Littlestone developed a simple deterministic on-line learning
algorithm for learning $k$-literal disjunctions. This algorithm
(called Winnow) keeps one weight for each variable and does
multiplicative updates to its weights. We develop a randomized
version of Winnow and prove bounds for an adaptation of the
algorithm ... more >>>

We present algorithms for learning depth two neural networks where the
hidden nodes are threshold gates with constant fan-in. The transfer
function of the output node might be more general: we have results for
the cases when the threshold function, the logistic function or the
identity function is ... more >>>