Backpropagation without Multiplication

The back propagation algorithm has been modified to work with(cid:173) out any multiplications and to tolerate comput.ations Numbers are represented in float.ing In this way, all the computations can be executed with shift and add operations. An estimate of a circuit implementatioll shows that a large network can be placed on a single chip, reaching more t.han 1 billion weight updat.es A speedup is also obtained on any machine where a mul(cid:173) tiplication is slower than a shift operat.ioJl.