arXiv subjects

Colin Ponce

Publications and source records attributed to Colin Ponce.

6 recordsLinked to original sources

arXiv2026

Skywing: A Platform for Decentralized Mathematical Computing in Unreliable Environments

Emerging edge, autonomous, and cyber-physical systems increasingly require mathematical computation across heterogeneous devices connected by unreliable communication networks. Traditional high-performance computing and distributed data-processing frameworks provide powerful abstractions for managed environments but are less suited to decentralized settings where centralized coordination, reliable communication, and global synchronization cannot be assumed. This paper presents Skywing, an open-source platform for decentralized mathematical computing in unreliable environments. Its programming model consists of three abstractions: agents represent participants in a decentralized computation, processors encapsulate algorithm-specific update rules, and iterations manage distributed execution. Skywing supports asynchronous operation, publish-subscribe communication, managed message handling, and the composition of independent algorithms into complex decentralized workflows. We demonstrate Skywing using representative algorithms from consensus, optimization, and numerical linear algebra. Experiments on the native Skywing runtime include Push Sum and Max Consensus, a composed monitoring and control workflow, resilient Push Sum under delayed communication, and resilient asynchronous Jacobi under malevolent data corruption. These demonstrations show that Skywing supports diverse decentralized algorithms while separating mathematical logic from communication and execution infrastructure. Skywing serves as both a deployment framework for decentralized applications and a research platform for developing resilient mathematical algorithms.

cs.DC↗

arXiv2022

Multilevel-in-Layer Training for Deep Neural Network Regression

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. We draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as \emph{multilevel-in-width} to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully-connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.

cs.LG↗

arXiv2022

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in-situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. A linear system with a more dense sparsity pattern is also explored. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

cs.DC↗

arXiv2020

Multiresolution Convolutional Autoencoders

We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a principled manner to encode new information in the higher resolution data based on its current performance of reconstruction. Basic transfer learning techniques are applied to ensure information learned from previous training steps can be rapidly transferred to the larger network. As a result, the network can dynamically capture different scaled features at different depths of the network. The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.

cs.LG↗

arXiv2014

FLiER: Practical Topology Update Detection Using Sparse PMUs

In this paper, we present a Fingerprint Linear Estimation Routine (FLiER) to identify topology changes in power networks using readings from sparsely-deployed phasor measurement units (PMUs). When a power line, load, or generator trips in a network, or when a substation is reconfigured, the event leaves a unique "voltage fingerprint" of bus voltage changes that we can identify using only the portion of the network directly observed by the PMUs. The naive brute-force approach to identify a failed line from such voltage fingerprints, though simple and accurate, is slow. We derive an approximate algorithm based on a local linearization and a novel filtering approach that is faster and only slightly less accurate. We present experimental results using the IEEE 57-bus, IEEE 118-bus, and Polish 1999-2000 winter peak networks.

eess.SY↗

arXiv2011

Unstructured Human Activity Detection from RGBD Images

Being able to detect and recognize human activities is essential for several applications, including personal assistive robotics. In this paper, we perform detection and recognition of unstructured human activity in unstructured environments. We use a RGBD sensor (Microsoft Kinect) as the input sensor, and compute a set of features based on human pose and motion, as well as based on image and pointcloud information. Our algorithm is based on a hierarchical maximum entropy Markov model (MEMM), which considers a person's activity as composed of a set of sub-activities. We infer the two-layered graph structure using a dynamic programming approach. We test our algorithm on detecting and recognizing twelve different activities performed by four people in different environments, such as a kitchen, a living room, an office, etc., and achieve good performance even when the person was not seen before in the training set.

cs.RO↗