Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering

We appreciate the time and effort taken to review our manuscript. We are happy to incorporate the reviewer's remarks into the revised version of our manuscript.

We address the listed weaknesses and questions one-by-one:

(minor) Fig 1 is slightly unclear — the caption should at least include some explanation of \nu, which is not specified until Sec 3

We thank the reviewer for catching this detail. We have updated the caption of Figure 1 in the revised manuscript. It is now explicitly specified what $\nu$ is.

Can the author clarify the results in Table 2 of the appendix? It appears that the performance gap between SCOPE and CLM is narrowing - can the authors explain why this might be happening?

We are unsure about what the reviewer means by "narrowing gap" between SCOPE and CLM in Table 2. Table 2 highlights that SCOPE consistently requires fewer admissibility checks compared to CLM across all our tasks. It would be great if the reviewer could provide additional details/clarification on this remark.

We thank the reviewer once again for supporting us in improving our manuscript.

We appreciate the time and effort taken to review our manuscript. The reviewer's feedback has highlighted areas where we can improve our explanations, and we are grateful for the opportunity to address all concerns.

Below, we address the listed weaknesses and questions one-by-one:

I find the empirical evaluation very difficult to asses both, on its own as well as in comparison to previous methods. To understand the effects of various parts of the proposed algorithms, it would be beneficial to perform ablation studies that could provide more insights into the effects of its individual components (e.g. the update function, the coverage level , etc.)

We agree. To provide insights into the effects of the various components, we have included comprehensive ablation studies in Appendix F (of the revised manuscript), analyzing different update functions, filter usage, and filter ordering. In the revised manuscript, we ensure these studies are more prominently referenced in the main text (specifically, in Section 5) to aid in assessment. Additionally, we have conducted new experiments with varying admissibility levels $\alpha \in \\{ 0.3, 0.35, 0.4 \\}$, which we have included in the revised manuscript.

I am not convinced about the benefits of the molecular example - when there is only one valid/admissable example, it seems to me that simple checking of the validity at the generation time for each generated specimen should be enough. I do not see the benefit of the proposed method in this setup. This also applies to the TriviaQA experiment.

To clarify, admissibility of the generated examples cannot be assessed at generation time for these tasks (and all other tasks). We can make this more concrete using TriviaQA: In the calibration set, the textual question correspecificallysponds to $x$ and the correct answer corresponds to $y^t$. The calibration set is a set of pairs $\\{ (x_i, y^t_i) \\}\_{i=1}^n$. This means that we can check for admissibility in the calibration set. At test time, however, admissibility cannot be checked. At test time, we only have access to the question $x_{n+1}$, but not the correct answer $y^t_{n+1}$. Thus, answers cannot be checked for admissibility. We have added a footnote on page 3 to clarify this point.

The algorithm requires an independent calibration set which seems to be very difficult to obtain in practice

In many real-world scenarios, calibration sets can be effectively obtained: For data sets where admissibility corresponds to an exact match, the calibration set can simply be obtained by setting some data aside from the training set. If admissibility does not correspond to an exact match (such as for a radiology report), admissibility should ideally be evaluated by a human domain-expert. While this is indeed costly, our method makes a great improvement over prior work, as clearly demonstrated in our experiments (see subsection 5.2).

In the presented experiments either boils down to something very trivial (single example being the valid one) or relying on another model which itself may be of uncertain quality.

As mentioned earlier, admissibility cannot be assessed at generation time, making our method essential even when only one valid example exists. In theory, this admissibility function can be any function, and the guarantee will hold for that specific function (as given by a machine or human). We use automated admissibility checks for experimental purposes only (see first paragraph of section 5.1). In practice, we believe that admissibility must be assessed by a human domain expert to prevent such uncertainty in the quality.

Further, I see similar issue with the update and filter functions which seem difficult to formulate reasonable in realistic scenarios

We demonstrate our method in the context of radiology report generation (Section 6, experiment 2), which is a highly relevant and realistic application/scenario. The same functions can be applied in different domains such as summarizing news articles (experiment 3), without requiring reformulations. We hope that this explanations clarifies concerns about the practicality in realistic scenarios and are happy to get back to this point if not.

