Analogical Minds

This talk will focus on our lab's extensive research on understanding and enhancing creative analogical reasoning. I will cover the development of the analogy finding matrix task, evidence for conscious augmentation of creative state during this task, and the real-world implications this ability has for college STEM education. I will also discuss recent research aimed at enhancing performance on this creative analogical reasoning task using both transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS).

Social learning and analogical reasoning both provide exponential opportunities for learning. These skills have largely been studied independently, but my future research asks how combining skills across previously independent domains could add up to more than the sum of their parts. Analogical reasoning allows individuals to transfer learning between contexts and opens up infinite opportunities for innovation and knowledge creation. Its origins and development, so far, have largely been studied in purely cognitive domains. Constraining analogical development to non-social domains may mistakenly lead researchers to overlook its early roots and limit ideas about its potential scope. Building a bridge between social learning and analogy could facilitate identification of the origins of analogical reasoning and broaden its far-reaching potential. In this talk, I propose that the early emergence of social learning, its saliency, and its meaningful context for young children provides a springboard for learning. In addition to providing a strong foundation for early analogical reasoning, the social domain provides an avenue for scaling up analogies in order to learn to learn from others via increasingly complex and broad routes.

Visual comparisons are ubiquitous, and they can also be an important source for learning (e.g., Gentner et al., 2016; Kok et al., 2013). In science, technology, engineering, and math (STEM), key information is often conveyed through figures, graphs, and diagrams (Mayer, 1993). Comparing within and across visuals is critical for gleaning insight into the underlying concepts, structures, and processes that they represent. This talk addresses how people make visual comparisons and how visual comparisons can be best supported to improve learning. In particular, the talk will present a series of studies exploring the Spatial Alignment Principle (Matlen et al., 2020), derived from Structure-Mapping Theory (Gentner, 1983). Structure-mapping theory proposes that comparisons involve a process of finding correspondences between elements based on structured relationships. The Spatial Alignment Principle suggests that spatially arranging compared figures directly – to support correct correspondences and minimize interference from incorrect correspondences – will facilitate visual comparisons. We find that direct placement can facilitate visual comparison in educationally relevant stimuli, and that it may be especially important when figures are less familiar. We also present complementary evidence illustrating the preponderance of visual comparisons in 7th grade science textbooks.

It is well established that the opportunity to compare learning stimuli in a novel word learning/extension task elicits a larger number of conceptually relevant generalizations than standard no-comparison conditions. I will present results suggesting that the effectiveness of comparison depends on factors such as semantic distance, number of training items, dimension distinctiveness and interactions with age. I will address these issues in the case of familiar and unfamiliar object nouns and relational nouns. The alignment strategies followed by children during learning and at test (i.e., when learning items are compared and how children reach a solution) will be described with eye-tracking data. We will also assess the extent to which children’s performance in these tasks are associated with executive functions (inhibition and flexibility) and world knowledge. Finally, we will consider these issues in children with cognitive deficits (Intellectual deficiency, DLD)

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 appear counter to theories of concept learning that posit when concepts are first learned they tend to be concrete (tied to specific contexts and features) and abstraction proceeds incrementally as learners encounter more examples. The current talk will not question the veracity of any of these findings but will present several others from my and others’ research on relational learning that suggests that when the perceptual or conceptual content becomes more complex, patterns of incremental abstraction re-emerge. Further, the specific contexts and task parameters that support or hinder abstraction reveal the underlying cognitive processes. I will then consider whether the models that posit simultaneous, immediate learning at multiple levels of abstraction can accommodate these more complex patterns.

The talk argues for a new approach to analysing analogical reasoning in scientific practice. Traditionally, philosophers of science tend to analyse analogical reasoning in either a top-down way or a bottom-up way. Examples of top-down approaches include Mary Hesse’s seminal work (1963) and Paul Bartha’s articulation model (2010), while most popular bottom-up approach is John Norton’s material approach (2018). I will address the problems of these traditional approaches and introduce an alternative approach, which is motivated by my exemplar-based approach to the history of science, defended in my recent book (2020).

