Growth bound for a single-hidden-layer sign network
= Growth bound for a single-hidden-layer sign network
A bias-free network with $p$ inputs, $m$ sign-activated hidden nodes, and a thresholded linear output satisfies
$$
s(\mathcal H,n)\leq(n+1)^{(p+1)m}.
$$
The hidden units contribute $s(\mathcal G,n)^m\leq(n+1)^{pm}$ sample patterns, and the output weights contribute $(n+1)^m$.