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Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
An Abstract Graph Machine(AGM) is an abstract model for distributed memory parallel stabilizing graph algorithms. A stabilizing algorithm starts from a particular initial state and goes through series of different state changes until it…
We present and analyze several strategies for improving the performance of stochastic variance-reduced gradient (SVRG) methods. We first show that the convergence rate of these methods can be preserved under a decreasing sequence of errors…
Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…
Deep neural networks have long been criticized for being black-box. To unveil the inner workings of modern neural architectures, a recent work \cite{yu2024white} proposed an information-theoretic objective function called Sparse Rate…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
Variational approximation, such as mean-field (MF) and tree-reweighted (TRW), provide a computationally efficient approximation of the log-partition function for a generic graphical model. TRW provably provides an upper bound, but the…
Scalability of graph neural networks remains one of the major challenges in graph machine learning. Since the representation of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes…
Graph representations are the generalization of geometric graph drawings from the plane to higher dimensions. A method introduced by Tutte to optimize properties of graph drawings is to minimize their energy. We explore this minimization…
Connectionist sequence models (e.g., RNNs) applied to musical sequences suffer from two known problems: First, they have strictly "absolute pitch perception". Therefore, they fail to generalize over musical concepts which are commonly…
The control of high-dimensional systems, such as soft robots, requires models that faithfully capture complex dynamics while remaining computationally tractable. This work presents a framework that integrates Graph Neural Network…
Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations…
Random graph models have been instrumental in characterizing complex networks, but chemical reaction networks (CRNs) are better represented as hypergraphs. Traditional models of random CRNs often reduce CRNs to bipartite graphs,…
We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries.…
Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting -- a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the…
Graphons have traditionally served as limit objects for dense graph sequences, with the cut distance serving as the metric for convergence. However, sparse graph sequences converge to the trivial graphon under the conventional definition of…
This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process…
Recurrent neural networks (RNNs) are a class of neural networks used in sequential tasks. However, in general, RNNs have a large number of parameters and involve enormous computational costs by repeating the recurrent structures in many…
With the prevalence of social media, the connectedness between people has been greatly enhanced. Real-world relations between users on social media are often not limited to expressing positive ties such as friendship, trust, and agreement,…
Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous…