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In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial integral terms appearing in the dynamics and the boundary…
Domain-specific adaptation is critical to maximizing the performance of pre-trained language models (PLMs) on one or multiple targeted tasks, especially under resource-constrained use cases, such as edge devices. However, existing methods…
In this paper, we give an in-depth analysis on the mathematical problem formulations and the probabilistic optimization explorations for some of the key components in Transformer model [33] in the field of generative AI. We explore and…
Combinatorial optimization is one of the fundamental research fields that has been extensively studied in theoretical computer science and operations research. When developing an algorithm for combinatorial optimization, it is commonly…
Large Language Models (LLMs) are increasingly used in empirical software engineering (ESE) to automate or assist annotation tasks such as labeling commits, issues, and qualitative artifacts. Yet the reliability and reproducibility of such…
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
The iterative and incremental nature of software development using models typically makes a model of a system incomplete (i.e., partial) until a more advanced and complete stage of development is reached. Existing model execution approaches…
Given the strong results of self-supervised models on various tasks, there have been surprisingly few studies exploring self-supervised representations for acoustic word embeddings (AWE), fixed-dimensional vectors representing…
In this paper, we present a new method for estimating the $L_2$-gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using semidefinite programming. It has previously been shown that,…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs)…
Covering all languages with a multilingual speech recognition model (MASR) is very difficult. Performing language extension on top of an existing MASR is a desirable choice. In this study, the MASR continual learning problem is…
Partial order reduction (POR) and net unfoldings are two alternative methods to tackle state-space explosion caused by concurrency. In this paper, we propose the combination of both approaches in an effort to combine their strengths. We…
Large language models have demonstrated remarkable capabilities, but their performance is heavily reliant on effective prompt engineering. Automatic prompt optimization (APO) methods are designed to automate this and can be broadly…
Parameter-efficient (PE) methods (like Prompts or Adapters) for adapting pre-trained language models (PLM) to downstream tasks have been popular recently. However, hindrances still prevent these methods from reaching their full potential.…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…
While frontier formal mathematics systems now routinely develop repository-scale proof engineering artifacts requiring multi-file coordination and semantic correctness beyond compilation, existing evaluation benchmarks remain focused on…
Automatic prompt optimization (APO) hinges on the quality of its evaluation signal, yet scoring every prompt candidate on the full training set is prohibitively expensive. Existing methods either fix a single evaluation subset before…
The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to…
We briefly review the inside-outside and EM algorithm for probabilistic context-free grammars. As a result, we formally prove that inside-outside estimation is a dynamic-programming variant of EM. This is interesting in its own right, but…