arXiv research

HA-SME models SGD dynamics with Hessian info for better escaping behaviors.

Quadratic models explain neural network behavior during training.

We state conjectures on the asymptotic behavior of the Masur-Veech volumes of strata in the moduli spaces of meromorphic quadratic differentials and on the asymptotics of their area Siegel-Veech constants as the genus tends to infinity.

We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential $q$ if we prescribe, in addition, the principal parts of $\sqrt q$ at the poles. This generalizes a theorem of Hubbard and …

Study describes splitting and filtration of Hodge bundle on quadratic differentials.

Consider a closed connected hypersurface in $\mathbb{R}^n$ with constant signature (k,l) of the second quadratic form, and approaching a quadratic cone at infinity. This hypersurface divides $\mathbb{R}^n$ into two pieces. We prove that one of them contains a k-dimensional subspace, and another contains a l-dimensional…

Abstract perspective on quadratic programming for optimal portfolio allocation.

We partially resolve a conjecture of Meeks on the asymptotic behavior of minimal surfaces in $\mathbb{R}^3$ with quadratic area growth.

Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the surface. We show that generically the index of the 3-web at a quadratic point is…

Gaussian equivalence fails for simple polynomial embeddings in quadratic scaling RF models.

New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $ε$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman eq…

Model asset pricing with habit formation in a large market.

Proposes r2SGLD for efficient constrained exploration in non-convex learning.

We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a…

Extends QHawkes to MQHawkes for analyzing financial co-jumps.

Studied how heavy-tailed behavior affects SGD's generalization in quadratic optimization.

The paper characterizes and studies compact subsets of complex projective space with specific line intersection properties.

Reinforcement learning (RL) has been successfully used to solve many continuous control tasks. Despite its impressive results however, fundamental questions regarding the sample complexity of RL on continuous problems remain open. We study the performance of RL in this setting by considering the behavior of the Least-S…

The paper studies new curvature properties in Finsler geometry.

Proposes sparse QSVM for better generalization and interpretability.

This paper introduces a method to incorporate risk sensitivity in RL using quadratic variation penalties.

We make use of wavelet transform to study the multi-scale, self similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scale…

We review geometrical properties of a static spacetime $(M,g)$, including geodesic completeness, causality, standard splittings, compact $M$, closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients $β$, $β^{-1}$ ($β= -g(K,K)$, being $K$ a …

Microscopic models describing a whole of economic interactions in a closed society are considered. The presence of a tax system combined with a redistribution process is taken into account, as well as the occurrence of tax evasion. In particular, the existence is postulated, in relation to the level of evasion, of diff…

Improved efficiency in HMC samplers reduces dissipative behavior.

The paper analyzes optimal execution strategies for traders with inventory processes influenced by Brownian motion.

Optimal trading strategy with predictor and costs, derived equations and shape.

We study the role of co-jumps in the interest rate futures markets. To disentangle continuous part of quadratic covariation from co-jumps, we localize the co-jumps precisely through wavelet coefficients and identify statistically significant ones. Using high frequency data about U.S. and European yield curves we quanti…

New model captures asymmetric rough volatility with Zumbach effect.

New study shows faster convergence of SGD and Kaczmarz methods.

In this paper we study $\varphi$-minimal surfaces in $\mathbb{R}^3$ when the function $\varphi$ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in $\mathbb{R}^2$. We describe a full classification of complete flat embedded $\varphi$-minimal surfaces i…

Develops a new fuzzy model using QPs and ewl2 regularization to improve local region behavior.

Study on Teichmüller rays' asymptotic behavior and distances.

New bound matches exact generalization error for quadratic Gaussian problem.

We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclide…

Quantum computing improves feature selection in machine learning.

Researchers disrupt Gaussian model inference to test adversarial attacks.

A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …

Given a negatively curved geodesic metric space $M$, we study the statistical asymptotic penetration behavior of (locally) geodesic lines of $M$ in small neighborhoods of points, of closed geodesics, and of other compact (locally) convex subsets of $M$. We prove Khintchine-type and logarithme law-type results for the s…

We analyze the slope gap distribution of Veech surfaces, finding finite non-analytic points and quadratic tail decay.

Study on how non-reversible diffusion processes affect homology on manifolds.

New method infers human sensorimotor costs from behavior.

Improved R-QDA classifier performs well in unbalanced data settings.

We quantify how co-jumps impact correlations in currency markets. To disentangle the continuous part of quadratic covariation from co-jumps, and study the influence of co-jumps on correlations, we propose a new wavelet-based estimator. The proposed estimation framework is able to localize the co-jumps very precisely th…

The main challenge for adaptive regulation of linear-quadratic systems is the trade-off between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the regulation of the underlying system (exploitation). To this end, optimism-based…

New algorithm reconstructs sparse networks in subquadratic time.

A new geometric flow $K$-flow on 3-manifolds shrinks or preserves homogeneous spheres.