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2021

Geometry of Linear Convolutional Networks

Kohn, Kathlén, Merkh, Thomas, Montúfar, Guido et al.

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We study the family of functions that are represented by a linear convolutional neural network (LCN).

These functions form a semi-algebraic subset of the set of linear maps from input space to output space.
In contrast, the families of functions represented by fully-connected linear networks form algebraic sets.
We observe that the functions represented by LCNs can be identified with polynomials that admit certain factorizations, and we use this perspective to describe the impact of the network's architecture on the geometry of the resulting function space.

Geometry of Linear Convolutional Networks · Around

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