Characterizing the Shape of Activation Space in Deep Neural Networks

The representations learned by deep neural networks are difficult to interpret in part due to their large parameter space and the complexities introduced by their multi-layer structure. We introduce a method for computing persistent homology over the graphical activation structure of neural networks, which provides access to the task-relevant substructures activated throughout the network for a given input. This topological perspective provides unique insights into the distributed representations encoded by neural networks in terms of the shape of their activation structures. We demonstrate the value of this approach by showing an alternative explanation for the existence of adversarial examples. By studying the topology of network activations across multiple architectures and datasets, we find that adversarial perturbations do not add activations that target the semantic structure of the adversarial class as previously hypothesized. Rather, adversarial examples are explainable as alterations to the dominant activation structures induced by the original image, suggesting the class representations learned by deep networks are problematically sparse on the input space

Learning-Based Constraint Satisfaction With Sensing Restrictions

In this paper we consider graph-coloring problems, an important subset of general constraint satisfaction problems that arise in wireless resource allocation. We constructively establish the existence of fully decentralized learning-based algorithms that are able to find a proper coloring even in the presence of strong sensing restrictions, in particular sensing asymmetry of the type encountered when hidden terminals are present. Our main analytic contribution is to establish sufficient conditions on the sensing behaviour to ensure that the solvers find satisfying assignments with probability one. These conditions take the form of connectivity requirements on the induced sensing graph. These requirements are mild, and we demonstrate that they are commonly satisfied in wireless allocation tasks. We argue that our results are of considerable practical importance in view of the prevalence of both communication and sensing restrictions in wireless resource allocation problems. The class of algorithms analysed here requires no message-passing whatsoever between wireless devices, and we show that they continue to perform well even when devices are only able to carry out constrained sensing of the surrounding radio environment