Structural Entropy Guided Agent for Detecting and Repairing Knowledge Deficiencies in LLMs

We sincerely appreciate your concise summary and insightful questions regarding SENATOR. Your points effectively highlight key aspects and potential areas for clarification in our work. We'll address each of your comments and questions below.

W1 & 2: KG Alignment and Performance with Incomplete/Absent KGs.

• KG Alignment with Evaluation Datasets: To clarify, for our experiments, we only utilized the medical/biological subsets of GPQA and MMLU. Our focus was specifically on evaluating SENATOR's effectiveness in enhancing LLMs' knowledge within the medical domain. Therefore, the questions from these benchmarks that fall outside of medical or biological topics were excluded from our evaluation. This ensures a consistent alignment between the domain of the SPOKE knowledge graph and the evaluation data used.
• Without KGs Altogether: SENATOR's core mechanism fundamentally relies on the KG serving as a structured external environment for the LLM to explore and discover its own knowledge deficiencies. The LLM acts as an "agent" navigating this map of interconnected concepts. Without a KG, the LLM would lack this organized landscape to systematically probe its knowledge boundaries and pinpoint its blind spots. Therefore, SENATOR, in its current form, cannot operate without an underlying KG. If the required knowledge truly doesn't exist in any structured form (i.e., is not representable as a KG), then detecting and acquiring it becomes a different, broader problem, falling outside SENATOR's current scope.
• With Incomplete or Noisy KGs: SENATOR is designed to function effectively even with incomplete KGs.
  • Our Monte Carlo Tree Search (MCTS) operates by exploring existing knowledge paths within the provided KG. It doesn't attempt to infer or complete missing parts of the graph. Instead, it focuses on systematically navigating the available structure to find areas where the LLM's uncertainty (quantified by Structural Entropy) is high.
  • The incompleteness of the KG does not inherently hinder this process; it simply means SENATOR will identify deficiencies within the knowledge that is represented and accessible in the graph, rather than in entirely missing sub-domains.
  • Noisy KGs are beyond the scope of SENATOR.

W3: Evaluation Dataset Format and Unstructured Generation Tasks

• Our synthetic data, as shown in Figure 6 of our paper, indeed consists of unstructured, open-ended QA pairs. These samples, generated by SENATOR, feature a question and a direct, free-form answer. This reflects the direct knowledge injection that SENATOR aims for—teaching the model to accurately respond to specific factual queries.
• However, for our main evaluation, we primarily used multiple-choice benchmarks such as MedQA, MedMCQA, and PubMedQA. This decision was driven by the current landscape of mainstream evaluation in the medical LLM field, where multiple-choice formats are widely adopted and enable standardized, quantitative comparisons across models, as seen in works like HuatuoGPT-o1 [1].
• While our direct evaluation is on multiple-choice tasks, the underlying training signal from SENATOR's synthetic data is designed to enhance the model's fundamental factual recall and understanding. This improved factual grounding is crucial for any downstream task, including open-ended generation. The ability to correctly provide a precise answer in an unstructured format (as learned from our synthetic data) directly supports improved performance in more complex, open-ended scenarios where factual accuracy is paramount. Though not directly evaluated for open-ended generation in this paper, we anticipate that the enhanced knowledge base provided by SENATOR would naturally translate to improved factual grounding in such tasks as well.

[1] HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs.

W4: Case Studies for Correction Examples.

We completely agree this would be a powerful demonstration. We are preparing to include additional case studies in the revised version of our paper. A case from MedQA is shown as follows:

A 4-week-old female newborn is brought to the physician because of increasing yellowing of her eyes and skin for 2 weeks. The mother has noticed that the girl's stools have become pale over the past week. She was breastfed since birth but her parents switched her to formula feeds recently after reading on the internet that breastfeeding could be the cause of her current symptoms. The patient was delivered vaginally at 38 weeks' gestation. Pregnancy and delivery were uncomplicated. She appears healthy. Vital signs are within normal limits. She is at the 50th percentile for length and at the 60th percentile for weight. Examination shows scleral icterus and jaundice. The liver is palpated 2 cm below the right costal margin. Cardiopulmonary examination shows no abnormalities. Neurologic examination shows no focal findings. Serum studies show: ...... Which of the following is the most likely diagnosis? A. Galactosemia B. Biliary atresia (correct) C. Crigler–Najjar syndrome D. Breast milk jaundice

Our synthetic data (QA Pair):

Question: Which disease is similar to bile duct disease, and presents symptom Obstructive Jaundice? Answer: Biliary atresia.

Evidence Path: Disease <bile duct disease> resembles disease <biliary atresia>,Disease <biliary atresia> presents symptom <Jaundice, Obstructive>,The symptom of <Jaundice, Obstructive> symptoms are presented in disease <collecting duct carcinoma> ……

The medical term Jaundice refers to the condition where an elevated level of bilirubin in the body causes the skin, sclera (the white part of the eye), and mucous membranes to turn yellow or green.

W5: Significance of KGs in LLM Knowledge Acquisition.

The reviewer has raised a thought-provoking point regarding the evolving role of knowledge graphs (KGs) amidst the power of natural language texts, retrieval, and autoregressive training for LLM knowledge. We appreciate this perspective and have considered it deeply. The reviewer's assumption is that large models can autonomously and reliably capture structured knowledge from vast amounts of free-text corpora. However, while state-of-the-art LLMs demonstrate impressive learning and generalization capabilities, their very nature as probabilistic models inherently introduces uncertainty. This means that when faced with massive volumes of knowledge, especially specialized or niche information, we lack clear insight into their confidence in specific factual statements. This fundamental uncertainty significantly undermines model reliability, particularly for applications in domains demanding high trustworthiness. This is where KGs crucially bridge the gap. Our work isn't about simply having LLMs learn from KGs. Instead, it's about leveraging KGs to systematically detect LLM knowledge deficiencies in a human-trustworthy manner, especially for complex, structured knowledge. As the number of knowledge entities grows, the complexity of structured knowledge increases exponentially. Relying solely on question-answering (QA) formats to detect comprehensive knowledge gaps becomes impractical. A systematic detection method is essential, and this is precisely why a KG-based approach is indispensable. KGs provide a verifiable, structured environment that allows us to:

