We thank the reviewer for recognizing the general usefulness of our task formulation and for commending our evaluation design. We'll now clarify some remaining confusions about the experiment designs.

1. Encoder Baseline and Regression Setup

RoBERTa-Large baseline: This serves as a strong ecoder-only baseline. Trained solely on UNLI, it processes the concatenation of the premise and hypothesis, and maps the [CLS] embedding through a linear layer to produce a scalar probability prediction.

Although our decoder models predict a categorical distribution over quantized bins, we ultimately compute the expected value under this distribution (via the Expected Label Scoring Rule) to obtain a scalar score, This makes it a regression model capable of predicting fine-grained probability scores, ensuring a fair comparison against encoder-only models with a regression head.

2. Does Simple Aggregation Suffice?

While rerunning all experiments with mean aggregation would be expensive, we can share observations that motivated our choice to include an LLM-judge. Two of the main authors have manually annotated 3-way preferences (win-loss-tie) on a small WANLI subset (50 examples ). We selected WANLI because its examples are shorter, contain more relevant premise–hypothesis pairs, and are easier for humans to understand. On this subset, we observed that the simple average and the LLM-as-a-judge methods produced large discrepancies in probability estimates (greater than 0.3). For each example, the two probabilities are randomly shuffled to avoid positional bias. We found a slight agreed preference of LLM-as-a-judge over simple average (win rate of 56%). Qualitatively, observing these examples we found that LLM-as-a-judge makes the distribution sharper and sometimes effectively down-weighted obviously incorrect responses.

3. Training Without Human-Annotated Ground Truth

We thank the reviewer for this thoughtful suggestion. As discussed in Section 5, there appears to be a distribution mismatch between human and LLM-generated labels. Building on prior work that focuses on aligning model uncertainty with human subjective uncertainty [1,2], we consider it a key objective for our model’s uncertainty estimates to reflect human belief. As noted in our general response, this alignment is essential for downstream tasks such as decision making and for building agents that understand the world in ways similar to humans. We view high-quality human labels (Please refer our detailed discussion regarding label quality to reviewer YjWc) as a critical resource in achieving this goal.

4. Concern on error introduced during the summary process

We thank the reviewer for their suggestion and propose to evaluate final score consistency before and after summarization. We achieve a spearman correlation of 0.984 on QwQ reasoning chains and nearly 1 spearman correlation on Deepseek’s reasonales, demonstrating high alignment between original and summarized reasoning chains.

5. Function of f(.)

Your understanding is very accurate. We use the center of each bin to convert the bins into scalars.

6. Meaning of mixture distribution

Thank you for pointing this out. We agree with the reviewer that q(t|x) might be a more consistent notation. We’ll make sure this gets updated in the next version, together with other writing improvements as discussed by the reviewer.

7. “Further Review”

Thank you for pointing this out. By further review we just mean that the LLM Judge will be used to compute confidence for these instances. We’ll make sure these will be made clear in the future. Also we would like to clarify that if an instance passes the discrepancy filter, all scores will be aggregated uniformly.

8. “Removing Modality“

EntailmentBank is originally proposed as a dataset of explanation trees where each inference step can be fully grounded. We extract probabilistic inference steps by removing modalities (possibly, necessarily, likely) and quantifiers (any, exists) etc. We’ll provide some examples in the appendix.

Reference

[1] Zhengping Jiang, Anqi Liu, and Benjamin Van Durme. Addressing the binning problem in calibration assessment through scalar annotations. Transactions of the Association for Computational Linguistics, 12:120–136, 2024a.

[2] Tongfei Chen, Zhengping Jiang, Adam Poliak, Keisuke Sakaguchi, and Benjamin Van Durme. Uncertain natural language inference. In Dan Jurafsky, Joyce Chai, Natalie Schluter, and Joel Tetreault (eds.), Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pp. 8772–8779, Online, July 2020. Association for Computational Linguistics. doi: 10.18653/v1/2020.acl-main.774. URL https://aclanthology.org/2020.acl-main.774.

