Related papers: Boltzmann Samplers for Colored Combinatorial Objec…
Instance segmentation is one of the actively studied research topics in computer vision in which many objects of interest should be separated individually. While many feed-forward networks produce high-quality segmentation on different…
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and…
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
Born-rule generative modeling, a central task in quantum machine learning, seeks to learn probability distributions that can be efficiently sampled by measuring complex quantum states. One hope is for quantum models to efficiently capture…
Text-to-image generation has recently seen remarkable success, granting users with the ability to create high-quality images through the use of text. However, contemporary methods face challenges in capturing the precise semantics conveyed…
The goal of this note is to present a combinatorial mechanism for counting certain objects associated to a variety X defined over a finite field. The basic example is that of counting conjugacy classes in GL_n(F_q), where X is the…
As robots become more ubiquitous and capable, it becomes ever more important to enable untrained users to easily interact with them. Recently, this has led to study of the language grounding problem, where the goal is to extract…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
A simply colored coalgebra is a coassociative counital coalgebra $C$ over an arbitrary ring $R$, which can be decomposed into a direct sum of two $R$-modules: one generated by set-like elements and another consisting of conilpotent…
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume…
In this paper, we study the problem of partitioning a graph into connected and colored components called blocks. Using bivariate generating functions and combinatorial techniques, we determine the expected number of blocks when the vertices…
We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…
Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic models that have recently been applied to a wide range of problems, including collaborative filtering, classification, and modeling motion capture data. While much…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…
We propose a new and, arguably, a very simple reduction of instance segmentation to semantic segmentation. This reduction allows to train feed-forward non-recurrent deep instance segmentation systems in an end-to-end fashion using…
Dramatic advances in generative models have resulted in near photographic quality for artificially rendered faces, animals and other objects in the natural world. In spite of such advances, a higher level understanding of vision and imagery…
Diffusion models have shown great promise in synthesizing visually appealing images. However, it remains challenging to condition the synthesis at a fine-grained level, for instance, synthesizing image pixels following some generic color…
We train generative 'up-convolutional' neural networks which are able to generate images of objects given object style, viewpoint, and color. We train the networks on rendered 3D models of chairs, tables, and cars. Our experiments show that…
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…