# Singleton-Optimized Conformal Prediction

arXiv: https://arxiv.org/abs/2509.24095 · HTML: https://mlsanity.com/paper/2509.24095/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 30 of 36)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Prediction Sets Adaptive to Unknown Covariate Shift](https://mlsanity.com/paper/2203.06126/) (2022)
- [PAC Prediction Sets Under Label Shift](https://mlsanity.com/paper/2310.12964/) (2023)
- [PAC Prediction Sets for Meta-Learning](https://mlsanity.com/paper/2207.02440/) (2022)
- [Conformal inference is (almost) free for neural networks trained with early stopping](https://mlsanity.com/paper/2301.11556/) (2023)
- [Conformal prediction after data-dependent model selection](https://mlsanity.com/paper/2408.07066/) (2024)
- [Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization](https://mlsanity.com/paper/2502.13030/) (2025)
- [Conformal Frequency Estimation using Discrete Sketched Data with Coverage for Distinct Queries](https://mlsanity.com/paper/2211.04612/) (2022)
- [On Volume Minimization in Conformal Regression](https://mlsanity.com/paper/2502.09985/) (2025)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)

## Built on by (most cited first, 2 of 2)

- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)

## Abstract (arXiv)

Conformal prediction can be used to construct prediction sets that cover the true outcome with a desired probability, but can sometimes lead to large prediction sets that are costly in practice. The most useful outcome is a singleton prediction-an unambiguous decision-yet existing efficiency-oriented methods primarily optimize average set size. Motivated by this, we propose a new nonconformity score that aims to minimize the probability of producing non-singleton sets. Starting from a non-convex constrained optimization problem as a motivation, we provide a geometric reformulation and associated algorithm for computing the nonconformity score and associated split conformal prediction sets in O(K) time for K-class problems. Using this score in split conformal prediction leads to our proposed Singleton-Optimized Conformal Prediction (SOCOP) method. We evaluate our method in experiments on image classification and LLM multiple-choice question-answering, comparing with standard nonconformity scores such as the (negative) label probability estimates and their cumulative distribution function; both of which are motivated by optimizing length. The results show that SOCOP increases singleton frequency (sometimes by over 20%) compared to the above scores, with minimal impact on average set size.