We thank the reviewer for their thoughtful feedback. However, we feel that there are some misalignment between what the main contributions of our works are, and how our experiments support our main research claims. We would like to kindly clarify regarding these two points.

1. Novelty and Contribution:

We respectfully clarify that while some of the methods in the paper are indeed unique (e.g., synthetic data creation), we consider the main contribution extends beyond methodology. A major contribution of the work is also about pinpointing this important but understudied problem of localized conditional probability inference and present an artifact that pushes the performance significantly beyond widely adopted solutions (ask-for-calibration, t/f logits as shown i n our additional experiments) We hope that through careful discussion of a highly effective training recipe and a comprehensive evaluation suite, we will motivate future research on realizing and studying the potential of LLM as a general probability estimator, which we believe can be a critical step in LLM reasoning. This work is not simply about proposing new methods. It is a task-driven study, anchored in practical needs for modeling uncertainty, and contributes tools, data, and benchmarks that the community can build upon.

2. Effectiveness of Synthetic Data:

We respectfully disagree with the reviewer’s assessment that synthetic data is helpful solely because it facilitates in-domain training. We carefully designed our evaluation suite to test generalization. The synthetic data is derived from ANLI and WANLI, totaling ~26k examples, which we specifically chose to be distinct from test data in our evaluation suite. In fact many of the tasks in our evaluation suite has very different data and label source and formulation from traditional NLI datasets, and the fact that our model can be applied to very different tasks like comparison and graph-based belief probabilistic inference effectively is a strong evidence of the wide-applicability of our problem formulation, as well as the generalizability of our model.

We acknowledge the ambiguity between "distillation" and "synthetic generation" in terminology. Our approach sits between both: we reuse existing input queries (like premises/hypotheses) but prompt LLMs for step-by-step reasoning on conditional probability. This process then allows us to synthesize final probabilistic labels that differ significantly from original categorical labels, enabling richer supervision and demonstrating that our method isn't merely a distillation process.

To further elaborate on our synthetic data construction and its motivation, we first illustrate the quality of initial LLM estimations. Here's the Spearman correlation with human annotations on the UNLI test split for the four models we used:

Despite individual model estimations not fully aligning with human annotation, we observed that the aggregation of agreement results increases performance. This insight directly motivated our agreement-based filtering strategy:

Subsequently, we apply a confidence-aware aggregation pipeline to assess the probability labels. We found that the LLM-as-a-judge approach sharpens the distribution and effectively down-weights obviously incorrect responses. For more details on this, please refer to our second discussion with Reviewer eG4a.

Thanks for your invaluable suggestions! Your feedback has been crucial in improving the quality of our paper. Let me address your concerns below.

1. Clarify the details of Synthetic data construction

Here are some key clarifications regarding our synthetic data construction:

• Prompts used to elicit probabilities from LLMs are included in Appendix C.
• For each example, we query four LLMs, two instruction-tuned models and two reasoning-augmented models, to independently generate probability estimates (see lines 298–300).
• Agreement-Based Filtering is performed at the example level. For a given input, if the range of predicted probabilities exceeds a predefined threshold, the example and all its associated reasonings are flagged for further review.
• Further review involves re-evaluation by a separate reasoning-enhanced LLM, which acts as a judge model. We choose DeepSeek-R1-Distill-Qwen-32B for its strong correlation with human judgments on UNLI and instruction following ability. This step ensures we select high-confidence pseudo-labels with high-quality rationale, and no human annotation is involved in this process.

2. Missing discussion with model calibration methods

We implement the True / False probing [1] and Thermometer calibration method [2]. The general ideas are simply decoding true and false logits then calibrated with temperature scaling. Results shows it does not always provide high correlation with humans, especially in comparison evaluation. Furthermore, since temperature scaling applies a monotonic change to output logits, it offers no benefit for ranking-based metrics like Spearman Correlation. Please refer to Overall Response Experiment (1) for more information.

