arXiv research

New result on group actions in CAT(0) spaces with vanishing escape rate.

We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statemen…

Improved sampling for Bayesian neural networks reduces vanishing acceptance rates and increases predictive accuracy.

The Weil-Petersson metric's curvature vanishes for surfaces with short geodesics.

Study on L2-boosting behavior as learning rate approaches zero.

Study the properties of SGD in non-vanishing learning rate regime.

Improved convergence rates for MLE in mixture models using penalized log-likelihood.

Study bounds growth rate of irreducible meanders, showing proportion vanishes.

Paper analyzes if GANs with adversarial features outperform standard supervised learning.

This paper contains some vanishing theorems for $L^2$ harmonic forms on complete Riemannian manifolds with a weighted Poincaré inequality and a certain lower bound of the curvature. The results are in the spirit of Li-Wang and Lam, but without assumptions of sign and growth rate of the weight function, so they can be a…

Study on solutions of degenerate equations on manifolds, linking behavior to geometry and decay rates.

We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken position…

TSGO optimizes gradients in tensor networks to avoid vanishing/exploding issues.

Gradient amplification boosts deep learning model performance without increasing training time.

Square metrics $F=\frac{(α+β)^2}α$ are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics $F=\frac{(bα+β)^2}α$. A characterization for such metrics to be of vanishing Douglas curvature is p…

Infinitesimal gradient boosting is a new algorithm derived from gradient boosting.

Study on convergence rates for optimal transport with regularization.

Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone loss functions, optimized on linearly separable data. Previous works assumed eit…

The paper explores growth rates and Perron numbers in Coxeter systems with low-dimensional Davis complexes.

The paper analyzes reg-SGD for convex problems, proving convergence and quantifying the rate of convergence.

New method finds optimal learning rates for neural nets.

We give another proof for a result of Brick stating that the simple connectivity at infinity is a geometric property of finitely presented groups. This allows us to define the rate of vanishing of $\p1i$ for those groups which are simply connected at infinity. Further we show that this rate is linear for cocompact latt…

New findings cast doubt on the role of $λ_{max}$ in generalizing neural networks.

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a stochastic variant in which the gradient is contaminated by noise, and study the resultin…

The paper develops methods to accurately locate change points in high-dimensional mean shift models.

The paper provides theoretical guarantees for optimized sampling in compressed sensing, showing error vanishes with more measurements.

The study bounds growth of Hodge numbers and computes $L^2$-Betti numbers for irregular varieties.

Active data collection improves convergence rates in operator learning.

We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial marke…

The paper explores how dynamic preconditioning affects the CLT in online averaging.

Ghost mechanism explains abrupt learning in RNNs, revealing constraints on optimization landscapes.

Paper proves multiplicative weight updates can train neural networks without learning rate tuning.

We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find that an observer's average uncertainty in the source state vanishes exponential…

In high dimensions, the mean and geometric median are nearly identical.

The paper constructs singularities for Lagrangian flow in Gibbons-Hawking spaces with vanishing mean curvature.

Calculates winning probability for three candidates based on support rates and information timing.

Vanishing long-term gradients are a major issue in training standard recurrent neural networks (RNNs), which can be alleviated by long short-term memory (LSTM) models with memory cells. However, the extra parameters associated with the memory cells mean an LSTM layer has four times as many parameters as an RNN with the…

In this paper, asymptotic results in a long-term growth rate portfolio optimization model under both fixed and proportional transaction costs are obtained. More precisely, the convergence of the model when the fixed costs tend to zero is investigated. A suitable limit model with purely proportional costs is introduced …

Estimates change point in high dimensional time series models.

The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.

The paper establishes convergence rates for MoE models in classification problems.

AdaGrad fails to adapt to Hölder-smoothness in composite optimization problems.

Step decay schedules improve convergence in non-convex optimization.

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …

We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to all…

Deep linear networks minimize sharpness, avoiding large eigenvalues.

Improved SEG method converges to Nash equilibrium in bilinear games.

Analyze message passing algorithms using free probability theory.