Topic: abstraction

Justin Chen introduces groups as collections of actions and explains their relationship to symmetry. The discussion uses accessible examples to show the power of abstraction, then considers the challenges of explaining group theory to non-specialists. Chen also reflects on his experience communicating mathematics and his plans for further study.

Category theorist Eugenia Cheng and Steven Strogatz explore how mathematical objects can be equivalent without being exactly equal. Cheng explains how abstraction reveals patterns and connections across different areas of mathematics, from geometry and topology to symmetry, and how category-theoretic thinking can illuminate situations in everyday life.

New tasks are often similar in structure to old ones. Animals that take advantage of such conserved or “abstract” task structures can master new tasks with minimal training. To understand the neural basis of this abstraction, we developed a novel behavioural paradigm for mice: the “ABCD” task, and recorded from their medial frontal neurons as they learned. Animals learned multiple tasks where they had to visit 4 rewarded locations on a spatial maze in sequence, which defined a sequence of four “task states” (ABCD). Tasks shared the same circular transition structure (… ABCDABCD …) but differed

In the past few years, there has been growing evidence that the basic ability for relational generalization starts in early infancy, with 3-month-olds seeming to learn relational abstractions with little training. Further, work with toddlers seem to suggest that relational generalizations are no more difficult than those based on objects, and they can readily consider both simultaneously. Likewise, causal learning research with adults suggests that people infer causal relationships at multiple levels of abstraction simultaneously as they learn about novel causal systems. These findings all app

Across species, humans are uniquely able to acquire deep relational systems of the kind needed for mathematics, science, and human language. Analogical comparison processes are a major contributor to this ability. Analogical comparison engages a structure-mapping process (Gentner, 1983) that fosters learning in at least three ways: first, it highlights common relational systems and thereby promotes abstraction; second, it promotes inferences from known situations to less familiar situations; and, third, it reveals potentially important differences between examples. In short, structure-mapping

The curse of dimensionality plagues models of reinforcement learning and decision-making. The process of abstraction solves this by constructing abstract variables describing features shared by different specific instances, reducing dimensionality and enabling generalization in novel situations. Here we characterized neural representations in monkeys performing a task where a hidden variable described the temporal statistics of stimulus-response-outcome mappings. Abstraction was defined operationally using the generalization performance of neural decoders across task conditions not used for tr

In 1955, John McCarthy and colleagues proposed an AI summer research project with the following aim: “An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves.” More than six decades later, all of these research topics remain open and actively investigated in the AI community. While AI has made dramatic progress over the last decade in areas such as vision, natural language processing, and robotics, current AI systems still almost entirely lack the ability to form humanlike concept

The curse of dimensionality plagues models of reinforcement learning and decision-making. The process of abstraction solves this by constructing abstract variables describing features shared by different specific instances, reducing dimensionality and enabling generalization in novel situations. We characterized neural representations in monkeys performing a task where a hidden variable described the temporal statistics of stimulus-response-outcome mappings. Abstraction was defined operationally using the generalization performance of neural decoders across task conditions not used for trainin

Wobble board-based Exergaming of different intensities provides a unique approach to enhance different cognitive and balance parameters . This study aims to determine that which of the cognitive and balance components are greatly affected by wobble board exergaming of different intensities in individuals with mild cognitive impairment (MCI).In this study ninety-seven MCI participants (MoCA 18-24, aged 50-75 years) were randomly assigned into mild, moderate, high intensity novel wobble board based exergaming, and control. All groups received 24 sessions (40 minutes/session, 3 times/week). Diffe