arXiv research

Study uses spectral risk for learning with heavy-tailed data.

Study heavy-tailed weights' impact on neural network's spectral distribution.

New models explain heavy-tailed behavior in neural networks.

Investigates spectral properties of neural networks, showing invariance under certain conditions.

Study on estimating rank-one tensors in noisy data with heavy tails.

This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that r…

Paper extends tail bounds to high-dimensional random objects on Riemannian manifolds.

Study uses satellite data to predict tailings dam collapse risk.

This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a quantile spectral beta representation of risk based on the decomposition of cova…

New insights into why neural networks generalize well.

Study uses detrended cross-correlation to analyze cryptocurrency market, revealing robust collective modes and distinguishing interdependencies.

We study the asymptotic behavior of the difference $Δρ^{X, Y}_α:= ρ_α(X + Y) - ρ_α(X)$ as $α\rightarrow 1$, where $ρ_α$ is a risk measure equipped with a confidence level parameter $0 < α< 1$, and where $X$ and $Y$ are non-negative random variables whose tail probability functions are regularly varying. The case where …

The difficulty of classification affects the weight matrices' heavy tail appearance in deep learning networks.

Efficiently estimates sparse mean from heavy-tailed data.

Heavy-tailed regularization improves deep neural network performance.

We prove exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates for certain Ruelle transfer operators for such flows.

New method estimates log-determinant using trace powers, avoiding classical limitations.

Muon optimizes Transformer training with heavy-tailed data, achieving optimal sample complexity.

The paper improves alignment methods for deep neural networks using geometric and spectral analysis.

Novel model captures high-dimensional copulas with spectral dynamics and regularization.

Paper tackles robust matrix completion with heavy-tailed noise.

Risk is an inherent feature of agricultural production and marketing and accurate measurement of it helps inform more efficient use of resources. This paper examines three tail quantile-based risk measures applied to the estimation of extreme agricultural financial risk for corn and soybean production in the US: Value …

New method reduces linear regret in high-dimensional bandit problems.

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming that the random vector has bounded mean and covariance. Polynomial-time solutio…

Method detects neural network equivalence via matrix ensembles and spectral analysis.

A new algorithm reduces the time and space complexity for multinomial logistic bandits.

We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the s…

Spectral measurements reveal hidden representation geometry in language model training.

Unified framework detects overfitting in crash classification models.

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …

Study uncovers scaling laws and spectral properties of shallow neural networks.

Positive weights improve kernel quadrature's accuracy.

Paper improves robust spectral clustering for noisy data.

Study finds the minimum number of finite Gaussian mixtures for best approximation.

The goal in extreme multi-label classification is to learn a classifier which can assign a small subset of relevant labels to an instance from an extremely large set of target labels. Datasets in extreme classification exhibit a long tail of labels which have small number of positive training instances. In this work, w…

AlphaPruning optimizes LLM pruning using HT-SR theory for better performance.

This paper develops a new theory for ensemble learning beyond variance reduction.

Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. Empirical and theoretical results clearly indicate th…

We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose ex…

A new method estimates parameters in heavy-tailed corrupted regression with unknown covariance and heterogeneous noise.

The paper proves geometric and spectral alignment for deep neural networks.

This work explains scaling laws as redundancy laws in deep learning.

We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal beha…

Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good prop…

Optimizes dividend control in a bankruptcy process using a special Levy process.

ACFS optimizes spectral risk under decision-dependent uncertainty using adaptive forest sampling.

New method models fat-tailed distributions with anisotropic tail-adaptive flows.