random matrix theory

Nov 12 2025

Understanding high-entropy random number generation for research: Leymosun Package

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PreambleThe idea of generating randomness via computers goes back to von Neumann's and his team of colleagues work in Princeton and Los Alamos. Even though, he was sceptical about the idea of generating randomness via computer programs, this practice is now almost a de-facto standard, so the name...

random number generators prng rng random matrix theory entropy random numbers

Nov 15 2021

Periodic Spectral Ergodicity Accurately Predicts Deep Learning Generalisation

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Preamble     Dali (1931), The Persistence of Memory (Wikipedia)One of the new mathematical concepts arise due to understanding of deep learning is called periodic spectral ergodicity (PSE). The cascading PSE (cPSE) propagates over deep learning layers which can also be used as a complexity...

deep learning random matrix theory periodic spectral ergodicity complexity theory spectral ergodicity quantum mechanics random matrices ergodic hypothesis

Jul 28 2021

Deep Learning in Mind a Gentle Introduction to Spectral Ergodicity

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Preamble    Figure: Monalisa on Eigenvector grids (Wikipedia)In the post, A New Matrix Mathematics for Deep Learning : Random Matrix Theory of Deep Learning, we have outlined a new mathematical concepts that are aimed at deep learning but in general belonging to applied mathematics. Here, we dive...

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Jul 21 2021

A New Matrix Mathematics for Deep Learning : Random Matrix Theory of Deep Learning

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Preamble     Figure: Definition of Randomness (Compagner 1991, Delft University)Development of deep learning systems (DLs)  increased our hopes to develop more autonomous systems. Based on the hierarchal learning of representations, deep learning defies the basic learning theory that beg the...

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Jun 29 2020

Conjugacy and Equivalence for Deep Neural Networks: Architecture compression to selection

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Preamble A recently shown phenomenon can classify deep learning architectures with only using the knowledge gained by trained weights [suezen20a]. The classification produces a measure of equivalence between two trained neural network and astonishingly captures a family of closely related...

learning machine learning deep learning random matrix theory statistical ensemble conjugate matrix ensembles supervised