Constrained Neural Networks

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The training of deep artificial neural networks has led to major breakthroughs in the automatic processing and analysis of image data within the last decade. Unfortunately, the significant expressive power of such approaches, currently comes at the price of lacking control: Even if a network has been trained to solve a specific task on millions of training examples, there are rarely any mechanisms to provably guarantee that its output follows a given (physical) data formation process, which can explicitly be stated as a (parametric) mathematical constraint. This lack of control is a severe problem due to two reasons,1. It ultimately limits the applicability of learning-based approaches in some safety-critical applications where constraints need to be satisfied, and2. it prevents the inclusion of prior knowledge to guide machine learning based techniques and reduce the amount of training data required to train faithful models. Therefore, the goal of this project is to study fundamental methodologies for provably constraining the output of neural networks to a predefined (parameterized) set. It builds upon the method of energy dissipating networks developed by the applicant that allows to iteratively minimize any smooth energy with a neural network by projecting onto the set of descent directions in its final layer. The technical goal of this proposal is to exploit the idea of energy dissipating networks to provably enforce constraints, e.g. by using the squared distance to the constraint set as an energy. Specific foci will be put on structured as well as non-convex constraint sets. Finally, effectiveness of constrained networks will be tested and verified in the applications of weakly supervised segmentation with shape prior constraints as well as graph matching problems.