This is an interim version of our Electronic Legal Deposit Catalogue-eJournals and eBooks while we continue to recover from a cyber-attack.
Asymptotics of representation learning in finite Bayesian neural networks*This article is an updated version of: Zavatone-Veth J, Canatar A, Ruben B and Pehlevan C 2021 Asymptotics of representation learning in finite Bayesian neural networks Advances in Neural Information Processing Systems vol 34 ed M Ranzato, A Beygelzimer, Y Dauphin, P S Liang and J Wortman Vaughan (New York: Curran Associates) pp 24765–77. (1st November 2022)
Record Type:
Journal Article
Title:
Asymptotics of representation learning in finite Bayesian neural networks*This article is an updated version of: Zavatone-Veth J, Canatar A, Ruben B and Pehlevan C 2021 Asymptotics of representation learning in finite Bayesian neural networks Advances in Neural Information Processing Systems vol 34 ed M Ranzato, A Beygelzimer, Y Dauphin, P S Liang and J Wortman Vaughan (New York: Curran Associates) pp 24765–77. (1st November 2022)
Main Title:
Asymptotics of representation learning in finite Bayesian neural networks*This article is an updated version of: Zavatone-Veth J, Canatar A, Ruben B and Pehlevan C 2021 Asymptotics of representation learning in finite Bayesian neural networks Advances in Neural Information Processing Systems vol 34 ed M Ranzato, A Beygelzimer, Y Dauphin, P S Liang and J Wortman Vaughan (New York: Curran Associates) pp 24765–77.
Abstract: Recent works have suggested that finite Bayesian neural networks may sometimes outperform their infinite cousins because finite networks can flexibly adapt their internal representations. However, our theoretical understanding of how the learned hidden layer representations of finite networks differ from the fixed representations of infinite networks remains incomplete. Perturbative finite-width corrections to the network prior and posterior have been studied, but the asymptotics of learned features have not been fully characterized. Here, we argue that the leading finite-width corrections to the average feature kernels for any Bayesian network with linear readout and Gaussian likelihood have a largely universal form. We illustrate this explicitly for three tractable network architectures: deep linear fully-connected and convolutional networks, and networks with a single nonlinear hidden layer. Our results begin to elucidate how task-relevant learning signals shape the hidden layer representations of wide Bayesian neural networks.