Researchers Establish Large Deviation Principles for Convolutional Bayesian Neural Networks
A new theoretical paper establishes large deviation principles (LDP) for convolutional neural networks in the infinite-channel regime, extending beyond previously known Gaussian process limits. The work applies to a broad class of CNN architectures with general receptive fields and derives LDPs for both conditional covariance matrices and posterior distributions. This represents the first such mathematical characterization for CNNs and advances theoretical understanding of deep learning behavior.
Researchers have proven a large deviation principle for convolutional neural networks (CNNs) with Gaussian initialization in the infinite-channel limit, filling a gap in theoretical machine learning. While prior work established that suitably scaled CNNs converge to Gaussian processes as channel numbers increase, behavior beyond this Gaussian limit remained poorly understood. The new result applies to a broad class of multidimensional CNN architectures with general receptive fields and establishes LDPs for conditional covariance matrices under Gaussian weight priors, as well as for posterior distributions conditioned on finite observations. The authors also provide streamlined proofs for concentration of conditional covariances and Gaussian equivalence of networks. This is claimed to be the first large deviation principle established for convolutional neural networks.
What's missing
The paper does not discuss practical implications or computational applications of these theoretical results, nor does it compare the tightness of these bounds to empirical observations in finite-channel networks used in practice.
What different sources said
- arXiv stat.MLCenter
Large deviation principles for convolutional Bayesian neural networks
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