Where Does Trust Break Down? A Quantitative Trust Analysis of Deep Neural Networks via Trust Matrix and Conditional Trust Densities

The advances and successes in deep learning in recent years have led to\nconsiderable efforts and investments into its widespread ubiquitous adoption\nfor a wide variety of applications, ranging from personal assistants and\nintelligent navigation to search and product recommendation in e-commerce. With\nthis tremendous rise in deep learning adoption comes questions about the\ntrustworthiness of the deep neural networks that power these applications.\nMotivated to answer such questions, there has been a very recent interest in\ntrust quantification. In this work, we introduce the concept of trust matrix, a\nnovel trust quantification strategy that leverages the recently introduced\nquestion-answer trust metric by Wong et al. to provide deeper, more detailed\ninsights into where trust breaks down for a given deep neural network given a\nset of questions. More specifically, a trust matrix defines the expected\nquestion-answer trust for a given actor-oracle answer scenario, allowing one to\nquickly spot areas of low trust that needs to be addressed to improve the\ntrustworthiness of a deep neural network. The proposed trust matrix is simple\nto calculate, humanly interpretable, and to the best of the authors' knowledge\nis the first to study trust at the actor-oracle answer level. We further extend\nthe concept of trust densities with the notion of conditional trust densities.\nWe experimentally leverage trust matrices to study several well-known deep\nneural network architectures for image recognition, and further study the trust\ndensity and conditional trust densities for an interesting actor-oracle answer\nscenario. The results illustrate that trust matrices, along with conditional\ntrust densities, can be useful tools in addition to the existing suite of trust\nquantification metrics for guiding practitioners and regulators in creating and\ncertifying deep learning solutions for trusted operation.\n