Reliable confidence is essential for trusting the outputs of LLMs, yet widely deployed post-trained LLMs (PoLLMs) typically compromise this trust with severe overconfidence. In contrast, we observe that their corresponding base LLMs often remain well-calibrated. This naturally motivates us to calibrate PoLLM confidence using the base LLM as a reference. This work proposes two ways to achieve this. A straightforward solution, BaseCal-ReEval, evaluates PoLLM's responses by feeding them into the base LLM to get average probabilities as confidence. While effective, this approach introduces additional inference overhead. To address this, we propose BaseCal-Proj, which trains a lightweight projection to map the final-layer hidden states of PoLLMs back to those of their base LLMs. These projected states are then processed by the base LLM's output layer to derive base-calibrated confidence for PoLLM's responses. Notably, BaseCal is an unsupervised, plug-and-play solution that operates without human labels or LLM modifications. Experiments across five datasets and three LLM families demonstrate the effectiveness of BaseCal, reducing Expected Calibration Error (ECE) by an average of 42.90% compared to the best unsupervised baselines.
Meta Review of Submission1065 by Area Chair mamp
This paper addresses overconfidence in post-trained LLMs by leveraging better-calibrated base-model signals. It proposes BaseCal: (1) ReEval, rescoring PoLLM answers with base-model token probabilities; (2) Proj, training a lightweight projection from PoLLM final-layer states to the base-model space and using the base head for low-cost confidence. Results on QA benchmarks (TriviaQA, NQ, SQuAD, WebQ; MMLU) reduce ECE vs. unsupervised baselines. However, this paper misses hallucination-specific challenge benchmarks weakens direct hallucination claims.
This paper gives a simple, practical way to make post-trained LLM confidence scores less overconfident by “borrowing” calibration from the base model. It works without labels, model changes, or expensive sampling, and shows solid ECE improvements across multiple QA benchmarks and model families—useful for safer, more reliable deployment.
Focus revisions on adding hallucination-specific benchmarks beyond standard QA: include TruthfulQA/HaluEval-style, adversarial and unanswerable questions, and grounded QA. Report not just ECE/Brier but also risk–coverage and abstention gains, plus breakdowns by hallucination type (fabricated facts, out-of-context claims, self-consistent errors).
Summary of the Discussion Phase for Submission1065
Dear (S)ACs,
We sincerely appreciate your time and dedication to the ACL community and the peer-review process. Below, we provide a brief summary of the rebuttal and the key points of our responses.
We are encouraged that all reviewers acknowledged the strengths of our work:
Method: "simple and intuitive, yet reasonable and effective" (#1 S1), "efficiency" (#2 S3), "easier to apply " and "practical" (#3 S2 S4)
Experiments: "thorough and solid" (#1 S1), "thorough" (#3 S3), and "strong empirical performance" (#2 S1)
"Novel insight" (#2 S2), "clear and intuitive idea" (#3 S1)
"Clear writing and easy to follow" (#1 S1)
We have actively engaged with all reviewers' feedback and provided substantial evidence to address their concerns. The main revisions and additional experiments are summarized as follows:
- Expanded Task Scope (#2 W1 W2 W3, #3 Suggestion 1)
- We clarify that our work primarily focuses on factual QA, aligning with mainstream calibration research, and our original experiments have been explicitly valued as "thorough" (#3, #1). While we note that ARR Guideline H13 generally considers the task beyond a paper's scope as "suggestions" rather than "reasons for rejection", we took this feedback seriously and addressed these suggestions with additional experiments.
- We conducted additional experiments on complex reasoning (MATH) and long-form generation (BioGen), and explored various aggregation methods for these tasks. These results further demonstrated the effectiveness and extensibility of our methods.
- Cross-Model Baselines (#1 Suggestion 1)
- We additionally extended existing baselines to cross-model variants and showed that our methods still significantly outperformed these enhanced baselines.
- Reliability of LLM-as-a-Judge (#3 W3)
- We conducted a human study that showed a 99% agreement rate between our automated judge and human annotators (Appendix A.2), confirming the reliability of our judgment.
- Downstream Utility (#3 W4)
- We demonstrated that the calibrated confidence obtained from BaseCal can substantially reduce error rates in downstream selective answering (Section 5.6), proving its practical value for risk-sensitive applications.
