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Entropy and mutual information in models of deep neural networks NeurIPS 2018 - Thursday Dec 06th - Spotlight Poster @ Room 210 & 230 AB #110 Marylou Gabri (LPS ENS), Andre Manoel (INRIA Saclay, Owkin), Clment Luneau, Jean Barbier,

  1. Entropy and mutual information in models of deep neural networks NeurIPS 2018 - Thursday Dec 06th - Spotlight Poster @ Room 210 & 230 AB #110 Marylou Gabrié (LPS ENS), Andre Manoel (INRIA Saclay, Owkin), Clément Luneau, Jean Barbier, Nicolas Macris (EPFL), Lenka Zdeborová (CEA Saclay), Florent Krzakala (LPS ENS)

  2. Motivations Information theoretic arguments to deep learning Theory of generalization: Shwartz-Ziv et al. 2017, Saxe et al. 2018, Goldfeld et al. 2018 etc. • • New regularizer: Chalk et al. 2016, Alemi et al. 2017, Kolchinsky et al. 2017, Belghazi et al. 2017, Zhao et al. 2018, Achille et al. 2018, Hjelm et al. 2018, etc. Computing mutual informations in neural networks … is tricky • Intractable Computing or yet more involved • Sampled based estimations (non-parametric, variational methods ) Kraskov et al. 2014, Kolchinsky et al. 2017, Belghazi et al. 2017, Goldfeld et al. 2018 etc. Less and less reliable as networks get large è Need for benchmark controlled case è Here 1) Restrict to models of DNNS, 2) Leveverage statistical physics replica method

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