Conformal Correction for Efficiency May be at Odds with Entropy
Senrong Xu, Tianyu Wang, Zenan Li, Yuan Yao, Taolue Chen, Feng Xu, Xiaoxing Ma
TL;DR
This paper investigates the trade-off between conformal prediction efficiency and model entropy, proposing an entropy-constrained correction method that improves efficiency while controlling entropy, validated on vision and graph datasets.
Contribution
It introduces an entropy-constrained conformal correction approach that balances efficiency and entropy, advancing the state-of-the-art in conformal prediction methods.
Findings
Significant efficiency improvements up to 34.4% under entropy constraints
Empirical and theoretical analysis of the efficiency-entropy trade-off
Effective on both computer vision and graph datasets
Abstract
Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or wrap the base model with an extra module using a conformal-aware inefficiency loss. In this work, we empirically and theoretically identify a trade-off between the CP efficiency and the entropy of model prediction. We then propose an entropy-constrained conformal correction method, exploring a better Pareto optimum between efficiency and entropy. Extensive experimental results on both computer vision and graph datasets demonstrate the efficacy of the proposed method. For instance, it can significantly improve the efficiency of state-of-the-art CP methods by up to 34.4%, given an entropy threshold.
Peer Reviews
Decision·Submitted to ICLR 2026
1. The investigation of the entropy and CP set size in this particular setting of conformal training is novel to the best of my knowledge. the framing is new and can be valuable for future research. 2. The theoretical results, though specific to a single score function, are well-motivated and provide interesting intuition. 3. The empirical results show promise in terms of prediction set size minimization relative to prior work. 4. The authors had valuable practical considerations in mind. I
1. **Limited scope of score functions**: the authors focus exclusively on the APS-type score functions. it remains unclear whether the observed entropy-efficiency tradeoff generalizes to other commonly used conformal scores such as 1-p(y|x), which is standard in split-conformal methods. At minimum, empirical evidence across multiple score functions would significantly strengthen the claims. 2. Theoretical results are again presented only considering the APS score. While generalizing the analys
- The paper provides a first rigorous analysis linking CP inefficiency and prediction entropy (Propositions 1-2, Theorem 3). - It identifies a real tension between compact prediction sets and calibrated uncertainty, which has been largely ignored by prior conformal training work. - The $EC^3$ objective combines focal loss and inefficiency regularization with entropy control; temperature scaling provides a simple yet effective Pareto traversal mechanism. - Extensive experiments across multiple ar
- The analysis focuses on adaptive conformal prediction (APS); extension to other CP variants (e.g., regression or non-adaptive scores) is not discussed. - The entropy parameter $\gamma$ and the temperature $T$ are hyperparameters tuned via grid search; no principled guidance for choosing them is provided. - While acknowledged in the Limitations section, empirical degradation in base model accuracy is not quantified or analyzed. - Some proofs (especially Proposition 2 and Theorem 3) rely on simp
- The paper includes a strong empirical evaluation, presenting results across several datasets with varying characteristics (i.e., number of classes). - The paper provides a clear justification for using **focal loss** in training adapters for Adaptive Prediction Sets (APS) non-conformity scores. It also provides a good theoretical connection between minimizing focal loss and maximizing entropy, leading to smaller prediction set sizes (**Theorem 3**, under the assumption $\mu \geq 0.5$). - Th
- The main weakness of the paper is the lack of comparison with APS using randomization, as introduced in [1]. The authors employ APS **without randomization** in their experiments. In other words, their implementation omits the second red and bolded term in the randomized non-conformity score: $$ V(x, y; u) = \sum_{i=1}^{y} \hat{\pi}_ {(i)}(x)~\textcolor{red}{\mathbf{- u \hat{\pi}_{(y)}(x) }} $$ for $u \sim U([0,1])$. Theoretically and empirically, randomized APS has been shown to **reduce set
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Taxonomy
TopicsAdvanced Graph Neural Networks · Explainable Artificial Intelligence (XAI) · Adversarial Robustness in Machine Learning