Related papers: Bean: A Language for Backward Error Analysis
This dissertation explores the design and implementation of programming languages that represent rounding error analysis through typing. In the first part of this dissertation, we demonstrate that it is possible to design languages for…
Backward stability is a desirable property for a well-designed numerical algorithm: given an input, a backward stable floating-point program produces the exact output for a nearby input. While automated tools for bounding the forward error…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps…
Large language models based on transformer architectures have become integral to state-of-the-art natural language processing applications. However, their training remains computationally expensive and exhibits instabilities, some of which…
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise which is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates are…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
In Grammatical Error Correction (GEC), sequence labeling models enjoy fast inference compared to sequence-to-sequence models; however, inference in sequence labeling GEC models is an iterative process, as sentences are passed to the model…
Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can…
We introduce seqBench, a parametrized benchmark for probing sequential reasoning limits in Large Language Models (LLMs) through precise, multi-dimensional control over several key complexity dimensions. seqBench allows systematic variation…
An important aspect of developing reliable deep learning systems is devising strategies that make these systems robust to adversarial attacks. There is a long line of work that focuses on developing defenses against these attacks, but…
Autoformalization, the process of transforming informal mathematical language into formal specifications and proofs remains a difficult task for state-of-the-art (large) language models. Existing works point to competing explanations for…
Over the last years, machine learning techniques have been applied to more and more application domains, including software engineering and, especially, software quality assurance. Important application domains have been, e.g., software…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
Lean processes focus on doing only necessery things in an efficient way. Artificial intelligence and Machine Learning offer new opportunities to optimizing processes. The presented approach demonstrates an improvement of the test process by…
Over the past decade, interval arithmetic (IA) has been utilized to determine tolerance bounds of phased array beampatterns. IA only requires that the errors of the array elements are bounded, and can provide reliable beampattern bounds…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Program errors can occur in any type of programming, and can manifest in a variety of ways, such as unexpected output, crashes, or performance issues. And program error diagnosis can often be too abstract or technical for developers to…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often leave the confidence parameter implicit. This work revisits…