# Selective Prediction from Agreement: A Lipschitz-Consistent Version Space Approach

arXiv: https://arxiv.org/abs/2605.02611 · HTML: https://mlsanity.com/paper/2605.02611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [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)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Beyond Perturbations: Learning Guarantees with Arbitrary Adversarial Test Examples](https://mlsanity.com/paper/2007.05145/) (2020)

## Abstract (arXiv)

We consider selective classification with abstention in the fixed-pool (or transductive) setting, where the unlabeled pool is given beforehand and only a subset of points can be queried for labels. Our main insight is to view selective prediction through agreement: given queried labels and Lipschitz margin constraints in an embedding space, the version space of Lipschitz-consistent classification heads is well defined. We obtain upper and lower Lipschitz margin bounds that define, for each pool point, a set of certified valid labels containing the prediction of every head in the version space. The model therefore predicts only when the label is forced (i.e., all consistent heads agree), and abstains otherwise. We also propose a monotone submodular geometric proxy for budgeted querying, and show that a greedy algorithm retains the standard approximation factor.