Spectral Norm in Learning Theory: Some Selected Topics

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Abstract

In this paper, we review some known results that relate the statistical query complexity of a concept class to the spectral norm of its correlation matrix. Since spectral norms are widely used in various other areas, we are then able to put statistical query complexity in a broader context. We briefly describe some non-trivial connections to (seemingly) different topics in learning theory, complexity theory, and cryptography. A connection to the so-called Hidden Number Problem, which plays an important role for proving bit-security of cryptographic functions, will be discussed in somewhat more detail.