Many tasks that are easy for humans are difficult for machines. In particular, while humans excel at tasks that require generalising across problems, machine systems notably struggle. One such task that has received a good amount of attention is the Synthetic Visual Reasoning Test (SVRT). The SVRT consists of a range of problems where simple visual stimuli must be categorised into one of two categories based on an unknown rule that must be induced. Conventional machine learning approaches perform well only when trained to categorise based on a single rule and are unable to generalise without extensive additional training to tasks with any additional rules. Multiple theories of higher-level cognition posit that humans solve such tasks using structured relational representations. Specifically, people learn rules based on structured representations that generalise to novel instances quickly and easily. We believe it is possible to model this approach in a single system which learns all the required relational representations from scratch and performs tasks such as SVRT in a single run. Here, we present a system which expands the DORA/LISA architecture and augments the existing model with principally novel components, namely a) visual reasoning based on the established theories of recognition by components; b) the process of learning complex relational representations by synthesis (in addition to learning by analysis). The proposed augmented model matches human behaviour on SVRT problems. Moreover, the proposed system stands as perhaps a more realistic account of human cognition, wherein rather than using tools that has been shown successful in the machine learning field to inform psychological theorising, we use established psychological theories to inform developing a machine system.

A common result is that comparison settings (i.e., several stimuli introduced simultaneously) favor conceptualization and generalization. However still little is known of the solving strategies used by children to compare and generalize novel words. Understanding the temporal dynamics of children’s solving strategies may help assess which processes underlie generalization. We tested children in noun and relational noun generalization tasks and collected eye tracking data. To analyze and interpret the data we followed predictions made by existing models of analogical reasoning and generalization. The data reveals clear patterns of exploration in which participants compare learning items before searching for a solution. Analyses of the beginning of trials show that early comparisons favor generalization and that errors may be caused by a lake of early comparison. Children then pursue their search in different ways according to the task. In this presentation I will present the generalization strategies revealed by eye tracking, compare the strategies from both tasks and confront them to existing models.

Analogy offers a new interpretation of a common concern in ethics: whether decision making includes or excludes a consideration of moral issues. This is often discussed as the moral awareness of decision makers and considered a motivational concern. The possible new interpretation is that moral awareness is in part a matter of expertise. Some failures of moral awareness can then be understood as stemming from novicehood. Studies of analogical transfer are consistent with the possibility that moral awareness is in part a matter of expertise, that as a result motivation is less helpful than some prior theorizing would predict, and that many adults are not as expert in the domain of ethics as one might hope. The possibility of expert knowledge of ethical principles leads to new questions and opportunities.

Human cognitive abilities seem qualitatively different from the cognitive abilities of other primates, a difference Penn, Holyoak, and Povinelli (2008) attribute to role-based relational reasoning—inferences and generalizations based on the relational roles to which objects (and other relations) are bound, rather than just the features of the objects themselves. Role-based relational reasoning depends on the ability to dynamically bind arguments to relational roles. But dynamic binding cannot be sufficient for relational thinking: Some non-human animals solve the dynamic binding problem, at least in some domains; and many non-human species generalize affordances to completely novel objects and scenes, a kind of universal generalization that likely depends on dynamic binding. If they can solve the dynamic binding problem, then why can they not reason about relations? What are they missing? I will present simulations with the LISA model of analogical reasoning (Hummel & Holyoak, 1997, 2003) suggesting that the missing pieces are multi-role integration (the capacity to combine multiple role bindings into complete relations) and structure mapping (the capacity to map different systems of role bindings onto one another). When LISA is deprived of either of these capacities, it can still generalize affordances universally, but it cannot reason symbolically; granted both abilities, LISA enjoys the full power of relational (symbolic) thought. I speculate that one reason it may have taken relational reasoning so long to evolve is that it required evolution to solve both problems simultaneously, since neither multi-role integration nor structure mapping appears to confer any adaptive advantage over simple role binding on its own.

Analogical reasoning remains foundational to the human ability to forge meaningful patterns within the sea of information that continually inundates the senses. Yet, meaningful patterns rely not only on the recognition of attributional similarities but also dissimilarities. Just as the perception of images rests on the juxtaposition of lightness and darkness, reasoning relationally requires systematic attention to both similarities and dissimilarities. With that awareness, my colleagues and I have expanded the study of relational reasoning beyond analogous reasoning and attributional similarities to highlight forms based on the nature of core dissimilarities: anomalous, antinomous, and antithetical reasoning. In this presentation, I will delineate the character of these relational reasoning forms; summarize procedures and measures used to assess them; overview key research findings; and describe how the forms of relational reasoning work together in the performance of complex problem solving. Finally, I will share critical next steps for research which has implications for instructional practice.

