Discovering Knowledge Deficiencies of Language Models on Massive Knowledge Base

We sincerely thank the reviewer for their detailed and insightful questions. This feedback is invaluable for improving the clarity of our work. We provide the following responses to address each point.

1. On the Influence of the Initial Passage Group

We recognize that the initial random batch could influence the search trajectory. To address this, we performed a specific experiment to measure the sensitivity of SEA to the initial seed selection. In our main experiments, the initial batch $B$ was created by uniformly sampling paragraphs from 13 predefined Wikipedia categories to ensure a broad starting point. However, in Appendix A (Query 6), we detail an additional experiment where we initialized SEA with a completely random batch of paragraphs from Wikipedia, with no category constraints at all. The results of this experiment are visualized in Figure 7. We found that the resulting error distributions were highly similar to those from our main experiment (Figure 6). For example, the same model clusters (e.g., gpt-4o, DeepSeek-V3, and o1-mini failing on similar topics) emerged independently of the starting point. This demonstrates that while the initial batch seeds the search, the iterative, error-driven nature of SEA is robust and consistently converges on a model's inherent knowledge deficiencies rather than being highly variable based on the start.

2. On Thresholds ($\xi$ and $\gamma$) and DAG Logic

We appreciate the reviewer pointing out the need for greater clarity here. Let us break down the logic.

Why $\xi = \gamma$? Setting $\xi = \gamma = 0.5$ is a design choice for simplicity, but the two thresholds serve different functions in the DAG.

• $\xi$ (Source Error Threshold): This threshold determines if a newly evaluated paragraph $p$ becomes a source error. It is based on the model's error rate for that single paragraph, $T_{\{p\}}$. If $T_{\{p\}} > \xi$, it is added to the source set $P_{\text{source}}$.
• $\gamma$ (Source Pruning Threshold): This threshold determines if an existing source error gets pruned. It is based on the cumulative error $\pi_{\mathcal{G}(p)}$, which is the average error across all of its descendants in the DAG.

You are correct that a newly added source error will not be immediately pruned. When a paragraph first becomes a source error, it has no descendants, so the pruning condition $\pi_{\mathcal{G}(p)}< \gamma$ does not apply. It can only be pruned in later steps after it has generated descendants whose average error rate is low, indicating it's no longer a fruitful path for discovering new errors.

Example of the Process: Given $\xi = \gamma = 0.5$.

• At step t: SEA evaluates paragraph $p_1$. The model's error rate $T_{\{p_1\}}$ is $0.8$. Since $0.8 > \xi$, $p_1$ is added to the source set. It has no descendants yet.
• Step t+1: Using $p_1$ as a source, SEA discovers and evaluates $p_2$ and $p_3$.
  • The model's error on $p_2$ is $T_{\{p_2\}}= 0.9$ (a new source error).
  • The model's error on $p_3$ is $T_{\{p_3\}}= 0.1$ (not a source error).
• Pruning Check for $p_1$: $p_1$ now has two descendants, $p_2$ and $p_3$. Its cumulative error is $\pi_{\mathcal{G}(p_1)} = (0.9 + 0.1) / 2 = 0.5$. Since $\pi_{\mathcal{G}(p_1)}$ is not less than $\gamma$, which is $0.5$, $p_1$ is not pruned and remains a source for the next step.

3. On Analyzing Various Values of $\xi$ and $\gamma$

Due to the budget limitation, we did not perform a detailed sweep of these hyperparameters. However, our ablation studies in Section 5 (Figure 4) provide a quantitative analysis of their impact. Specifically, the "w/o Pruning" variant is equivalent to setting the pruning threshold $\gamma$ to 0. The results show a clear performance drop compared to the full SEA framework, demonstrating that the pruning mechanism is crucial for performance. The gap between SEA and the "w/o Pruning" variant increases over time, indicating that low-quality sources that haven't been pruned by the cumulative error start negatively affecting SEA. This quantitatively validates the importance of the pruning component governed by the $\gamma$ threshold.