The main text of the paper (section 9) spills over to page 11. As per the call for papers, there is a strict 10 page limit on the main text and the call suggests a desk reject in case of violations of this limit.

We assure the reviewer that the main text ends on page 10. The content on page 11 is the reproducibility statement, which complies with the conference guidelines and does not count towards the page limit. We cite the ICLR 2025 Author Guidelines:

This optional reproducibility statement will not count toward the page limit, but should not be more than 1 page.

Dear authors, thank you for your responses. Some further thoughts.

• Ablations - thank you for these. Yes, these indeed provide some additional useful insights. The Scope-Gen gen only seems to perform very well and I believe it would be worth to provide the reader with more info to help understanding, what's happenning. Why do you explore the addmissibility level in such a narrow interval (0.3-0.4)? Would significantly lower or higher values behave similarly? I may have missed it but is there any conclusion / recommendation for the count/sum/max measures?
• Admissibility - ah, I see, ok
• How to obtain calibration sets - would be worth mentioning in the main text
• Trivial problems - ah, I see, ok
• Update and filter funcitons - ok
• Human evaluation - ok
• quantile - ok
• post-evaluation - good.

I appreciate the clarificaitons and I find that the updates improved the paper. I have increased my score to weak accept.

We are happy to hear that the reviewer appreciates our clarifications. We would like to add three more remarks regarding the response:

Yes, these indeed provide some additional useful insights. The Scope-Gen gen only seems to perform very well and I believe it would be worth to provide the reader with more info to help understanding, what's happenning.

We have included a brief dicussion about the additional experiments in Appendix F.2. There exists another SCOPE-Gen configuration that works better in terms of minimizing prediction set size for MIMIC-CXR and CNN/DM, at the cost of slightly more required admissibility checks. We have decided to include this "configuration 2" in the experiments of our revised manuscript.

Why do you explore the addmissibility level in such a narrow interval (0.3-0.4)? Would significantly lower or higher values behave similarly?

Much lower admissibility levels would not behave similarly, because the performance of the underlying model sets a limit on which admissibility levels are theoretically possible to achieve. For example, if a model does not achieve a single admissible answer within the $`max`$ amount of tries for more than $30 \\%$ of questions, we see that admissible sets cannot be achieved for level $\alpha < 0.3$, independent of the method that is used. Thus, setting $\alpha$ even lower will result in rejected calibrations, as outlined in Section 4.2. We thus decided to only demonstrate a range for $\alpha$ that is theoretically achievable across all experiments. We decided to elucidate on this point in Appendix F.2 of our revised manuscript. We thank the reviewer for bringing this to our attention.

I may have missed it but is there any conclusion / recommendation for the count/sum/max measures?

We thank the reviewer for this question. In general, the optimal non-conformity measure depends on the experiment and admissibility level. It is thus difficult to make a general recommendation. We decided to include a small discussion around this point in Appendix F.2, using the experimental results.

We appreciate the time and effort taken to review our manuscript. We are glad to incorporate the comments and suggestions into the revised version.

We address the listed weaknesses and questions one-by-one:

The paper lacks a theoretical analysis detailing how effectively the proposed method reduces the required admissibility checks and prediction set size.

We note that the amount of required admissibility checks is upper bounded by the amount of checks required for CLM. Regarding theoretical analysis, we observe that the mentioned effectiveness depends highly on the used non-conformity measure. Thus, a theoritical analysis is likely to be bounded to a very specific setting without possibilities for generalization.

The sequential generation and filtering process may introduce additional computational costs by generating a large number of samples before the filtering stage.

We appreciate the reviewer's correct observation. Although the filtering process does introduce a computational overhead over standard i.i.d. sampling, we believe it is justified by the significant advantages it offers. The filtering step enables our method to work with any generative model (generating i.i.d. samples) without requiring modifications to the model architecture, thus providing broad applicability.

If avoiding computational cost is of great importance, one potential strategy would be to adjust the sampling parameters of the generative model. For instance, sampling from a language model at a lower temperature can reduce the generation of low-quality examples. Additionally, existing methods for generating diverse (non-i.i.d.) prediction sets (e.g., [1, 2]) could be integrated with our approach. In such cases, the filtering steps will remove fewer examples, while still maintaining the admissibility control guarantee.