1. Systematically Probe Deficiencies: Unlike unstructured text, KGs enable targeted, structured exploration (as with our SE-based MCTS) to pinpoint exactly what an LLM doesn't know.
2. Ensure Trustworthiness: The explicit, symbolic nature of KGs allows for greater transparency and auditability, fostering human trust in the knowledge acquisition process.
3. Handle Complexity: KGs are inherently designed to represent complex, relational knowledge in a way that is difficult for LLMs to consistently and reliably extract from raw text alone. Furthermore, the feasibility of KG-based approaches is high. There's already a lot of existing domain-specific KGs (e.g., as surveyed in "Domain-specific Knowledge Graphs: A Survey"), which can readily serve as the structured environment for our framework. Therefore, we believe KGs remain profoundly relevant, not as a replacement for textual knowledge or retrieval, but as essential tools that enable LLMs to achieve higher levels of factual precision, reliability, and systematic self-correction in specialized domains where human trust is paramount.

W6: Modern KG+LLM References.

Thank you for the helpful suggestion and for pointing us to this recent work. We are glad to incorporate Hron et al. (COLM) into our discussion, as it provides valuable insights into the interplay between knowledge graphs and language models, particularly around hallucinations and their detectability. We agree this line of work is highly relevant and complementary to SENATOR. While Hron et al. focus on training LLMs directly on KGs to mitigate hallucination, our work instead addresses the challenge of detecting and targeting knowledge deficiencies in pretrained LLMs by leveraging KG structure for guided data synthesis. We believe both approaches share the broader goal of enhancing factual reliability in LLMs, and we are happy to include a discussion in the revised version.

We hope above responses addresses all your comments and questions, further clarifying the significance and unique contributions of SENATOR.

We sincerely appreciate your thoughtful review and insightful observations. Your feedback has been invaluable in helping us clarify and strengthen our contribution. We would like to address your concerns as follows:

W1 and Q1&3: Dependency on High-Quality KGs, Performance with Incomplete/Noisy KGs, and Domain Generalizability

Having experienced the wave of knowledge engineering, many fields now have knowledge graphs, as mentioned in the survey "Domain-specific Knowledge Graphs: A Survey."

• Without KGs Altogether: SENATOR's core mechanism fundamentally relies on the KG serving as a structured external environment for the LLM to explore and discover its own knowledge deficiencies. The LLM acts as an "agent" navigating this map of interconnected concepts. Without a KG, the LLM would lack this organized landscape to systematically probe its knowledge boundaries and pinpoint its blind spots. Therefore, SENATOR, in its current form, cannot operate without an underlying Knowledge Graph. If the required knowledge truly doesn't exist in any structured form, detecting and acquiring it becomes a different, broader problem outside SENATOR's scope.
• With Incomplete or Noisy KGs: SENATOR is designed to function effectively even with incomplete or noisy KGs.
  • Our Monte Carlo Tree Search (MCTS) operates by exploring existing knowledge paths within the provided KG. It doesn't attempt to infer or complete missing parts of the graph. Instead, it focuses on systematically navigating the available structure to find areas where the LLM's uncertainty (quantified by Structural Entropy) is high.
  • The incompleteness of the KG does not inherently hinder this process; it simply means SENATOR will identify deficiencies within the knowledge that is represented and accessible in the graph, rather than in entirely missing sub-domains.
  • While noise in the KG might introduce some irrelevant paths, our Structural Entropy (SE)-based reward mechanism, which quantifies LLM uncertainty, would naturally assign lower rewards to paths the LLM already knows well (even if noisy), thereby de-emphasizing them in the exploration process. This inherent filtering mechanism helps mitigate the impact of noise.
• Domain Generalizability (Law, Science, etc.): We intentionally focused our current study on the medical domain for a strategic reason: data annotation in specialized, vertical domains like medicine is significantly more challenging and resource-intensive compared to general domains. This makes a targeted data synthesis approach like SENATOR particularly valuable where high-quality, domain-specific data is scarce.
  • While our empirical evidence is limited to medicine, the fundamental principles of SENATOR are designed to be domain-agnostic:
    • Knowledge Graph Agnostic: SENATOR's methodology operates on the structural properties of a knowledge graph and the LLM's uncertainty over its paths, independent of domain-specific semantics.
    • LLM Agnostic: We've demonstrated its effectiveness across different LLM architectures (Llama-3 and Qwen2).
    • Uncertainty-Guided Exploration: The use of Structural Entropy for MCTS is a general approach to identify areas of high LLM uncertainty.
  • Therefore, we anticipate strong potential for SENATOR's application in other knowledge-intensive vertical domains where structured factual information is prevalent, such as law, finance, or other scientific disciplines, provided a relevant knowledge graph is available.

W2 & Q2: Lack of Comparison with Alternative KG Exploration Strategies & Choice of Structural Entropy

• Why Structural Entropy? We chose Structural Entropy (SE) specifically as the exploration reward because it allows us to define and detect knowledge deficiencies at a sub-graph or path level, which is a unique and powerful aspect of our framework.

  • Unlike simpler measures that might only consider the LLM's uncertainty on individual facts (e.g., a single triplet) or on isolated sequences, Structural Entropy quantifies the aggregate uncertainty within a structured knowledge path. It considers both the LLM's confidence in individual triplets and the topological organization of those triplets within the graph, providing a more comprehensive understanding of complex knowledge gaps. This allows us to target systemic deficiencies embedded within relational knowledge structures.

