de en es fr nl pl pt sv zh

statistical physics

Numerical stability showcase: Ranking with SoftMax or Boltzmann factor

msuzen

Preamble Image: Babylonian table for computation (Wikipedia)Probably, one of the most important aspects of computational work in quantitative fields, such as physics and data sciences is stability of numerical computations. It implies given inputs, outputs should not wildly deviates to large...

machine learning statistical learning statistical physics numerical analysis connectionist machine learning statistics

Inducing time-asymmetry on reversible classical statistical mechanics via Interventional Thermodynamic Ensembles (ITEs).

msuzen

Preamble Probably, one of the most fundamental issue in classical statistical mechanics is extending reversible dynamics to many-particle systems that behaves irreversibly. In other words, how time's arrow appears even though constituted systems evolves in reversible dynamics. This is the main...

thermodynamics causality statistical physics dynamical systems statistical ensemble causal inference

Loschimidt's Paradox and Causality: Can we establish Pearlian expression for Boltzmann's H-theorem?

msuzen

Boltzmann (Wikipedia)Post covers the papers: H-theorem do-conjecture, M. Süzen,  arxiv:2310.01458 (2023) PreambleProbably the most important achievement for humans is the ability to produce scientific discoveries, that  helps us objectively understand how nature works and build artificial tools...

thermodynamics causality applied mathematics statistical physics statistical mechanics mathematical philosophy theoretical physics

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

msuzen

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...

thermodynamics probability deep learning statistical physics statistics quantum mechanics statistical mechanics probabilistic models statistical analysis

Bayesian rabbit holes: Decoding conditional probability with non-commutative algebra

msuzen

Preamble    The White Rabbit (Wikipedia)A novice analyst or even experienced (data) scientist would have thought that the bar notation $|$ in representing conditional probability carries some different operational mathematics. Primarily when written in explicit distribution functions $p(x|y)$....

data science statistical physics statistics conditional data mining bayesianism statistical mechanics probabilistic models statistical analysis

A misconception in ergodicity: Identify ergodic regime not ergodic process

msuzen

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

Physics origins of the most important statistical ideas of recent times

msuzen

Figure: Maxwell's handwritings, state diagram (Wikipedia)PreambleThe modern statistics now move into an emerging field called data science that amalgamate many different fields from high performance computing to control engineering. However, the emergent behaviour from researchers in machine...

machine learning data science statistical physics statistics data mining interpretable machine learning freshman physics newtonian physics cooperative phenomenon

Deep Learning in Mind a Gentle Introduction to Spectral Ergodicity

msuzen

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

Book review: A tutorial introduction to the mathematics of deep learning

msuzen

Preamble Artificial Intelligence Engines:An introduction to the Mathematics of Deep Learning by Dr James V. Stone the book and Github repository. (c) 2019 Sebtel Press Deep learning and associated connectionist approaches are now applied routinely in industry and academic research from image...

machine learning deep learning statistical learning statistical physics linear algebra mathematics of neural networks connectionist machine learning classsification