# BOLT: Universal Classifier Training via a Bayes-Error Upper Bound

arXiv: https://arxiv.org/abs/2501.07754 · HTML: https://mlsanity.com/paper/2501.07754/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Optimal Bounds between f-Divergences and Integral Probability Metrics](https://mlsanity.com/paper/2006.05973/) (2020)
- [Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification](https://mlsanity.com/paper/2202.00395/) (2022)
- [Evaluating State-of-the-Art Classification Models Against Bayes Optimality](https://mlsanity.com/paper/2106.03357/) (2021)
- [Learning to Benchmark: Determining Best Achievable Misclassification Error from Training Data](https://mlsanity.com/paper/1909.07192/) (2019)
- [Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errors](https://mlsanity.com/paper/2405.11547/) (2024)

## Built on by (most cited first, 1 of 1)

- [Revisiting GAN with Bayes-Optimal Discrimination](https://mlsanity.com/paper/2510.25609/) (2025)

## Abstract (arXiv)

This work introduces a novel approach to compute a universal upper bound on the Bayes error rate (BER) from classifier-output samples, which serves as a Bayes-error-related performance criterion for the underlying classification task. We show that the bound is tight in the binary case and characterize the max-sum gap that appears in the aggregate multiclass formulation. Based on this bound, we define a new loss function, called Bayes optimal learning threshold (BOLT), for training parameterized classifiers. For each data sample, the BOLT loss computes a term whose expectation upper-bounds the Bayes error, so that during training the model parameters can be updated toward minimizing this bound. Numerical experiments with both synthetic and real-world datasets show that, in the reported settings, BOLT training often attains lower held-out classification error than cross-entropy training.