• Comparison to Simpler Measures: To directly demonstrate the efficacy of our SE-guided selection, we have conducted quantitative comparisons against simpler knowledge-gap targeting strategies:

  • Random Walk: A baseline that explores the KG without any guidance, simulating unguided traversal through entities and relations.
  • Prob-Prob [1,2]: A sequence-based baseline using intrinsic LLM confidence scores. Specifically, it uses the product of token probabilities to estimate model certainty.
  • Instruction-tuning: This corresponds to the "w/ instruction tuning" setting in our paper, where the original medical training data (MedQA,MedMCQA,PubMedQA) is reformatted into instruction-style prompts to improve the model’s general instruction-following ability and domain alignment.

  [1] Teaching Large Language Models to Express Knowledge Boundary from Their Own Signals

  [2] Reinforced Internal-External Knowledge Synergistic Reasoning for Efficient Adaptive Search Agent

Our experimental results, presented in the table below, clearly show the advantage of SENATOR's SE-guided approach:

As evident, SENATOR consistently outperforms both the "Random Walk" (undirected exploration) and "Prob-Prob" (sequence-based uncertainty) baselines. This quantitatively demonstrates that our SE-guided MCTS effectively leverages the structural information of the KG to pinpoint true knowledge deficiencies, leading to superior performance gains compared to simpler or non-graph-aware uncertainty measures.

We hope these clarifications address your concerns and highlight the unique contributions and practical effectiveness of SENATOR. We're open to further discussion if you have any additional questions.

We appreciate the reviewer's thorough review and insightful comments, which have helped us identify areas for improvement. We're encouraged that the reviewer recognizes the importance of our problem, the soundness of our motivation and methodology, and the effectiveness of our experimental results. Below, we address each point raised.

W1: Missing Implementation Details

• Determining Knowledge Boundaries (Criteria and Thresholds): Our method defines knowledge boundaries by identifying areas where the LLM exhibits the highest uncertainty. To select these highly deficient paths for data synthesis, we employ a thresholding mechanism. This is defined in the collect_paths_above_threshold function within our supplementary material's kg_mcts.py file. Here, we select knowledge paths whose cumulative SE reward exceeds a predefined threshold (e.g., paths with a total SE reward m>20).

• Model Used for QA Sample Generation: To clarify, for each base model used in our experiments, the entire SENATOR pipeline, including both the knowledge deficiency detection phase (where it acts as the "Agent") and the subsequent data synthesis phase, is executed using that same base model. This adheres to a self-improvement paradigm. For instance, when we evaluate Qwen2, Qwen2 itself explores the KG, and then Qwen2 also generates the QA samples based on the identified deficient paths. The same principle applies when Llama-3 is the base model.

• Hyperparameter Sensitivity: We did not perform deliberate hyper-parameter tuning in our initial submission. Under fixed hyper-parameters and random seeds, the model already surpasses all baselines. Thank you for the suggestion, and we will analyze this further in the revised manuscript.

W2: SFT for Knowledge Injection and Potential Data Leakage

• Justifying SFT for Targeted Knowledge Injection: While CPT is indeed commonly used for broad knowledge ingestion, our SENATOR framework specifically focuses on highly targeted and precise knowledge injection to remedy identified deficiencies. Our synthetic data is generated as simple, atomic QA pairs, as clearly illustrated in Figure 6. This format consists of a single question and its corresponding correct answer. This is fundamentally different from the complex, multi-turn dialogues or intricate instruction-following formats often seen in general instruction tuning. The simplicity and specificity of our QA pairs make SFT an exceptionally effective and precise method for directly injecting these identified, discrete factual knowledge points and relationships into the model. The primary goal here is not to broadly align the model with new conversational styles or instructions, but rather to teach it specific facts and relational knowledge that it currently lacks.
• Addressing Stylistic Similarity and Data Leakage Concerns:
  • Stylistic Similarity: Our ablation study in Table 1 directly addresses this. When we fine-tuned our models solely with general domain instruction data (the "w/ instruction tuning" setting), we saw only marginal performance improvements, and in some cases, even a slight drop, compared to the base models. It's worth noting that this instruction tuning step converts the original medical training set into instruction-style prompts. This not only boosts the model's ability to follow instructions but also reinforces some of its domain-specific medical knowledge. However, our results clearly suggest that simply aligning the model's style or improving its general instruction-following doesn't inherently lead to significant factual knowledge gains in our specialized medical domain. The substantial performance uplift consistently appears only when we incorporate our SENATOR-synthesized data (the "w/ synthetic data + IT" setting). This definitively shows that the performance improvements come from fixing the model's actual knowledge deficiencies with our targeted synthetic data, not just from stylistic alignment.
  • Data Leakage: We have meticulously addressed the possibility of data leakage. As illustrated in Figure 8, our test data formats (e.g., MedQA's multiple-choice questions) are structurally distinct from the simple QA pair format of our synthetic data (Figure 6). This significant structural dissimilarity inherently reduces the likelihood that performance gains are due to format overlap. More critically, we have diligently cross-referenced our entire synthetic dataset with all test datasets and have not found any identical QA samples. This ensures that our reported evaluation results genuinely reflect the model's improved knowledge and reasoning abilities, rather than simple memorization or direct data leakage.

W3: Insufficient Experimental Evaluation & Efficiency Analysis.

• Comparison with Structure-Aware Knowledge Injection: Structure-aware knowledge injection integrates external knowledge into models while preserving its structural relationships. Our core innovation is enabling an LLM to self-explore its knowledge gaps within KGs. Our knowledge injection (SFT) phase, which uses data from detected deficiencies, serves primarily to validate our deficiency detection via SE+MCTS.

• Sufficiency of Ablation Study. we introduce additional baselines representing alternative knowledge-gap targeting strategies:

  • Random Walk: A baseline that explores the KG without any guidance, simulating unguided traversal through entities and relations.
  • Prob-Prob [1,2]: A sequence-based baseline using intrinsic LLM confidence scores. Specifically, it uses the product of token probabilities to estimate model certainty.
  • Instruction-tuning: This corresponds to the "w/ instruction tuning" setting in our paper.

