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→ . For a compression using a parity tree with K 2 hidden units, the rate distortion
function, which is known as the theoretical limit for compression, is derived where the code length becomes
infinity.