And/or trade-off in artificial neurons: impact on adversarial robustness

Since its discovery in 2013, the phenomenon of adversarial examples has attracted a growing amount of attention from the machine learning community. A deeper understanding of the problem could lead to a better comprehension of how information is processed and encoded in neural networks and, more in general, could help to solve the issue of interpretability in machine learning. Our idea to increase adversarial resilience starts with the observation that artificial neurons can be divided in two broad categories: AND-like neurons and OR-like neurons. Intuitively, the former are characterised by a relatively low number of combinations of input values which trigger neuron activation, while for the latter the opposite is true. Our hypothesis is that the presence in a network of a sufficiently high number of OR-like neurons could lead to classification "brittleness" and increase the network's susceptibility to adversarial attacks. After constructing an operational definition of a neuron AND-like behaviour, we proceed to introduce several measures to increase the proportion of AND-like neurons in the network: L1 norm weight normalisation; application of an input filter; comparison between the neuron output's distribution obtained when the network is fed with the actual data set and the distribution obtained when the network is fed with a randomised version of the former called "scrambled data set". Tests performed on the MNIST data set hint that the proposed measures could represent an interesting direction to explore.