Empiricism without Magic: Transformational Abstraction in Deep Convolutional Neural Networks

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain

Dealing with abstraction: Case study generalisation as a method for eliciting design patterns

Developing a pattern language is a non-trivial problem. A critical requirement is a method to support pattern writers with abstraction, so as they can produce generalised patterns. In this paper, we address this issue by developing a structured process of generalisation. It is important that this process is initiated through engaging participants in identifying initial patterns, i.e. directly dealing with the 'cold-start' problem. We have found that short case study descriptions provide a productive 'way into' the process for participants. We reflect on a 1-year interdisciplinary pan-European research project involving the development of almost 30 cases and over 150 patterns. We provide example cases, detailing the process by which their associated patterns emerged. This was based on a foundation for generalisation from cases with common attributes. We discuss the merits of this approach and its implications for pattern development

Learning by Seeing by Doing: Arithmetic Word Problems

Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty

Don't Just Listen, Use Your Imagination: Leveraging Visual Common Sense for Non-Visual Tasks

Artificial agents today can answer factual questions. But they fall short on questions that require common sense reasoning. Perhaps this is because most existing common sense databases rely on text to learn and represent knowledge. But much of common sense knowledge is unwritten - partly because it tends not to be interesting enough to talk about, and partly because some common sense is unnatural to articulate in text. While unwritten, it is not unseen. In this paper we leverage semantic common sense knowledge learned from images - i.e. visual common sense - in two textual tasks: fill-in-the-blank and visual paraphrasing. We propose to "imagine" the scene behind the text, and leverage visual cues from the "imagined" scenes in addition to textual cues while answering these questions. We imagine the scenes as a visual abstraction. Our approach outperforms a strong text-only baseline on these tasks. Our proposed tasks can serve as benchmarks to quantitatively evaluate progress in solving tasks that go "beyond recognition". Our code and datasets are publicly available

Abstraction and context in concept representation

This paper develops the notion of abstraction in the context of the psychology of concepts, and discusses its relation to context dependence in knowledge representation. Three general approaches to modelling conceptual knowledge from the domain of cognitive psychology are discussed, which serve to illustrate a theoretical dimension of increasing levels of abstraction

What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery