Provably Strict Generalisation Benefit for Equivariant Models

It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the simplest case of linear models, this paper provides the first p...

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Bibliographic Details
Published inarXiv.org
Main Authors Elesedy, Bryn, Zaidi, Sheheryar
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.07.2021
Subjects
Function space
Invariants
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Summary:It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the simplest case of linear models, this paper provides the first provably non-zero improvement in generalisation for invariant/equivariant models when the target distribution is invariant/equivariant with respect to a compact group. Moreover, our work reveals an interesting relationship between generalisation, the number of training examples and properties of the group action. Our results rest on an observation of the structure of function spaces under averaging operators which, along with its consequences for feature averaging, may be of independent interest.
ISSN:2331-8422