The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often employed as the primary means for computing PCA, a process that indispensably includes the step of centering - the subtraction of the mean location from the data set. In our study, we delve into a detailed exploration of the influence of this critical yet often ignored or downplayed data centering step. Our research meticulously investigates the conditions under which two PCA embeddings, one derived from SVD with centering and the other without, can be viewed as aligned. As part of this exploration, we analyze the relationship between the first singular vector and the mean direction, subsequently linking this observation to the congruity between two SVDs of centered and uncentered matrices. Furthermore, we explore the potential implications arising from the absence of centering in the context of performing PCA via SVD from a spectral analysis standpoint. Our investigation emphasizes the importance of a comprehensive understanding and acknowledgment of the subtleties involved in the computation of PCA. As such, we believe this paper offers a crucial contribution to the nuanced understanding of this foundational statistical method and stands as a valuable addition to the academic literature in the field of statistics.
Recent research in decoding methods for Natural Language Generation (NLG) tasks has shown that the traditional beam search and greedy decoding algorithms are not optimal, because model probabilities do not always align with human preferences. Stronger decoding methods, including Quality Estimation (QE) reranking and Minimum Bayes' Risk (MBR) decoding, have since been proposed to mitigate the model-perplexity-vs-quality mismatch. While these decoding methods achieve state-of-the-art performance, they are prohibitively expensive to compute. In this work, we propose MBR finetuning and QE finetuning which distill the quality gains from these decoding methods at training time, while using an efficient decoding algorithm at inference time. Using the canonical NLG task of Neural Machine Translation (NMT), we show that even with self-training, these finetuning methods significantly outperform the base model. Moreover, when using an external LLM as a teacher model, these finetuning methods outperform finetuning on human-generated references. These findings suggest new ways to leverage monolingual data to achieve improvements in model quality that are on par with, or even exceed, improvements from human-curated data, while maintaining maximum efficiency during decoding.
The Lipschitz bound, a technique from robust statistics, can limit the maximum changes in the output concerning the input, taking into account associated irrelevant biased factors. It is an efficient and provable method for examining the output stability of machine learning models without incurring additional computation costs. Recently, Graph Neural Networks (GNNs), which operate on non-Euclidean data, have gained significant attention. However, no previous research has investigated the GNN Lipschitz bounds to shed light on stabilizing model outputs, especially when working on non-Euclidean data with inherent biases. Given the inherent biases in common graph data used for GNN training, it poses a serious challenge to constraining the GNN output perturbations induced by input biases, thereby safeguarding fairness during training. Recently, despite the Lipschitz constant's use in controlling the stability of Euclideanneural networks, the calculation of the precise Lipschitz constant remains elusive for non-Euclidean neural networks like GNNs, especially within fairness contexts. To narrow this gap, we begin with the general GNNs operating on an attributed graph, and formulate a Lipschitz bound to limit the changes in the output regarding biases associated with the input. Additionally, we theoretically analyze how the Lipschitz constant of a GNN model could constrain the output perturbations induced by biases learned from data for fairness training. We experimentally validate the Lipschitz bound's effectiveness in limiting biases of the model output. Finally, from a training dynamics perspective, we demonstrate why the theoretical Lipschitz bound can effectively guide the GNN training to better trade-off between accuracy and fairness.
I study the measurement of scientists' influence using bibliographic data. The main result is an axiomatic characterization of the family of citation-counting indices, a broad class of influence measures which includes the renowned h-index. The result highlights several limitations of these indices: they are not suitable to compare scientists across different fields, and they cannot account for indirect influence. I explore how these limitations can be overcome by using richer bibliographic information.
Philosophical research in AI has hitherto largely focused on the ethics of AI. In this paper we, an ethicist of belief and a machine learning scientist, suggest that we need to pursue a novel area of philosophical research in AI - the epistemology of AI, and in particular an ethics of belief for AI. Here we take the ethics of belief, a field that has been defined in various ways, to refer to a sub-field within epistemology. This subfield is concerned with the study of possible moral, practical, and other non-alethic dimensions of belief. And in this paper, we will primarily be concerned with the normative question within the ethics of belief regarding what agents - both human and artificial - ought to believe, rather than with descriptive questions concerning whether certain beliefs meet various evaluative standards such as being true, being justified or warranted, constituting knowledge, and so on. We suggest four topics in extant work in the ethics of (human) belief that can be applied to an ethics of AI belief: doxastic wronging by AI; morally owed beliefs; pragmatic and moral encroachment on AI beliefs; and moral responsibility for AI beliefs. We also indicate two relatively nascent areas of philosophical research that haven't yet been generally recognized as ethics of AI belief research, but that do fall within this field of research in virtue of investigating various moral and practical dimensions of belief: the epistemic and ethical decolonization of AI; and epistemic injustice in AI.
