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of 19
pro vyhledávání: '"Hamdan, Jad"'
We present a unified approach to obtain scaling limits of neural networks using the genus expansion technique from random matrix theory. This approach begins with a novel expansion of neural networks which is reminiscent of Butcher series for ODEs, a
Externí odkaz:
http://arxiv.org/abs/2407.08459
Autor:
Arguin, Louis-Pierre, Hamdan, Jad
We derive precise upper bounds for the maximum of the Riemann zeta function on short intervals on the critical line, showing for any $\theta\in(-1,0]$, the set of $t\in [T,2T]$ for which $$\max_{|h|\leq \log^\theta T}|\zeta(\tfrac{1}{2}+it+ih)|>\exp\
Externí odkaz:
http://arxiv.org/abs/2405.06474
Autor:
Hamdan, Jad
We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi--free and bi--Boolean independence under finite third moment assumptions. The proofs rely on the constr
Externí odkaz:
http://arxiv.org/abs/2305.06960
Autor:
Devroye, Luc, Hamdan, Jad
We propose a simple algorithm to generate random variables described by densities equaling squared Hermite functions. Using results from random matrix theory, we utilize this to generate a randomly chosen eigenvalue of a matrix from the Gaussian Unit
Externí odkaz:
http://arxiv.org/abs/2304.03741
We investigate properties of neural networks that use both ReLU and $x^2$ as activation functions and build upon previous results to show that both analytic functions and functions in Sobolev spaces can be approximated by such networks of constant de
Externí odkaz:
http://arxiv.org/abs/2301.13091
Autor:
Devroye, Luc, Hamdan, Jad
We propose a novel, simple density estimation algorithm for bounded monotone densities with compact support under a cellular restriction. We show that its expected error ($L_1$ distance) converges at a rate of $n^{-1/3}$, that its expected runtime is
Externí odkaz:
http://arxiv.org/abs/2203.08006
Publikováno v:
Australasian Journal of Combinatorics 84,3 (2022), 357-374
This paper concerns the lattice $L_n$ of subsets of $\{1,\ldots,n\}$ that are arithmetic progressions, under the inclusion order. For $n\geq 4$, this poset is not graded and thus not semimodular. We give three independent proofs of the fact that for
Externí odkaz:
http://arxiv.org/abs/2106.05949
We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results allow us t
Externí odkaz:
http://arxiv.org/abs/2105.03195
Autor:
Hamdan, Jad
This short note presents a proof of the Free Central Limit Theorem for probability measures with finite third moment using the renormalization group approach. We construct a contractive renormalization group map over the space of probability measures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::675167a44c15d0564075353a42c74b57
http://arxiv.org/abs/2305.06960
http://arxiv.org/abs/2305.06960
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