  Deep learning's successes are often attributed to its ability to
automatically discover new representations of the data, rather than relying on
handcrafted features like other learning methods. We show, however, that deep
networks learned by the standard gradient descent algorithm are in fact
mathematically approximately equivalent to kernel machines, a learning method
that simply memorizes the data and uses it directly for prediction via a
similarity function (the kernel). This greatly enhances the interpretability of
deep network weights, by elucidating that they are effectively a superposition
of the training examples. The network architecture incorporates knowledge of
the target function into the kernel. This improved understanding should lead to
better learning algorithms.
