Towards generalizable neuro-symbolic reasoners

Doctor of PhilosophyDepartment of Computer ScienceMajor Professor Not ListedSymbolic knowledge representation and reasoning and deep learning are fundamentally different approaches to artificial intelligence with complementary capabilities. The former are transparent and data-efficient, but they are sensitive to noise and cannot be applied to non-symbolic domains where the data is ambiguous. The latter can learn complex tasks from examples, are robust to noise, but are black boxes; require large amounts of --not necessarily easily obtained-- data, and are slow to learn and prone to adversarial examples. Either paradigm excels at certain types of problems where the other paradigm performs poorly. In order to develop stronger AI systems, integrated neuro-symbolic systems that combine artificial neural networks and symbolic reasoning are being sought. In this context, one of the fundamental open problems is how to perform logic-based deductive reasoning over knowledge bases by means of trainable artificial neural networks. Over the course of this dissertation, we provide a brief summary of our recent efforts to bridge the neural and symbolic divide in the context of deep deductive reasoners. More specifically, We designed a novel way of conducting neuro-symbolic through pointing to the input elements. More importantly we showed that the proposed approach is generalizable across new domain and vocabulary demonstrating symbol-invariant zero-shot reasoning capability. Furthermore, We have demonstrated that a deep learning architecture based on memory networks and pre-embedding normalization is capable of learning how to perform deductive reason over previously unseen RDF KGs with high accuracy. We are applying these models on Resource Description Framework (RDF), first-order logic, and the description logic EL+ respectively. Throughout this dissertation we will discuss strengths and limitations of these models particularly in term of accuracy, scalability, transferability, and generalizabiliy. Based on our experimental results, pointer networks perform remarkably well across multiple reasoning tasks while outperforming the previously reported state of the art by a significant margin. We observe that the Pointer Networks preserve their performance even when challenged with knowledge graphs of the domain/vocabulary it has never encountered before. To our knowledge, this work is the first attempt to reveal the impressive power of pointer networks for conducting deductive reasoning. Similarly, we show that memory networks can be trained to perform deductive RDFS reasoning with high precision and recall. The trained memory network's capabilities in fact transfer to previously unseen knowledge bases. Finally will talk about possible modifications to enhance desirable capabilities. Altogether, these research topics, resulted in a methodology for symbol-invariant neuro-symbolic reasoning

Explaining Deep Learning Hidden Neuron Activations using Concept Induction

One of the current key challenges in Explainable AI is in correctly interpreting activations of hidden neurons. It seems evident that accurate interpretations thereof would provide insights into the question what a deep learning system has internally \emph{detected} as relevant on the input, thus lifting some of the black box character of deep learning systems. The state of the art on this front indicates that hidden node activations appear to be interpretable in a way that makes sense to humans, at least in some cases. Yet, systematic automated methods that would be able to first hypothesize an interpretation of hidden neuron activations, and then verify it, are mostly missing. In this paper, we provide such a method and demonstrate that it provides meaningful interpretations. It is based on using large-scale background knowledge -- a class hierarchy of approx. 2 million classes curated from the Wikipedia Concept Hierarchy -- together with a symbolic reasoning approach called \emph{concept induction} based on description logics that was originally developed for applications in the Semantic Web field. Our results show that we can automatically attach meaningful labels from the background knowledge to individual neurons in the dense layer of a Convolutional Neural Network through a hypothesis and verification process.Comment: Submitted to IJCAI-2

On the Potential of Logic and Reasoning in Neurosymbolic Systems using OWL-based Knowledge Graphs

Knowledge graphs feature ever more frequently as symbolic components in neurosymbolic research and systems. But even though a central concern of neurosymbolic AI is to combine neural learning with symbolic reasoning, relatively little neurosymbolic research focuses on leveraging the logical representation and reasoning capabilities of OWL-based knowledge graphs. The objective of this position paper is to inspire more neurosymbolic researchers to embrace the OWL and the Semantic Web by raising awareness of the benefits, capabilities, and applications of OWL-based knowledge graphs, particularly with respect to logical reasoning. We describe the ecosystem of open W3C standards-based resources available that support the adoption and use of OWL-based knowledge graphs; we describe tools that exist for engineering custom OWL ontologies tailored to particular research needs; we discuss the encoding of background KG knowledge in subsymbolic embedding spaces and various applications of this approach; we discuss and illustrate the reasoning capabilities of OWL-based knowledge graphs; and we describe several promising directions for research that focus on leveraging these reasoning capabilities. We also discuss the specialised resources needed to undertake research on OWL-based knowledge graphs in neurosymbolic systems. We use the example of NeSy4VRD, an image dataset with a custom-designed companion OWL ontology. The scarcity of this kind of resource should be addressed to accelerate research in this field

Exploring mathematics learners’ problem-solving skills in circle geometry in South African schools : (a case study of a high school in the Northern Cape Province)

This study examined “problem solving skills in circle geometry concepts in Euclidean Geometry. This study was necessitated by learners’ inability to perform well with regards to Euclidean Geometry in general and Circle Geometry in particular. The use of naturalistic observation case study research (NOCSR) study was employed as the research design for the study. The intervention used for the study was the teaching of circle geometry with Polya problem solving instructional approach coupled with social constructivist instructional approach. A High School in the Northern Cape Province was used for the study. 61 mathematics learners (grade 11) in the school served as participants for the first year of the study, while 45 mathematics learners, also in grade 11, served as participants for the second year of the study. Data was collected for two consecutive years: 2018 and 2019. All learners who served as participants for the study did so willingly without been coerced in any way. Parental consent of all participants were also obtained. The following data were collected for each year of the research intervention: classroom teaching proceedings’ video recordings, photograph of learners class exercises (CE), field notes and the end-of-the- Intervention Test (EIT). Direct interpretations, categorical aggregation and a problem solving rubric were used for the analysis of data. Performance analysis and solution appraisal were also used to analyse some of the collected data. It emerged from the study that the research intervention evoked learners’ desire and interest to learn circle geometry. Also, the research intervention improved the study participants’ performance and problem solving skills in circle geometry concepts. Hence, it is recommended from this study that there is the need for South African schools to adopt the instructional approach for the intervention: Polya problem solving instructional approach coupled with social constructivist instructional approach, for the teaching and learning of Euclidean geometry concepts.Mathematics EducationM. Sc. (Mathematics Education