no code implementations • 21 Feb 2024 • Dominik Schröder, Daniil Dmitriev, Hugo Cui, Bruno Loureiro
For a large class of feature maps we provide a tight asymptotic characterisation of the test error associated with learning the readout layer, in the high-dimensional limit where the input dimension, hidden layer widths, and number of training samples are proportionally large.
1 code implementation • 1 Feb 2023 • Dominik Schröder, Hugo Cui, Daniil Dmitriev, Bruno Loureiro
Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest.
no code implementations • 13 Apr 2022 • Dominik Schröder, Diederick Vermetten, Hao Wang, Carola Doerr, Thomas Bäck
In this work, we build on the recent study of Vermetten et al. [GECCO 2020], who presented a data-driven approach to investigate promising switches between pairs of algorithms for numerical black-box optimization.
1 code implementation • NeurIPS 2021 • Vanessa Piccolo, Dominik Schröder
We extend the previous results to the case of additive bias $Y=f(WX+B)$ with $B$ being an independent rank-one Gaussian random matrix, closer modelling the neural network infrastructures encountered in practice.
no code implementations • 11 Mar 2021 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the quadratic form of a general deterministic matrix on the eigenvectors of an $N\times N$ Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large $N$ limit.
Probability Mathematical Physics Mathematical Physics 60B20, 15B52
no code implementations • 19 Feb 2021 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices $W$ and provide an optimal error bound on their fluctuation with very high probability.
Probability Mathematical Physics Functional Analysis Mathematical Physics Operator Algebras 60B20, 15B52, 46L54
no code implementations • 24 Dec 2020 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$ viewed as an entire matrix $f(W)$.
Probability Mathematical Physics Mathematical Physics 60B20, 15B52
no code implementations • 24 Dec 2020 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension.
Probability Mathematical Physics Mathematical Physics 60B20, 15B52, 58J51, 81Q50
