Related papers: Random generation of combinatorial structures: Bol…
A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling…
Given a subset of size $k$ of a very large universe a randomized way to find this subset could consist of deleting half of the universe and then searching the remaining part. With a probability of $2^{-k}$ one will succeed. By probability…
Generative semantic hashing is a promising technique for large-scale information retrieval thanks to its fast retrieval speed and small memory footprint. For the tractability of training, existing generative-hashing methods mostly assume a…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
The Boltzmann Machine (BM) is a neural network composed of stochastically firing neurons that can learn complex probability distributions by adapting the synaptic interactions between the neurons. BMs represent a very generic class of…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice. The method is based on ideas of the author and David Wilson for using ``coupling…
We investigate how machine learning models acquire the ability to compose music and how musical information is internally represented within such models. We develop a composition algorithm based on a restricted Boltzmann machine (RBM), a…
Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
The restricted Boltzmann machine (RBM) is a representative generative model based on the concept of statistical mechanics. In spite of the strong merit of interpretability, unavailability of backpropagation makes it less competitive than…
A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random…
Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have…