While we did not receive further replies during the discussion phase, we believe our additional experiments and detailed responses have resolved the reviewers' concerns. Given these points, we respectfully request that our rebuttal and contributions be considered in the meta-review process. We sincerely trust the (S)ACs’ judgment in ensuring a fair evaluation, and greatly appreciate your attention to these matters.
Best regards,
Authors
Official Review of Submission1065 by Reviewer #1
Inspired by prior work showing that base LLMs can retain superior calibration properties, the authors propose an unsupervised, plug-and-play framework for calibrating preference-optimized LLMs (PoLLMs). Two calibration strategies are introduced: (1) directly using confidence scores estimated from the base model for each sampled output, and (2) learning a lightweight linear projection that maps the logits of the fine-tuned LLM to the final-layer space of the base model, thereby reducing the inference cost associated with repeatedly querying the base model. Experimental results demonstrate that the proposed framework is highly effective and substantially mitigates overconfidence across diverse datasets, model scales, and existing post-training strategies.
- The paper is clearly written and easy to follow. The proposed methods are simple and intuitive, yet reasonable and effective.
- The experimental evaluation is thorough and solid. The authors validate the effectiveness of their approach from multiple perspectives, across different LLM families and a variety of task types.
There are no major issues, but some minor notation errors that do not affect the main contributions.
- The function
- Although the framework avoids repeated base-model inference at test time, training the lightweight mapping still requires passing data through the base model, which incurs substantial computation. In this sense, the computational burden is shifted rather than entirely eliminated.
The construction of
There are no concerns with this submission
Response to reviewer #1
Dear Reviewer #1,
We sincerely appreciate your constructive review and supportive score. We are encouraged that you found our approach intuitive, reasonable, and effective, and that you valued the solid experiments and clear writing.
W1. Notation problems in Equations (1) and (3)
Thanks for pointing out the notation issues. We have fixed them in the revised manuscript. Specifically, in Eq. (1), we define
W2. The compute cost at test time is shifted to training rather than removed.
We agree that the computational burden is shifted to training rather than removed. We will refine our description to be more accurate.
This is a deliberate design trade-off: we prioritize inference-time efficiency, as inference latency directly affects user experience and deployment. In contrast, the offline and one-time training cost does not impact deployment and is entirely acceptable. Moreover, our training cost is minor, as BaseCal-Proj only requires about 3k questions for training and only updates the parameters of a lightweight projection layer.
S1. Self-assessment may be a source of overconfidence in P(True). Comparing with baselines using a third-party model to provide confidence.
Thank you for this constructive suggestion. We conduct cross-model variants of the P(True) and Verbalization baselines, where a third-party model provides confidence estimates. Concretely, for responses generated by Llama3.1-8B-Instruct, we use Qwen2.5-7B-Instruct to compute confidence, yielding P(True) w/ Qwen and Verbalization w/ Qwen. (It is inappropriate to utilize base models for these cross-model baselines, given their reliance on instruction-following capacities [1].)
From the results in the following table, we draw two findings:
(1) A third-party model slightly reduces miscalibration. Your intuition is correct: Using a third-party model (Qwen) generally lowers the ECE compared to self-assessment, confirming that cross-model estimation mitigates part of the self-overconfidence.
(2) Our method remains significantly better than these cross-model baselines. In this setting, the cross-model baselines use a third-party model to produce confidence, which helps avoid the potential overconfidence induced by self-assessment. Even comparing with them, both BaseCal-Proj and BaseCal-ReEval still achieve substantially lower ECE, supporting our core insight that the base model serves as a strong reference to calibrate PoLLMs.
| method | WebQ (ECE) | TriviaQA (ECE) |
|---|---|---|
| P(True) | 0.4581 | 0.2476 |
| P(True) w/ Qwen | 0.3977 | 0.2239 |
| Verbalization | 0.3565 | 0.1769 |
| Verbalization w/ Qwen | 0.3433 | 0.2151 |
| BaseCal-Proj | 0.2091 | 0.0387 |
| BaseCal-ReEval | 0.1873 | 0.0309 |
[1] Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback. EMNLP 2023
We hope these clarifications have fully addressed your concerns. If you have any further suggestions, please feel free to reach out.
Official Review of Submission1065 by Reviewer #2
The paper addresses the overconfidence problem inherent in post-trained large language models (PoLLMs), which often assign high probability to incorrect responses. Based on the observation that base LLMs remain well-calibrated compared to their post-trained counterparts, the authors propose BaseCal, an unsupervised framework that uses the base model as a reference.
