arxiv: 2604.16830 · v1 · submitted 2026-04-18 · 💻 cs.LG · cs.AI

Recognition: unknown

The Illusion of Certainty: Decoupling Capability and Calibration in On-Policy Distillation

Caiming Xiong, Chien-Sheng Wu, Jiaxin Zhang, Qinglin Chen, Qinyuan Ye, Xiangyu Peng

Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:41 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords on-policy distillationmodel calibrationoverconfidencelanguage modelspost-traininginformation mismatchself-distillation

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The pith

On-policy distillation boosts task accuracy but traps models in severe overconfidence due to an information mismatch between training and deployment.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that on-policy distillation improves task performance while causing systematic overconfidence in language models. The cause is that teacher supervision draws on privileged context available only during training, whereas the deployed model must assess its own confidence with strictly less information. A sympathetic reader would care because deployed systems require accurate uncertainty reporting for safety and reliability, not merely correct answers. The authors formalize why teacher-conditioned success is an invalid target for deployment confidence, as it induces entropy collapse and optimism bias. They introduce CaOPD to replace self-reported confidence with empirical confidence estimated from model rollouts and distill the revised targets through the existing pipeline.

Core claim

We identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that est

What carries the argument

The information mismatch between privileged teacher context during training and limited deployment-time information, which renders teacher-conditioned success an invalid target for confidence and produces optimism bias in the distilled model.

If this is right

OPD will produce models whose accuracy rises while calibration worsens as training or scale increases.
Gains in capability from distillation will not automatically yield accurate self-reported confidence.
CaOPD can maintain competitive task accuracy while reaching Pareto-optimal calibration.
The calibration gains of CaOPD extend to out-of-distribution inputs and continual learning settings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Any distillation method that supplies richer context at training time than available at deployment may separate capability gains from calibration.
Post-training pipelines could benefit from treating empirical confidence estimation as an explicit, separate objective.
The observed decoupling may help explain why some instruction-tuned models remain overconfident on factual errors.

Load-bearing premise

That empirical confidence estimated from model rollouts provides a valid and superior target for distillation that avoids the optimism bias without introducing new selection effects or variance issues in the confidence labels.

What would settle it

A controlled experiment in which CaOPD models still exhibit overconfidence on deployment tasks with limited context, or in which rollout-derived confidence targets show no calibration improvement over standard OPD, would falsify the proposed remedy.

Figures

Figures reproduced from arXiv: 2604.16830 by Caiming Xiong, Chien-Sheng Wu, Jiaxin Zhang, Qinglin Chen, Qinyuan Ye, Xiangyu Peng.

**Figure 1.** Figure 1: The Scaling Law of Miscalibration. (Left) Mean Confidence vs. Accuracy on Science Q&A. Almost all modern LLMs are trapped in the red Overconfidence Zone, exhibiting massive calibration gaps. Scaling up capability does not resolve this blind optimism. (Right) CaOPD structurally eliminates this bias by decoupling capability from calibration. It pulls the model back to the ideal calibration line, enabling a c… view at source ↗

**Figure 2.** Figure 2: Optimization trajectories. CaOPD perfectly matches the accuracy improvements [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Generalization of Calibrated Confidence. Evaluation on the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Decoupling Capability from Calibration across Model Scales. As Qwen3 scales [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Overview of the CaOPD Framework. The pipeline consists of five stages: (1) querying the student for a base response with verbalized confidence, (2) approximating the true empirical confidence via student rollouts and an objective verifier, (3) revising the completion by replacing the original confidence tokens with the empirical success rate, (4) constructing the privileged teacher context with the same re… view at source ↗

**Figure 6.** Figure 6: Effect of rollout sample size and confidence distributions. [PITH_FULL_IMAGE:figures/full_fig_p037_6.png] view at source ↗

