Check out https://arxiv.org/pdf/1909.11522.pdf where we do some similar analysis of perceptrons but in higher dimensions. Theorem 4.1 shows that there is an anti-entropy bias—in other words, functions with either mostly 0s or mostly 1s are exponentially more likely to show up than expected under a uniform prior—which holds for perceptrons of any dimension. This proves a (fairly trivial) bias towards simple functions, although it doesn’t say anything about why a function like 010101010101… appears more frequently than other functions in the maximum-entropy class.
Check out https://arxiv.org/pdf/1909.11522.pdf where we do some similar analysis of perceptrons but in higher dimensions. Theorem 4.1 shows that there is an anti-entropy bias—in other words, functions with either mostly 0s or mostly 1s are exponentially more likely to show up than expected under a uniform prior—which holds for perceptrons of any dimension. This proves a (fairly trivial) bias towards simple functions, although it doesn’t say anything about why a function like 010101010101… appears more frequently than other functions in the maximum-entropy class.