Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models

Responses (1/2)

We thank the reviewer for the constructive review, and appreciating for our experiments and general motivation. We are also thankful for the useful feedback. We have made revisions to our manuscript as well as performed additional experiments following the reviewer's suggestions. ## Uncertainty vs Confidence Apologize for this confusion. To clarify, in short, $U$ is a property of the model's perceived posterior and depends only on $x$ (see L3-5 in Section 3.1, and Eq 1). $C$ depends on both $x$ and the answer $\mathbf{s}$ (L2-L3 of Section 3.2 and Eq 2). We have updated Section 3.2 to further clarify this. > Confidence scores are defined based on the token probabilities, which are not available in black-box inference settings Just want to clarify that Eq(1) and Eq(2) are only one possible uncertainty/confidence (that are however mainstream). Exact definition is just anything taking the form of $U(x)$ and $C(x,\mathbf{s})$. We hope the updated section 3.2 and the example helps clarify this. ## Non-QA NLP applications (We assume "data-to-text" means tasks like captioning. Please let us know if this is a misunderstanding.) Other NLP applications like data-to-text are definitely something we plan to explore next. This paper mostly just follows existing UQ literature and uses QA as it is the easiest to perform evaluation on it. Evaluation in general is still quite hard. In fact, we have seen very recent explorations on using model-predicted likelihoood as confidence scores on X-ray report generation task (but they also judge the quality of the report with ROUGE). We believe that a lot of the ideas are transferrable and we would like note that CoQA is to some extent "data-to-text" except that the data is in textual form as well. Our methods do not assume that the input has to be text, as we are only comparing the generations' similarities. If the input is data, we think there are two possible solutions: We skip the data (image or audio) and directly use Jaccard or NLI model on the question and answers, OR; We fine-tune a domain-specific NLI model by training a "bridging" module that "translates" the other modalities to embeddings that the NLI model understands.

Responses (2/2)

## Why UQ for NLG is important > In the introduction it's presented that LLMs are gaining attention -> it's crucial to quantify their uncertainty. After reading the paper, I still have to ask why? It seems crucial to improve their accuracy. Is the only rational for improving their uncertainty so that their accuracy can be improved, e.g. by blocking uncertain outputs? Or is there other reasons as well? To begin with, improving the accuracy is important, but selective generation (i.e. blocking uncertain outputs) is not just about improving accuracy. For example, an influential work [1] in selective classification (an area with a similar motivation, but with much more literature) aims at providing risk guarantees after the selection. Secondly, if improving accuracy *on the un-rejected samples* is important, then finding a good UQ measure for such selective generation task is also important as a better UQ measure could lead to higher accuracy at the same rejection rate. A bad UQ, such as the "Random" baseline in Table 1, leads to no improvement. Finally, selective generation/classification is one of the most important applications of UQ, but in general UQ is about conveying this information about uncertainty to the decision maker (human or algorithm) [2]. In UQ literature, people tend to focus on AUROC to check whether the UQ measure is reliable, and we also use AUARC (a metric related to selective generation) as we think it is more directly related to real-world applications. They are both machinery to probe the reliability of UQ measure, whose true importance is due to that decision-making processes intrinsically need to have a reliablity measure on the prediction. [1] Geifman, Yonatan, and Ran El-Yaniv. "Selective classification for deep neural networks." Advances in neural information processing systems 30 (2017). [2] Seoni, Silvia, Vicnesh Jahmunah, Massimo Salvi, Prabal Datta Barua, Filippo Molinari, and U. Rajendra Acharya. "Application of uncertainty quantification to artificial intelligence in healthcare: A review of last decade (2013–2023)." Computers in Biology and Medicine (2023): 107441. ## UQ vs Calibration > How is the issue of model calibration different? (See end of Section 2 for a discussion, and a newly added Appendix C.5 for calibration experiments.) The UQ we focus on tries to find a measure of uncertainty or confidence that is *discriminative* of what's uncertain and what's not. In other words, we care about whether the *ranking* of our UQ measure could effectively predict the reliability of the answers. This is also why most literature uses AUROC as an evaluation metric. Calibration cares about the discrepancy between the predicted probability and the frequency. (Such "discriminative-ness" is often referred to as "sharpness" and is considered orthogonal to calibration [3].) In the extreme case - if we know the model's accuracy is 0.6 on average, and we keep predicting a answer's confidence is 0.6 regardless of the answer, we get something that is prefectly calibrated, yet this constant confidence is not useful because it doesn't tell us which answer is more reliable than others (i.e. not "sharp"). [3] Gneiting, T., Balabdaoui, F., and Raftery, A. E. Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69 (2):243–268, 2007.

