-Techniques from,coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory stores n -tuple of + 1's. The components change depending on a hardlimited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products of m fundamental memories, one hopes to be able to recover a certain one of the no memories by using an initial n-tuple probe vector less than a Hamming distance n/2 away from the ftindamental memory. If WI fundamental memories are chosen at random, the maximum asympotic value of m in order that most of the no original memories are exactly recoverable is n/(2log n). With the added restriction that every one of the m fundamental memories be recoverable exactly, rrl can be no more than n/(4log n) asymptotically as n approaches infinity. Extensions are also considered, in particular to capacity under qnantization of the outer-product connection matrijr. This quantized memory capacity problem is closely related to the capacity of the quantized Gaussian channel.

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Classical and recent results in statistical pattern recognition and learning theory are reviewed in a two-class pattern classification setting. This basic model best illustrates intuition and analysis techniques while still containing the essential features and serving as a prototype for many applications. Topics discussed include nearest neighbor, kernel, and histogram methods, Vapnik-Chervonenkis theory, and neural networks. The presentation and the large (thogh nonexhaustive) list of references is geared to provide a useful overview of this field for both specialists and nonspecialists.