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Leveraging second-order information about the loss at the scale of deep networks is one of the main lines of approach for improving the performance of current optimizers for deep learning. Yet, existing approaches for accurate full-matrix…
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
Single-event upset (SEU) fault tolerance for systems-on-chip (SoCs) in radiation-heavy environments is often addressed by architectural fault-tolerance approaches protecting individual SoC components (e.g., cores, memories) in isolation.…
This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled…
Fault tolerance is a property which needs deeper consideration when dealing with streaming jobs requiring high levels of availability and low-latency processing even in case of failures where Quality-of-Service constraints must be adhered…
Intrusion Detection Systems (IDS) are developed to protect the network by detecting the attack. The current paper proposes an unsupervised feature selection technique for analyzing the network data. The search capability of the…
System prompts for LLM-based coding agents are software artifacts that govern agent behavior, yet lack the testing infrastructure applied to conventional software. We present Arbiter, a framework combining formal evaluation rules with…
Machine unlearning offers a promising solution to privacy and safety concerns in large language models (LLMs) by selectively removing targeted knowledge while preserving utility. However, current methods are highly sensitive to downstream…
In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time auxiliary classical computation, we construct a fault tolerance protocol with constant-space and $\widetilde{O}(\log N)$-time overhead, where…
In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular…
Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than preconditioners based on incomplete block factorizations. Lower…
We are interested in obtaining approximate solutions to parameterized linear systems of the form $A(\mu) x(\mu) = b$ for many values of the parameter $\mu$. Here $A(\mu)$ is large, sparse, and nonsingular, with a nonlinear analytic…
The Helmholtz equation poses significant computational challenges due to its oscillatory solutions, particularly for large wavenumbers. Inspired by the Schur complement system for elliptic problems, this paper presents a novel…
Machine learning (ML) models often exhibit bias that can exacerbate inequities in biomedical applications. Fairness auditing, the process of evaluating a model's performance across subpopulations, is critical for identifying and mitigating…
As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of "early fault tolerance" where limited error correction is available. We propose a framework for designing early…
Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement.…
Modern machine learning frameworks support very large models by incorporating parallelism and optimization techniques. Yet, these very techniques add new layers of complexity, introducing silent errors that severely degrade model…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…
Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At…