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quantum mechanics

Differentiating ensembles and sample spaces: Alignment between statistical mechanics and probability theory

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Preamble Sample space is the primary concept introduced in any probability and statistics books and in papers. However, there needs to be more clarity about what constitutes a sample space in general: there is no explicit distinction between the unique event set and the replica sets. The...

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...