Deep Neural Networks, Generic Universal Interpolation, and Controlled ODEs

DOI10.1137/19M1284117zbMath1485.93062arXiv1908.07838OpenAlexW3089885363MaRDI QIDQ5037577

Josef Teichmann, Martin Larsson, Christa Cuchiero

Publication date: 1 March 2022

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.07838

zbMATH Keywords

Lie bracketsHörmander conditionuniversal interpolationcontrolled dynamical systemsdeep neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Controllability (93B05) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (11)

Interpolation and approximation via momentum ResNets and neural ODEs ⋮ Turnpike in optimal control of PDEs, ResNets, and beyond ⋮ Stochastic integrals and Gelfand integration in Fréchet spaces ⋮ Large Sample Mean-Field Stochastic Optimization ⋮ Control on the manifolds of mappings with a view to the deep learning ⋮ Neural networks in Fréchet spaces ⋮ Universal regular conditional distributions via probabilistic transformers ⋮ Neural ODE Control for Classification, Approximation, and Transport ⋮ Pricing options on flow forwards by neural networks in a Hilbert space ⋮ Control of partial differential equations via physics-informed neural networks ⋮ Reinforcement learning and stochastic optimisation

Uses Software

• FFJORD
• torchdiffeq
• ANODEs

Cites Work

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• Just interpolate: kernel ``ridgeless regression can generalize
• A proposal on machine learning via dynamical systems
• Defining relations for classical Lie algebras of polynomial vector fields.
• On Everywhere Dense Imbedding of Free Groups in Lie Groups
• Approximation by superpositions of a sigmoidal function

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