We study an infinite-dimensional optimization problem that aims to identify the Nemytskii operator in the nonlinear part of a prototypical semilinear elliptic partial differential equation (PDE) which minimizes the distance between the PDE-solution and a given desired state. In contrast to previous works, we consider this identification problem in a low-regularity regime in which the function inducing the Nemytskii operator is a-priori only known to be an element of $H^1_{loc}(\mathbb{R})$. This makes the studied problem class a suitable point of departure for the rigorous analysis of training problems for learning-informed PDEs in which an unknown superposition operator is approximated by means of a neural network with nonsmooth activation functions (ReLU, leaky-ReLU, etc.). We establish that, despite the low regularity of the controls, it is possible to derive a classical stationarity system for local minimizers and to solve the considered problem by means of a gradient projection method. The convergence of the resulting algorithm is proven in the function space setting. It is also shown that the established first-order necessary optimality conditions imply that locally optimal superposition operators share various characteristic properties with commonly used activation functions: They are always sigmoidal, continuously differentiable away from the origin, and typically possess a distinct kink at zero. The paper concludes with numerical experiments which confirm the theoretical findings.
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Computational argumentation has become an essential tool in various fields, including artificial intelligence, law, and public policy. It is an emerging research field in natural language processing that attracts increasing attention. Research on computational argumentation mainly involves two types of tasks: argument mining and argument generation. As large language models have demonstrated strong abilities in understanding context and generating natural language, it is worthwhile to evaluate the performance of LLMs on various computational argumentation tasks. This work aims to embark on an assessment of LLMs, such as ChatGPT, Flan models and LLaMA2 models, under zero-shot and few-shot settings within the realm of computational argumentation. We organize existing tasks into six main categories and standardise the format of fourteen open-sourced datasets. In addition, we present a new benchmark dataset on counter speech generation, that aims to holistically evaluate the end-to-end performance of LLMs on argument mining and argument generation. Extensive experiments show that LLMs exhibit commendable performance across most of these datasets, demonstrating their capabilities in the field of argumentation. Our analysis offers valuable suggestions for evaluating computational argumentation and its integration with LLMs in future research endeavors.
The presence of toxic and gender-identity derogatory language in open-source software (OSS) communities has recently become a focal point for researchers. Such comments not only lead to frustration and disengagement among developers but may also influence their leave from the OSS projects. Despite ample evidence suggesting that diverse teams enhance productivity, the existence of toxic or gender identity discriminatory communications poses a significant threat to the participation of individuals from marginalized groups and, as such, may act as a barrier to fostering diversity and inclusion in OSS projects. However, there is a notable lack of research dedicated to exploring the association between gender-based toxic and derogatory language with a perceptible diversity of open-source software teams. Consequently, this study aims to investigate how such content influences the gender, ethnicity, and tenure diversity of open-source software development teams. To achieve this, we extract data from active GitHub projects, assess various project characteristics, and identify instances of toxic and gender-discriminatory language within issue/pull request comments. Using these attributes, we construct a regression model to explore how they associate with the perceptible diversity of those projects.
Classification algorithms using Transformer architectures can be affected by the sequence length learning problem whenever observations from different classes have a different length distribution. This problem causes models to use sequence length as a predictive feature instead of relying on important textual information. Although most public datasets are not affected by this problem, privately owned corpora for fields such as medicine and insurance may carry this data bias. The exploitation of this sequence length feature poses challenges throughout the value chain as these machine learning models can be used in critical applications. In this paper, we empirically expose this problem and present approaches to minimize its impacts.
This manuscript presents a methodical examination of the utilization of Artificial Intelligence in the assessment of emotions in texts related to healthcare, with a particular focus on the incorporation of Natural Language Processing and deep learning technologies. We scrutinize numerous research studies that employ AI to augment sentiment analysis, categorize emotions, and forecast patient outcomes based on textual information derived from clinical narratives, patient feedback on medications, and online health discussions. The review demonstrates noteworthy progress in the precision of algorithms used for sentiment classification, the prognostic capabilities of AI models for neurodegenerative diseases, and the creation of AI-powered systems that offer support in clinical decision-making. Remarkably, the utilization of AI applications has exhibited an enhancement in personalized therapy plans by integrating patient sentiment and contributing to the early identification of mental health disorders. There persist challenges, which encompass ensuring the ethical application of AI, safeguarding patient confidentiality, and addressing potential biases in algorithmic procedures. Nevertheless, the potential of AI to revolutionize healthcare practices is unmistakable, offering a future where healthcare is not only more knowledgeable and efficient but also more empathetic and centered around the needs of patients. This investigation underscores the transformative influence of AI on healthcare, delivering a comprehensive comprehension of its role in examining emotional content in healthcare texts and highlighting the trajectory towards a more compassionate approach to patient care. The findings advocate for a harmonious synergy between AI's analytical capabilities and the human aspects of healthcare.