The framework consists of two methods:
- BaseCal-ReEval: A direct approach that re-evaluates PoLLM responses by feeding them into the base model to obtain average token probabilities as confidence scores.
- BaseCal-Proj: A more efficient approach that trains a lightweight linear projection to map PoLLM final-layer hidden states back to the base model's representation space. The projected states are then passed through the base model’s output layer to derive confidence. Experiments conducted on five datasets and three model families (Qwen, Llama, Olmo) demonstrate that BaseCal reduces the Expected Calibration Error (ECE) by an average of 42.90% compared to existing unsupervised baselines.
- Strong Empirical Performance: BaseCal consistently outperforms unsupervised baselines like Verbalization and Semantic Entropy across three major model families (Qwen, Llama, Olmo) and five diverse benchmarks
- Novel Insight: The paper identifies that base models retain superior calibration signals that are recoverable even after post-training.
- Efficiency: BaseCal-Proj is particularly efficient, introducing negligible inference overhead by only having a single auxiliary layer.
- Inappropriate Scope of Claims: While the paper aims to enhance calibration for "general QA tasks," the experimental evaluation is strictly limited to short-form QA benchmarks (TriviaQA, NQ, SQuAD, WebQ) where models are explicitly prompted to "answer the question briefly". The effectiveness of the proposed signals in more complex, open-ended scenarios remains unproven.
- Limited Task Generalization of Averaging Strategy: The methodology relies on average aggregation of all token probabilities to derive a single confidence score for the entire response. This approach is inherently ill-suited for creative writing or long-form generation, where a response may contain a mixture of factual and hallucinated segments. The current "all-or-nothing" confidence score lacks the granularity required to identify localized errors in long-form or complex reasoning tasks.
- Uncertainty in Reasoning and Complex Tasks: Beyond simple fact-retrieval, there is no evidence that the simple mapping or averaging approach can effectively capture the calibration requirements for multi-step reasoning or highly creative tasks. The reliance on such a simple aggregation strategy without testing on diverse task categories leaves a significant gap in the framework’s claimed general-purpose utility.
- Fine-grained Evaluation: To better support the claim of general QA calibration, the authors should test the framework on long-form generation datasets. Specifically, I suggest implementing a sliding window aggregation or sentence-level scoring to determine if BaseCal can pinpoint specific hallucinations within a longer text rather than just scoring the entire sequence.
- Task Diversity: It would be beneficial to include tasks beyond fact-retrieval, such as summarization or logical reasoning, to verify if the base model's calibration signals remain superior and recoverable across different cognitive demands.
There are no concerns with this submission
Seeking your valuable feedback on our response
Dear Reviewer #2,
We hope this message finds you well.
We are deeply grateful for your thorough review. We have provided detailed clarifications and additional experiments in response to your valuable feedback.
As the discussion period draws to a close, we would like to hear your thoughts on our response, including whether it adequately addresses your concerns. If you have any updated thoughts, we would be grateful to hear them.
Thank you again for your time and insightful engagement.
Best regards,
Authors
Response to Reviewer #2 (1/2)
Dear Reviewer #2,
We sincerely appreciate your time and effort on our work! We are grateful that you acknowledge the strengths of our work, particularly in the novel insight, strong empirical performance, and method efficiency.
In the following response, we address your comments point-by-point, with similar questions and suggestions grouped together for clarity.
W1. Claim "general QA tasks," but only test on short-form QA with "answer the question briefly" prompts.
(1) Our original use of the term "general QA" was intended to contrast our free-form QA setting with the constrained "multiple-choice" format in prior calibration work [1]. We acknowledge that this terminology was too broad and have corrected it throughout the paper to avoid any possible confusion.
(2) Our evaluation follows the standard protocols of mainstream calibration research [2, 3, 4, 5], primarily focusing on factual (short-form) QA. This evaluation covers 4 widely adopted QA benchmarks and the MMLU dataset, which spans 57 different tasks (e.g., elementary mathematics, formal logic, etc.). We believe these diverse experiments are sufficient to support the scope of our study.
(3) To further mitigate your concern, we also validate our method with additional experiments on complex reasoning tasks with CoT prompts. See our response to “W3 & S2” for full details.
