MARGIN: Uncovering Deep Neural Networks using Graph Signal Analysis

Interpretability has emerged as a crucial aspect of machine learning, aimed at providing insights into the working of complex neural networks. However, existing solutions vary vastly based on the nature of the interpretability task, with each use case requiring substantial time and effort. This paper introduces MARGIN, a simple yet general approach to address a large set of interpretability tasks ranging from identifying prototypes to explaining image predictions. MARGIN exploits ideas rooted in graph signal analysis to determine influential nodes in a graph, which are defined as those nodes that maximally describe a function defined on the graph. By carefully defining task-specific graphs and functions, we demonstrate that MARGIN outperforms existing approaches in a number of disparate interpretability challenges.Comment: Technical Repor

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

Input and Weight Space Smoothing for Semi-supervised Learning

We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the minimality of the resulting representation, the other insensitivity to nuisance variability. We propose a method to perform such smoothing, which combines known input-space smoothing with a novel weight-space smoothing, based on a min-max (adversarial) optimization. The resulting Adversarial Block Coordinate Descent (ABCD) algorithm performs gradient ascent with a small learning rate for a random subset of the weights, and standard gradient descent on the remaining weights in the same mini-batch. It achieves comparable performance to the state-of-the-art without resorting to heavy data augmentation, using a relatively simple architecture