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.

<script>

(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');

ga('create', 'UA-59662816-1', 'auto');
ga('send', 'pageview');

</script>