In cognitive development, learning more than the input provides is a central challenge. This challenge is especially evident in learning the meaning of numbers. Integers – and the quantities they denote – are potentially infinite, as are the fractional values between every integer. Yet children’s experiences of numbers are necessarily finite. Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input. However, retrieving proper analogy requires cognitive supports. In this talk, I seek to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning. To examine these hypotheses, I will present a series of educational intervention studies with third-to-fifth graders. Results showed that a short, unsupervised intervention of spatial alignment between integers and fractions on number lines produced broad and durable gains in fractional magnitudes. Additionally, training on conceptual knowledge of fractions – that fractions denote magnitude and can be placed on number lines – facilitates explicit analogical reasoning. Together, these studies indicate that analogies can play an important role in rational number learning with the help of number lines as schemas. These studies shed light on helpful practices in STEM education curricula and instructions.

Dominant theories of analogical thinking postulate that making an analogy consists in discovering that two superficially different situations share isomorphic systems of similar relations. According to this perspective, the comparison between the two situations may eventually lead to the construction of a schema, which retains the structural aspects they share and deletes their specific contents. We have developed a new approach to analogical thinking, whose purpose is to explain a particular type of analogies: those in which the analogs are exemplars of a schema-governed category (e.g., two instances of robbery). As compared to standard analogies, these comparisons are noteworthy in that a well-established schema (the schema-governed category) mediates each one of the subprocesses involved in analogical thinking. We argue that the category assignment approach is able to provide a better account of how the analogical subprocesses of retrieval, mapping, re-representation, evaluation and inference generation are carried out during the processing of this specific kind of analogies. The arguments presented are accompanied by brief descriptions of some of the studies that provided support for this approach.

In popular media, there is often a connection drawn between the advent of awareness in artificial agents and those same agents simultaneously achieving human or superhuman level intelligence. In this talk, I will examine the validity and potential application of this seemingly intuitive link between consciousness and intelligence. I will do so by examining the cognitive abilities associated with three contemporary theories of conscious function: Global Workspace Theory (GWT), Information Generation Theory (IGT), and Attention Schema Theory (AST), and demonstrating that all three theories specifically relate conscious function to some aspect of domain-general intelligence in humans. With this insight, we will turn to the field of Artificial Intelligence (AI) and find that, while still far from demonstrating general intelligence, many state-of-the-art deep learning methods have begun to incorporate key aspects of each of the three functional theories. Given this apparent trend, I will use the motivating example of mental time travel in humans to propose ways in which insights from each of the three theories may be combined into a unified model. I believe that doing so can enable the development of artificial agents which are not only more generally intelligent but are also consistent with multiple current theories of conscious function.

Previous experiments have shown that a comparison of two written narratives highlights their shared relational structure, which in turn facilitates the retrieval of analogous narratives from the past (e.g., Gentner, Loewenstein, Thompson, & Forbus, 2009). However, analogical retrieval occurs across domains that appear more conceptually distant than merely different narratives, and the deepest analogies use matches in higher-order relational structure. The present study investigated whether comparison can facilitate analogical retrieval of higher-order relations across written narratives and abstract symbolic problems. Participants read stories which became retrieval targets after a delay, cued by either analogous stories or letter-strings. In Experiment 1 we replicated Gentner et al. who used narrative retrieval cues, and also found preliminary evidence for retrieval between narrative and symbolic domains. In Experiment 2 we found clear evidence that a comparison of analogous letter-string problems facilitated the retrieval of source stories with analogous higher-order relations. Experiment 3 replicated the retrieval results of Experiment 2 but with a longer delay between encoding and recall, and a greater number of distractor source stories. These experiments offer support for the schema induction account of analogical retrieval (Gentner et al., 2009) and show that the schemas abstracted from comparison of narratives can be transferred to non-semantic symbolic domains.

Analogical reasoning is one of the most complex cognitive functions in humans that allows abstract thinking, high-level reasoning, and learning. Based on analogical reasoning, one can extract an abstract and general concept (i.e., an analogy schema) from a familiar situation and apply it to a new context or domain (i.e., analogy transfer). These processes allow us to solve problems we never encountered before and generate new ideas. However, the place of analogy transfer in problem solving mechanisms is unclear. This presentation will describe several experiments with three main findings. First, we show how analogy transfer facilitates problem-solving, replicating existing empirical data largely based on the radiation/fortress problems with four new riddles. Second, we propose a new experimental task that allows us to quantify analogy transfer. Finally, using science network methodology, we show how restructuring the mental representation of a problem can predict successful solving of an analogous problem. These results shed new light on the cognitive mechanism underlying solution transfer by analogy and provide a new tool to quantify individual abilities.

