As I got deeper and deeper understanding of the world, both in theoretical and practical way, I am fascinated by the fact that different concepts in different fields can always build a correspondence between one another. Which can be said so, that one concept are continuously rediscovered over and over again, by different group of people with different background. Or maybe we can even guess that this phenomenon reveals an astonishing truth that the world is built up deductively, using some minimal set of elements.

Put aside this philosophy thinking, I do appreciate the correspondence I found during my long journey of learn&study, the list are, but not limited to, as below:

• the correspondence between Bayesian variational inference, second law of thermodynamics, and information theory

• the correspondence between quantum computing and Bayesian statistics, linked by the concept of tensor

• the correspondence between MCMC(markov chain monte carlo sampling) and dynamics, linked by HMC algorithm

• the correspondence between sequential monte carlo, generative diffusion model and adiabatic quantum computing

• the correspondence between the symmetry concept and group theory, the symmetry preseving and equivariant operator

• the correspondence between the category theory and functional programming(Monad as a very famous example)

• the correspondence between natural deduction and typed lambda calculus, revealed by Curry-Horward correspondence

In this series of posts, I would like to talk about these correspondences and other interesting topics I encountered in daily life.