Concept
Hyperplane
Related publications (29)
Finite Littlestone Dimension Implies Finite Information Complexity
Michael Christoph Gastpar, Aditya Pradeep, Ido Nachum
We prove that every online learnable class of functions of Littlestone dimension d admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the information complexity of ...
2022Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions
In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to satisfy in addition ...
2022Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances
Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot
We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with layers of minimal widths reaches a zero-loss minimum at $ r_1^*! \c ...
2021A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bezout's identities
Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180 degrees rotation. Thus, crystallographic models of twinning require the determination of the sho ...
INT UNION CRYSTALLOGRAPHY2021Affine Combination of Diffusion Strategies Over Networks
Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strate ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020Stochastic Frank-Wolfe for Composite Convex Minimization
A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed fo ...
2019A Conditional Gradient-Based Augmented Lagrangian Framework
This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template or are too slow ...
2019From Tarski's Plank Problem to Simultaneous Approximation
A slab (or plank) is the part of the d-dimensional Euclidean space that lies between two parallel hyperplanes. The distance between the these hyperplanes is called the width of the slab. It is conjectured that the members of any infinite family of slabs wi ...
Mathematical Assoc Amer2017New Moduli For Banach Spaces
Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...
Tusi Mathematical Research Group2017The number of double-normals in space
Given a set V of points in , two points p, q from V form a double-normal pair, if the set V lies between two parallel hyperplanes that pass through p and q, respectively, and that are orthogonal to the segment pq. In this paper we study the maximum number ...
Springer2016