Consistency-based Black-box Uncertainty Quantification for Text-to-SQL by Similarity Aggregation

We thank the reviewer for their valuable feedback and suggestions. We provide responses to specific questions and comments below.

Re: scope:

We clarify that the scope of our work is broad and that the proposed approach is applicable to numerous tasks. Although UQ for text-to-SQL is our main motivation, we showed generalizability to tasks such as QA in Section 5.4. Also, perhaps there is some misunderstanding about the baselines, but we have included a broad suite of those including verbalized and white-box approaches (not just consistency-based approaches). We would appreciate any suggestions that the reviewer may have to further highlight breadth of our work.

Re: conformal prediction references:

We thank the reviewer for the references. While conformal prediction for LLMs is interesting and clearly related to uncertainty quantification/estimation, the goal is different in that it aims to find a prediction set that contains the desired result with confidence guarantees. The target tasks in the suggested papers are for QA or summarization, where algorithms generate multiple answers to cover the correct answer. The evaluation metrics for conformal prediction are the coverage rate and the prediction set size. In contrast, the goal of our paper is to find a well-calibrated confidence estimate that reduces the calibration error. The two suggested papers cannot be suitable baselines fir our purposes.

Responses to Questions

”Open-source models allow users to access their internal states, while API-based LLMs do not. However, exploring open-source models for black-box approaches seems a bit self-contradictory.”

The reviewer is correct that API-based LLMs are often the ones without access to internal states. Note that our methods apply just as much to API-based LLMs, but our experiments were restricted to open-source LLMs for practical reasons.

”Why is a verbalized method introduced as white-box? (Line 186). Some verbalization methods do not require access to logits (e.g., qualifying phrases).”

We agree that some verbalized methods are not white-box, as the reviewer indicates, but the one mentioned in this line happens to be white-box as it needs the logit for the True or False output. We will clarify this in our revision.

”In terms of paper organization, if the proposed method works well for question-answering datasets (also, are they all long-sequence generation tasks?), I'm curious why the authors titled the paper UQ for text-to-SQL. Is there a specific reason behind this decision?”

We chose to focus our paper on estimating well-calibrated confidences for the text-to-SQL task, as this is the main motivation behind the work. This choice requires specifying information such as related work, choice of metrics, datasets, etc. Section 5.4 is intended to show generalizability of the work to QA (which is the sole focus of some related work) and show broad scope of the proposed approach. Also, to clarify, some of the QA datasets involve short generation tasks.

We hope that we addressed the reviewer’s main concerns, particularly about scope of the work, which seems to be a major factor in the reviewer’s rating. If this is indeed the case, we request them to consider increasing their rating.

We thank the reviewer for their valuable feedback and suggestions. We provide responses to specific questions and comments below.

Re: evidence about implicit underlying assumption behind consistency-based approaches:

We have indeed observed empirical evidence for the underlying assumption about consistency; for instance, the mean similarity between correct generations is less than that between incorrect generations across datasets. Fig. 1 is a visualization of the assumption, although it is qualitative and only covers a few queries. We stress that the results of the work provide evidence for the assumption, since they would not generally hold if the assumption did not hold at least to some degree.

Re: Fig. 1(b):

We agree with the reviewer’s observation about Fig. 1(b). However, we note that this instance indicates importantly that the consistency assumption does not hold the same way for all instances — it is a statistical assumption, i.e. holds generally but not to all instances. However, we appreciate the point about showing examples and will consider adding some in the Appendix.

Re: ACE metric computation:”

We provided a short description of the ACE metric computation in line 346. Space-permitting, we will add more detail here.

Re: results in Tables 1 and 2:

We have already used bold font to highlight the best results in both tables. Was the bold font hard to identify? We will see how we can make the results clearer.

Re: comment: “The proposed similarity method can evaluate if the model knows these inputs, but how does it perform with data the model hasn't seen?”

We are not sure we understand this comment correctly — we clarify that the approach is intended to work for unseen instances. For the low data methods, we assume that the nature of sampling is the same across training and test sets, but that’s the only assumption being made.

Responses to Questions

”AUROC and AUARC could shown the accuracy of the model on text-to-SQL task?”

We clarify that it is not our intent to improve execution accuracy of the underlying task but to estimate well-calibrated confidences. AUROC gauges how well one can distinguish between correct and incorrect generations using confidences, and AUARC gauges how performance changes as confidence is used to determine which instances to abstain from answering.

”The hyper-parameter m in line 233 and B in line 349 is same?:

No, they are different — m is the number of generations/samples and B is the number of bins for computing adaptive calibration error (ACE).

Some setting like "bayes-beta" is not clear it's meaning.

Thanks for pointing this out — we will try to make it clearer. Bayes-beta refers to the proposed approach of Bayesian aggregation with Beta distributions.

