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Dependence between Bayesian neural network units

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Abstract

The connection between Bayesian neural networks and Gaussian processes gained a lot of attention in the last few years, with the flagship result that hidden units converge to a Gaussian process limit when the layers width tends to infinity. Underpinning this result is the fact that hidden units become independent in the infinite-width limit. Our aim is to shed some light on hidden units dependence properties in practical finite-width Bayesian neural networks. In addition to theoretical results, we assess empirically the depth and width impacts on hidden units dependence properties.
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hal-03449211 , version 1 (26-11-2021)

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Mariia Vladimirova, Julyan Arbel, Stéphane Girard. Dependence between Bayesian neural network units. BDL 2021 - Workshop. Bayesian Deep Learning NeurIPS, Dec 2021, Montreal, Canada. pp.1-9. ⟨hal-03449211⟩
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