[图书][B] Metric algebraic geometry
P Breiding, K Kohn, B Sturmfels - 2024 - library.oapen.org
Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …
geometry. Building on classical foundations, it offers practical tools for the 21st century …
On the minimal algebraic complexity of the rank-one approximation problem for general inner products
K Kozhasov, A Muniz, Y Qi, L Sodomaco - arXiv preprint arXiv:2309.15105, 2023 - arxiv.org
We study the algebraic complexity of Euclidean distance minimization from a generic tensor
to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Veronese …
to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Veronese …
The geometry of the deep linear network
G Menon - arXiv preprint arXiv:2411.09004, 2024 - arxiv.org
This article provides an expository account of training dynamics in the Deep Linear Network
(DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results …
(DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results …
Geometry of lightning self-attention: Identifiability and dimension
NW Henry, GL Marchetti, K Kohn - arXiv preprint arXiv:2408.17221, 2024 - arxiv.org
We consider function spaces defined by self-attention networks without normalization, and
theoretically analyze their geometry. Since these networks are polynomial, we rely on tools …
theoretically analyze their geometry. Since these networks are polynomial, we rely on tools …
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 …
determinantal variety. We investigate the subvariety of functions that are equivariant or …
[HTML][HTML] The geometry of the neuromanifold
K Kohn - Collections, 2024 - siam.org
Machine learning with neural networks works quite well for a variety of applications, even
though the underlying optimization problems are highly nonconvex. Yet despite researchers' …
though the underlying optimization problems are highly nonconvex. Yet despite researchers' …
On the Geometry and Optimization of Polynomial Convolutional Networks
We study convolutional neural networks with monomial activation functions. Specifically, we
prove that their parameterization map is regular and is an isomorphism almost everywhere …
prove that their parameterization map is regular and is an isomorphism almost everywhere …
Algebraic Complexity and Neurovariety of Linear Convolutional Networks
V Shahverdi - arXiv preprint arXiv:2401.16613, 2024 - arxiv.org
In this paper, we study linear convolutional networks with one-dimensional filters and
arbitrary strides. The neuromanifold of such a network is a semialgebraic set, represented by …
arbitrary strides. The neuromanifold of such a network is a semialgebraic set, represented by …
[PDF][PDF] A Complete Bibliography of Publications in the SIAM Journal on Applied Algebra and Geometry
NHF Beebe - 2024 - netlib.org
A Complete Bibliography of Publications in the SIAM Journal on Applied Algebra and
Geometry Page 1 A Complete Bibliography of Publications in the SIAM Journal on Applied …
Geometry Page 1 A Complete Bibliography of Publications in the SIAM Journal on Applied …