Resilience, Interpretability, and Scale in Large Complex Systems

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Throughout my research career I have been interested in image processing problems with an explicit notion of hierarchy or scale.  In the last five to ten years, multi-scale algorithms have transformed into what are now known as convolutional neural networks (CNNs) or deep networks, a family of approaches which now dominates nearly every aspect of data analysis and computer vision.  Although these deep networks have remarkable performance, to some extent this appearance of invincibility is quite misplaced. In particular, their nonlinearity and size means that these networks are essentially uninterpretable, that there is no way to answer how the 100-million parameters in some 100-layer black box reached a certain conclusion. Furthermore, there is the unsettling observation that networks, reporting 99.9% accuracy, in fact fail for other very elementary problems. If such networks are to be used in healthcare or autonomous vehicles or countless other life-critical applications, then a degree of interpretability and network resilience is essential, and indeed is slowly being mandated by some governments. The following inter-related summaries outline the exploratory research objectives proposed under my Discovery Grant: 1. Resilience and Interpretability of Deep Networks: The unusual aspects of deep learning - fantastically robust on certain test sets, and then bafflingly catastrophic errors on others - hint at unusual patterns of learning. Since the network essentially lives in a 100-million dimensional space, visualizing the learned classification boundaries is completely out of the question, yet some insight into the learning process is essential in producing more resilient networks with more predictable learning outcomes and some degree of interpretability. 2. The role of Scale in Large Networks: Deep networks and related strategies suffer from a high computational complexity and from a limited predictability as to when the approach will or will not work. It is ambiguous how or when scale may implicitly be introduced by machine learning, although anecdotally it is known that learned filters frequently show scale-related patterns. The goal of this work is to explicitly introduce scale dependence, whether at the inputs, transferred from other networks, or explicitly into the network architecture. 3. Large Complex Systems and Nonlinear Networks: Deep networks are, in a sense, just unusually large complex nonlinear systems. However complex systems research has had relatively little connection to research into deep networks.  I would like to consider whether aspects of resilience in complex systems might lead to insights on related questions of resilience in large networks, not that the algorithm would be the same, but whether understanding of resilience might translate. All of these topics and skills are in demand across a wide range of industries, leading to outstanding training and future employment opportunities for HQP.