**Figure 7.** Figure 7: Training dynamics across model scales. Left: Larger models (14B, 32B) exhibit highly efficient optimization, rapidly converging to a near-zero loss. Right: While small models (0.6B, 1.7B) initially struggle with the strict confidence formatting instructions, CaOPD acts as a strong corrective alignment force, driving their format adherence to > 90% within the first 100 steps. ing the continuous empirical co… view at source ↗

read the original abstract

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper flags a real overconfidence problem in on-policy distillation from info mismatch and proposes rollout-based CaOPD as a fix, but the estimator risks new variance and bias without clear proof it works better.

read the letter

The core observation is that on-policy distillation lifts task accuracy while trapping models in overconfidence, and the authors link this to teacher supervision using privileged context that the deployed model lacks. They formalize an optimism bias from entropy collapse and introduce CaOPD to swap in empirical confidence targets estimated from student rollouts instead of teacher signals, then distill the revised outputs through the usual pipeline. Experiments reportedly show this keeps capability competitive while reaching better calibration that holds up out of distribution and in continual learning.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that on-policy distillation (OPD) improves language model task accuracy but induces severe overconfidence, formalized as a 'Scaling Law of Miscalibration' arising from an information mismatch: teacher supervision uses privileged context unavailable at deployment. It theoretically shows that this leads to entropy collapse and optimism bias, making teacher-conditioned success invalid for calibration. The proposed CaOPD framework replaces self-reported confidence with empirical estimates from student rollouts and distills accordingly, with experiments demonstrating Pareto-optimal calibration, maintained capability, and robust generalization to out-of-distribution and continual learning settings.

Significance. If the theoretical formalization and experimental results hold, this work would be significant for LLM post-training research. It demonstrates that capability gains from distillation do not imply calibration and introduces a practical framework (CaOPD) to address miscalibration while preserving performance. The emphasis on treating confidence as a separate objective, combined with the open-sourced code, could influence deployment practices where reliable uncertainty is needed.

major comments (3)

Abstract: The theoretical formalization of the information mismatch, entropy collapse, and optimism bias is asserted without any equations, definitions of key terms, or derivation steps. This is load-bearing for the central claim that teacher-conditioned success is not a valid target for deployment-time confidence, as it remains unclear whether the bias definition is independent of the fitted quantities used in the proposed fix.
Abstract: The CaOPD method relies on rollout-based empirical confidence as the distillation target, but provides no analysis or bounds on variance, selection bias from trajectory filtering, or finite-sample effects (especially at low per-prompt success rates). This is load-bearing for whether the estimator resolves the claimed optimism bias without introducing new miscalibration issues.
Abstract: Claims of experimental support for the Scaling Law of Miscalibration, Pareto-optimal calibration, and robust OOD/continual learning generalization lack any quantitative details, metrics, baselines, rollout counts, or error analysis, making it impossible to assess the strength or reproducibility of the findings.

minor comments (2)

Abstract: The acronym 'CaOPD' is introduced without expansion on first use.
Abstract: The description of experiments mentions 'various models and domains' but provides no specifics on tasks, model sizes, or evaluation metrics, which would aid clarity even at the abstract level.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight opportunities to strengthen the clarity of the abstract and the rigor of supporting analyses. We address each major comment point by point below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

Referee: Abstract: The theoretical formalization of the information mismatch, entropy collapse, and optimism bias is asserted without any equations, definitions of key terms, or derivation steps. This is load-bearing for the central claim that teacher-conditioned success is not a valid target for deployment-time confidence, as it remains unclear whether the bias definition is independent of the fitted quantities used in the proposed fix.

Authors: We appreciate this observation regarding the abstract's conciseness. The full manuscript provides the complete theoretical formalization in Section 3, including explicit definitions of the information mismatch, entropy collapse, and optimism bias, along with derivation steps showing that teacher-conditioned success is not a valid target. The optimism bias is defined via the information asymmetry between training and deployment and is independent of the specific quantities fitted in CaOPD. To address the concern, we will revise the abstract to briefly reference these key theoretical elements and their implications for the central claim. revision: partial
Referee: Abstract: The CaOPD method relies on rollout-based empirical confidence as the distillation target, but provides no analysis or bounds on variance, selection bias from trajectory filtering, or finite-sample effects (especially at low per-prompt success rates). This is load-bearing for whether the estimator resolves the claimed optimism bias without introducing new miscalibration issues.