  [1] Teaching Large Language Models to Express Knowledge Boundary from Their Own Signals

  [2] Reinforced Internal-External Knowledge Synergistic Reasoning for Efficient Adaptive Search Agent

As shown in the table: SENATOR consistently outperforms both the "Random Walk" and "Prob-Prob" baselines for both Qwen2-7B and Llama-3-8B, demonstrating the superior effectiveness of our SE-guided MCTS for knowledge deficiency detection.

• Efficiency Analysis of MCTS: Assuming a fixed number of simulations $N$ (e.g., $N = 100$ in our setup), and a knowledge path length (tree depth) of $H$ (our knowledge paths have a length of 5, implying $H = 4$ steps from the root to a terminal node), the size of the MCTS tree is influenced by the average number of neighbor nodes (relations) for an entity, which we denote as $M$. In general, the number of nodes visited is proportional to $M \times H$. Therefore, the time complexity of the MCTS component can be approximated as: $\mathcal{O}(N \times M \times H)$.In our specific setting, this translates to: $\mathcal{O}(100 \times M \times 4) = \mathcal{O}(400M)$ (since this is inference rather than training, the actual speed is on the order of seconds).

Q1: "Agent" Terminology: We appreciate the suggestion regarding the "Agent" terminology. Our choice of "Agent" is deliberate and central to emphasizing the active, exploratory role of the LLM in the knowledge deficiency detection phase. The SENATOR framework is composed of two distinct parts:

1. Knowledge Deficiency Detection: In this crucial first stage, the LLM acts as an agent within the Knowledge Graph (KG) environment. Guided by Monte Carlo Tree Search (MCTS) and our proposed Structural Entropy (SE) reward, it actively navigates and makes strategic decisions to explore the KG, specifically pinpointing knowledge paths where the model exhibits high uncertainty. This involves dynamic decision-making and navigation within a structured knowledge space.
2. Knowledge Synthesis and Repair: The second stage, while employing more conventional methods like Supervised Fine-Tuning (SFT) or Continued Pre-Training (CPT) for model repair, directly leverages the high-quality, targeted knowledge paths discovered by the LLM as an agent in the first stage. Thus, the "Agent" terminology specifically refers to the LLM's proactive, decision-making role in exploring and identifying deficiencies within the KG, which is the core novelty of SENATOR. We believe this distinction is vital to understanding our core contribution.

Q2: Learning Rate and Batch Size. We sincerely apologize for the misunderstanding caused by the batch size notation in Table A2. The value "1" in the table indeed refers to the per-GPU batch size. As stated in the Resource Requirement section, we conducted our experiments using 8 NVIDIA A100-40G GPUs. Therefore, the effective global batch size was 64. We regret this imprecision and will explicitly clarify this in the revised Table A2 and its accompanying text to avoid any confusion. Regarding the learning rate, we followed the setting used in prior work for similar fine-tuning tasks, rather than performing explicit hyperparameter tuning. For consistency and fairness, we used the same set of hyperparameters across all models and settings during the SFT phase, without optimizing them specifically for SENATOR.

We hope these clarifications address your concerns and look forward to further in-depth discussions.

Thank you for your continued engagement and for your insightful questions, which help us to further refine and clarify our work. We will address each of your concerns below.

W1: Hyperparameter Selection

You've asked how our hyperparameters were selected and what insights this process provides. We appreciate this question as it speaks to the reproducibility and practical application of our method.

To ensure our training process was both robust and based on established best practices, we adopted the hyperparameter settings from the open-source code for the InstructGPT project's SFT stage. Specifically, we followed the guidelines detailed in the paper's Appendix C.1 Details of SFT training [1], which describes their rigorous process of using geometric searches to tune learning rates and epochs.

InstructGPT uses an LR of 9.65e-6 and a batch size of 32.

[1] Training language models to follow instructions with human feedback

Our decision to not modify these settings was a deliberate choice to build our work on a well-validated and empirically effective foundation. This approach provides two key insights:

1. Reproducibility: It demonstrates that SENATOR does not require a complex, domain-specific hyperparameter search. It can achieve significant performance gains using a standard, proven fine-tuning regimen.
2. Practicality: It suggests that the effectiveness of our framework is driven by the quality and targeted nature of the synthetic data generated by SENATOR, rather than highly optimized, brittle training parameters. This makes our method more accessible and easier to apply for future work.

W2: Data Leakage Detection

We have a clear and rigorous procedure in place to ensure no data leakage between our synthesized data and the test sets. We consider a synthesized QA pair to have potential leakage if there is a significant overlap in entities with any QA pair in the test set.

Our procedure is as follows:

1. Unit of Comparison: The primary unit of comparison is the QA pair, which we define as a (Question, Answer) tuple.
2. Entity Extraction: For every QA pair in both our synthesized dataset and the test set, we automatically extract the core entities (e.g., diseases, genes, drugs).
3. Overlap Criterion: We define an overlap as when the entities in a synthesized QA pair are a superset of the entities in any test set QA pair.

This rigorous check, which goes beyond simple text-based token overlap, ensures that no synthesized data directly corresponds to a test question, preventing any form of data leakage and guaranteeing the integrity of our evaluation.

W3: Conceptual Advantages & MCTS Cost

You've asked about the conceptual advantages of our approach over methods like "Structure-aware Domain Knowledge Injection" and the computational cost of MCTS.

Conceptual Advantages: We believe there is a fundamental difference between our work and the one you cited. While that paper focuses on giving LLMs a better structural perception by preprocessing unstructured text into hierarchical data, SENATOR focuses on using a pre-existing KG to detect the LLM's own internal knowledge deficiencies.

The core advantage of our approach is that it is a targeted, self-probing framework. We don't just add general knowledge; we systematically identify what specific knowledge is missing first by using the LLM's own uncertainty as a guide. This is more efficient because it avoids generating redundant data for knowledge the LLM already possesses. It's a method for finding "unknown unknowns" that other, less targeted approaches cannot achieve.

