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ergodic hypothesis

A misconception in ergodicity: Identify ergodic regime not ergodic process

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Preamble     Figure 1: Two observable's approach to ergodicity for Bernoulli Trials. Ergodicity appears in many fields, in physics, chemistry and natural sciences but in economics to machine learning as well. Recall that, ergodicity in physics and mathematical definition diverges significantly due...

economics statistical physics statistics bernoulli trails statistical mechanics stochastic processes ergodic hypothesis

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

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...

machine learning statistical physics random matrix theory spectral ergodicity interpretable machine learning statistical mechanics ergodic hypothesis

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...

machine learning deep learning linear algebra random matrix theory complexity theory probabilistic models ergodic hypothesis complex networks multidimensional arrays freeman dyson ising-lenz model