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EpiCaR: Knowing What You Don't Know Matters for Better Reasoning in LLMs

Jewon Yeom, Jaewon Sok, Seonghyeon Park, Jeongjae Park, Taesup Kim

TL;DR

EpiCaR is proposed as a training objective that jointly optimizes reasoning performance and calibration, and instantiate it within an iterative supervised fine-tuning framework using explicit self-evaluation signals, achieving Pareto-superiority over standard baselines in both accuracy and calibration.

Abstract

Improving the reasoning abilities of large language models (LLMs) has largely relied on iterative self-training with model-generated data. While effective at boosting accuracy, existing approaches primarily reinforce successful reasoning paths, incurring a substantial calibration cost: models become overconfident and lose the ability to represent uncertainty. This failure has been characterized as a form of model collapse in alignment, where predictive distributions degenerate toward low-variance point estimates. We address this issue by reframing reasoning training as an epistemic learning problem, in which models must learn not only how to reason, but also when their reasoning should be trusted. We propose epistemically-calibrated reasoning (EpiCaR) as a training objective that jointly optimizes reasoning performance and calibration, and instantiate it within an iterative supervised fine-tuning framework using explicit self-evaluation signals. Experiments on Llama-3 and Qwen-3 families demonstrate that our approach achieves Pareto-superiority over standard baselines in both accuracy and calibration, particularly in models with sufficient reasoning capacity (e.g., 3B+). This framework generalizes effectively to OOD mathematical reasoning (GSM8K) and code generation (MBPP). Ultimately, our approach enables a 3X reduction in inference compute, matching the K=30 performance of STaR with only K=10 samples in capable models.

EpiCaR: Knowing What You Don't Know Matters for Better Reasoning in LLMs

TL;DR

EpiCaR is proposed as a training objective that jointly optimizes reasoning performance and calibration, and instantiate it within an iterative supervised fine-tuning framework using explicit self-evaluation signals, achieving Pareto-superiority over standard baselines in both accuracy and calibration.

Abstract

Improving the reasoning abilities of large language models (LLMs) has largely relied on iterative self-training with model-generated data. While effective at boosting accuracy, existing approaches primarily reinforce successful reasoning paths, incurring a substantial calibration cost: models become overconfident and lose the ability to represent uncertainty. This failure has been characterized as a form of model collapse in alignment, where predictive distributions degenerate toward low-variance point estimates. We address this issue by reframing reasoning training as an epistemic learning problem, in which models must learn not only how to reason, but also when their reasoning should be trusted. We propose epistemically-calibrated reasoning (EpiCaR) as a training objective that jointly optimizes reasoning performance and calibration, and instantiate it within an iterative supervised fine-tuning framework using explicit self-evaluation signals. Experiments on Llama-3 and Qwen-3 families demonstrate that our approach achieves Pareto-superiority over standard baselines in both accuracy and calibration, particularly in models with sufficient reasoning capacity (e.g., 3B+). This framework generalizes effectively to OOD mathematical reasoning (GSM8K) and code generation (MBPP). Ultimately, our approach enables a 3X reduction in inference compute, matching the K=30 performance of STaR with only K=10 samples in capable models.
Paper Structure (86 sections, 8 equations, 6 figures, 10 tables, 1 algorithm)

This paper contains 86 sections, 8 equations, 6 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Iterative Reasoning & Self-Improvement
  4. Calibration Cost & Alignment Tax
  5. Calibration & Uncertainty Estimation
  6. Preliminaries
  7. Problem Formulation and Verbalized Confidence
  8. Evaluation Metrics: Calibration and Discrimination
  9. The Epistemic Cost of Iterative Training
  10. Methodology
  11. Iterative Dual-Loop Framework
  12. Internalizing Evaluation Task
  13. Adaptive Injection Decoding (AID)
  14. Experimental Setup
  15. Datasets
  16. ...and 71 more sections

Figures (6)

  • Figure 1: Pareto-Superior Improvement in Reasoning and Reliability. We visualize the relative improvement in reasoning accuracy ($\Delta$ Accuracy, %) and reliability ($\Delta$ ECE reduction) compared to the base model (at the origin). Solid and dashed arrows represent the trajectories of our proposed EpiCaR and the STaR baseline, respectively. While standard iterative SFT often incurs a trade-off (Calibration Cost Zone), our method consistently drives diverse model families (Llama-3 and Qwen-3) into the Pareto-Superior Zone, achieving simultaneous gains in both task performance and uncertainty calibration.
  • Figure 2: Inference-time Scaling on MATH-500. Visual representation of ensemble accuracy across sample sizes $K$. Our framework paired with CISC achieves superior scaling efficiency, outperforming STaR and establishing a new frontier for compute-optimal reasoning.
  • Figure 3: Reliability Diagram: MATH (Standard). Comparison of calibration performance between the base model, STaR, and EpiCaR on the MATH dataset.
  • Figure 4: Reliability Diagram: MATH (Slow Thinking). Visualizing how internalized calibration interacts with inference-time "slow thinking" behaviors.
  • Figure 5: Reliability Diagram: GSM8K (Zero-Shot). Evaluation of epistemic uncertainty calibration in an out-of-distribution mathematical reasoning context.
  • ...and 1 more figures