Reference

[1] Tian, Katherine, et al. "Just ask for calibration: Strategies for eliciting calibrated confidence scores from language models fine-tuned with human feedback." arXiv preprint arXiv:2305.14975 (2023).

[2] Shen, Maohao, et al. "Thermometer: Towards Universal Calibration for Large Language Models." arXiv preprint arXiv:2403.08819 (2024).

Thank you for your thoughtful and constructive review. We appreciate your engagement with our work and address each of your concerns below:

1. Connection between LLM Regression and Uncertainty Calibration

As we discussed in our general response, the specific regression task that we formulate here is closely related to instance-wise-calibration. We want to reiterate that our formulation is more general than calibrated classification. additional Experiment (1), Table 1, clearly shows that simple post-hoc calibration is not sufficient for our task, while Experiment (2) shows that our approach directly induces more calibrated classifiers for unseen tasks. Our formulation empowers LLMs to directly reason about uncertainty in continuous outcome spaces, leveraging their commonsense and linguistic knowledge.

2. On the Use of "Well-Calibrated Probabilistic Predictions"

We acknowledge that achieving truly calibrated probability estimates, especially in subjective reasoning tasks, is a significant challenge. Nevertheless, previous studies offer compelling evidence supporting the quality of UNLI annotations:

• UNLI annotations have been carefully curated with strict qualification criteria and detailed hyperparameter tuning. [2]
• UNLI labels have been shown to correspond very well to more traditional classification calibration notions in ChaosNLI [1]
• Subjective probability annotation can be significantly improved through annotator quality control [1], and careful interface design [5]

3. "Real-World" Application of Our Model

We appreciate the desire to see more directly applied decision-making tasks. While our benchmark tasks are drawn from standard datasets, they are structured to reflect real-world belief modeling workflows:

• Intrinsic Evaluation involves estimating probabilities for uncertain claims.
• Comparison Evaluation simulates defeasible reasoning—deciding between competing hypotheses.
• Structural Evaluation involves multi-step probabilistic reasoning and is designed to emulate real-world decision-making workflows, such as multi-hop question answering and scientific claim verification. This serves as a downstream application for our model by introducing uncertainty during the reasoning process. For instance, we assess commonsense and temporal reasoning capabilities on the Bayesian inference framework BIRD [4].

4. Conditional Probability Estimation Task

We emphasize that our framework is general-purpose and not limited to NLI. As noted in Section 3.1, conditional probability estimation is broadly applicable, for example, in information-seeking, risk assessment, or legal reasoning. Prior work often limits regression to function approximation (e.g., curve fitting) [3]; our work extends it to reasoning under uncertainty in open-domain texts.

5. Suggestion for Writing

• The “textual outcomes” in line 128 refer to individual claims or propositions over which probabilities are estimated.
• In line 213, “token” refers to the special bin-associated tokens used for label discretization during training.
• Typos such as “LLMyielding” will be corrected in the final revision.
• We will revise Table 1’s caption to explain the metric types, and the meaning of bold and underline (first and second place, respectively). We compute Spearman Correlation for intrinsic tasks and classification metrics for Comparison and Structural Reasoning tasks [lines 270, 295].

6. Statistic of Synthetic Data

We generated synthetic data on the UNLI test split (3040 examples) and found a high correlation with human annotations. Our method even surpassed the average performance of five GPT-4o runs using the same prompting. We also observed that the correlation of aggregated results on the UNLI test set increases as the discrepancy among LLMs decreases. For further verification on how "LLM-as-a-judge" improves over simple score averaging, please refer to our response to Reviewer eG4a.

We thank the Area Chair for the thoughtful reminder. As the end of the rebuttal period approaches, we sincerely encourage the reviewers to share their feedback and insights on both our submission and response.