1. Hybrid Orthogonal Projection & Estimation (HOPE)

Each hidden layer in neural networks can be formulated as one HOPE model

• The HOPE model combines a linear orthogonal projection and a mixture model under a unied generative modelling framework;
• The HOPE model can be used as a novel tool to probe why and how NNs work;
• The HOPE model provides several new learning algorithms to learn NNs either supervisedly or unsupervisedly.