As for InfiFusion [3], no code has been made publicly available in its published paper, making it impossible for us to reproduce it. Additionally, as an explicit LLM fusion scheme, the performance reported in the InfiFusion paper does not show significant improvements compared to FuseChat, the baseline we selected, and its design is similar to that of FuseChat. Therefore, the results of FuseChat can, to some extent, roughly represent the performance of InfiFusion. We have further clarified this point in the revised version of the paper. We again appreciate your valuable suggestions.

[1]Condor: Enhance LLM Alignment with Knowledge-Driven Data Synthesis and Refinement, in ACL 25.

[2]Language models are super mario: Absorbing abilities from homologous models as a free lunch, in ICML 24.

[3]InfiFusion: A Unified Framework for Enhanced Cross-Model Reasoning via LLM Fusion

Response To Cons #3 & Question #1

We appreciate the reviewer's insightful feedback. Among the comparative baselines, explicit model fusion baselines do not actually generate text during operation, making it impossible to directly compare the number of generated tokens across methods. However, in Table 3 of the appendix, we have provided statistics on the actual total running time (in minutes) of each baseline method and Bohdi on each target model when using 8 A100 GPUs, allowing for a fair comparison of the practical efficiency of each method. Across all target models, Bohdi's actual running time is consistently shorter than that of other baselines. This result practically demonstrates Bohdi's efficiency advantage over other baselines. In the final version of the paper, we will move this result to the main text to present Bohdi's efficiency advantage more clearly to readers. We again appreciate the reviewer's valuable suggestions, which are very important for enhancing the quality of our work.

Response To Question #2

We appreciate the reviewer's valuable question. In response to your inquiry, we compared the data generated by Bohdi with the test task data across all four target model settings, and found that the number of overlaps between the generated data and the test data is zero. This further confirms that there is no overlap between the collected QA pairs and the test data. We have further elaborated on this result in the experimental section of the revised manuscript. We again appreciate the reviewer's insightful question.

Response To Reviewer ShRp

We appreciate the reviewer's meticulous examination and valuable feedback, which are of great significance to our manuscript. Below, we will provide point-by-point responses to each of your comments and suggestions.

Response To Weakness #1

We appreciate the reviewer's valuable comments. In line with your feedback, we have added a dedicated section in the appendix of the revised manuscript to present and discuss the quality of synthetic data. Here, we briefly showcase a piece of data from the path Mathematics - Algebra - Linear Algebra. Due to space constraints, we have omitted part of the response here:

Example: Q: Consider two matrices, A = \\begin{pmatrix} 2 & 4 \\\\ 3 & 6 \\end{pmatrix} and B = \\begin{pmatrix} 1 & 2 \\\\ 0.5 & 1 \\end{pmatrix}. Compare the eigenvalues and eigenvectors of $A$ and $B$. Discuss the properties of these matrices based on their eigenvalues and eigenvectors, and summarize your findings in a table format.

A: ...... Matrix A: ...... Eigenvalues: \n The characteristic equation for matrix $A$ is given by ...... Thus, the eigenvalues are $\\lambda_1 = 0$ and $\\lambda_2 = 8$.\n\n2. Eigenvectors:\n - For $\\lambda_1 = 0$:\n ...... we can choose $x = 2$ and $y = -1$ as a solution ...... ### Matrix B: ......\n\n### Summary Table\n\n| Property/Matrix | A | B |\n|---|---|---|\n| Eigenvalues | 0, 8 | 0, 2 |\n| Eigenvectors | (2, -1), (2, 3) | (2, -1), (2, 1) |\n| Properties | $A$ has one zero eigenvalue and one non-zero eigenvalue. It is singular and non-invertible.<br> $A$'s eigenvectors are not orthogonal. ...... |\n\n

The question in the above example data involves comparing the eigenvalues of a matrix and requires an answer in table format. The generated response correctly solves this problem and strictly follows the requirement to present the answer in a table, thus demonstrating full correctness and completeness, which indicates that the synthetic data is of high quality.

Furthermore, the randomness introduced by the Beta distribution sampling serves as the foundation for ensuring diversified and parallel domain exploration, as discussed in Section 2.3. However, it does not unduly affect the stability of the algorithm. Existing research has also provided solid guarantees for the convergence of such sampling algorithms [1][2]. Meanwhile, in the ablation experiment illustrated in Figure 7 of the supplementary materials, we visualized the domain structure generated when Llama3.2-3B-Instruct is used as the target model, with statistics showing that as the number of source models increases, the generated domains still encompass most of the domains observed when there are fewer source models. This strongly confirms the stability of the overall domain expansion.