We hope that we have addressed the reviewer’s main concerns, and if this is indeed the case, we request them to consider increasing their rating.

We thank the reviewer for their valuable feedback and suggestions. We provide responses to specific questions and comments below.

Re: improving text-to-SQL performance:

Note that it is not our intent to improve performance of the underlying task. We are interested in estimating well-calibrated confidence estimates, just like other work on UQ. This is the main objective of our proposed UQ module (for a text-to-SQL system).

Re: Fig 1:

We thank the reviewer for spotting this discrepancy. This figure has 35 samples per query but the experiments use 30 samples per query. The figure itself is correct but the caption needs to be changed. We will either modify the plots or the caption accordingly.

Identical outputs are indeed allowed and are handled the same as any other output pair, where pairwise similarity becomes 0 for such outputs. Fig. 1 is just a visualization to convey the consistency assumption that is implicit in consistency-based approaches, so such outputs would be overlapping in the visualization.

Re: proposed baseline and effect of generations:

We make an important clarification — the Kuhn et al. 2022 work on semantic entropy is NOT a suitable baseline for our work. Their use of natural language inference is crucial to their method and this does not make sense for SQL outputs — what does it mean for a SQL query to entail another one? We have cited this paper several times and even mentioned why it is not suitable for text-to-SQL in line 491. Note also that Lin et al. 2024 has shown superior performance over Kuhn et al. 2022 on QA tasks, and we use that as a baseline in our work.

We thank the reviewer for the excellent suggestion of ablation on number of generations and will add this in the Appendix.

Re: repeated generations:

Yes, repeated generations are indeed allowed — please see our answer above about overlapping outputs.

We believe we have addressed most of the reviewer’s concerns, including unsuitability of a proposed baseline, fixing a caption error in Figure 1, and clarifying that repeated generations are allowed. If they agree, we hope they will consider increasing their rating.

We thank the reviewer for their feedback. It appears though that they have misunderstood several aspects of the paper, so we clarify matters by responding to specific questions and comments below.

Re: the following comments about metrics: “The metric (ROUGE) used to evaluate the method could only reflect the syntactic similarity but hard to evaluate semantic-level correlation. There is only 1 semantic-level metric (sentence bert) to evaluate the method … The similarity measurement may not be reliable. Therefore, the results obtained from those experiments are possibly meaningless and the conclusion of this paper is ungrounded.”

Firstly, the phrase “metric (ROUGE) used to evaluate the method” is factually incorrect — the metrics used for evaluation are ACE, AUROC, and AUARC. We believe the reviewer is referring instead to the choice of similarity metric. They seem to have however completely missed that 1) the output (for most of the paper) is SQL, and 2) we have used numerous similarity measures (see Section 3.2 on page 4) spanning syntactic, semantic, and SQL-specific metrics. Various experiments discuss the implications of the choice of similarity metric. We have even explained our conjecture for why syntactic similarity measures such as ROUGE may be doing well for UQ for text-to-SQL starting around line 463. The scope of the experiments is much broader than the comment suggests and the conclusions are very much meaningful, given the extensive nature of the empirical study.

Re: motivation and scope:

The motivation for the work is clearly stated in Section 1. Text-to-SQL is a hugely consequential task and widely studied in the AI and data communities. We chose to focus on the task as it has complexities that go beyond QA tasks. Section 5.4 even discusses the generality of the ideas by conducting experiments on QA datasets. The scope of our work is in fact broader than numerous papers published previously on QA tasks alone, since we experiment with more datasets (see Kuhn et al. 2022 and Lin et al. 2024 for comparison).

Re: awkward language in lines 46-75:

Could the reviewer please specify the lines that are unclear? This paragraph seems clear to us and is important to appreciate the motivation of the work. Specific feedback will help us in our revision.

Re: comments about verbalization and consistency: “It’s unclear that how this method tackles “over confidence” from LLMs. It’s possible that LLM has a false belief and it doesn’t matter with how the LLM evaluate itself (line 94: ”when asking LLMs for probabilities). It’s strange that the paper mentions so. What if the model generates very similar text samples but all of them are wrong? Could the proposed similarity based method handle this case?”

We address yet another misunderstanding — our method does NOT ask LLMs to provide confidences; it is a non-verbalized method and merely uses LLM outputs. Note that consistency-based approaches all make assumptions about consistency and the correctness of LLM generations. If this is not the case and an LLM consistently provides highly similar incorrect answers, then this will not be accounted for by ANY consistency-based method, including ours. No method is perfect but we have empirically shown that our proposed method performs better than relevant baselines, particularly for the ACE evaluation metric.

We hope our responses have clarified misunderstandings and request the reviewer to completely re-evaluate the work and update their rating accordingly.