We thank and agree with the reviewer for the issue that the potential for circular evaluation and bias is a critical issue in LLM research. In our paper, we have shown our efforts into mitigating these risks. We also make further clarification in the following:

Clarifying the Role of the Generator and Ensuring Quality

We want to clarify that the external LLM (gpt-4o) in our framework does not act as a subjective "judge" but as a structured data-to-question generation tool. Its role is to convert a factual paragraph from the Wikipedia knowledge base into a multiple-choice question where the answer is explicitly contained within the provided text. The final evaluation of the model being tested is not based on another LLM's opinion, but on an objective comparison against the ground truth from the source document. To address the concern about the generator's own biases or blind spots, we implemented a rigorous human validation process.

Human Evaluation of Generated Questions: We thoroughly evaluated the questions created by our gpt-4o generator. Five college-level students were tasked with verifying the generated questions and answers by cross-referencing them with the original source paragraphs from the knowledge base.

100% Pass Rate: Out of 1,000 randomly sampled questions generated by SEA, this evaluation achieved a 100% human pass rate. This result confirms that the generated questions are factually grounded and that their correct answers are verifiably present in the source text.

Objective Evaluation: The final accuracy is computed by simply comparing the testee model's chosen option with the ground truth answer derived directly from the source paragraph. This deterministic process removes the subjectivity and potential leakage associated with using an LLM for qualitative evaluation.

This methodology of using a powerful LLM for structured content generation from source documents has also been adopted by other recent work in the field, such as AutoBencher. Our robust validation process ensures that our framework reliably identifies the true knowledge deficiencies of the tested models rather than being an artifact of the generator.

Dear Reviewer cJFu,

We sincerely thank you for your detailed and thoughtful review of our paper. We have done our best to address the concerns you raised, especially regarding the dependence on an external generator and your other valuable points. Your feedback is crucial for improving our work.

As the discussion deadline is approaching, we wanted to kindly check if our responses have clarified these issues. If any aspect of our explanation remains unclear, we are ready to provide further details immediately.

We are highly encouraged if your concerns have been addressed, and we are on standby to offer any additional clarification needed before the deadline passes.

Thank you again for your time and guidance.

Best,

Authors

We sincerely thank the reviewer’s thoughtful feedback and questions. We provide the following clarifications to address the requested details.

On the Rationale for DAG Modeling

Rationale: The primary purpose of the relation DAG is to identify and model systematic weaknesses within the language model. Large language models often exhibit correlated failure patterns, where errors are not isolated but are concentrated in specific knowledge areas. The DAG structure allows us to model these relationships explicitly by tracing error propagation paths. By representing paragraphs that induce errors (source errors) as nodes, we can track how one error-prone topic leads to the discovery of other, semantically similar error-prone topics over time. This helps us understand if a model has a fundamental deficiency in, for example, "chronological reasoning" within the broader domain of "history."

Edge Construction: The principles are based on semantic similarity and error propagation. An edge is constructed as follows: At each step $t$, we have a set of source error paragraphs, $P_{\text{source}}^{(t)}$, collected according to LLM’s incorrect answer. We use these source errors to find a new batch of error-inducing paragraphs in the next step, $P_{\text{source}}^{(t+1)}​$, by retrieving semantically similar candidates as in Figure 1. A directed edge is drawn from a paragraph $p \in P_{\text{source}}^{(t)}​$ to its semantically similar descendants in $P_{\text{source}}^{(t+1)}​$ that also induce errors. To ensure the graph remains acyclic, we remove any newly discovered source errors from the knowledge base $K$, which prevents them from being discovered again and creating loops.

On the Initial Seed Selection

Selection Process: For our main experiments, the initial batch $B$ was constructed by uniformly retrieving 40 paragraphs from 13 predefined top-level Wikipedia categories. This was done to ensure a broad and category-agnostic starting point for the error discovery process for all models, facilitating a fair comparison.