Authors: This is a valid point. While the manuscript discusses the rollout-based estimator, we agree that explicit analysis of its statistical properties is needed. We will add a dedicated subsection providing theoretical bounds on estimator variance, analysis of selection bias from trajectory filtering, and finite-sample effects (with particular attention to low per-prompt success rates). This will be supported by additional derivations and targeted experiments to confirm the estimator addresses the optimism bias without new miscalibration. revision: yes
Referee: Abstract: Claims of experimental support for the Scaling Law of Miscalibration, Pareto-optimal calibration, and robust OOD/continual learning generalization lack any quantitative details, metrics, baselines, rollout counts, or error analysis, making it impossible to assess the strength or reproducibility of the findings.

Authors: We acknowledge that the abstract summarizes results at a high level. The full manuscript details quantitative results in Section 5, including specific metrics (e.g., ECE), accuracy values, baselines, rollout counts, and error analysis from repeated runs. We will revise the abstract to include key quantitative highlights and ensure all experimental parameters, metrics, and reproducibility details are explicitly stated in the main text and appendix. revision: partial

Circularity Check

0 steps flagged

No significant circularity in claimed derivation

full rationale

The paper reports an empirical Scaling Law of Miscalibration observed under OPD, attributes it conceptually to an information mismatch between privileged teacher context and deployment-time inputs, and introduces CaOPD as a distinct method that substitutes rollout-estimated empirical success rates for self-reported confidence. No equations, formal derivations, or self-citations are presented that reduce the central claims or the proposed fix to the original inputs by construction. The theoretical formalization is framed as a perspective on the mismatch rather than a self-referential proof, and the rollout target is a new quantity not equivalent to the teacher-conditioned supervision it replaces. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review limits visibility into parameters and assumptions; the core relies on the unshown formalization of information mismatch and the validity of rollout-based empirical confidence.

axioms (1)

domain assumption Teacher-conditioned success under privileged context is not a valid target for deployment-time confidence
Stated directly as the traced failure mode in the abstract.

invented entities (1)

CaOPD framework no independent evidence
purpose: Estimates empirical confidence from rollouts and distills revised response
New method introduced to address the identified mismatch.

pith-pipeline@v0.9.0 · 5534 in / 1320 out tokens · 54445 ms · 2026-05-10T06:41:06.469739+00:00 · methodology

discussion (0)

Forward citations

Cited by 2 Pith papers

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KL for a KL: On-Policy Distillation with Control Variate Baseline
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vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensiv...
Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training
cs.LG 2026-05 unverdicted novelty 5.0

Sparse RL on a strong teacher followed by dense distillation to the student outperforms direct GRPO on the student for math tasks, with a forward-KL + OPD bridge enabling further gains.

Reference graph

Works this paper leans on

11 extracted references · cited by 2 Pith papers

[1]

In standard OPD, val(c) would typically be near 1.0, reflecting the teacher’s optimism inherited during training

Generate Verbalized Confidence:Given an input prompt x, the model (in student mode, i.e., conditioned only on x) generates a complete trajectory y= (a , c), where a is the reasoning trajectory and c is the confidence segment. In standard OPD, val(c) would typically be near 1.0, reflecting the teacher’s optimism inherited during training
[2]

We sampleK inde- pendent rollouts (ak, ck)∼π θ(· |x) and evaluate each with an objective task verifier to compute the empirical success rate ˆµ(x) = 1 K ∑K k=1 R(x, ak)