Regarding the impact of randomly selecting the Leader Model, we conducted experiments where each of the three source models was fixed as the Leader Model, and compared these with the current scheme of randomly selecting the Leader Model, using Llama3.2-3B-Instruct as the target model. The results presented in the table below show that randomly selecting the Leader Model yields more stable performance. Since each model has inherent judgment biases, which can lead to unbalanced performance, random selection of the Leader can better counteract the negative effects of such biases. Therefore, the randomness introduced by the random selection of the Leader Model and the Beta distribution random sampling does not have a negative impact on the stability of the algorithm.

[1]Analysis of Thompson Sampling for the Multi-armed Bandit Problem, in JMLR.

[2]An Information-Theoretic Analysis for Thompson Sampling with Many Actions, in NeurIPS.

Response To Weakness #2

We appreciate the reviewer's constructive suggestions, which are crucial for enhancing the quality of our work.

We appreciate the reviewer's constructive suggestions. The primary purpose of the structural differences between the source models and target model used is to ensure heterogeneity between models, which aligns with the focus of our research.

Regarding the selection logic for target models, we aimed to cover the most widely accessed and used mainstream model types, thus choosing Qwen2.5-7B-Instruct, Gemma2-9B-IT, and Llama3.1-8B-Instruct. These three models, with comparable parameter sizes, form the main body of our experiments. To further verify the effectiveness and generalization ability of our method, we also included Llama3.2-3B-Instruct, a model with a smaller parameter size, as a target model. Due to space constraints, these results are reported in Table 1 of the main text and Table 2 of the appendix, fully demonstrating the universality of our method across target models of different structures and scales.

In summary, we have fully considered controlled comparisons of parameter sizes in model selection, including both model combinations with similar parameter sizes and models of different scales. Meanwhile, selecting models from different companies is intended to ensure the premise of heterogeneity and strengthen the persuasiveness of our experimental results by using the most mainstream open-source models available. Furthermore, in each set of experiments, all compared methods were conducted under the same source and target model settings, thus ensuring the fairness and consistency of the experiments. We have clearly elaborated on the above content in the revised version. We again appreciate your valuable suggestions, which are vital for improving the clarity of our work.

Response To Weakness #3 & Question #3

We appreciate the reviewer's insightful comments. Regarding the cost of constructing and managing the hierarchical tree, we will address this from two dimensions: the number of models and the number of domains.

1. Concerning the number of models: When the number of involved LLMs increases, the cost rises linearly with the number of LLMs. However, any scheme built on multiple LLMs will inevitably face this objective cost increase due to a larger number of LLMs, which is also true for all the methods we compared with. New domains generated through the Sprout operation are fixed as new components of the tree after generation, so Sprout is typically executed a limited number of times. The response collection in the Harvest operation is only related to the amount of generated data—for each piece of data generated, responses from each model need to be collected once. Similar operations are equally necessary for other baselines, whether explicitly or implicitly fused. Thus, while an increase in model parameters leads to higher costs, this is an unavoidable objective cost increase for any current method.

2. Concerning the cost from an increase in the number of domains: The computational cost brought by more domains is mainly reflected in the sampling process of the TS algorithm. However, this process does not require direct participation of any LLM; it only involves variable sampling based on the Beta distribution parameters. The computational effort required here is merely O(1) floating-point operations per data point. Even when sampling across 1000 domains, this can be completed in less than 0.001 seconds on a regular consumer-grade CPU. Moreover, our method involves sampling across at most several hundred domains (see Figure 6 in the main text). Therefore, the efficiency cost from an increase in the number of domains and their management is almost negligible. Additionally, in Table 3 of our Appendix, we have provided statistics on the actual total running time (in minutes) of each baseline method and Bohdi on each target model when using 8 A100 GPUs, which practically demonstrates Bohdi's efficiency advantage over other baselines.

We again appreciate your valuable comments.

Response To Question #1

We appreciate your valuable question. In response to this, all instructions involved in Bohdi can be found in Appendix F. For examples of data and analysis of data quality, please refer to our response to weakness #1.

