Solomonoff's general theory of inference and the Minimum Description Length
principle formalize Occam's razor, and hold that a good model of data is a
model that is good at losslessly compressing the data, including the cost of
describing the model itself. Deep neural networks might seem to go against this
principle given the large number of parameters to be encoded.
We demonstrate experimentally the ability of deep neural networks to compress
the training data even when accounting for parameter encoding. The compression
viewpoint originally motivated the use of variational methods in neural
networks. Unexpectedly, we found that these variational methods provide
surprisingly poor compression bounds, despite being explicitly built to
minimize such bounds. This might explain the relatively poor practical
performance of variational methods in deep learning. On the other hand, simple
incremental encoding methods yield excellent compression values on deep
networks, vindicating Solomonoff's approach.

通过实验证明，即使考虑到参数编码，深度神经网络仍能够压缩训练数据，而这种压缩视角最初激励了神经网络中变分方法的使用。我们发现，这些变分方法提供了惊人的较差压缩界限，这可能解释了变分方法在深度学习中相对较差的实际性能。另一方面，简单的增量编码方法在深度网络上产生了出色的压缩效果，从而证明了 Solomonoff 的方法。