This survey is meant to provide an introduction to the fundamental theorem of linear algebra and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to linear algebra. Specifically, we provide some details and proofs of some results from (Strang, 1993). We then describe the fundamental theorem of linear algebra from different views and find the properties and relationships behind the views. The fundamental theorem of linear algebra is essential in many fields, such as electrical engineering, computer science, machine learning, and deep learning.

Robots in our daily surroundings are increasing day by day. Their usability and acceptability largely depend on their explicit and implicit interaction capability with fellow human beings. As a result, social behavior is one of the most sought-after qualities that a robot can possess. However, there is no specific aspect and/or feature that defines socially acceptable behavior and it largely depends on the situation, application, and society. In this article, we investigate one such social behavior for collocated robots. Imagine a group of people is interacting with each other and we want to join the group. We as human beings do it in a socially acceptable manner, i.e., within the group, we do position ourselves in such a way that we can participate in the group activity without disturbing/obstructing anybody. To possess such a quality, first, a robot needs to determine the formation of the group and then determine a position for itself, which we humans do implicitly. The theory of f-formation can be utilized for this purpose. As the types of formations can be very diverse, detecting the social groups is not a trivial task. In this article, we provide a comprehensive survey of the existing work on social interaction and group detection using f-formation for robotics and other applications. We also put forward a novel holistic survey framework combining all the possible concerns and modules relevant to this problem. We define taxonomies based on methods, camera views, datasets, detection capabilities and scale, evaluation approaches, and application areas. We discuss certain open challenges and limitations in current literature along with possible future research directions based on this framework. In particular, we discuss the existing methods/techniques and their relative merits and demerits, applications, and provide a set of unsolved but relevant problems in this domain.

Given a Boolean specification between a set of inputs and outputs, the problem of Boolean functional synthesis is to synthesise each output as a function of inputs such that the specification is met. Although the past few years have witnessed intense algorithmic development, accomplishing scalability remains the holy grail. The state-of-the-art approach combines machine learning and automated reasoning to efficiently synthesise Boolean functions. In this paper, we propose four algorithmic improvements for a data-driven framework for functional synthesis: using a dependency-driven multi-classifier to learn candidate function, extracting uniquely defined functions by interpolation, variables retention, and using lexicographic MaxSAT to repair candidates. We implement these improvements in the state-of-the-art framework, called Manthan. The proposed framework is called Manthan2. Manthan2 shows significantly improved runtime performance compared to Manthan. In an extensive experimental evaluation on 609 benchmarks, Manthan2 is able to synthesise a Boolean function vector for 509 instances compared to 356 instances solved by Manthan--- an increment of 153 instances over the state-of-the-art. To put this into perspective, Manthan improved on the prior state-of-the-art by only 76 instances.

Machine learning on sets towards sequential output is an important and ubiquitous task, with applications ranging from language modelling and meta-learning to multi-agent strategy games and power grid optimization. Combining elements of representation learning and structured prediction, its two primary challenges include obtaining a meaningful, permutation invariant set representation and subsequently utilizing this representation to output a complex target permutation. This paper provides a comprehensive introduction to the field as well as an overview of important machine learning methods tackling both of these key challenges, with a detailed qualitative comparison of selected model architectures.

Recently, dense passage retrieval has become a mainstream approach to finding relevant information in various natural language processing tasks. A number of studies have been devoted to improving the widely adopted dual-encoder architecture. However, most of the previous studies only consider query-centric similarity relation when learning the dual-encoder retriever. In order to capture more comprehensive similarity relations, we propose a novel approach that leverages both query-centric and PAssage-centric sImilarity Relations (called PAIR) for dense passage retrieval. To implement our approach, we make three major technical contributions by introducing formal formulations of the two kinds of similarity relations, generating high-quality pseudo labeled data via knowledge distillation, and designing an effective two-stage training procedure that incorporates passage-centric similarity relation constraint. Extensive experiments show that our approach significantly outperforms previous state-of-the-art models on both MSMARCO and Natural Questions datasets.

Artificial Intelligence is, without a doubt, one of the Fourth Industrial Revolution's primary growth engines. The benefits and business potential inherent in this technology are immense. Improving customer experience, automating business processes, real-time information analysis, improving cyber protection capabilities, and implementing autonomous applications are just a few examples of these benefits. However, and similarly to other types of new and groundbreaking technologies, we must consider the latent risks in implementing Artificial Intelligence in an uncontrolled manner. Considering such risks is evidently even more urgent as Artificial Intelligence has now become so vastly used that it affects every aspect of our personal and professional life and used in scale, in large sectors of the economy.

In the age of big data, data processing and analytics are fundamental, ubiquitous, and crucial to many organizations which undertake a digitalization journey to improve and transform their businesses and operations. Data analytics typically entails other key operations such as data acquisition, data cleansing, data integration, modeling, etc., before insights could be extracted. Big data can unleash significant value creation across many sectors such as health care and retail[56]. However, the complexity of data (e.g., high volume, high velocity, and high variety) presents many challenges in data analytics and hence renders the difficulty in drawing meaningful insights. To tackle the challenge and facilitate the data processing and analytics efficiently and effectively, a lot of algorithms and techniques have been designed and numerous learning systems have also been developed by researchers and practitioners such as Spark MLlib[63], and Rafiki[104]. To support fast data processing and accurate data analytics, a huge number of algorithms rely on rules that are developed based on human knowledge and experience. For example, Shortest-job-first is a scheduling algorithm that chooses the job with the smallest execution time for the next execution. However, without fully exploiting characteristics of the workload, it can achieve inferior performance compared to DRL-based scheduling algorithm [58].

Regulators have signalled an interest in adopting explainable AI(XAI) techniques to handle the diverse needs for model governance, operational servicing, and compliance in the financial services industry. In this short overview, we review the recent technical literature in XAI and argue that based on our current understanding of the field, the use of XAI techniques in practice necessitate a highly contextualized approach considering the specific needs of stakeholders for particular business applications.

Rapid progress in natural language processing has led to its utilization in a variety of industrial and enterprise settings, including in its use for information extraction, specifically named entity recognition and relation extraction, from documents such as engineering manuals and field maintenance reports. While named entity recognition is a well-studied problem, existing state-of-the-art approaches require large labelled datasets which are hard to acquire for sensitive data such as maintenance records. Further, industrial domain experts tend to distrust results from black box machine learning models, especially when the extracted information is used in downstream predictive maintenance analytics. We overcome these challenges by developing three approaches built on the foundation of domain expert knowledge captured in dictionaries and ontologies. We develop a syntactic and semantic rules-based approach and an approach leveraging a pre-trained language model, fine-tuned for a question-answering task on top of our base dictionary lookup to extract entities of interest from maintenance records. We also develop a preliminary ontology to represent and capture the semantics of maintenance records. Our evaluations on a real-world aviation maintenance records dataset show promising results and help identify challenges specific to named entity recognition in the context of noisy industrial data.

The K-means algorithm is a method for dividing a set of data points into distinct clusters, or groups, based on similar attributes. It is an unsupervised learning algorithm which means it does not require labeled data in order to find patterns in the dataset. K-means is an approachable introduction to clustering for developers and data scientists interested in machine learning. In this article, you will learning how to implement k-means entirely from scratch and gain a strong understanding of the k-means algorithm. The goal of clustering is to divide items into groups such that objects in a group are more similar than those outside the group. Stepping aside from programming for a second, we can gain a better understanding of clusters.