Each hidden layer in neural networks can be formulated as one HOPE model [1]

• 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.

Reference:
[1] Shiliang Zhang and Hui Jiang, “Hybrid Orthogonal Projection and Estimation (HOPE): A New Framework to Probe and Learn Neural Networks,” arXiv:1502.00702.

Software:
The matlab codes to reproduce the MNIST results in [1] can be downloaded here.