Constrained Neural Networks

深度人工神经网络的训练在过去十年中导致了图像数据自动处理和分析的重大突破。不幸的是，这些方法的显著表现力目前是以缺乏控制为代价的：即使一个网络已经被训练来解决数百万个训练示例的特定任务，也很少有任何机制可以证明其输出遵循给定的（物理）数据形成过程，这可以明确地表示为（参数）数学约束。这种缺乏控制是一个严重的问题，由于两个原因，1。它最终限制了基于学习的方法在一些需要满足约束的安全关键应用中的适用性。它防止了包含先验知识来指导基于机器学习的技术，并减少了训练忠实模型所需的训练数据量。 因此，本项目的目标是研究可证明地将神经网络的输出约束到预定义（参数化）集合的基本方法。它建立在由申请人开发的能量耗散网络的方法之上，该方法允许通过投影到其最终层中的下降方向集合上来迭代地最小化具有神经网络的任何平滑能量。该提案的技术目标是利用能量耗散网络的思想来可证明地强制约束，例如通过使用到约束集的平方距离作为能量。具体重点将放在结构化以及非凸约束集。最后，将测试和验证的约束网络的有效性，在弱监督分割与形状先验约束，以及图匹配问题的应用。

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.