This paper studies the over-parameterization of deep neural networks using Fisher Information Matrix from information geometry. We identify several surprising trends in structure its eigenspectrum, and how this relates to eigenspectrum data correlation matrix. topology predictions model develop a "model reduction'' method for networks. ongoing investigation hypothesizes certain universal FIM th...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

In this paper we consider the problem of decomposing a simple polygon into subpolygons that exclusively use vertices of the given polygon. We allow two types of subpolygons: pseudo-triangles and convex polygons. We call the resulting decomposition PTconvex. We are interested in minimum decompositions, i.e., in decomposing the input polygon into the least number of subpolygons. Allowing subpolyg...

For a connected graph G with at least two vertices and S a subset of vertices, the convex hull [S]G is the smallest convex set containing S. The hull number h(G) is the minimum cardinality among the subsets S of V (G) with [S]G = V (G). Upper bound for the hull number of strong product G⊠H of two graphs G and H is obtainted. Improved upper bounds are obtained for some class of strong product gr...

In this note we show that a non-degenerated polytope in IRn with n+k, 1 ≤ k < n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes. 0 Introduction and notations The canonical Euclidean inner product in IR is denoted by 〈·, ·〉, the norm in `p is denoted by ‖ · ‖p, 1 ≤ p ≤ ∞. By a convex body K ⊂ IR we shall always ...

We consider a finite set of lattice points and their convex hull. The author previously gave a geometric proof that the sumsets of these lattice points take over the central regions of dilated convex hulls, thus revealing an interesting connection between additive number theory and geometry. In this paper, we will see an algebraic proof of this fact when the convex hull of points is a simplex, ...

Assume that we are given a set of points some of which are black and the rest are white. The goal is to find a set of convex polygons with maximum total area that cover all white points and exclude all black points. We study the problem on three different settings (based on overlapping between different convex polygons): (1) In case convex polygons are permitted to have common area, we present ...

Sparsity-inducing norm has been a powerful tool for learning robust models with limited data in high dimensional space. By imposing such norms as constraints or regularizers in an optimization setting, one could bias the model towards learning sparse solutions, which in many case have been proven to be more statistically efficient [Don06]. Typical sparsityinducing norms include `1 norm [Tib96] ...

A convex polygon is defined as a sequence (V0, . . . , Vn−1) of points on a plane such that the union of the edges [V0, V1], . . . , [Vn−2, Vn−1], [Vn−1, V0] coincides with the boundary of the convex hull of the set of vertices {V0, . . . , Vn−1}. It is proved that all sub-polygons of any convex polygon with distinct vertices are convex. It is also proved that, if all sub-(n − 1)-gons of an n-g...