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

Dynamic Integration of Value Information into a Common Probability Currency as a Theory for Flexible Decision Making

Decisions involve two fundamental problems, selecting goals and generating actions to pursue those goals. While simple decisions involve choosing a goal and pursuing it, humans evolved to survive in hostile dynamic environments where goal availability and value can change with time and previous actions, entangling goal decisions with action selection. Recent studies suggest the brain generates concurrent action-plans for competing goals, using online information to bias the competition until a single goal is pursued. This creates a challenging problem of integrating information across diverse types, including both the dynamic value of the goal and the costs of action. We model the computations underlying dynamic decision-making with disparate value types, using the probability of getting the highest pay-off with the least effort as a common currency that supports goal competition. This framework predicts many aspects of decision behavior that have eluded a common explanation