It is shown that high order feedforward neural nets of constant depth with piecewise
polynomial activation functions and arbitrary real weights can be simulated for boolean
inputs and outputs by neural nets of a somewhat larger size and depth with heaviside
gates and weights ... more >>>

We show the following hardness results for monotone learning and approximation of monotone circuit size:

1. Under the Randomised Exponential-Time Hypothesis (rETH), it requires time $n^{\Omega(\log n)}$ to PAC-learn monotone formulas with $n$ input bits and size $s(n) = n$ by monotone circuits of size $n^{(\log n)^{1-\epsilon}}$, for every $\epsilon ... more >>>