MCTS Computational Cost: We appreciate you pushing for more clarity on this. As detailed in our previous response, we have measured the additional computational cost of MCTS. For our Llama-3-8B model on 8 A100 GPUs, generating a single synthetic QA pair with MCTS takes approximately 0.38 seconds. This is an additional cost of 0.26 seconds compared to a standard inference run (0.12 seconds). While this demonstrates that the SENATOR process takes longer per sample than standard inference, it is crucial to recognize that this is a one-time computational cost for generating a high-quality, targeted training dataset. Our method's efficiency is not measured by the speed of a single inference, but by its ability to achieve significant performance gains with a small, highly targeted dataset. For instance, our SENATOR-enhanced Llama-3-8B model, which outperforms the UltraMedical model, was trained on only 26k synthetic samples. This is a mere 6.34% of the 410k samples used to train UltraMedical. The total time for our entire data synthesis and SFT process remains a fraction of the cost of large-scale pre-training or continual pre-training, making it a highly efficient solution for targeted knowledge repair.

We fully agree with your concern and that of Reviewer 6gHM regarding the use of the term "agent." We understand that using terminology that deviates from a commonly accepted meaning can create an unnecessary cognitive burden on the reader. We will remove the term "agent" from our final manuscript. Instead, we will describe our approach as a "closed-loop, self-improvement framework" which more accurately and precisely reflects the nature of our method.

Please allow us to thank you again for reviewing our paper and the valuable feedback.

Please let us know if our response has properly addressed your concerns. We are more than happy to answer any additional questions during the discussion period. Your feedback will be greatly appreciated.

We appreciate the reviewer's comprehensive summary and insightful feedback. We are encouraged that the reviewer recognizes the strengths of our work, including the novel use of structural entropy within MCTS, the evaluation on relevant medical benchmarks, and the demonstrated efficiency of SENATOR. We address each point below.

W1&2: Evaluation Scope and Comparison to Alternative Knowledge-Gap Targeting Strategies.

Our work takes a novel stance by defining knowledge boundaries at a sub-graph level, which distinguishes us from prior methods that primarily focus on text-based uncertainty or individual triplets. For instance, while methods like LAMA's Language Models as Knowledge Bases? explore triplet-level confidence using self-information (e.g., $I(u, \rho, v) = -\log_2 P(v \mid u, \rho)$ ), SENATOR extends this by considering the collective uncertainty of an entity and its neighboring relations: $d_u = \sum_{v \in \mathcal{N}(u)} I(u, \rho, v)$ , and further aggregates this over entire knowledge paths via Structural Entropy. This enables us to identify systemic knowledge deficiencies embedded within the KG's topology. To validate the effectiveness of our SE-guided knowledge boundary identification, we introduce additional baselines representing alternative knowledge-gap targeting strategies:

• Random Walk: A baseline that explores the KG without guidance, simulating unguided sampling.
• Prob-Prob [1,2]: A sequence-based baseline using intrinsic LLM confidence scores. Specifically, it uses the product of token probabilities to estimate model certainty.
• Instruction-tuning: This corresponds to the "w/ instruction tuning" setting in our paper, where the original medical training data (MedQA,MedMCQA,PubMedQA) is reformatted into instruction-style prompts to improve the model’s general instruction-following ability and domain alignment.

[1] Teaching Large Language Models to Express Knowledge Boundary from Their Own Signals

[2] Reinforced Internal-External Knowledge Synergistic Reasoning for Efficient Adaptive Search Agent

The table below presents these new quantitative comparisons:

As shown in the table: SENATOR consistently outperforms both the "Random Walk" and "Prob-Prob" baselines for both Qwen2-7B and Llama-3-8B, demonstrating the superior effectiveness of our SE-guided MCTS for knowledge deficiency detection.

W3 and Q1: Domain Generality and KG Completeness.

• Domain Generality: Our study focuses on the medical domain due to its high demand for reliability, LLMs' persistent challenges with precise factual recall in this specialized field, and the high cost of data annotation. This makes targeted knowledge remediation via SENATOR exceptionally valuable. Crucially, SENATOR's core principles are domain-agnostic. Our methodology operates on KG structural properties and LLM path uncertainty, not domain-specific semantics. Any domain representable by a KG can theoretically leverage SENATOR, and its adaptability is shown across Llama-3 and Qwen2.
• Regarding Incomplete and Noisy KGs: SENATOR leverages the existing KG to find LLM uncertainties within represented knowledge. Our MCTS explores existing paths; it doesn't infer missing parts. Thus, SENATOR effectively identifies deficiencies even with incomplete KGs. And noise issue is beyond the scope of SENATOR.

Q2: Quantitative Analysis of Synthetic Data Quality.

As detailed in Appendix A.4 "Data Filtering," we have previously analyzed the quality of our synthetic data. To gain deeper insights into the impact of synthetic data quality on knowledge injection performance, we further analyzed the performance of Llama-3 and Qwen2 when trained on unfiltered, lower-quality samples. SENATOR employs a multi-tiered evaluation mechanism (including checks for format consistency, logical coherence, and hallucination avoidance) to ensure high-quality synthetic data for knowledge injection. The table below demonstrates the downstream impact of unfiltered synthetic data (i.e., data that contains potential errors or inconsistencies) compared to our carefully filtered data:

As shown, using synthetic data without filtering ("w/o filtering" rows) leads to a noticeable degradation in performance compared to using our filtered data ("w/ SENATOR" rows), and in some cases, even performs worse than the model trained without any synthetic data at all (only "w/ instruction tuning"). This quantitatively highlights the critical role of our data filtering module in ensuring the quality and positive impact of the synthesized knowledge.

We hope these clarifications address your concerns and highlight the unique contributions and practical effectiveness of SENATOR. We're open to further discussion if you have any additional questions.