Responses

We thank the reviewer for the constructive review and acknowledging our contributions vis-a-vis experiments and presentation, as well as for providing useful feedback. In pursuance to the suggestions made by the reviewer, we have made revisions to our manuscript, and performed some additional experiments. ## ECE or ACE (calibration measures) Thank you for the suggestion. We tried to distinguish the focus of our paper at the end of Section 2. Just like in our baseline papers, we focus on the uncertainty estimation, and we care more about the *ranking* of such measures - that is, whether a high confidence means highly reliable prediction or accuracy. All uncertainty or confidence estimates could be conformalized or calibrated to bear concrete meaning in the frequentist sense, by using a calibration dataset. There is a large collection of calibration literature that we can leverage here. In repsonse to your suggestion, we have also run additional experiments using histogram binning to calibrate all methods, and report the ACE in the Appendidx C.3. ## Additional Reference Thank you for the suggestion and we have included this reference to our revision for completeness. After reading the paper, we found that this method is more suitable for questions with exact answers (e.g. multiple choice or arithmetics) as the consistency-based component requires comparing exact matches of predictions, which is quite hard to achieve for examples like Figure 6 in the Appendix. The "verbalized confidence" is similar to the P(true) baseline we tried. ## Use of model embeddings > Would this method (using model embeddings) give better confidence or uncertainty estimates in those settings as well? Thank you for the question. While we did not perform the experiments ourselves (and is not a black-box method), we noticed that our baseline paper's (Kuhn et al. 2023) official implementation tried this idea. As it was not used nor reported in their paper, it is probably not performing well.