W2 & S1. Limited task generalization of the averaging strategy to the long-form generation task.
We thank the reviewer for highlighting the unique challenges of confidence calibration in long-form generation. We first clarify the scope of our contribution and then provide additional long-form generation results, as follows:
(1) Our primary goal is not to design a sophisticated aggregation strategy for long-form calibration. Instead, this work primarily focuses on the fundamental calibration task of factual QA, where the key problem is to estimate the LLM’s confidence for a specific fact. Factual QA is still an active and challenging problem, and remains the primary focus of current mainstream calibration works [2,3,4,5]. Aligning with them ensures a fair and direct validation of our methods against prior baselines.
(2) Although this work primarily focuses on factual QA, we have conducted an additional long-form experiment to address your concerns. By extending our method with a straightforward fact-level aggregation, we demonstrate its extensibility to long-form scenarios.
- Setup. We use the BioGen [8] dataset, which prompts LLMs to write long biographies. Similar to prior work [8,9], we use GPT-5.2 to extract atomic facts from the generated biography and verify each fact’s correctness based on retrieved documents. The goal in long-form generation calibration is to align fact-level confidence with fact correctness. Due to time constraints, we test Llama-3.1-8B-Instruct on a randomly sampled 20% subset of BioGen, totaling 633 facts.
- Fact-level confidence aggregation. Following [8], for each atomic fact, we locate the corresponding response segment (longest common substring) and use the average token probability over that segment as the fact confidence.
As shown in the table below, even with a simple fact-level aggregation, BaseCal-ReEval still improves calibration on long-form generation. This preliminary evidence suggests the signal of the base model remains beneficial in long-form settings. In future work, we will explore more suitable aggregation strategies for our method to further improve calibration in long-form generation.
| Method | ECE | BS |
|---|---|---|
| Vanilla | 0.4156 | 0.3323 |
| BaseCal-ReEval | 0.4036 | 0.3210 |
Case study. The following table shows the extracted facts and their confidence scores. For an incorrect fact, BaseCal-ReEval assigns lower confidence than Vanilla; for a correct fact, it assigns higher confidence.
- Generated biography: "Waka Flocka Flame, born Donald Verrus Figgins Jr., is an American rapper and entrepreneur. Born on March 12, 1986, ....."
| Fact | Correctness | BaseCal-ReEval Confidence | Vanilla Confidence |
|---|---|---|---|
| Waka Flocka Flame was born Donald Verrus Figgins Jr | False | 0.0303 | 0.0636 |
| Waka Flocka Flame is an American rapper and entrepreneur | True | 0.4726 | 0.4187 |
Response to Reviewer #2 (2/2)
W3 & S2. More diverse tasks, such as multi-step reasoning, and more aggregation strategies.
While our primary focus is on factual QA, which remains the standard and mainstream testbed for confidence calibration [2, 3, 4, 5], we acknowledge that extending our methods to reasoning tasks is an important direction.
To directly address your concern, we conducted additional experiments on the challenging MATH dataset [6], a standard benchmark for complex mathematical reasoning, and explored more aggregation strategies.
- Diverse aggregations: Following recent work on confidence aggregation for reasoning [10], we implement Tail Average Aggregation, which averages the probabilities over the last 25 tokens. Compared to the original strategy that averages over the entire responses, tail averaging focuses on the final step, which is often more critical for reasoning correctness.
- Experiment settings: To elicit long, multi-step reasoning, we prompted Llama-3.1-8B-Instruct with 5-shot CoT examples using the instruction: "Think step by step, and then provide the final result."
The results in the following table show:
- Our methods still bring significant gains in multi-step reasoning.
- Our approach shows consistent improvements across all tested aggregations, and the task-specific strategy Tail Aggregation further improves BaseCal-Proj, reducing ECE to 0.4015.
| Aggregation | Method | ECE | BS |
|---|---|---|---|
| Average | Vanilla | 0.4916 | 0.4738 |
| Average | BaseCal-Proj | 0.4452 | 0.4367 |
| Tail Average | Vanilla | 0.5213 | 0.4556 |
| Tail Average | BaseCal-Proj | 0.4015 | 0.3944 |
We hope these clarifications have fully addressed your concerns. If you have any further suggestions, please feel free to reach out.