We recognize the trade-off between computational cost and generality of our method. To address this point, we have incorporated a discussion paragraph called "Computational Demand vs. Generality" (Appendix I) of the revised manuscript. We thank the reviewer for bringing this important point to our attention.

The calibration process, which involves sample splitting for generation and each filtering stage, may require extra ground-truth samples to determine accurate threshold (lambda) values.

This is a good point and it is discussed in Section 7 (now Appendix I in the revised manuscript). However, we would like to stress that our method tends to yield better empirical results than prior work, in spite of data splitting. Considering the vast amount of data required to train/fine-tune a generative model, we believe that setting aside a data sample of size around $n=600$ should not be of significant practical concern.

[1] Corso, Gabriele, et al. "Particle Guidance: Non-IID Diverse Sampling with Diffusion Models." International Conference on Learning Representations (2023).

[2] Vilnis, Luke, et al. "Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models." International Conference on Machine Learning (2023).

We appreciate the time and effort taken to review our manuscript. We are delighted to hear that you appreciate the novelty and clarity of our work. We address the mentioned weaknesses and questions one-by-one:

There are now a bunch of papers on using conformal wrappers for filtering long form generations by dividing them into segments and then scoring. I think it would have been great to evaluate on such tasks as well, as generally QA type tasks are a bit too easy.

We thank the reviewer for pointing out these interesting concurrent related works. We are happy to incorporate them into our manuscript and discuss their relationship to ours. We see that these conformal wrappers are beneficial for long text responses. However, a critical assumption for such methods to be practical is that text responses indeed consist of multiple distinct claims with little coherence, so that the returned text response is meaningful and assessable without the removed claims. This assumption may not hold in the context of QA tasks, where responses typically need to be more coherent and holistic and cannot be divided into sub-claims. We incorporated this discussion into our related work section (Section 6).

Sampling multiple times and expecting a correct response can be quite compute-intensive.

We thank the reviewer for raising this aspect to our attention. This is a good point. We have incorporated an additional paragraph to our discussion section (Appendix I in the revised manuscript), where we discuss this aspect and sketch architecture-specific measures that may reduce the computational cost during inference, in comparison to i.i.d. sampling. During calibration, we note that SCOPE-Gen is vastly more efficient than the most similar existing approach to ours (CLM). We have also added a sentence to elevate this point in our results section (Section 5.2).

We furthermore address the reviewer's questions:

I might have missed it, but do at least a fraction of the experiments report some kind of human evaluation? I think to validate the method, at least some of it might be reasonable. While using another generative model (as a judge or to generate a calibration set) is popular, it still presents an incomplete analysis.

We agree with the reviewer. However, such an endeavor requires extensive collaboration with domain experts, which is beyond the current scope. The present work is meant as a methodological contribution. We note that the admissibility control guarantee holds irrespective of what (or who) the admissibility function is. We are, however, in the process of initiating a partnership with medical professionals to apply our method in real-world settings involving human evaluations. We plan to explore this in future work and believe that our current study lays the essential groundwork for these applications.

The authors might also want to discuss the works on conditional language validity by Cherian https://arxiv.org/abs/2406.09714 and also the earlier work by Mohri and Hashimoto https://arxiv.org/abs/2402.10978. Further, there is also a literature on confidence scoring which is often used for fine-tuning and reducing hallucinations. e.g. Kuhn et al. https://arxiv.org/abs/2302.09664, Lin et al. https://arxiv.org/abs/2305.19187, Wang and Holmes https://web3.arxiv.org/abs/2406.05213. It would be useful to include a brief discussion of these and how conformal methods might be used to calibrate such scores. It would help to bridge the two somewhat separate lines of enquiry together.

We thank the reviewer for pointing out these works to us. As mentioned earlier, we have included the mentioned works about conformal wrappers that chunk long answers into smaller claims in the revised version of our manuscript (see Section 6). Regarding the mentioned non-conformal methods, we decided to incorporate them into our discussion section (now Appendix I) as an additional paragraph called "Reducing Hallucination without Guarantees", because the relation is somewhat speculative and more of a venue for future work.

We sincerely thank the reviewer for the insightful comments, which have helped us present a more comprehensive overview of the field.