Neural Belief Reasoner

TL;DR

This paper introduces the neural belief reasoner (NBR), a generative model that uses belief functions instead of probability distributions, demonstrating its effectiveness in reasoning tasks and robust image classification.

Contribution

It presents NBR, a novel model combining neural networks with belief functions, and applies it to reasoning and robust digit classification tasks.

Findings

NBR performs multi-hop reasoning with uncertainty and conflicting information.

NBR achieves high robustness in MNIST digit classification without adversarial training.

The model maintains 99.1% accuracy on natural images while resisting adversarial attacks.

Abstract

This paper proposes a new generative model called neural belief reasoner (NBR). It differs from previous models in that it specifies a belief function rather than a probability distribution. Its implementation consists of neural networks, fuzzy-set operations and belief-function operations, and query-answering, sample-generation and training algorithms are presented. This paper studies NBR in two tasks. The first is a synthetic unsupervised-learning task, which demonstrates NBR's ability to perform multi-hop reasoning, reasoning with uncertainty and reasoning about conflicting information. The second is supervised learning: a robust MNIST classifier for 4 and 9, which is the most challenging pair of digits. This classifier needs no adversarial training, and it substantially exceeds the state of the art in adversarial robustness as measured by the L2 metric, while at the same time maintains 99.1% accuracy on natural images.