Thank you for this valuable feedback. You've correctly identified that comparing SENATOR against other knowledge injection paradigms is essential for properly contextualizing our method. We agree that providing this context is important, and we've conducted a new experiment to address your point.

• Our core argument is that SENATOR's main innovation lies in its deficiency detection mechanism (Stage 1), which uses a novel, systematic approach to identify what knowledge is missing. The subsequent fine-tuning is the repair stage (Stage 2) that validates this detection. This makes our method fundamentally different from paradigms that simply add knowledge without first systematically identifying the gaps.

• To address your concern, we've added a Retrieval-Augmented Generation (RAG) approach as a new baseline on the Qwen2-7B model. We believe this is a more suitable comparison than Knowledge Editing (KE) at this time, as current KE techniques [1,2] are not mature enough, especially for life-long (sequential) editing [3,4] or batch editing [5], and can often lead to model corruption [6], making them difficult to use in a robust comparative study.

    [1] Locating and Editing Factual Associations in GPT  (ROME)
  
    [2] SetKE: Knowledge Editing for Knowledge Elements Overlap
  
    [3] WilKE: Wise-Layer Knowledge Editor for Lifelong Knowledge Editing
  
    [4] MELO: Enhancing Model Editing with Neuron-Indexed Dynamic LoRA
  
    [5] Mass-Editing Memory in a Transformer (MEMIT)
  
    [6] Unveiling the Pitfalls of Knowledge Editing for Large Language Models
  

• For our RAG experiment based [7] , we used e5-base-v2[8] as the retriever and a medical subset of Wikipedia as our local knowledge base. The results are provided in the updated table below, integrated with our existing baselines:

   [7] Flashrag: A modular toolkit for efficient retrieval-augmented generation research
  
   [8] Text embeddings by weakly-supervised contrastive pre-training.
  

Comparison with Retrieval-Augmented Generation (RAG)

As the results show, SENATOR achieves a significantly higher average performance than the RAG baseline (61.20 vs. 54.63). This demonstrates the key difference between our approaches. RAG provides temporary, on-the-fly access to external information, which can sometimes be less reliable or harder for the LLM to integrate into its final reasoning. In contrast, SENATOR performs permanent knowledge injection by directly repairing the model's internal knowledge gaps through fine-tuning, making the model more inherently capable and reliable from the outset.

While RAG and SENATOR are distinct paradigms, this experiment shows that our method for systematic knowledge repair is a highly effective approach for building more robust and knowledgeable models.

Thank you for your valuable feedback. You've correctly identified a point that deserves more attention. While we agree that the performance gap on the Qwen2-7B model for the MedQA and MedMCQA average might appear limited, we believe your observation overlooks the full picture of our experimental results and the core value of our method.

As shown in Table 1 of our paper, SENATOR provides a substantial and consistent improvement over instruction-tuning on the Llama-3-8B base model across all benchmarks. However, the true strength of SENATOR becomes even more apparent when we analyze the challenging GPQA datasets, which contain complex, structured knowledge that our method is specifically designed to address.

When we look at the full performance table, the gap between SENATOR and instruction-tuning on Qwen2-7B is significantly more pronounced on these tougher benchmarks:

As this table shows, on the MedQA and MedMCQA benchmarks, SENATOR provides a modest but consistent improvement over instruction-tuning. However, the gains on the GPQA datasets are dramatic:

• On GPQA Genetics, SENATOR's score of 40.0 is a substantial improvement over instruction-tuning's 22.5, an increase of 44% relative to the instruction-tuning baseline.
• Similarly, on GPQA Molecular Biology, SENATOR's 40.12 score is significantly higher than instruction-tuning's 35.80.

When we consider the average performance across all five benchmarks, SENATOR's score of 52.74 is a far more convincing and substantial improvement over instruction-tuning's 47.67.

This demonstrates that SENATOR's unique value is not just in achieving consistent gains on medical knowledge questions, but in its ability to systematically pinpoint and repair deficiencies in challenging, structured knowledge areas where conventional methods fall short. This is precisely the problem our framework is designed to solve, and the full experimental results clearly highlight this unique strength.

Thank you for your detailed and constructive feedback. We appreciate your careful reading of our rebuttal and your dedication to ensuring the rigor of the experimental validation.

We would like to directly address your concern regarding the fairness of the experimental comparisons, which you rightly note was also a key point raised by Reviewer 6gHM. We agree that a rigorously controlled experiment, with comparisons made on the same base models, is essential to definitively prove that our performance gains originate from the SENATOR method itself.

To address this specific and crucial point, we have conducted a new, controlled experiment using a state-of-the-art medical LLM built on the exact same base model as our SENATOR-enhanced model.

Our new baseline is UltraMedical, a powerful medical LLM also based on Llama-3-8B. By comparing our SENATOR-enhanced Llama-3-8B model directly against UltraMedical, we can effectively isolate the impact of our framework from that of the base model's capabilities. The results are presented below:

As this table clearly shows, our SENATOR-enhanced Llama-3-8B model significantly outperforms the UltraMedical model (58.90 Avg. vs. 54.21 Avg.). This new, rigorously controlled experiment provides strong evidence that the performance gains are a direct result of our targeted knowledge repair and not simply a more capable base model. This conclusively demonstrates the effectiveness of the SENATOR framework itself.

Dear Reviewer ugoP,

We would like to sincerely thank you for your helpful comments. We hope our response has adequately addressed your concerns. We take this as a great opportunity to improve our work and hope the additional evidence and clarifications warrant your favorable reassessment. We would be very grateful if you could kindly give any feedback to our rebuttal.

Best Regard,

Paper 1319 Author(s)

We're truly grateful for your in-depth review and insightful feedback. It's encouraging to see you acknowledge the novelty and strong motivation behind our framework, along with our comprehensive ablation studies, effective visualizations, and the overall clear structure of our paper. We've addressed each of your points below.

W1 & Q1: Baseline Comparisons and Model Version Discrepancy.

