# Multi-Condition Conformal Selection

arXiv: https://arxiv.org/abs/2510.08075 · HTML: https://mlsanity.com/paper/2510.08075/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Conformal Alignment: Knowing When to Trust Foundation Models with Guarantees](https://mlsanity.com/paper/2405.10301/) (2024)
- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [Conformal Prediction with Learned Features](https://mlsanity.com/paper/2404.17487/) (2024)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [Optimized Conformal Selection: Powerful Selective Inference After Conformity Score Optimization](https://mlsanity.com/paper/2411.17983/) (2024)
- [Multivariate Conformal Selection](https://mlsanity.com/paper/2505.00917/) (2025)
- [Selection from Hierarchical Data with Conformal e-values](https://mlsanity.com/paper/2501.02514/) (2025)
- [Conformal Prediction as Bayesian Quadrature](https://mlsanity.com/paper/2502.13228/) (2025)
- [Diversifying Conformal Selections](https://mlsanity.com/paper/2506.16229/) (2025)
- [Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift](https://mlsanity.com/paper/2405.10302/) (2024)
- [One Sample is Enough to Make Conformal Prediction Robust](https://mlsanity.com/paper/2506.16553/) (2025)
- [Revamping Conformal Selection With Optimal Power: A Neyman--Pearson Perspective](https://mlsanity.com/paper/2502.16513/) (2025)

## Built on by (most cited first, 4 of 4)

- [Provable Training Data Identification for Large Language Models](https://mlsanity.com/paper/2510.09717/) (2025)
- [Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables](https://mlsanity.com/paper/2604.11305/) (2026)
- [Provable Joint Decontamination for Benchmarking Multiple Large Language Models](https://mlsanity.com/paper/2605.21543/) (2026)
- [Null-Calibrated Conformal Selection via Target-Membership Scores](https://mlsanity.com/paper/2606.22336/) (2026)

## Abstract (arXiv)

Selecting high-quality candidates from large-scale datasets is critically important in resource-constrained applications such as drug discovery, precision medicine, and the alignment of large language models. While conformal selection methods offer a rigorous solution with False Discovery Rate (FDR) control, their applicability is confined to single-threshold scenarios (i.e., y > c) and overlooks practical needs for multi-condition selection, such as conjunctive or disjunctive conditions. In this work, we propose the Multi-Condition Conformal Selection (MCCS) algorithm, which extends conformal selection to scenarios with multiple conditions. In particular, we introduce a novel nonconformity score with regional monotonicity for conjunctive conditions and a global Benjamini-Hochberg (BH) procedure for disjunctive conditions, thereby establishing finite-sample FDR control with theoretical guarantees. The integration of these components enables the proposed method to achieve rigorous FDR-controlled selection in various multi-condition environments. Extensive experiments validate the superiority of MCCS over baselines, its generalizability across diverse condition combinations, different real-world modalities, and multi-task scalability.