arXiv subjects

David E. Stewart

Publications and source records attributed to David E. Stewart.

6 recordsLinked to original sources

arXiv2026

Enhancing Coherence of Spin Centers in p-n Diodes via Optimization Algorithms

Solid-state spin defects hold great promise as building blocks for various quantum technologies. Embedding spin centers in $p$-$n$ diodes under reverse bias has proved to be a powerful strategy to narrow the optical linewidth and increase spin coherence, while also enabling control of the photoluminescence wavelength via Stark shift. Given the multitude of parameters influencing spin centers in diodes (e.g., doping densities and profiles, temperature, bias voltage, spin center position), a question that has not yet been answered is: which set of these design parameters maximizes spin center coherence? In this work, we address this question by developing a scaled gradient descent optimization algorithm that minimizes the optical linewidth of spin centers by combining the numerical solution of a diode's Poisson equation with calculated charge noise from the non-depleted regions. Our optimization is performed for both single- and multiple-parameter cases for divacancies in SiC $p$-$i$-$n$ diodes, including reverse-bias voltage, doping density and profile, and diode total length. Importantly, the optimization is subject to realistic physical constraints, such as small operating bias voltages, avoidance of the dielectric breakdown regime and physical thresholds for doping density. Additionally, due to the leakage current at reverse bias voltages, we develop a new formalism to investigate its influence on coherence. We show that the corresponding noise can be mitigated by implanting spin defects away from the diode's surfaces. Our work provides guidance on experimentally relevant diodes for hosting spin centers with the narrowest optical linewidths and longest coherence times.

quant-ph↗

arXiv2025

Training Autoencoders Using Stochastic Hessian-Free Optimization with LSMR

Hessian-free (HF) optimization has been shown to effectively train deep autoencoders (Martens, 2010). In this paper, we aim to accelerate HF training of autoencoders by reducing the amount of data used in training. HF utilizes the conjugate gradient algorithm to estimate update directions. Instead, we propose using the LSMR method, which is known for effectively solving large sparse linear systems. We also incorporate Chapelle & Erhan (2011)'s improved preconditioner for HF optimization. In addition, we introduce a new mini-batch selection algorithm to mitigate overfitting. Our algorithm starts with a small subset of the training data and gradually increases the mini-batch size based on (i) variance estimates obtained during the computation of a mini-batch gradient (Byrd et al., 2012) and (ii) the relative decrease in objective value for the validation data. Our experimental results demonstrate that our stochastic Hessian-free optimization, using the LSMR method and the new sample selection algorithm, leads to rapid training of deep autoencoders with improved generalization error.

cs.LG↗

arXiv2023

A Smoothing Algorithm for l1 Support Vector Machines

A smoothing algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important measure of its cost for very large datasets. The algorithm uses smoothing for the hinge-loss function, and an active set approach for the $\ell^{1}$ penalty. The smoothing parameter $α$ is initially large, but typically halved when the smoothed problem is solved to sufficient accuracy. Convergence theory is presented that shows $\mathcal{O}(1+\log(1+\log_+(1/α)))$ guarded Newton steps for each value of $α$ except for asymptotic bands $α=Θ(1)$ and $α=Θ(1/N)$, with only one Newton step provided $ηα\gg1/N$, where $N$ is the number of data points and the stopping criterion that the predicted reduction is less than $ηα$. The experimental results show that our algorithm is capable of strong test accuracy without sacrificing training speed.

math.OC↗

arXiv2023

A $k$-medoids Approach to Exploring Districting Plans

Researchers and legislators alike continue the search for methods of drawing fair districting plans. A districting plan is a partition of a state's subdivisions (e.g. counties, voting precincts, etc.). By modeling these districting plans as graphs, they are easier to create, store, and operate on. Since graph partitioning with balancing populations is a computationally intractable (NP-hard) problem most attempts to solve them use heuristic methods. In this paper, we present a variant on the $k$-medoids algorithm where, given a set of initial medoids, we find a partition of the graph's vertices to admit a districting plan. We first use the $k$-medoids process to find an initial districting plan, then use local search strategies to fine-tune the results, such as reducing population imbalances between districts. We also experiment with coarsening the graph to work with fewer vertices. The algorithm is tested on Iowa and Florida using 2010 census data to evaluate the effectiveness.

math.CO↗

arXiv2020

gBeam-ACO: a greedy and faster variant of Beam-ACO

Beam-ACO, a modification of the traditional Ant Colony Optimization (ACO) algorithms that incorporates a modified beam search, is one of the most effective ACO algorithms for solving the Traveling Salesman Problem (TSP). Although adding beam search to the ACO heuristic search process is effective, it also increases the amount of work (in terms of partial paths) done by the algorithm at each step. In this work, we introduce a greedy variant of Beam-ACO that uses a greedy path selection heuristic. The exploitation of the greedy path selection is offset by the exploration required in maintaining the beam of paths. This approach has the added benefit of avoiding costly calls to a random number generator and reduces the algorithms internal state, making it simpler to parallelize. Our experiments demonstrate that not only is our greedy Beam-ACO (gBeam-ACO) faster than traditional Beam-ACO, in some cases by an order of magnitude, but it does not sacrifice quality of the found solution, especially on large TSP instances. We also found that our greedy algorithm, which we refer to as gBeam-ACO, was less dependent on hyperparameter settings.

cs.NE↗

arXiv2018

Smoothed Hinge Loss and $\ell^{1}$ Support Vector Machines

A new algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important measure of its cost for very large data sets. The algorithm uses smoothing for the hinge-loss function, and an active set approach for the $\ell^{1}$ penalty.

math.OC↗