Impact on Results: We investigated the sensitivity of SEA to the initial seeds. In Appendix A (Query 6), we present an experiment where we initiated SEA with a completely random initial batch, without any topic or category constraints. The results, visualized in Figure 7, show that SEA discovers similar failure patterns and error distributions as in the main experiment (Figure 6). For example, gpt-4o, DeepSeek-V3, and o1-mini still form a distinct error cluster, regardless of the different starting points. This demonstrates that while the initial seed starts the search, the iterative, error-driven nature of SEA is robust and consistently converges on the model's intrinsic knowledge deficiencies.

On Experiment Details

Experimental Dataset and Structure: As described in Section 4 (Knowledge base details), our experiments are conducted on a massive knowledge base collected from English Wikipedia, comprising 7.1M documents and 28.8M paragraphs. SEA dynamically samples from this knowledge base. The "dataset" for evaluation is generated on-the-fly. For each paragraph $p$ selected by SEA, we use a generator LLM (gpt-4o) to create multiple-choice questions.

Impact of Thresholds: The thresholds $\xi$ (for identifying a source error) and $\gamma$ (for pruning the source error set) were set to 0.5 for our experiments.Due to the budget limitation, we did not perform a detailed sweep of these hyperparameters. However, our ablation studies in Section 5 (Figure 4) provide a quantitative analysis of their impact. Specifically, the "w/o Pruning" variant is equivalent to setting the pruning threshold $\gamma$ to 0. The results show a clear performance drop compared to the full SEA framework, demonstrating that the pruning mechanism is crucial for performance. The gap between SEA and the "w/o Pruning" variant increases over time, indicating that low-quality sources that haven't been pruned by the cumulative error start negatively affecting SEA. This quantitatively validates the importance of the pruning component governed by the $\gamma$ threshold.

Dear Reviewer PkVq,

Thank you for your valuable feedback and insightful questions. We appreciate your positive assessment of our work.

We have provided a detailed response addressing your points regarding the DAG modeling rationale, initial seed selection, and experimental details. We have also included a case analysis to visually demonstrate the process and outcomes of our framework, as you suggested.

As the discussion deadline is approaching, we wanted to gently check if our revisions and responses have addressed your concerns. Your feedback is very important to us, and we would be grateful to know if any points remain unclear. We are available to provide further clarification as needed before the deadline.

Thank you again for your time and effort in reviewing our paper.

Thanks,

Authors

On Clarifying Methodological Details (Random Sampling)

Thanks for pointing this out. As described in the implementation details in Section 4 (Implementation details L165), this step occurs after the "Top-k Error Related Retrieval". At each step, SEA first retrieves the top-k semantically similar candidates from the knowledge base (we use $k=50$) for each error. From this retrieved set of $50\times |P_{\text{incorr}}|$ paragraphs, we then randomly sample a smaller batch (40 paragraphs) to form the error-related batch $E$ for evaluation in the current step. The purpose of this random sampling is twofold: (1) It introduces stochasticity into the ascent process, helping the search escape local optima and explore a wider area within the high-error region of the embedding space, and (2) it keeps the per-step evaluation cost fixed and manageable, preventing the evaluation batch size from growing uncontrollably.

We thank the reviewer for their constructive feedback and valuable suggestions. We have carefully considered the comments and provide the following clarifications to address the raised concerns.

On the Experiment Setting on Initial Batch and Sensitivity Analysis

We appreciate the reviewer's concern regarding the potential for the initial batch to introduce bias. We would like to clarify our experimental setup and provide further evidence of SEA's robustness to the initial batch selection.

Implementation Details: For the experiments presented in the main paper (e.g., Figures 2, 3, 5, and 6), the same initial batch was used for all models to ensure a fair and consistent comparison. This initial batch was randomly and uniformly retrieved 40 paragraphs from 13 predefined top-level Wikipedia categories. This strategy was chosen to provide a broad, category-balanced starting point for the error discovery process.