Responses

We are grateful to the reviewer for the constructive comments. To begin, we would like to emphasize that this paper focuses on the uncertainty quantification of the LLM, and the experiment setups largely follow the white-box baseline (Kuhn et al. 2023). We have made revisions to our manuscript as well as performed additional experiments following the reviewer's suggestions. Below we present responses to each of the points raised: ## Clarification of Details. > what DeBERTa model used for NLI? Was it trained using NLI data? For a fair comparison, we followed (Kuhn et al. 2023) and used the same official pretrained DeBERTa-large on hugginface, which was fine-tuned on MNLI data. More training details of this model could be found on the model card of `deberta-large-mnli` on huggingface. ## Uncertainty vs Confidence We apologize for the confusion here. The structure was that 3.1 defines uncertainty and 3.2 defines confidence (which is different). $U$ is a property of the model's perceived posterior and depends only on $x$ (see L3-5 in Section 3.1, and Eq 1). $C$ depends on both $x$ and the answer $\mathbf{s}$ (L2-L3 of Section 3.2 and Eq 2). These are commonly used terms in two somewhat disconnected domains and we have made updates to Section 3.2 to emphasize this distinction. ## Recommended Variation / Why a particular method outperforms Thank you for the constructive question/suggestion. In section 5.3, under *Uncertainty Measures*, our conclusion was that the similarity measure (Section 4.1) seems more important than variants proposed in Section 4.2. We hypothesize that "entail" works better because generally the output space is huge, and for two generations, "not contradicting" is likely not a sufficient indicator of low-uncertainty (as they can both be bad random responses). We have updated section 5.3 and Appendix B.7 with examples to reflect this hypothesis. ## GPT evaluation We would like to clarify that the number of evaluations is *99* per dataset instead of 33 (33 per (model, dataset) pair * 3 models) The number of total human evaluations is chosen basing on (Kuhn et al. 2023), which evaluated 200 answers for two datasets (we have 297 on three). We tried our best to verify the reliability of GPT evaluation, but the verification process is actually quite slow, as for CoQA we need to read the passage first before judging the answers, and even for TriviaQA or NQ, sometimes seemingly unrelated answers are just two names of the same person and require careful research. We agree that a larger-scale human evaluation with mulitple annotators is more desirable, but the main focus of this paper is UQ, and we think the topic of automatic evaluation is an important research area by itself. Existing UQ literature almost always use purely lexical measures like ROUGE-based automatic evaluation, and we believe the GPT evaluation is better (please refer to Appendix B.3 for a discussion). To address your concern, we increased the number of annotations to 200 per dataset (50 per (model, dataset) * 4 models) and the new accuracies are 89.4/96.5/93 for coqa/trivia/nq. Using the same annotations, the ROUGE-L based metric's accuracy is 81.5/93.5/85. If we construct a confidence interval we could reject that "GPT and ROUGE are equally good" (our estimate is that further shrinking the confidence interval by half requires about 20 hours of annotation time). We found that llama2 (newly added) tends to generate different expressions of the same answer, which is sometimes judged incorrect by GPT. Excluding llama2, the GPT accuracies are 90.6/98/94 for coqa/trivia/nq. ## Other Questions > What is the reasoning for a_{NLI, contra}? If you use a standard NLI model which has three classes, Eq 4 (right) would take into account the entailment and neutral class (since it is 1-p_{contra}, is that correct? $a_{NLI, contra}$ accounts for both neutral and entailment. We could consider the difference between $a_{NLI, contra}$ and $a_{NLI, entail}$ as whether we think "neutral" is closer to “similar” or “dissimilar”. > Unclear why uncertainty is used for expected accuracy and model confidence for individual accuracy. The setting of uncertainty + individual accuracy was in Table 11 (now 10), and we discuss in Appendix C.2 why we choose not to include it in the main text. Essentially, since $U$ does not depend on a particular generation (i.e. it is a property of the model's posterior, for a random generation), we think it should be used to predict the (estimated) expected accuracy (which also depends on the posterior/a random generation). > Provide examples on when the uncertainty and confidence estimation aligns/doesn't align with the prediction We've added more examples (e.g. Fig 5-7) in the Appendix in the updated pdf, but we are not entirely sure with what you mean by aligning with the prediction. Could you check if the new examples address your concerns, or clarify your suggestion? Thank you!

Responses

We appreciate the positive feedback on the soundness and overall contribution of our work---we are glad that the reviewer found it intuitive and interesting. However, we would also like to take this opportunity to respond to some concerns regarding the clarity/presentation of our work. We have made revisions to our manuscript as well as performed additional experiments following the reviewer's suggestions. ## Analysis on the impact of similarity functions Thank you for this constructive suggestion. We had some discussion in Appendix B.7. To clarify this further, we have updated section 5.3 and Appendix B.7 with some examples to reflect our hypothesis. Newly added text is reflected in blue. ## Discussion of advantages over baselines Thank you for the suggestion. The only two black-box baselines are NumSet nad LexiSim. NumSet is discrete, so our method (EigV in particular) has an advantage over it as it's more granular. LexiSim is purely lexical based, and we have some discussion of why meaning-based measures are more useful in Appendix right before B.4. We have also updated the appendix B.7 to include discussion and example of why the proposed measures are better than the baselines. ## Readability of Table 1-3 Thank you for the feedback! If you notice, we had already moved most of the results to the Appendix, but due to the large number of experiments we ran it is quite hard to reduce the information. The general message is that the middle rows ("Ours") tend to perform better. We have followed your suggestion and also moved AUROC (Table 3) to the Appendix now. ## Questions > Have you tried other similarity measures, such as cosine similarity, using existing word embeddings? This is an interesting idea and seems related to the Jaccard similarity. We just finished running some experiments using the largest Glove embedding (glove.840B.300d) where an answer's embedding is computed as the average embedding of its words, and it performs significantly worse than Jaccard. While we haven't fully explored this idea due to limited time, we did notice that the baseline paper (Kuhn et al. 2023) seems to have tried the sentence embeddings in their code release but didn't use it in the paper, and we assumed that sentence embedding-based method didn't work well. > Is there any reason for the definition of the degree matrix? The degree matrix (Eq.7) was used because it seems like quite a straightforward measure of ``dispersion'', as $C_{deg}$ is just the average distance to other nodes.