A mathematical theory is presented for the representation of knowledge in the form of a directed acyclic hierarchy of objects in a category where all paths between any given pair of objects are required to be equal. The conditions under which knowledge update, in the form of the sesqui-pushout rewriting of an object in a hierarchy, can be propagated to the rest of the hierarchy, in order to maintain all required path equalities, are analysed: some rewrites must be propagated forwards, in the direction of the arrows, while others must be propagated backwards, against the direction of the arrows, and, depending on the precise form of the hierarchy, certain composability conditions may also be necessary. The implementation of this theory, in the ReGraph Python library for (simple) directed graphs with attributes on nodes and edges, is then discussed in the context of two significant use cases.

With the strengthening of data privacy and security, traditional data centralization for AI faces huge challenges. Moreover, isolated data existing in various industries and institutions is grossly underused and thus retards the advance of AI applications. We propose a possible solution to these problems: knowledge federation. Beyond the concepts of federated learning and secure multi-party computation, we introduce a comprehensive knowledge federation framework, which is a hierarchy with four-level federation. In terms of the occurrence time of federation, knowledge federation can be categorized into information level, model level, cognition level, and knowledge level. To facilitate widespread academic and commercial adoption of this concept, we provide definitions free from ambiguity for the knowledge federation framework. In addition, we clarify the relationship and differentiation between knowledge federation and other related research fields and conclude that knowledge federation is a unified framework for secure multi-party computation and learning.

Machine teaching is an algorithmic framework for teaching a target hypothesis via a sequence of examples or demonstrations. We investigate machine teaching for temporal logic formulas -- a novel and expressive hypothesis class amenable to time-related task specifications. In the context of teaching temporal logic formulas, an exhaustive search even for a myopic solution takes exponential time (with respect to the time span of the task). We propose an efficient approach for teaching parametric linear temporal logic formulas. Concretely, we derive a necessary condition for the minimal time length of a demonstration to eliminate a set of hypotheses. Utilizing this condition, we propose a myopic teaching algorithm by solving a sequence of integer programming problems. We further show that, under two notions of teaching complexity, the proposed algorithm has near-optimal performance. The results strictly generalize the previous results on teaching preference-based version space learners. We evaluate our algorithm extensively under a variety of learner types (i.e., learners with different preference models) and interactive protocols (e.g., batched and adaptive). The results show that the proposed algorithms can efficiently teach a given target temporal logic formula under various settings, and that there are significant gains of teaching efficacy when the teacher adapts to the learner's current hypotheses or uses oracles.

When it comes to bias and artificial intelligence, there is a common belief that algorithms are only as good as the numbers plugged into them. But the focus on algorithmic bias being concentrated entirely on data has meant we have ignored two aspects of this problem: the deep limitations of existing algorithms and, more importantly, the role of human problem solvers. Powerful as they may be, most of our algorithms only mine correlational relationships without understanding anything about them. My research has found that massive data sets on jobs, education and loans contain more spurious correlations than meaningful causal relationships. It is ludicrous to assume these algorithms will solve problems that we do not understand.

How can we enable machines to make sense of the world, and become better at learning? To approach this goal, I believe viewing intelligence in terms of many integral aspects, and also a universal two-term tradeoff between task performance and complexity, provides two feasible perspectives. In this thesis, I address several key questions in some aspects of intelligence, and study the phase transitions in the two-term tradeoff, using strategies and tools from physics and information. Firstly, how can we make the learning models more flexible and efficient, so that agents can learn quickly with fewer examples? Inspired by how physicists model the world, we introduce a paradigm and an AI Physicist agent for simultaneously learning many small specialized models (theories) and the domain they are accurate, which can then be simplified, unified and stored, facilitating few-shot learning in a continual way. Secondly, for representation learning, when can we learn a good representation, and how does learning depend on the structure of the dataset? We approach this question by studying phase transitions when tuning the tradeoff hyperparameter. In the information bottleneck, we theoretically show that these phase transitions are predictable and reveal structure in the relationships between the data, the model, the learned representation and the loss landscape. Thirdly, how can agents discover causality from observations? We address part of this question by introducing an algorithm that combines prediction and minimizing information from the input, for exploratory causal discovery from observational time series. Fourthly, to make models more robust to label noise, we introduce Rank Pruning, a robust algorithm for classification with noisy labels. I believe that building on the work of my thesis we will be one step closer to enable more intelligent machines that can make sense of the world.