Approximate True Confidence:Instead of trusting the single-pass verbalized confidence, we estimate the student’s actual competence via empirical execution. We sampleK inde- pendent rollouts (ak, ck)∼π θ(· |x) and evaluate each with an objective task verifier to compute the empirical success rate ˆµ(x) = 1 K ∑K k=1 R(x, ak). This serves as a statistically ...
[3]

We take the student’s reasoning trajectorya from Step 1, but explicitly discard its original confidence segment c

Revise the Completion (Target Replacement):This is the core decoupling step of CaOPD. We take the student’s reasoning trajectorya from Step 1, but explicitly discard its original confidence segment c. We construct the revised completion ˜y= (a , ˆµ(x)) by overwriting the confidence tokens with the string representation of the empirical success rate. This ...
[4]

open-book

Construct Revised Teacher Context:To ensure the model learns advanced reasoning capabilities, we construct a privileged context z by prepending the user question with environmental feedback, ground-truth demonstrations, or correct solutions, creating an “open-book” setting for the teacher. Crucially, the confidence score withinz — originally near 1.0 — is...
[5]

Nc1ccn(Cc2ccc(Cl)cc2C(F)(F)F)

Compute Reverse KL Loss:Both the student πθ(· | ˜y<t, x) and the teacher πθ(· | ˜y<t, x, ˜z) perform a forward pass on the revised completion ˜y. The per-token reverse KL divergence (Equation (7)) is computed between these two distributions. As discussed in Section 4.2, this naturally decomposes into aCapability Cloningcomponent at reasoning positions and...
[6]

EMA Teacher Tracking:In self-distillation, the teacher is the same model with different conditioning (Section 2.1). To stabilize the teacher’s distribution during training, we maintain an Exponential Moving Average (EMA) (Tarvainen & Valpola, 2017) copy of the model weightsθ ema, updated at every gradient step:θ ema ←(1−α)θ ema +α θ. The teacher distribut...

2017
[7]

The engine generates a fresh batch of K studentrollouts (ak, ck)∼π θ(· |x) for each prompt on-the-fly

Dynamic Rollout Generation:Periodically during training, the latest model weights θ are synchronized to a high-throughput inference engine (vLLM (Kwon et al., 2023)). The engine generates a fresh batch of K studentrollouts (ak, ck)∼π θ(· |x) for each prompt on-the-fly

2023
[8]

The empirical success rate ˆµ(x) = 1 K ∑K k=1 R(x,a k)is computed strictly from thiscurrentbatch of rollouts

Online Target Computation:These newly generated student rollouts are immediately evaluated by the objective task verifier R(x, ak). The empirical success rate ˆµ(x) = 1 K ∑K k=1 R(x,a k)is computed strictly from thiscurrentbatch of rollouts
[9]

amortized offline

Target Replacement:The freshly computed ˆµ(x) is used to construct the revised comple- tion ˜yand revised teacher context ˜zfor the subsequent gradient optimization steps. This online, on-policy generation mechanism ensures that the supervision signal for confi- dence dynamically adapts to the model’s learning trajectory. As the model becomes more capable...

2022
[10]

• SDFT(Shenfeld et al., 2026) andSDPO(Hübotter et al., 2026): These represent the current state-of-the-art in on-policy self-distillation

Capability-Focused Paradigms.These methods primarily optimize for task success (capability) and serve to empirically illustrate the severe overconfidence degradation typical in standard post-training pipelines. • SDFT(Shenfeld et al., 2026) andSDPO(Hübotter et al., 2026): These represent the current state-of-the-art in on-policy self-distillation. The mod...

2026
[11]

Calibration Forgetting

Calibration-Aware RL Methods.To demonstrate that CaOPD is superior not only to standard distillation but also to specialized calibration techniques, we benchmark against state-of-the-art methods that explicitly shape rewards to penalize miscalibration. • RLCR(Damani et al., 2025): A reinforcement learning approach that integrates proper scoring rules (suc...

2025