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fellow, ieee Arithmetic coding provides an eeective mechanism for removing redundancy in the encoding of data. We show how arithmetic coding works and describe an eecient implementation that uses table lookup as a fast alternative to arithmetic operations. The reduced-precision arithmetic has a provably negligible eeect on the amount of compression achieved. We can speed up the implementation further by use of parallel processing. We discuss the role of probability models and how they provide probability information to the arithmetic coder. We conclude with perspectives on the comparative advantages and disadvantages of arithmetic coding.

Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical self-supervised learning that may relate to the function of bottom-up and top-down cortical processing pathways.

An unsupervised learning algorithm for a multilayer network of stochastic neurons is described. Bottom-up "recognition" connections convert the input into representations in successive hidden layers, and top-down "generative" connections reconstruct the representation in one layer from the representation in the layer above. In the "wake" phase, neurons are driven by recognition connections, and generative connections are adapted to increase the probability that they would reconstruct the correct activity vector in the layer below. In the "sleep" phase, neurons are driven by generative connections, and recognition connections are adapted to increase the probability that they would produce the correct activity vector in the layer above.

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