Reference
[1] Your Pre-trained LLM is Secretly an Unsupervised Confidence Calibrator. NIPS 2025
[2] Annotation-Efficient Honesty Alignment via Confidence Elicitation and Calibration. ICLR 2026
[3] Towards Harmonized Uncertainty Estimation for Large Language Models. ACL 2025
[4] Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback. EMNLP 2023
[5] Detecting hallucinations in large language models using semantic entropy. Nature 2024
[6] Measuring Mathematical Problem Solving With the MATH Dataset. NIPS 2021
[7] Qwen3 Technical Report
[8] Factscore: Fine-grained atomic evaluation of factual precision in long form text generation. EMNLP 2023
[9] LitCab: Lightweight Language Model Calibration over Short- and Long-form Responses. ICLR 2024
[10] Deep Think with Confidence. Arxiv 2025
Official Review of Submission1065 by Reviewer #3
This paper addresses the problem that post-trained language models often express overly confident answers, even when they are wrong. It proposes using the corresponding base model as a reference to recalibrate confidence, either by re-evaluating the generated answer with the base model or by learning a small projection that approximates the base model’s confidence signal with little extra cost. Experiments across several models and question-answering datasets show that this approach substantially improves confidence calibration without requiring labels or modifying the original models.
- The paper introduces a clear and intuitive idea by using the base model as a reference instead of relying only on signals from the post-trained model.
- The method works without labelled data, which makes it easier to apply in settings where annotations are expensive or unavailable.
- Experiments are thorough and cover multiple models, datasets, and post-training methods, strengthening the empirical claims.
- The lightweight projection variant offers a practical trade-off between performance and computation cost.
- The approach assumes that base models are reliably calibrated in all settings, but this assumption is only tested on a limited set of tasks and models.
- The projection method requires access to internal model states and output layers, which limits its usefulness for closed or API-only models.
- Confidence quality is evaluated mainly with automatic judging, which may introduce noise or bias into the reported calibration results.
- The method focuses on calibration metrics and does not clearly show how improved confidence changes real downstream decisions or user outcomes.
- The added complexity of maintaining both base and post-trained models may reduce practicality in real deployment settings.
- Evaluate the method on more types of tasks to show it works beyond question answering.
- Provide stronger evidence that base models are consistently well calibrated in harder or different settings.
- Show more clearly how better confidence helps in real applications, such as deciding when not to answer.
- Investigate ways to apply the method without needing access to internal model representations.
There are no concerns with this submission
Response to reviewer #3 (1/2)
Dear Reviewer #3,
We sincerely appreciate your constructive review and supportive score. We are encouraged that you found our work clear and intuitive, appreciated its label-free applicability, and valued the thoroughness of our experiments.
In the following response, we address your comments point-by-point, with similar questions and suggestions grouped together for clarity.
W1 & S2. Assuming that base models are reliably calibrated in all settings, but only test on a limited set of settings.
(1) We appreciate the reviewer for highlighting the empirical premise behind our approach: base models commonly exhibit better calibration than post-trained LLMs (PoLLMs). Importantly, this is not an isolated assumption introduced by our work, but rather a phenomenon increasingly observed by recent works [1,2,3]. Multiple recent studies [1,2,3] have reported that post-training procedures such as instruction tuning and preference optimization tend to increase overconfidence relative to base models, suggesting that post-training may distort calibration.
Our contribution builds upon this widely observed phenomenon by proposing a practical mechanism to recover the calibration signal from base models to PoLLMs.
(2) We empirically verify this assumption across various settings, covering the multi-choice dataset MMLU and 4 widely used QA datasets following mainstream calibration works [4,5,6]. The tested model covers 3 model families (Llama, Qwen, and Olmo), multiple scales, and 3 different post-training strategies. Given the broad empirical support across diverse settings, together with the consistent finding in prior literature [1,2,3], we believe this premise is well supported within the scope of this paper. Identifying rare edge cases where it may fail is an interesting direction for future work.
[1] Restoring Calibration for Aligned Large Language Models: A Calibration-Aware Fine-Tuning Approach. ICML 2025
[2] Towards Objective Fine-tuning: How LLMs' Prior Knowledge Causes Potential Poor Calibration? ACL 2025
[3] Taming overconfidence in llms: Reward calibration in rlhf. ICLR 2025
[4] Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback. EMNLP 2023
[5] Towards Harmonized Uncertainty Estimation for Large Language Models. ACL 2025
[6] Detecting hallucinations in large language models using semantic entropy. Nature 2024
W2 & S4. The projection method requires access to internal model states and output layers, which limits its usefulness for closed or API-only models.
