Here's my understanding after giving the paper a once-over: the authors decompose a convnet with linear activations (instead of, say, ReLUs, as is common) and p

Here's my understanding after giving the paper a once-over: the authors decompose a convnet with linear activations (instead of, say, ReLUs, as is common) and product-pooling layers (instead of, say, average- or max- pooling layers, as is common) into tensors[1] that have the same structure as a quantum many-body wave function. In other words, this convnet is equivalent to such a function. This equivalence allows the authors to use quantum entanglement measures to quantify this convnet’s ability to model the correlation structures of its inputs (i.e., its "expresiveness"), and tie that ability to the number of feature maps in each convolutional layer. I LOVE seeing these kinds of connections across different fields. [1] By "tensor" I mean this: https://en.wikipedia.org/wiki/Tensor https://en.wikipedia.org/wiki/Tensor