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@INPROCEEDINGS{Fischer:1029334,
      author       = {Fischer, Kirsten and Lindner, Javed and Dahmen, David and
                      Ringel, Zohar and Krämer, Michael and Helias, Moritz},
      title        = {{C}ritical feature learning in deep neural networks},
      reportid     = {FZJ-2024-05061},
      year         = {2024},
      abstract     = {A key property of neural networks driving their success is
                      their ability to learn features from data. Understanding
                      feature learning from a theoretical viewpoint is an emerging
                      field with many open questions. In this work we capture
                      finite-width effects with a systematic theory of network
                      kernels in deep non-linear neural networks. We show that the
                      Bayesian prior of the network can be written in closed form
                      as a superposition of Gaussian processes, whose kernels are
                      distributed with a variance that depends inversely on the
                      network width N . A large deviation approach, which is exact
                      in the proportional limit for the number of data points
                      P=αN→∞, yields a pair of forward-backward equations for
                      the maximum a posteriori kernels in all layers at once. We
                      study their solutions perturbatively to demonstrate how the
                      backward propagation across layers aligns kernels with the
                      target. An alternative field-theoretic formulation shows
                      that kernel adaptation of the Bayesian posterior at
                      finite-width results from fluctuations in the prior: larger
                      fluctuations correspond to a more flexible network prior and
                      thus enable stronger adaptation to data. We thus find a
                      bridge between the classical edge-of-chaos NNGP theory and
                      feature learning, exposing an intricate interplay between
                      criticality, response functions, and feature scale.},
      month         = {Jul},
      date          = {2024-07-21},
      organization  = {The Forty-first International
                       Conference on Machine Learning, Wien
                       (Austria), 21 Jul 2024 - 27 Jul 2024},
      subtyp        = {After Call},
      cin          = {IAS-6},
      cid          = {I:(DE-Juel1)IAS-6-20130828},
      pnm          = {5232 - Computational Principles (POF4-523) / 5234 -
                      Emerging NC Architectures (POF4-523) / RenormalizedFlows -
                      Transparent Deep Learning with Renormalized Flows
                      (BMBF-01IS19077A) / MSNN - Theory of multi-scale neuronal
                      networks (HGF-SMHB-2014-2018) / ACA - Advanced Computing
                      Architectures (SO-092)},
      pid          = {G:(DE-HGF)POF4-5232 / G:(DE-HGF)POF4-5234 /
                      G:(DE-Juel-1)BMBF-01IS19077A /
                      G:(DE-Juel1)HGF-SMHB-2014-2018 / G:(DE-HGF)SO-092},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/1029334},
}