The reviewer pointed out a critical issue regarding our chosen baselines, noting a discrepancy between models built on Llama-2 (like Chat-Doctor, Med-Alpaca, PMC-LLaMA) and our use of Llama-3 and Qwen2 as base models. The reviewer rightly argue this makes fair comparisons difficult and strongly recommend either retraining all models on a consistent base (e.g., Llama-2) or including results from newer medical LLMs. We appreciate your valuable suggestion regarding baseline selection, and we agree that comparisons on the same, up-to-date base models are ideal.

• Focus on Open-Source and Comparable Models: Our work primarily aims to enhance open-source, white-box LLMs, and we prioritize comparing models of similar scale. This approach ensures our methods are reproducible and allows for a fair assessment of SENATOR's performance on currently prevalent base models.
• Newer Medical LLM Baselines Added: To provide a more comprehensive comparison as you suggested, we've incorporated the performance of BioMistral-7B and Meditron-7B. These are leading open-source medical LLMs of comparable size to our base models (Llama-3-8B and Qwen2-7B). Here's an updated snapshot of the results:

As this table shows, SENATOR-enhanced models (Llama-3-8B and Qwen2-7B) consistently outperform these new medical LLM baselines on MedQA and MedMCQA, and remain highly competitive on PubMedQA. This further strengthens our claim about SENATOR's effectiveness in addressing knowledge deficiencies.

• Consideration for Closed-Source Models (GPT-4 etc.): Regarding the evaluation of closed-source models like GPT-4o, GPT-4.1, or Claude, we chose not to include them for two main reasons:
  • Methodological Constraint: SENATOR's core mechanism relies on an LLM's ability to self-explore its knowledge deficiencies by measuring its intrinsic uncertainty (via Structural Entropy) during Monte Carlo Tree Search within a Knowledge Graph. This process requires fine-grained access to the model's internal probabilities and outputs, which isn't feasible with black-box, API-only models like GPT-4 or Claude. We simply can't reliably get the necessary uncertainty signals from these models to guide our deficiency detection.
  • Research Focus: Our work primarily focuses on enhancing open-source, white-box LLMs, promoting reproducibility and accessibility within the research community. So, while we appreciate the suggestion for broader comparisons, our current evaluation scope aligns with SENATOR's nature and technical requirements.

W2 & Q3: Scope of Evaluation, Generalizability, and KG Applicability to Other Domains.

Our study focuses on the medical domain due to its high demand for reliability, LLMs' persistent challenges with precise factual recall in this specialized field, and the high cost of data annotation. This makes targeted knowledge remediation via SENATOR exceptionally valuable.

• Domain Generalizability: Crucially, SENATOR's core principles are domain-agnostic. Our methodology operates on KG structural properties and LLM path uncertainty, not domain-specific semantics. Any domain representable by a KG can theoretically leverage SENATOR, and its adaptability is shown across Llama-3 and Qwen2.
• Suitability for Knowledge-Intensive Domains: It's important to emphasize that SENATOR is tailored for knowledge-intensive tasks. This design is based on a core assumption: LLMs act as implicit knowledge bases, and our goal is to uncover and fill their factual knowledge deficiencies. For domains like mathematical reasoning tasks (e.g., GSM8K, AIME2024) or tool learning/function-calling (e.g., BFCL V3, ToolAlpaca), SENATOR might not be directly applicable for two key reasons:
  1. Lack of Suitable Knowledge Graphs: These domains often lack structured, KG-style representations. SENATOR relies on semi-structured KGs as an agent for the LLM's internal knowledge space and as a source for synthetic data generation.
  2. Nature of the Task: In mathematical reasoning or tool-use tasks, model failure often stems from missing algorithmic ability, procedural logic, or execution errors—not from missing factual knowledge. Therefore, high structural entropy in a KG (if one even exists) wouldn't necessarily map to meaningful deficiencies for these domains. The detected uncertainty wouldn't correspond to missing facts but rather to an LLM's inability to perform a reasoning step or execute an algorithm correctly.

W3: MCTS Computational Cost and Efficiency Analysis.

• Time Complexity: Assuming a fixed number of simulations $N$ (e.g., $N = 100$ in our setup), and a knowledge path length (tree depth) of $H$ (our knowledge paths have a length of 5, implying $H = 4$ steps from the root to a terminal node), the size of the MCTS tree is influenced by the average number of neighbor nodes (relations) for an entity, which we denote as $M$. In general, the number of nodes visited is proportional to $M \times H$. Therefore, the time complexity of the MCTS component can be approximated as: $\mathcal{O}(N \times M \times H)$.In our specific setting, this translates to: $\mathcal{O}(100 \times M \times 4) = \mathcal{O}(400M)$ (since this is inference rather than training, the actual speed is on the order of seconds). .

W4: Accuracy of Uncertainty Selection.

Thank you for this insightful question. To assess whether our Structural Entropy (SE)-based selection truly identifies knowledge gaps, we've conducted an additional analysis to directly address this.

• Validating Uncertainty Selection Accuracy: We tested Qwen2-7B on 5,000 synthetic samples generated by SENATOR (based on Qwen2) from high-uncertainty knowledge paths. These represent areas where the model was least confident.
  • Results (Zero-Shot setting):
    • Exact Match Score (EM): 0%. (EM measures the percentage of predictions that match the ground truth exactly.)
    • F1 Score: 6.87%. (The F1 Score is the harmonic mean of precision and recall.)
  • Example Question: "What disease is similar to thyroid gland carcinoma, with symptom dysphonia and neck pain? Answer: Head and neck cancer."
• Conclusion: The extremely low EM and F1 scores directly confirm that Qwen2-7B indeed lacked the knowledge required to answer these questions accurately prior to supervised fine-tuning. This quantitatively validates that our SE-driven selection mechanism effectively identifies genuine, intrinsic knowledge deficiency regions within the model.

Q2: Clarification on "Agent-Based" Terminology.

