Statistical mechanics of lossy compression using multilayer perceptrons.

Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a treelike committee machine (committee tree) and treelike parity machine (parity tree) whose transfer functions are monotonic. For compression using a committee tree, a lower bound of achievable distortion becomes small as the number of hidden units K increases. However, it cannot reach the Shannon bound even where K-->infinity. For a compression using a parity tree with K> or =2 hidden units, the rate distortion function, which is known as the theoretical limit for compression, is derived where the code length becomes infinity.