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zbMATH Open
Article . 2021
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SIAM Journal on Mathematics of Data Science
Article . 2021 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2019
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Implicit Deep Learning

Implicit deep learning
Authors: Laurent El Ghaoui; Fangda Gu; Bertrand Travacca; Armin Askari; Alicia Y. Tsai;

Implicit Deep Learning

Abstract

Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only implicitly defined. The implicit framework greatly simplifies the notation of deep learning, and opens up many new possibilities, in terms of novel architectures and algorithms, robustness analysis and design, interpretability, sparsity, and network architecture optimization.

Related Organizations
Keywords

FOS: Computer and information sciences, Numerical optimization and variational techniques, Computer Science - Machine Learning, deep learning, Machine Learning (stat.ML), robustness, deep equilibrium models, Perron-Frobenius theory, Machine Learning (cs.LG), Neural nets and related approaches to inference from stochastic processes, fixed-point equations, Implicit function theorems, Jacobians, transformations with several variables, adversarial attacks, Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Optimization and Control

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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    38
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 1%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
38
Top 10%
Top 10%
Top 1%
Green
gold