Architectural patterns provide a reusable architectural solution for commonly recurring problems that can assist in designing software systems. In this regard, self-awareness architectural patterns are specialized patterns that leverage good engineering practices and experiences to help in designing self-awareness and self-adaptation of a software system. However, domain knowledge and engineers' expertise that is built over time are not explicitly linked to these patterns and the self-aware process. This linkage is important, as it can enrich the design patterns of these systems, which consequently leads to more effective and efficient self-aware and self-adaptive behaviours. This paper is an introductory work that highlights the importance of synergizing domain expertise into the self-awareness in software systems, relying on well-defined underlying approaches. In particular, we present a holistic framework that classifies widely known representations used to obtain and maintain the domain expertise, documenting their nature and specifics rules that permits different levels of synergies with self-awareness. Drawing on such, we describe mechanisms that can enrich existing patterns with engineers' expertise and knowledge of the domain. This, together with the framework, allow us to codify an intuitive step-by-step methodology that guides engineer in making design decisions when synergizing domain expertise into self-awareness and reveal their importances, in an attempt to keep 'engineers-in-the-loop'. Through three case studies, we demonstrate how the enriched patterns, the proposed framework and methodology can be applied in different domains, within which we quantitatively compare the actual benefits of incorporating engineers' expertise into self-awareness, at alternative levels of synergies.

This dissertation explores the integration of learning and analogy-making through the development of a computer program, called Analogator, that learns to make analogies by example. By "seeing" many different analogy problems, along with possible solutions, Analogator gradually develops an ability to make new analogies. That is, it learns to make analogies by analogy. This approach stands in contrast to most existing research on analogy-making, in which typically the a priori existence of analogical mechanisms within a model is assumed. The present research extends standard connectionist methodologies by developing a specialized associative training procedure for a recurrent network architecture. The network is trained to divide input scenes (or situations) into appropriate figure and ground components. Seeing one scene in terms of a particular figure and ground provides the context for seeing another in an analogous fashion. After training, the model is able to make new analogies between novel situations. Analogator has much in common with lower-level perceptual models of categorization and recognition; it thus serves as a unifying framework encompassing both high-level analogical learning and low-level perception. This approach is compared and contrasted with other computational models of analogy-making. The model's training and generalization performance is examined, and limitations are discussed.

Through play children (and adults) learn how to use their imaginations, to experiment with different ways of doing things. This might seem like it has relevance only for their self-development, but it's also through imagination and experimentation that the human race as a collective arrives at the solutions to its problems. As such, it's vital that we encourage children and people more generally to use their imaginations and to experiment, and it's to this end that LEGO, of all things, has an important role to play in nurturing the next generation of engineers, scientists and problem solvers. And we're not just talking about informal play with LEGO here, since one organization in particular has taken it upon itself to incorporate the famous Danish toy in competitions and workshops, all of which aim to instil a love for science and engineering in children. This organization is FIRST (For Inspiration and Recognition of Science and Technology), a not-for-profit public charity based in New Hampshire that works to inspire young people to pursue careers and education in STEM (science, technology, engineering and mathematics) subjects. Beginning in 1999, it partnered with the LEGO Group itself to launch the FIRST LEGO League, tapping into the LEGO brand to bring children to science.

The recent usage of technical systems in human-centric environments leads to the question, how to teach technical systems, e.g., robots, to understand, learn, and perform tasks desired by the human. Therefore, an accurate representation of knowledge is essential for the system to work as expected. This article mainly gives insight into different knowledge representation techniques and their categorization into various problem domains in artificial intelligence. Additionally, applications of presented knowledge representations are introduced in everyday robotics tasks. By means of the provided taxonomy, the search for a proper knowledge representation technique regarding a specific problem should be facilitated.