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and computability theory is very old, and this paper extends this connection in new ways. In one direction, we counter the main trend in both computability theory and combinatory logic of heading straight to undecidability. Instead, this paper proposes using several very small equational logics to examine results in computability theory itself. These logics are decidable via term rewriting. We argue that they have something interesting to say about computability theory. They are closely related to fragments of combinatory logic which are decidable, and so this paper contributes to the study of such fragments. The paper has a few surprising results such as a classification of quine programs (programs which output themselves) in two decidable fragments. The classification goes via examination of normal forms in term rewriting systems, hence the title of the paper. The classification is an explanation of why all quine programs (in any language) are "pretty much the same, except for inessential details." In addition, we study the relational structure whose objects are the programs with the relation "p expresses q" meaning that if the program p is run on nothing, then it eventually outputs the program q.
Nowadays many research articles are prefaced with research highlights to summarize the main findings of the paper. Highlights not only help researchers precisely and quickly identify the contributions of a paper, they also enhance the discoverability of the article via search engines. We aim to automatically construct research highlights given certain segments of a research paper. We use a pointer-generator network with coverage mechanism and a contextual embedding layer at the input that encodes the input tokens into SciBERT embeddings. We test our model on a benchmark dataset, CSPubSum, and also present MixSub, a new multi-disciplinary corpus of papers for automatic research highlight generation. For both CSPubSum and MixSub, we have observed that the proposed model achieves the best performance compared to related variants and other models proposed in the literature. On the CSPubSum dataset, our model achieves the best performance when the input is only the abstract of a paper as opposed to other segments of the paper. It produces ROUGE-1, ROUGE-2 and ROUGE-L F1-scores of 38.26, 14.26 and 35.51, respectively, METEOR score of 32.62, and BERTScore F1 of 86.65 which outperform all other baselines. On the new MixSub dataset, where only the abstract is the input, our proposed model (when trained on the whole training corpus without distinguishing between the subject categories) achieves ROUGE-1, ROUGE-2 and ROUGE-L F1-scores of 31.78, 9.76 and 29.3, respectively, METEOR score of 24.00, and BERTScore F1 of 85.25.
This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is critical for high-dimensional analysis and stands in contrast to classical metrics ({\it e.g.}, the Wasserstein metric). The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD. Examples of the selected test function spaces include the reproducing kernel Hilbert spaces, Barron space, and flow-induced function spaces. Three applications of the proposed metrics are presented: 1. The convergence of empirical measure in the case of random variables; 2. The convergence of $n$-particle system to the solution to McKean-Vlasov stochastic differential equation; 3. The construction of an $\varepsilon$-Nash equilibrium for a homogeneous $n$-player game by its mean-field limit. As a byproduct, we prove that, given a distribution close to the target distribution measured by our metric and a certain representation of the target distribution, we can generate a distribution close to the target one in terms of the Wasserstein metric and relative entropy. Overall, we show that the proposed class of metrics is a powerful tool to analyze the convergence of empirical measures in high dimensions without CoD.
Tensor Processing Units (TPUs) are specialized hardware accelerators for deep learning developed by Google. This paper explores the performance of TPU with a focus on AI and its implementation in edge computing. It first provides an overview of TPUs, specifically their design in relation to neural networks, their general architecture, compilation techniques and supporting frameworks. Furthermore, we provide a comparative analysis of Cloud and Edge TPU performance against other counterpart chip architectures. It is then discussed how TPUs can be used to speed up AI workloads. The results show that TPUs can provide significant performance improvements both in cloud and edge computing. Additionally, we address the need for further research for the deployment of more architectures in the Edge TPU, as well as the need for the development of more robust comparisons in edge computing.
Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.
This paper offers a comprehensive review of the research on Natural Language Generation (NLG) over the past two decades, especially in relation to data-to-text generation and text-to-text generation deep learning methods, as well as new applications of NLG technology. This survey aims to (a) give the latest synthesis of deep learning research on the NLG core tasks, as well as the architectures adopted in the field; (b) detail meticulously and comprehensively various NLG tasks and datasets, and draw attention to the challenges in NLG evaluation, focusing on different evaluation methods and their relationships; (c) highlight some future emphasis and relatively recent research issues that arise due to the increasing synergy between NLG and other artificial intelligence areas, such as computer vision, text and computational creativity.