There has been a recent surge of interest in the question of whether and how deep learning algorithms might be capable of abstract reasoning, much of which has centered around datasets based on Raven’s Progressive Matrices (RPM), a visual analogy problem set commonly employed to assess fluid intelligence. This has led to the development of algorithms that are capable of solving RPM-like problems directly from pixel-level inputs. However, these algorithms require extensive direct training on analogy problems, and typically generalize poorly to novel problem types. This is in stark contrast to human reasoners, who are capable of solving RPM and other analogy problems zero-shot — that is, with no direct training on those problems. Indeed, it’s this capacity for zero-shot reasoning about novel problem types, i.e. fluid intelligence, that RPM was originally designed to measure. I will present some results from our recent efforts to model this capacity for zero-shot reasoning, based on an extension of a recently proposed approach to analogical mapping we refer to as Probabilistic Analogical Mapping (PAM). Our RPM model uses deep learning to extract attributed graph representations from pixel-level inputs, and then performs alignment of objects between source and target analogs using gradient descent to optimize a graph-matching objective. This extended version of PAM features a number of new capabilities that underscore the flexibility of the overall approach, including 1) the capacity to discover solutions that emphasize either object similarity or relation similarity, based on the demands of a given problem, 2) the ability to extract a schema representing the overall abstract pattern that characterizes a problem, and 3) the ability to directly infer the answer to a problem, rather than relying on a set of possible answer choices. This work suggests that PAM is a promising framework for modeling human zero-shot reasoning.

With the Donders Inclusion Seminars, we celebrate diversity. Please join us on Apr. 21st 2021 at 15.00 (CET) as we next welcome Dr. Silvy Collin of Tilburg University on Crowdcast. Her seminar is entitled "Schemas and schema-mediated memory". To read the abstract and register for the event visit: https://www.crowdcast.io/e/donders-inclusion-3

1. Embedding is all you need: A machine learning way to analyse white matter tractography streamlines - Dr Shenjun Zhong, Monash Biomedical Imaging Embedding white matter streamlines with various lengths into fixed-length latent vectors enables users to analyse them with general data mining techniques. However, finding a good embedding schema is still a challenging task as the existing methods based on spatial coordinates rely on manually engineered features, and/or labelled dataset. In this webinar, Dr Shenjun Zhong will discuss his novel deep learning model that identifies latent space and solves the problem of streamline clustering without needing labelled data. Dr Zhong is a Research Fellow and Informatics Officer at Monash Biomedical Imaging. His research interests are sequence modelling, reinforcement learning and federated learning in the general medical imaging domain. 2. Application of artificial intelligence in correcting motion artifacts and reducing scan time in MRI - Dr Kamlesh Pawar, Monash Biomedical imaging Magnetic Resonance Imaging (MRI) is a widely used imaging modality in clinics and research. Although MRI is useful it comes with an overhead of longer scan time compared to other medical imaging modalities. The longer scan times also make patients uncomfortable and even subtle movements during the scan may result in severe motion artifact in the images. In this seminar, Dr Kamlesh Pawar will discuss how artificial intelligence techniques can reduce scan time and correct motion artifacts. Dr Pawar is a Research Fellow at Monash Biomedical Imaging. His research interest includes deep learning, MR physics, MR image reconstruction and computer vision.

Existing accounts of analogical transfer highlight the importance of comparison-based schema abstraction in aiding retrieval of relevant prior knowledge from memory. In this talk, we discuss an alternative view, the category status hypothesis—which states that if knowledge of a target principle is represented as a relational category, it is easier to activate as a result of categorizing (as opposed to cue-based reminding)—and briefly review supporting evidence. We then further investigate this hypothesis by designing study tasks that promote different facets of category-level representations and assess their impact on spontaneous analogical transfer. A Baseline group compared two analogous cases; the remaining groups experienced comparison plus another task intended to impact the category status of the knowledge representation. The Intension group read an abstract statement of the principle with a supporting task of generating a new case. The Extension group read two more positive cases with the task of judging whether each exemplified the target principle. The Mapping group read a contrast case with the task of revising it into a positive example of the target principle (thereby providing practice moving in both directions between type and token, i.e., evaluating a given case relative to knowledge and using knowledge to generate a revised case). The results demonstrated that both Intension and Extension groups led to transfer improvements over Baseline (with the former demonstrating both improved accessibility of prior knowledge and ability to apply relational concepts). Implications for theories of analogical transfer are discussed.