We appreciate you raising this point about our use of "agent-based" terminology, given that our method doesn't involve explicit tool use often associated with agentic LLMs. We want to clarify why we refer to our approach as agentic and which aspects of agent behavior are leveraged within the SENATOR framework. Specifically, the LLM acts as an agent navigating a KG environment:

• Environment & State: The KG serves as the environment, with each entity representing a state.
• Actions: At each entity, the agent chooses among connected relations to move to a new state (entity).
• Reward Signal: The Structural Entropy (SE) associated with knowledge paths serves as the intrinsic reward signal for the agent. This MCTS-based exploration, driven by SE as a reward signal, embodies the LLM's purposeful, adaptive decision-making and navigation within the knowledge space to identify its own uncertainties. This fundamentally differs from a traditional LLM acting merely as a data generator, which typically lacks such proactive exploration and decision-making capabilities. Therefore, we believe the term "Agent" accurately captures this active role the LLM plays within our framework.

We hope these clarifications address your concerns and highlight the unique contributions and practical effectiveness of SENATOR. We're open to further discussion if you have any additional questions.

• The reviewer asked for comparisons to other popular uncertainty estimation methods like perplexity-based or verbal confidence approaches. We agree this is a valid and important point, and we have addressed it with our "Prob-Prob" baseline. This baseline serves as a strong, widely recognized measure of sequence-based uncertainty. It utilizes the product of token probabilities to estimate a model's certainty over a full sequence, which is a direct and popular method akin to perplexity-based approaches. This baseline provides a robust, non-graph-aware alternative to our Structural Entropy-guided approach.

• As shown in our updated results table, SENATOR consistently and significantly outperforms the "Prob-Prob" baseline (58.90 Avg. vs. 55.62 Avg. for Llama-3-8B). This numerical difference quantitatively demonstrates the superior effectiveness of our structural, graph-aware uncertainty measure. By leveraging the rich relational information within KGs, SENATOR is able to identify more genuine and complex knowledge gaps than purely sequence-based confidence measures, leading to superior performance gains.

The reviewer has correctly highlighted that an algorithmic explanation of latency is not a substitute for real-world performance numbers. We have conducted a new experiment to measure the actual inference latency of our MCTS-based data synthesis process.

• For our primary experimental setup (Llama-3-8B on 8 A100 GPUs using the Vllm framework), the latency for generating a single high-quality synthetic QA pair using our MCTS framework is approximately 0.38 seconds. This includes the full MCTS process (exploration and tree expansion) and the final generation of the QA pair. In contrast, a simple zero-shot inference for a single question on the same model takes an average of 0.12 seconds.

• While this demonstrates that the SENATOR process takes longer per sample than standard inference, it is crucial to recognize that this is a one-time computational cost for generating a high-quality, targeted training dataset. Our method's efficiency is not measured by the speed of a single inference, but by its ability to achieve significant performance gains with a small, highly targeted dataset. For instance, our SENATOR-enhanced Llama-3-8B model, which outperforms the UltraMedical model, was trained on only 26k synthetic samples. This is a mere 6.34% of the 410k samples used to train UltraMedical. The total time for our entire data synthesis and SFT process remains a fraction of the cost of large-scale pre-training or continual pre-training, making it a highly efficient solution for targeted knowledge repair.

Thank you for your continued engagement and for providing a refined critique of our work. We appreciate you pushing us to further strengthen our comparisons and analyses. We have taken your feedback to heart and have conducted new experiments and analysis to address your concerns directly.

Response to Baseline Comparisons.

We fully agree with your core concern that comparing models on the same base is crucial for a fair assessment. While retraining all existing medical LLM baselines (such as PMC-Llama) on Llama-3 is unfortunately infeasible due to their unique, diverse, and often proprietary training data, we have implemented a solution that directly addresses your recommendation.

• To provide a truly fair and direct comparison, we have added a new, strong baseline: UltraMedical, an open-source medical LLM that is also built on the Llama-3-8B base model. This allows for a direct, like-for-like comparison, ensuring that any performance difference is due to our SENATOR framework and not the data augmentation.

Llama-3-8B-UltraMedical is an open-access large language model (LLM) specialized in biomedicine. Developed by the Tsinghua C3I Lab, this model aims to enhance medical examination access, literature comprehension, and clinical knowledge. Building on the foundation of Meta's Llama-3-8B, Llama-3-8B-UltraMedical is trained on our UltraMedical dataset, which includes 410,000 diverse entries comprising both synthetic and manually curated samples.

• Furthermore, as you suggested, we have also included a strong API-based model, GPT-4, to provide a performance upper bound on the benchmarks.

The updated results are presented in the table below:

As this table clearly shows:

• SENATOR-enhanced Llama-3-8B outperforms the UltraMedical model (58.90 Avg. vs. 54.21 Avg.), a model trained specifically for the medical domain on the same base model. This provides definitive evidence that the performance gains are a direct result of our targeted deficiency detection and data synthesis framework, not merely data augmentation.
• GPT-4 and Qwen2.5-72B-Instruct establish a clear upper bound, as expected, demonstrating the challenge of our benchmarks and providing context for the performance of all other open-source models.

We appreciate your direct feedback on the "agent" metaphor. We understand your concern that this term can be overly broad and misleading when tool usage is not a part of the framework. We agree with your sentiment that the metaphor should not be introduced if it risks misinterpretation.

To avoid any confusion, we will remove the "agent-based" terminology from our final manuscript. Instead, we will describe our approach as a "closed-loop, self-improvement framework". Our goal was to convey that the model is not a passive recipient of data but is an active participant that systematically and autonomously probes its own knowledge boundaries to identify areas of deficiency. We believe this new phrasing more accurately and precisely captures the core contribution of SENATOR without the baggage of tool-use connotations.

Please allow us to thank you again for reviewing our paper and the valuable feedback.

Please let us know if our response has properly addressed your concerns. We are more than happy to answer any additional questions during the discussion period. Your feedback will be greatly appreciated.