Response To Question #2

We appreciate your insightful comments.

Regarding the comprehensiveness of target models, we aimed to cover the most widely accessed and used mainstream model types, thus selecting four target models: Qwen2.5-7B-Instruct, Gemma2-9B-IT, Llama3.1-8B-Instruct, and Llama3.2-3B-Instruct. Due to space constraints, the results with Llama3.1-8B-Instruct and Qwen2.5-7B-Instruct as target models are recorded in Table 2 of the appendix, where Bohdi still shows significant advantages over other baselines. In the final version of the paper, we will also move this part of the results to the main text.

As for the logic behind selecting baselines, we chose FuseChat3.0, the current state-of-the-art implicit heterogeneous model fusion baseline, and FuseChat, the most representative explicit fusion baseline. Additionally, to validate the effectiveness of Bohdi as an implicit model fusion scheme, we included a baseline that directly collects data for SFT and Condor, a baseline that performs data synthesis based on a static label tree. We have further emphasized this baseline selection logic in the experimental section of the revised version. We again appreciate your valuable suggestions.

Response To Reviewer YY3V

We sincerely appreciate the reviewer’s thorough and exacting review. Your comments and suggestions are pivotal to improving our manuscript. We provide a point-by-point response below.

Response To Weakness #1

We appreciate the reviewer's insightful feedback.

For comprehensive design, Bohdi incorporates multiple components and mechanisms. To ensure readers fully grasp its functionality, we've utilized various presentation methods. Beyond the main methodology in the body of the paper and operational details in the appendix of the supplementary materials, we include schematic diagrams for each component and the overall framework (Figures 2 and 3 in the main text). Crucially, Appendix B.4 provides a highly detailed pseodocode of the entire algorithm's workflow, and Appendix F contains all associated LLM instructions. We believe this offers readers a thorough understanding of our algorithm's operational logic and specific procedures.

Regarding code availability, we commit to including a link to the open-source code in the final version of the paper. This will clearly outline all running, evaluation, and environment setup instructions, along with links to the Bohdi-fused model weights, as promised in our checklist. We hope you understand our decision not to directly include the full code at this stage, as it serves to protect our original work. We again appreciate your valuable comments.

Response To Weakness #2

We appreciate the reviewer's valuable feedback.

To clarify, all our reported improvements and declines are determined relative to the base model's performance on its corresponding task. For instance, when the target model is Llama3.2-3B-Instruct, Bohdi improves its BBH accuracy to 54.90% from the vanilla Llama3.2-3B-Instruct's 53.86%, marking a 1.93% relative increase over the original model. For overall average performance, the Bohdi-fused Llama3.2-3B-Instruct achieves an average accuracy of 50.79%, which is an 8.83% relative improvement compared to the vanilla Llama3.2-3B-Instruct's 46.67%. We've explicitly noted this clarification in the revised manuscript to enhance reader understanding. We again appreciate the reviewer's valuable suggestions, which have been highly helpful in enhancing the clarity of our paper.

Response To Weakness #3

We appreciate the reviewer's meticulous examination and insightful suggestions. We have taken note of this point and made revisions accordingly in the updated version. Additionally, we have conducted a thorough review and polishing of the entire manuscript. We again appreciate your insightful comments, which play an important role in refining the details of our work.

Response To Weakness #4

We appreciate the reviewer's constructive suggestions. Following your advice, we conducted experiments where each of the three source models was fixed as the Leader Model, and compared these with the current scheme of randomly selecting the Leader Model, using Llama3.2-3B-Instruct as the target model. The results are presented in the table below. In comparison, the scheme of randomly selecting the Leader Model demonstrates more balanced performance gains and achieves the best average (AVG) performance. While fixing a single model as the Leader may yield better results in certain individual tasks than random selection, it often leads to unbalanced performance due to the inherent biases of each model. Randomly selecting the Leader can better counteract the negative impacts of such biases and alleviate the issue of performance imbalance.

Furthermore, in the current version of the manuscript, we have also verified the approach of using a Reward Model for Answer evaluation in the ablation experiment shown in Figure 4. The results indicate that randomly selecting a Leader Model from the source models for evaluation remains a more optimal strategy. We again appreciate the reviewer's valuable suggestions, which are of great significance for enhancing the quality of our work.