A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Review of information plane analyses in neural networks, highlighting mixed results and methodological challenges.
The Information Plane theory predicts autoencoders do not compress input information.
We give a criterion for a projective surface to become a quotient of a fake projective plane. We also give a detailed information on the elliptic fibration of a -elliptic surface that is the minimal resolution of a quotient of a fake projective plane. As a consequence, we give a classification of -h…
Results on -dimensional topological planes are scattered in the literature. It is the aim of the present paper to give a survey of these geometries, in particular of information obtained after the appearance of the treatise Compact Projective Planes or not included in this book. For some theorems new proofs are give…
Certain biological neurons demonstrate a remarkable capability to optimally compress the history of sensory inputs while being maximally informative about the future. In this work, we investigate if the same can be said of artificial neurons in recurrent neural networks (RNNs) trained with maximum likelihood. Empirical…
Study of elementary planes in Apollonian orbifold with unusual equidistribution.
We show that under certain symmetry, the images of complete harmonic embeddings from the complex plane into the hyperbolic plane is completely determined by the geometric information of the vertical measured foliation and is independent of the horizontal measured foliation of the corresponding Hopf differentials.
The paper extends curve deformation methods in Minkowski plane.
In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These two quantities are complementary and are jointly applied to information behavior…
Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the dynamics of learning and the design of autoencoders, a special type of deep lea…
High quality reconstruction with interventional C-arm cone-beam computed tomography (CBCT) requires exact geometry information. If the geometry information is corrupted, e. g., by unexpected patient or system movement, the measured signal is misplaced in the backprojection operation. With prolonged acquisition times of…
In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case…
New method recovers curvature from heat diffusion data.
TSVQR captures heterogeneous and asymmetric data using quantile regression.
Explains a theorem about curves in the plane.
The abstract aims to generalize classical curve concepts to uniquely define complex curves.
New algorithms solve convex optimization problems with limited memory.
Classifies compact radio sources in the Galactic plane using machine learning.
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to . We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plan…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
The study classifies semiaffine stable planes into affine, projective, or punctured projective planes.
Stable planes are locally isomorphic to classical projective planes.
Only vertical planes are asymptotic to other planes in 3D space.
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by Morse Theory, we algorithmically produce a PL approximation of the original shape …
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective ho…
The paper discusses Nirenberg's work on geometric problems and his personality.
Analyzing deep neural networks (DNNs) via information plane (IP) theory has gained tremendous attention recently as a tool to gain insight into, among others, their generalization ability. However, it is by no means obvious how to estimate mutual information (MI) between each hidden layer and the input/desired output, …
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
Criteria for sharksfin and deltoid singularities from plane to plane, with applications.
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…
The study explores conformal planes with finite areas.
For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…
Applications of machine learning tools to problems of physical interest are often criticized for producing sensitivity at the expense of transparency. To address this concern, we explore a data planing procedure for identifying combinations of variables -- aided by physical intuition -- that can discriminate signal fro…
We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.
This thesis explores bifoliated planes and their group actions from Anosov flows.
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
Two proofs show that removing a loop from a plane circuit splits the plane.
For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with fixed boundary conditions and prescribed singular pattern, by which we mean the com…
The paper classifies singularities of plane congruences and affine distance functions.
Computed distortion coefficients for the α-Grushin plane.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
Weak lensing maps contain information beyond two-point statistics on small scales. Much recent work has tried to extract this information through a range of different observables or via nonlinear transformations of the lensing field. Here we train and apply a 2D convolutional neural network to simulated noiseless lensi…
New harmonic maps to hyperbolic plane via Bäcklund transformation.
Study compact plane waves, showing they are essentially standard.
The paper examines asymptotic lines of plane fields in 3D space.
A 6-regular triangulation for hyperbolic plane created.
The role of credit rating agencies has been under severe scrutiny after the subprime crisis. In this paper we explore the relationship between credit ratings and informational efficiency of a sample of thirty nine corporate bonds of US oil and energy companies from April 2008 to November 2012. For that purpose, we use …
Study local and global aspects of complex plane curve embeddings.