Related papers: A general class of invariant diffusion processes i…
As one of the most popular and sought-after generative models in the recent years, diffusion models have sparked the interests of many researchers and steadily shown excellent advantage in various generative tasks such as image synthesis,…
A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
We propose an additional category of dimensionless groups based on the principle of {\it entropic similarity}, defined by ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes.…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…
Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Diffusion models are learning pattern-learning systems to model and sample from data distributions with three functional components namely the forward process, the reverse process, and the sampling process. The components of diffusion…
In this paper we shall prove the weak convergence of the associated diffusion processes of regular subspaces with monotone characteristic sets for a fixed Dirichlet form. More precisely, given a fixed 1-dimensional diffusion process and a…
We give a new proof of some characteristic-free fundamental theorems in invariant theory first proved in C. De Concini and C. Procesi, A characteristic free approach to invariant theory, Adv. Math. 21 (1976), 330--354. We treat the action…
The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…