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I was going to add a tweet but it didn't go through. What's interesting here is not that a random network would work, it's that training this random network does not improve its performance. It's a sign there's a fundamental flaw with how we think about the setup.
If random projections work at all, it should be very easy to tune these random projections to get a better network. No reason to believe the random weights were a local minimum.
It was also the main idea behind Rosenblatt's original Perceptrons. He is not given enough credit for that, imo.
Here they remove the last FC layer of many conv networks architectures and substitute it w/ a random projection and achieve similar results to the FC onehttps://arxiv.org/abs/1801.04540
If you remove a trained layer, add a random one, and then train a new layer on top, what you're looking at is just whether the random layer is destructive or not (with enough units, it's likely overcomplete, so not destructive). This is very different and not surprising
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