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.
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…
Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical ensemble of asset-price covariances from a single instance of financial data sets…
Persistence diagrams from random matrices follow RMT universality, offering a new spectral diagnostic.
We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random …
We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance matrix is defined and we proved that the set of such matrices is everywhere dense …
Study on random matrices in deep neural networks with IID entries.
Random matrix analysis reveals that neural network weights are mostly random, with some indicating learned information.
We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.
In a noiseless linear estimation problem, one aims to reconstruct a vector x* from the knowledge of its linear projections y=Phi x*. There have been many theoretical works concentrating on the case where the matrix Phi is a random i.i.d. one, but a number of heuristic evidence suggests that many of these results are un…
We uncover scaling laws and statistical structure in complex datasets.
The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some prev…
Study on linear regression with dependent covariates, proving universality and error characterization.
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
This paper shows universality in spectrum behavior for random inner-product kernel matrices in polynomial regime.
New insights into model robustness for random features and NTK models.
The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite restrictive in practice. More specifically, the methods assume that: a) the observed indic…
Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important difference is that the population covariance matrices, which are assumed to be non-random…
New tool detects 'fleeting modes' causing excess risk in financial markets.
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the …
A new machine learning model uses matrix exponentials for universal approximation.
We demonstrate that in residual neural networks (ResNets) dynamical isometry is achievable irrespectively of the activation function used. We do that by deriving, with the help of Free Probability and Random Matrix Theories, a universal formula for the spectral density of the input-output Jacobian at initialization, in…
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994--95 (ii) 30-min returns of 881 US stock…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particulary universal) space to the properties of distance …
This paper shows how to estimate distances in latent space of random graphs using entropic OT.
New models explain heavy-tailed behavior in neural networks.
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal -matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that c…
New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.
Stochastic configuration networks (SCNs) as a class of randomized learner model have been successfully employed in data analytics due to its universal approximation capability and fast modelling property. The technical essence lies in stochastically configuring hidden nodes (or basis functions) based on a supervisory m…
Optimal subspace embedding with near-optimal sparsity for high-dimensional data.
The study proves Gaussian universality of deep random features learning.
We introduce a class of metrics on gauge theoretic moduli spaces. These metrics are made out of the universal matrix that appears in the universal connection construction of M. S. Narasimhan and S. Ramanan. As an example we construct metrics on the c_{2}=1 SU(2) moduli space of instantons on R^4 for various universal m…
We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes in neural networks. The universality result implies that the random ReLU features…
GNNs with random node initialization are shown to be universally expressive.
The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters advancing conventional randomized approaches constrained with a fixed scope of rand…
New pivoting strategy improves trace norm contraction in low-rank approximation.
Study exact limits of matrix reconstruction from noisy projections.
A novel algorithm for unbiased graph kernel estimation with subquadratic time complexity.
Improved matrix approximation using randomized algorithms.
Random feature models approximate functions in Banach spaces efficiently.
Study reveals a universal formula for knotting in random equilateral polygons.
Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
Proposes a robust portfolio method for large asset universes.
In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the tail behavior of various matrix functions, e.g., arbitrary matrix norms, the absol…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…
Study shows exponential growth of Laplacian determinant on random hyperbolic surfaces.
The paper proves universality in optimization problems with i.i.d. random vectors.