Related papers: Combinatorial generation via permutation languages…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…

A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…

Genetic programming (GP) is an evolutionary computation technique to solve problems in an automated, domain-independent way. Rather than identifying the optimum of a function as in more traditional evolutionary optimization, the aim of GP…

This paper discusses the permutations that are generated by rotating $k \times k$ blocks of squares in a union of overlapping $k \times (k+1)$ rectangles. It is found that the single-rotation parity constraints effectively determine the…

A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings…

Generating images from a single sample, as a newly developing branch of image synthesis, has attracted extensive attention. In this paper, we formulate this problem as sampling from the conditional distribution of a single image, and…

There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…

We introduce a novel framework to build a model that can learn how to segment objects from a collection of images without any human annotation. Our method builds on the observation that the location of object segments can be perturbed…

Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…

Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take…

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of…

Generative design refers to computational design methods that can automatically conduct design exploration under constraints defined by designers. Among many approaches, topology optimization-based generative designs aim to explore diverse…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…

In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several…

This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…

Image generation remains a fundamental problem in artificial intelligence in general and deep learning in specific. The generative adversarial network (GAN) was successful in generating high quality samples of natural images. We propose a…