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control system that has optimization parameters. We describe a subspace procedure to cope with the setting when the matrix-valued function is of large size. The proposed subspace procedure solves a sequence of reduced problems obtained by restricting the matrix-valued function to small subspaces, whose dimensions increase gradually. It possesses desirable features such as the global convergence of the minimal values of the reduced problems to the minimal value of the original problem, and a superlinear convergence exhibited by the decay in the errors of the minimizers of the reduced problems. In mathematical terms, the problem we consider is a large-scale nonconvex minimax eigenvalue optimization problem such that the eigenvalue function appears in the constraint of the inner maximization problem. Devising and analyzing a subspace framework for the minimax eigenvalue optimization problem at hand with the eigenvalue function in the constraint require special treatment that makes use of a Lagrangian and dual variables. There are notable advantages in minimizing the pseudospectral abscissa over maximizing the distance to instability or minimizing the $\mathcal{H}_\infty$ norm; the optimized pseudospectral abscissa provides quantitative information about the worst-case transient growth, and the initial guesses for the parameter values to optimize the pseudospectral abscissa can be arbitrary, unlike the case to optimize the distance to instability and $\mathcal{H}_\infty$ norm that would normally require initial guesses yielding asymptotically stable systems.
Identifying scientific publications that are within a dynamic field of research often requires costly annotation by subject-matter experts. Resources like widely-accepted classification criteria or field taxonomies are unavailable for a domain like artificial intelligence (AI), which spans emerging topics and technologies. We address these challenges by inferring a functional definition of AI research from existing expert labels, and then evaluating state-of-the-art chatbot models on the task of expert data annotation. Using the arXiv publication database as ground-truth, we experiment with prompt engineering for GPT chatbot models to identify an alternative, automated expert annotation pipeline that assigns AI labels with 94% accuracy. For comparison, we fine-tune SPECTER, a transformer language model pre-trained on scientific publications, that achieves 96% accuracy (only 2% higher than GPT) on classifying AI publications. Our results indicate that with effective prompt engineering, chatbots can be used as reliable data annotators even where subject-area expertise is required. To evaluate the utility of chatbot-annotated datasets on downstream classification tasks, we train a new classifier on GPT-labeled data and compare its performance to the arXiv-trained model. The classifier trained on GPT-labeled data outperforms the arXiv-trained model by nine percentage points, achieving 82% accuracy.
We prove impossibility results for adaptivity in non-smooth stochastic convex optimization. Given a set of problem parameters we wish to adapt to, we define a "price of adaptivity" (PoA) that, roughly speaking, measures the multiplicative increase in suboptimality due to uncertainty in these parameters. When the initial distance to the optimum is unknown but a gradient norm bound is known, we show that the PoA is at least logarithmic for expected suboptimality, and double-logarithmic for median suboptimality. When there is uncertainty in both distance and gradient norm, we show that the PoA must be polynomial in the level of uncertainty. Our lower bounds nearly match existing upper bounds, and establish that there is no parameter-free lunch.
Most diffusion models assume that the reverse process adheres to a Gaussian distribution. However, this approximation has not been rigorously validated, especially at singularities, where t=0 and t=1. Improperly dealing with such singularities leads to an average brightness issue in applications, and limits the generation of images with extreme brightness or darkness. We primarily focus on tackling singularities from both theoretical and practical perspectives. Initially, we establish the error bounds for the reverse process approximation, and showcase its Gaussian characteristics at singularity time steps. Based on this theoretical insight, we confirm the singularity at t=1 is conditionally removable while it at t=0 is an inherent property. Upon these significant conclusions, we propose a novel plug-and-play method SingDiffusion to address the initial singular time step sampling, which not only effectively resolves the average brightness issue for a wide range of diffusion models without extra training efforts, but also enhances their generation capability in achieving notable lower FID scores. Code and models are released at //github.com/PangzeCheung/SingDiffusion.
This work delves into the complexities of machine unlearning in the face of distributional shifts, particularly focusing on the challenges posed by non-uniform feature and label removal. With the advent of regulations like the GDPR emphasizing data privacy and the right to be forgotten, machine learning models face the daunting task of unlearning sensitive information without compromising their integrity or performance. Our research introduces a novel approach that leverages influence functions and principles of distributional independence to address these challenges. By proposing a comprehensive framework for machine unlearning, we aim to ensure privacy protection while maintaining model performance and adaptability across varying distributions. Our method not only facilitates efficient data removal but also dynamically adjusts the model to preserve its generalization capabilities. Through extensive experimentation, we demonstrate the efficacy of our approach in scenarios characterized by significant distributional shifts, making substantial contributions to the field of machine unlearning. This research paves the way for developing more resilient and adaptable unlearning techniques, ensuring models remain robust and accurate in the dynamic landscape of data privacy and machine learning.
This study investigates a strongly-coupled system of partial differential equations (PDE) governing heat transfer in a copper rod, longitudinal vibrations, and total charge accumulation at electrodes within a magnetizable piezoelectric beam. Conducted within the transmission line framework, the analysis reveals profound interactions between traveling electromagnetic and mechanical waves in magnetizable piezoelectric beams, despite disparities in their velocities. Findings suggest that in the open-loop scenario, the interaction of heat and beam dynamics lacks exponential stability solely considering thermal effects. To confront this challenge, two types of boundary-type state feedback controllers are proposed: (i) employing static feedback controllers entirely and (ii) adopting a hybrid approach wherein the electrical controller dynamically enhances system dynamics. In both cases, solutions of the PDE systems demonstrate exponential stability through meticulously formulated Lyapunov functions with diverse multipliers. The proposed proof technique establishes a robust foundation for demonstrating the exponential stability of Finite-Difference-based model reductions as the discretization parameter approaches zero.
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