EC84-408 Grain as Food

Extension Circular 84-408: This circular talks about various cereal grains. Most of these grains are important to Nebraska’s economy

Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such group actions are translations or $90^\circ$ rotations on images. For such equivariant or invariant subvarieties, we provide an explicit description of their dimension, their degree as well as their Euclidean distance degree, and their singularities. We fully characterize invariance for arbitrary permutation groups, and equivariance for cyclic groups. We draw conclusions for the parameterization and the design of equivariant and invariant linear networks, such as a weight sharing property, and we prove that all invariant linear functions can be learned by linear autoencoders.Comment: 24 pages, 2 figures, comments welcome

EC84-408 Grain as Food

Extension Circular 84-408: This circular talks about various cereal grains. Most of these grains are important to Nebraska’s economy

The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices

We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over a linear space of symmetric matrices. We obtain new formulae for the ML degree, one via Schubert calculus, and another using Segre classes from intersection theory. We settle the case of codimension one models, and characterize the degenerate case when the ML degree is zero.Comment: 21 pages and 1 figur

Redescrição do tipo de equinoparyphium singularis (Lutz, 1924) comb. para Stephanoprora singularis (Lutz, 1924) (Trematoda, Equinostomatidae)

Os autores redescrevem e apresentam figuras originais do exemplar tipo de Stephanoprora singularis (Lutz, 1924) propondo uma nova combinação: Equinoparyphium singularis (Lutz, 1924) comb. n.The authors redescribe and present original figures of the type of S. singularis (Lutz, 1924) proposing a new combination: Equinoparyphium singularis (Lutz, 1924) n. comb