Statistical mechanics of lossy compression using multilayer perceptrons

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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.

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