A mind-boggling analogy between machine learning and quantum physics

A recent paper published in PNAS titled “The Fermi-Dirac distribution provides a calibrated probabilistic output for binary classifiers” caught my attention, because it describes a surprising relationship between machine learning and quantum physics. In fact, surprising is an understatement. Mind-boggling is more like it. According to the analogy developed by the authors, positive samples in binary classification problems are like… fermions?! What?! I decided that I should try to understand the gist of this paper, at least to the extent that I can.
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How many photons get into your eyes?

A recent paper shows that our vision is so sensitive to light that human subjects can detect the presence of one single photon shot into their retinas. While scientists have been trying to establish the lower limit of visual sensitivity for a very long time, and it is generally accepted that a small number of photons are sufficient for detection since the 40’s, new advances in quantum optics finally allow us to manipulate light at single photon precision, and it is the first time that direct evidence for single photon sensitivity is demonstrated in a psychological experiment.
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