We thank the reviewer for raising this point. While we agree that users cannot access internal states through APIs, we argue that confidence estimation is fundamentally a backend feature to be deployed by Model-as-a-Service (MaaS) providers (e.g., OpenAI, Google) to ensure reliability, similar to "logprobs" provided in current APIs.
From the perspective of MaaS providers, both the base and post-trained models are internally accessible to them, where BaseCal-Proj is fully applicable. More importantly, BaseCal-Proj only adds a lightweight projection module and introduces negligible inference overhead at test time. This makes our method explicitly well-suited for high-throughput industrial deployment.
W3. Confidence quality is evaluated mainly with automatic judging, which may introduce noise or bias into the reported calibration results.
We thank the reviewer for pointing out that LLM-as-a-judge may introduce noise. To mitigate this concern, our work (i) follows the standard judging protocol in mainstream calibration works [7,8,9], and (2) conducted a human verification on 100 randomly sampled instances, achieving 99% agreement with human annotation (also shown in Appendix A.2). This further demonstrates the effectiveness of the judging in our task.
[7] Just ask for calibration: Strategies for eliciting calibrated confidence scores from language models fine-tuned with human feedback. EMNLP 2023
[8] LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations. ICLR 2025
[9] Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models. TMLR 2024
Response to reviewer #3 (2/2)
W4 & S3. How can better confidence help in real applications, such as deciding when not to answer?
In Sec 5.6, we have demonstrated that better confidence directly improves decision-making by abstaining when confidence is below a threshold. Here, we briefly summarize the key findings and results below (see Sec. 5.6 for full details).
The following table compares the error rate among accepted predictions across different confidence thresholds using Vanilla vs. BaseCal-Proj confidence. Across all thresholds, BaseCal-Proj yields a substantially lower error rate than Vanilla. This demonstrates that improved calibration directly translates into safer decision policies under selective answering.
| Threshold | Error rate (%) with Vanilla confidence | Error rate (%) with BaseCal-Proj confidence |
|---|---|---|
| 0.50 | 47.2 | 35.8 |
| 0.60 | 45.1 | 30.2 |
| 0.70 | 41.4 | 22.9 |
| 0.80 | 35.6 | 15.0 |
| 0.90 | 25.7 | 8.6 |
W5. The added complexity of maintaining both base and post-trained models may reduce practicality in real deployment settings.
We acknowledge that BaseCal-ReEval introduces some deployment overhead by maintaining the base model. However, this overhead is still smaller than the methods requiring multiple samplings [10].
To explicitly resolve this overhead, we further propose BaseCal-Proj, which does not require maintaining the base model during inference. Instead, it employs a lightweight linear projection to derive confidence from the PoLLM's final-layer hidden states. BaseCal-Proj serves as a highly efficient alternative to BaseCal-ReEval, achieving comparable performance with nearly negligible inference overhead. This makes it highly practical for real-world deployment settings.
[10] Detecting hallucinations in large language models using semantic entropy. Nature 2024
S1. Evaluate the method on more types of tasks to show it works beyond question answering.
Thanks for these constructive suggestions.
(1) We first clarify that our evaluation already extends beyond simple QA by including MMLU [11], a standard benchmark for assessing general LLM capabilities, which covers 57 diverse tasks (e.g., elementary mathematics, formal logic, etc.).
(2) As your suggestion, we add an experiment beyond question answering on the challenging mathematical reasoning task MATH [12]. We prompt the model with “Think step by step, and then provide the final result” using 5 CoT examples, which encourages long, multi-step reasoning. As shown in the following table, we find:
Our method shows significant improvements in the multi-step reasoning task. This further supports our core insight that the base model can serve as a strong reference to calibrate post-trained LLMs.
| Method | ECE | BS |
|---|---|---|
| Vanilla | 0.4916 | 0.4738 |
| BaseCal-Proj | 0.4452 | 0.4367 |
[11] Measuring Massive Multitask Language Understanding. ICLR 2021
[12] Measuring Mathematical Problem Solving With the MATH Dataset. NIPS 2021
We hope these clarifications have fully addressed your concerns. If you have any further suggestions, please feel free to reach out.