CQnet：凸几何解释和约束神经网络轨迹
CQnet: convex-geometric interpretation and constraining neural-network trajectories
摘要：
我们介绍了CQnet，一个起源于CQ算法的神经网络，用于解决凸分裂可行性问题和向前向后分裂。CQnet的轨迹可以解释为粒子，它们通过点到集合距离函数跟踪不断变化的约束集，同时在每一层都是另一个约束集的元素。CQnet不仅仅是一种凸几何解释，它还适应学习和确定性约束，这些约束可能是样本或数据特定的，并且每个层和输出都能满足。此外，CQnet中的状态在每一层都朝着另一个约束集前进。我们提供的稳定性/非扩张性的最小假设的证明。约束处理和稳定性的结合使CQnet成为各种任务的候选者，其中先验知识存在于网络状态或输出上。
英文摘要：
We introduce CQnet, a neural network with origins in the CQ algorithm for solving convex split-feasibility problems and forward-backward splitting. CQnet's trajectories are interpretable as particles that are tracking a changing constraint set via its point-to-set distance function while being elements of another constraint set at every layer. More than just a convex-geometric interpretation, CQnet accommodates learned and deterministic constraints that may be sample or data-specific and are satisfied by every layer and the output. Furthermore, the states in CQnet progress toward another constraint set at every layer. We provide proof of stability/nonexpansiveness with minimal assumptions. The combination of constraint handling and stability put forward CQnet as a candidate for various tasks where prior knowledge exists on the network states or output.
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