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.
CatNet controls FDR in LSTM models using SHAP feature importance and Gaussian mirrors.
problem Controlling False Discovery Rate (FDR) in LSTM models with feature selection.
method CatNet uses SHAP values for feature importance and Gaussian Mirror algorithm for FDR control. It introduces a kernel-based independence measure to handle feature correlations.
result CatNet reduces overfitting and improves model interpretability on simulated and real-world data.
Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic gradient algorithm (SGD), where instead of updating the weight vector along the nega…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack either scalability or rigorous guarantees. To tackle this challenge, we propose …
Deep Gaussian Processes with polynomial kernels can collapse rapidly without proper hyperparameter tuning.
problem The collapse of Deep Gaussian Processes with polynomial kernels without careful hyperparameter tuning.
method Analysis using the Berry-Esseen Theorem and observation of prior behavior.
result The prior of a Deep Gaussian Process collapses rapidly towards zero or places negligible mass on low norm functions without proper hyperparameter tuning.
We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare …
We describe mirror symmetry on higher dimensional tori, paying special attention to the behaviour of D-branes under mirror symmetry. To find the mirror D-branes the description of mirror symmetry on D-branes due to Ooguri, Oz en Yin is used. This method allows us to deal with the coisotropic D-branes recently introduce…
Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds.
We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups G2 and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twisted connected sum G2 manifolds, mirrors of such Spin(7) manifolds can be fou…
In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.
A standard introduction to online learning might place Online Gradient Descent at its center and then proceed to develop generalizations and extensions like Online Mirror Descent and second-order methods. Here we explore the alternative approach of putting Exponential Weights (EW) first. We show that many standard meth…
Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference networks for a flexible inference. Unfortunately, for such networks, minibatch tra…
Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond. By necessity, most theoretical guarantees revolve around convex-concave (or even linear) problems; however, making theoretical inroads towards effici…
This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian torus fibrations. We explore this conjecture without reference to the special La…
Optimal classifiers derived from GMMs are approximated by deep neural networks.
problem Binary classification of high-dimensional overlapping Gaussian mixtures.
method Closed-form expressions for Bayes optimal decision boundaries derived from GMMs' eigenstructure. Empirical validation through synthetic and real-world data.
result Deep neural networks approximate optimal classifiers for GMMs, with decision thresholds related to covariance eigenvectors.
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G2 manifolds. For a given G2 manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of $G_2…
Find first (0,2) mirror symmetry examples on Hopf surfaces.
problem Find (0,2) mirror symmetry on compact non-Kähler manifolds.
method Use Borisov's approach with vertex algebras and chiral de Rham complex. Study Killing spinors on quadratic Lie algebras and embeddings of superconformal vertex algebras.
result Construct first (0,2) mirror pairs of Hopf surfaces.
Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…