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.
The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codim…
This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have symmetries with hidden extensions, then we further extend these to hidden symmetries of…
We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of th…
This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian non…
Supervised learning frequently boils down to determining hidden and bright parameters in a parameterized hypothesis space based on finite input-output samples. The hidden parameters determine the attributions of hidden predictors or the nonlinear mechanism of an estimator, while the bright parameters characterize how h…
Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We exhibit examples that illustrate the need for a more general model and discuss de…
We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain Monte Carlo to move between solutions. In contrast, we assume that the number of hi…
Hidden Markov Neural Networks balance adaptation and forgetting in time-series data.
problem Balancing adaptation to new data and forgetting outdated information in time-series forecasting.
method Modeling weights as hidden states of a Hidden Markov model, using a filtering algorithm for learning a variational approximation of the posterior distribution over weights, and employing sequential Bayes by Backprop with variational DropConnect for regularization.
result Achieves strong predictive performance and effective uncertainty quantification on various tasks.
This paper is concerned with the sparsification of the input-hidden weights of ELM (Extreme Learning Machine). For ordinary feedforward neural networks, the sparsification is usually done by introducing certain regularization technique into the learning process of the network. But this strategy can not be applied for E…
A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the relations to other variables in the model and determining the number of states of …
The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.
problem Integrating the hidden M-algebra into a super-Lie group to model super-exceptional spacetimes.
method Left-invariant extension of the decomposed M-theory 3-form, providing a computer-checked re-derivation and streamlined conception of super-Lie groups.
result Lattice subgroups of the hidden M-group allow toroidal compactification of hidden dimensions, akin to topological T-duality.
Multilabel classification is an important problem in a wide range of domains such as text categorization and music annotation. In this paper, we present a probabilistic model, Multilabel Logistic Regression with Hidden variables (MLRH), which extends the standard logistic regression by introducing hidden variables. Hid…
Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on E=[0,∞]d\{(0,0,...,0)} and models another regular variation on the sub-cone E(2)=E\∪i=1dLi, where Li is the $i…
In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional ∫1+Kγ2ds, depending both on length and curvature K. We fix starting and ending points as well as initial and final directions. For this functional we discuss the problem o…
A neural network with a single hidden layer can't represent certain multivariable functions.
problem Representing certain multivariable functions with a neural network having only one hidden layer.
method Developed a continuum version of a one-hidden-layer neural network with ReLU activation, and proved constraints on its parameters and second derivative.
result Existence of a smooth binary function that cannot be precisely represented by any such neural network.
We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent activity levels that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of inferring human mobility on sub-daily time scales from, for example, mobile phone …
A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<\infty, Riemannian cover of M which is not the lift of any isometry. In this paper we characterize the locally symmetric metric(s) on a closed, arithmetic manifold as the unique metric with infinitely many hidden symmetries.