Random-Set Neural Networks (RS-NN)

TL;DR

The paper introduces Random-Set Neural Networks (RS-NN), a novel classification method that models uncertainty with belief functions, improving confidence estimation, out-of-distribution detection, and robustness in safety-critical applications.

Contribution

RS-NN is the first approach to predict belief functions over classes using random set mathematics, capturing epistemic uncertainty and scaling to large architectures.

Findings

Outperforms Bayesian and ensemble methods in accuracy and uncertainty estimation

Effectively detects out-of-distribution samples across multiple benchmarks

Demonstrates robustness to adversarial attacks and provides statistical guarantees

Abstract

Machine learning is increasingly deployed in safety-critical domains where erroneous predictions may lead to potentially catastrophic consequences, highlighting the need for learning systems to be aware of how confident they are in their own predictions: in other words, 'to know when they do not know'. In this paper, we propose a novel Random-Set Neural Network (RS-NN) approach to classification which predicts belief functions (rather than classical probability vectors) over the class list using the mathematics of random sets, i.e., distributions over the collection of sets of classes. RS-NN encodes the 'epistemic' uncertainty induced by training sets that are insufficiently representative or limited in size via the size of the convex set of probability vectors associated with a predicted belief function. Our approach outperforms state-of-the-art Bayesian and Ensemble methods in terms of accuracy, uncertainty estimation and out-of-distribution (OoD) detection on multiple benchmarks (CIFAR-10 vs SVHN/Intel-Image, MNIST vs FMNIST/KMNIST, ImageNet vs ImageNet-O). RS-NN also scales up effectively to large-scale architectures (e.g. WideResNet-28-10, VGG16, Inception V3, EfficientNetB2 and ViT-Base-16), exhibits remarkable robustness to adversarial attacks and can provide statistical guarantees in a conformal learning setting.