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Stateful ODE-Nets using Basis Function Expansions
Alejandro Queiruga · N. Benjamin Erichson · Liam Hodgkinson · Michael Mahoney

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @

The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems. In this work, we reconsider formulations of the weights as continuous-in-depth functions using linear combinations of basis functions which enables us to leverage parameter transformations such as function projections. In turn, this view allows us to formulate a novel stateful ODE-Block that handles stateful layers. The benefits of this new ODE-Block are twofold: first, it enables incorporating meaningful continuous-in-depth batch normalization layers to achieve state-of-the-art performance; second, it enables compressing the weights through a change of basis, without retraining, while maintaining near state-of-the-art performance and reducing both inference time and memory footprint. Performance is demonstrated by applying our stateful ODE-Block to (a) image classification tasks using convolutional units and (b) sentence-tagging tasks using transformer encoder units.

Author Information

Alejandro Queiruga (Google)
N. Benjamin Erichson (University of Pittsburgh)
Liam Hodgkinson (UC Berkeley)
Michael Mahoney (UC Berkeley)

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