Sensitivity to Initial Batch: To directly address the sensitivity question, we conducted an additional experiment where SEA was initiated with a completely random set of paragraphs from Wikipedia, without any category constraints. The results of this experiment are presented in Figure 7 and discussed in Appendix A (Query 6). The analysis shows that even with a different, entirely random start, SEA discovers similar failure patterns and distributions. For instance, gpt-4o, DeepSeek-V3, and o1-mini still share similar failure clusters, as do Qwen2.5-72B-Instruct and DeepSeek-R1-Distill-Llama-70B. This demonstrates that SEA's iterative, similarity-based search effectively converges on a model's inherent weaknesses, regardless of the specific starting points.

On the Diversity and Spread of Discovered Errors

We thank the reviewer for pointing out the need for a more systematic analysis of error diversity. We believe that Section 6 ("Analyzing LLMs from the Discovery Results") provides a detailed, qualitative, and quantitative analysis of the diversity of errors found by SEA, and we further clarify as follows:

Quantitative and Systematic Analysis: In Figure 6, we visualize the discovered source errors ($p ∈ P_{\text{source}}$) for each model using t-SNE. The visualization is color-coded by model and uses different markers for 13 distinct Wikipedia categories. This visualization clearly shows that SEA does not merely concentrate on a few clusters but identifies diverse error patterns across a wide range of topics. For example, we observe distinct clusters of errors for different models and groups of models. gpt-4o-mini and DeepSeek-R1 exhibit unique error clusters, while gpt-4o, DeepSeek-V3, and o1-mini overlap significantly in the "culture and the arts" category.

Error Pattern Analysis: To further analyze the types of errors, we aggregated them from the question level to the model level for specific clusters. As detailed in Table 2, we analyzed the error patterns for models in clusters 3 and 5. For cluster 3 (gpt-4o, DeepSeek-V3, o1-mini), common failure patterns included "Challenging in Chronological Analysis" and "Unfamiliar with Locational Details". For cluster 5 (Qwen2.5-72B-Instruct, Llama-3.3-70B-Instruct, etc.), failures often involved "Challenges with Chronological and Historical Data" and "Inaccurate Interpretation of Patterns and Trends". This analysis demonstrates that SEA uncovers systematic and recurring failure modes, offering deep insights into model weaknesses beyond a simple error count.

On the Comparison with ACD and Cost Analysis

Fairness of ACD Comparison: The reviewer notes that SEA and ACD have different search strategies. We acknowledge this difference; it is precisely this distinction that highlights SEA's novel contribution. While ACD discards similar proposals to broaden its search, SEA intentionally leverages semantic similarity to previously observed failures to efficiently discover new errors. Our comparison focuses on the ultimate goal of both frameworks: to discover as many model deficiencies as possible within a given budget. We compare the number of "error tasks" from ACD with the number of "source errors" from SEA, as both represent identified categories of model misinformation. The results, which show SEA finding up to 40.7x more errors, demonstrate the superior efficiency of our error-ascent approach for the task of knowledge deficiency discovery.

Computational Costs for Retrieval and Embedding: The computational cost for retrieval and embedding is negligible compared to the LLM inference cost. We use a single 4090 GPU for the sentence transformer model serving, embedding similarity calculation in SEA, and document embedding pre-processing.

Dear Reviewer cTGP:

We sincerely appreciate your efforts in reviewing this paper! We tried our best to address your specific concerns regarding the initial batch sensitivity, the diversity of discovered errors, the comparison with the ACD baseline, and clarifications on methodological details. Your suggestions and feedback are very important to us.

The discussion deadline is approaching. We wanted to check if our responses have helped clarify these points. If you need any more clarification, we are happy to provide it as soon as possible.

We are highly encouraged if your concerns have been addressed.

Thanks!

Authors