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Research questionHow can fixed-dimensional subspaces of one-dimensional convolutional filters be parametrized injectively as smooth closed projective varieties?Representing a layer by a filter subspace removes dependence on the ordering of its filters, but distinct subspaces could still induce the same convolutional operators. The resulting projective image may also have undesirable closure or singularity behavior that must be characterized.
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Latest papersRecent research connected to this question, newest first.Grassmann--Plücker Parametrization of Convolutional Filter Subspaces: Regularity and Closed EmbeddingsThe setting is one-dimensional finite-stride convolution with an injective filter-to-operator map and fixed-dimensional subspaces represented through Grassmannians and Plücker coordinates. The supplied results establish injectivity, closed embedding, singleton fibers, and smoothness of the projective image; the k=4, q=2 computer-algebra calculation is illustrative rather than a replacement for the general proof.research paper · Sep 3, 2026
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