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Learning informative representations of data is one of the primary goals ofdeep learning, but there is still little understanding as to whatrepresentations a neural network actually learns. To better understand this,subspace match was recently proposed as a method for assessing the similarityof the representations learned by neural networks. It has been shown that twonetworks with the same architecture trained from different initializationslearn representations that at hidden layers show low similarity when assessedwith subspace match, even when the output layers show high similarity and thenetworks largely exhibit similar performance on classification tasks. In thisnote, we present a simple example motivated by standard results in commutativealgebra to illustrate how this can happen, and show that although the subspacematch at a hidden layer may be 0, the representations learned may be isomorphicas vector spaces. This leads us to conclude that a subspace match comparison oflearned representations may well be uninformative, and it points to the needfor better methods of understanding learned representations.

Subspace Match Probably Does Not Accurately Assess the Similarity of Learned Representations