Related papers: Probabilistic Graphical Models and Tensor Networks…

Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the…

We present a new approach to the design of deep networks for natural language processing (NLP), based on the general technique of Tensor Product Representations (TPRs) for encoding and processing symbol structures in distributed neural…

Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…

We propose the Binary Diffusion Probabilistic Model (BDPM), a generative framework specifically designed for data representations in binary form. Conventional denoising diffusion probabilistic models (DDPMs) assume continuous inputs, use…

Dense image alignment from RGB-D images remains a critical issue for real-world applications, especially under challenging lighting conditions and in a wide baseline setting. In this paper, we propose a new framework to learn a pixel-wise…

Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard…

With the incredible results achieved from generative pre-trained transformers (GPT) and diffusion models, generative AI (GenAI) is envisioned to yield remarkable breakthroughs in various industrial and academic domains. In this paper, we…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

Diffusion models are at the vanguard of generative AI research with renowned solutions such as ImageGen by Google Brain and DALL.E 3 by OpenAI. Nevertheless, the potential merits of diffusion models for communication engineering…

Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

Pairwise network models such as the Gaussian Graphical Model (GGM) are a powerful and intuitive way to analyze dependencies in multivariate data. A key assumption of the GGM is that each pairwise interaction is independent of the values of…

We present a means of formulating and solving the well known structure-and-motion problem in computer vision with probabilistic graphical models. We model the unknown camera poses and 3D feature coordinates as well as the observed 2D…

Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…

We propose DenseHMM - a modification of Hidden Markov Models (HMMs) that allows to learn dense representations of both the hidden states and the observables. Compared to the standard HMM, transition probabilities are not atomic but composed…

We propose a general modeling and inference framework that composes probabilistic graphical models with deep learning methods and combines their respective strengths. Our model family augments graphical structure in latent variables with…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…

In this paper, we propose a semantic communication approach based on probabilistic graphical model (PGM). The proposed approach involves constructing a PGM from a training dataset, which is then shared as common knowledge between the…

Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs) are widely used structured models, both of which can be represented as factor graph grammars (FGGs), a powerful formalism capable of describing a wide range of…