Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

Learning Universal Predictors

Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data. Broad exposure to different tasks leads to versatile representations enabling general problem solving. But, what are the limits of meta-learning? In this work, we explore the potential of amortizing the most powerful universal predictor, namely Solomonoff Induction (SI), into neural networks via leveraging meta-learning to its limits. We use Universal Turing Machines (UTMs) to generate training data used to expose networks to a broad range of patterns. We provide theoretical analysis of the UTM data generation processes and meta-training protocols. We conduct comprehensive experiments with neural architectures (e.g. LSTMs, Transformers) and algorithmic data generators of varying complexity and universality. Our results suggest that UTM data is a valuable resource for meta-learning, and that it can be used to train neural networks capable of learning universal prediction strategies.Comment: 32 pages, 11 figure

Innovative use of educational technology in the second language classroom : design principles for teaching and

M.Ed. (ICT in Education)The use of information and communications technologies (ICT’s) is essential to build capacity in education. This is regarded as one of the strategic thrusts for the national development plan focusing on the development of 21st century skills in the information age. ICT’s offer many new learning opportunities when integrated into languages and in particular, when addressing the preparation and presentation of speeches in the second language classroom. Prepared speeches are not only difficult, but tend to become boring due to the fact that learners battle with pronunciation, grammar and language structure. By using primary school learners, in groups of not more than 8, learners were expected to work in collaboration to prepare a viral video production, that would replace the traditional speech. Participants had to rely on drama and computer skills to create a 90 second viral video that would promote healthy eating habits. By using Google Translate, Windows Moviemaker and digital cameras, learners had to translate from English to Afrikaans, write storyboards and finally create a video production. The data collection in this research is of a quantitative nature. The research involves a deeper look at the theory underpinning teaching and learning with technologies, as well as the notion of transformative action which is based in Cultural Historical and Activity Theory (CHAT). Draft design principles were distilled from informal interviews, reflective diaries and a set of questions to clarify experiences of all learner

An analysis of within-compound associations in spatial learning

The nature of spatial learning has been argued to be qualitatively different from that of associative learning. Compelling evidence for this argument is provided by experiments showing a lack of typical associative cue competition between spatial and non-spatial cues. However, this lack of cue-competition is also evident in wholly nonspatial experiments and has been explained by the presence of within-compound associations: an associative phenomenon. This thesis aims to determine whether such associations can explain similar cue-competition failures in spatial learning. In a series of experiments it is shown that these within-compound associations exist between spatial and non-spatial cues in the rat, and that they can account for the frequent failure to observe typical cue-competition between these cues. In addition, it is demonstrated that the extent to which this failure occurs depends upon the relative salience of the cues in question. In related experiments, it is also shown that these within-compound associations between spatial and non-spatial cues exist in humans. However, manifestation of these associations appears to depend on the gender of the participant, with associations forming in males but not in females. Further experiments suggest that this difference is likely due to the fact that the females are much less able to learn about the spatial cues in question. It is argued that spatial learning need not be qualitatively different from associative learning if such associative phenomena as within-compound associations are accounted for

Chinese Postgraduate Students in a British University: Their Learning Experiences and Learning Beliefs

This thesis is an ethnographic study of a group of Chinese postgraduate students in a British university as they become adjusted to the culture of teaching and learning in the new learning environment during their first year of overseas study. It focuses on these Chinese students’ initial perceptions of British teaching and learning practices compared with their inherited culture of learning and how they make adjustments, emotionally, cognitively, and behaviourally, in order to make their learning successful, with the result of changes and developments in their conceptions and beliefs about knowing and learning. The present study seeks to draw together understanding from the fields of intercultural adaptation theories, tertiary students’ conceptions of learning research, and the interface of culture and learning, i.e. cultures of learning, to explore the impact of studying abroad on students’ intellectual development and personal growth so as to inform international and intercultural education

Communication in virtual world spaces; an exploration of the layers and resources employed in a multimodal, informal language learning experience.

In my thesis I explore the interplay between the different layers employed in communication when a small number of people interact and exchange views in a virtual world, Second Life. I investigate how geographical, physical reality intrudes on virtual reality, and the effect this has on identity and communication. Furthermore, I trace how the interface between the different modes and spaces, such as ‘in world’ voice, the Internet and the ‘real physical world’, blend in communication. The study involved video recordings of the meetings and interaction in Second Life between a small number of participants. The participants comprised international students, preparing to study at a UK university, home students in the same university and the researcher. This occurred in my plot of land on Edunation Island in Second Life. Ultimately, I, the researcher, explored how adopting an avatar in a virtual world affects communication. My approach to this research was a qualitative, in depth study of selected scenes and interactions. I use a visual narrative approach to present an analysis of the interactions between participants, the environment and references to modes or spaces external to the virtual spaces. I theorise on the interactions from the view of language as a social practice with its principal purpose for communication. I evaluate the success of communication between the participants on the merit of their understanding of each other, and in so doing I reject the structuralist view of language where needing to be ‘accurate’ and where only the ‘expert’ speaker can be accepted as correct

Students' ideas about different representations of the past : South Korean adolescents interpret historical film

This thesis explores the ways in which secondary school students interpret different\ud representations of the past as portrayed in the film. It focuses on the question of how they set\ud the film director's view within a sociocultural context, and how they conceptualise what\ud constitutes acceptable historical knowledge. Ninety-six secondary school students in South\ud Korea viewed two sets of historical films that vary in terms of authorship, period, and genre.\ud The viewings were followed by semi-structured interviews, which aimed to investigate a\ud range of students' approaches to different representations produced at a given place and time.\ud This thesis argues that acknowledging the structuring of historical knowledge as a part of\ud cultural practice enabled students to make a shift in their picture of the past: from the idea of\ud the past as being reproduced to that of the past as being organised and reconstructed. A range\ud of ideas about historical knowledge, from a direct report of the event through an\ud idiosyncratic interpretation of a literary past to systematic mediation of historical reality, was\ud identified.\ud Through analysis of students' approaches to revision of the past, this thesis also discusses the\ud relationship between ideas about the role of perspective in history and ideas about the\ud reconfiguration of the past for the present. Students tended to assume that more committed\ud perspectives were likely to subject historical representations to greater revision of history.\ud Students' ideas about changing representations of the past reflected their presuppositions\ud about change of viewpoints in historical enquiry, mainly either in an empirical or cultural\ud sense rather than in a methodological sense.\ud Given students' tendency to conceive historical representations as being subject to\ud perspective mainly fuelled by present interests, it is crucial to provide an opportunity for\ud them to frame an historical account as an answer to a particular question, attributing a\ud positive role to perspectival views of the past