Although analogical reasoning has been assumed to involve insight and its associated “aha!” experience, the relationship between these phenomena has never been directly probed empirically. In this study we investigated the relationship between representational change and the “aha!” experience during analogical reasoning. A novel set of verbal analogy stimuli were developed for use as an insight task. Across two experiments, participants reported significantly stronger aha moments and showed greater evidence of representational change on trials with more semantically distant analogies. Further, the strength of reported aha moments was correlated with the degree to which participants’ descriptions of the analogies changed over the course of each trial. Lastly, we probed the individual differences associated with a tendency to report stronger "aha" experiences, particularly related to mood, curiosity, and reward responsiveness. The findings shed light on the affective components of analogical reasoning and suggest that measuring affective responses during such tasks may elucidate novel insights into the mechanisms of creative analogical reasoning.

Children's emerging ability to acquire and apply relational same-different concepts is often cited as a defining feature of human cognition, providing the foundation for abstract thought. Yet, young learners often struggle to ignore irrelevant surface features to attend to structural similarity instead. I will argue that young children have--and retain--genuine relational concepts from a young age, but tend to neglect abstract similarity due to a learned bias to attend to objects and their properties. Critically, this account predicts that differences in the structure of children's environmental input should lead to differences in the type of hypotheses they privilege and apply. I will review empirical support for this proposal that has (1) evaluated the robustness of early competence in relational reasoning, (2) identified cross-cultural differences in relational and object bias, and (3) provided evidence that contextual factors play a causal role in relational reasoning. Together, these studies suggest that the development of abstract thought may be more malleable and context-sensitive than initially believed.

This talk will focus on the idea that the kind of similarity driving analogical retrieval is determined by the kind of features encoded regarding the source and the target cue situations. Emphasis will be put on educational perspectives in order to show the influence of world semantics on learners’ problem representations and solving strategies, as well as the difficulties arising from semantic incongruence between representations and strategies. Special attention will be given to the recoding of semantically incongruent representations, a crucial step that learners struggle with, in order to illustrate a promising path for going beyond informal strategies.

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.

Hongjing Lu will present a new computational model of Probabilistic Analogical Mapping (PAM, in collaboration with Nick Ichien and Keith Holyoak) that finds systematic correspondences between inputs generated by machine learning. The model adopts a Bayesian framework for probabilistic graph matching, operating on semantic relation networks constructed from distributed representations of individual concepts (word embeddings created by Word2vec) and of relations between concepts (created by our BART model). We have used PAM to simulate a broad range of phenomena involving analogical mapping by both adults and children. Our approach demonstrates that human-like analogical mapping can emerge from comparison mechanisms applied to rich semantic representations of individual concepts and relations. More details can be found https://arxiv.org/ftp/arxiv/papers/2103/2103.16704.pdf

In human and non-human animals, conceptual knowledge is partially organized according to low-dimensional geometries that rely on brain structures and computations involved in spatial representations. Recently, two separate lines of research have investigated cognitive maps, that are associated with the hippocampal formation and are similar to world-centered representations of the environment, and image spaces, that are associated with the parietal cortex and are similar to self-centered spatial relationships. I will suggest that cognitive maps and image spaces may be two manifestations of a more general propensity of the mind to create low-dimensional internal models, and may play a role in analogical reasoning and metaphorical thinking. Finally, I will show some data suggesting that the metaphorical relationship between colors and emotions can be accounted for by the structural alignment of low-dimensional conceptual spaces.

Abstract relations are considered the pinnacle of human cognition, allowing analogical and logical reasoning, and possibly setting humans apart from other animal species. Such relations cannot be represented in a perceptual code but can easily be represented in a propositional language of thought, where relations between objects are represented by abstract discrete symbols. Focusing on the abstract relations same and different, I will show that (1) there is a discontinuity along ontogeny with respect to the representations of abstract relations, but (2) young infants already possess representations of same and different. Finally, (3) I will investigate the format of representation of abstract relations in young infants, arguing that those representations are not discrete, but rather built by juxtaposing abstract representations of entities.

Analogies are widely used by teachers and coaches of different movement disciplines, serving a role during the learning phase of a new skill, and honing one’s performance to a competitive level. In previous studies, analogies improved motor control in various tasks and across age groups. Our study aimed to evaluate the efficacy of analogies throughout the learning process, using kinematic measures for an in-depth analysis. We tested whether applying analogies can shorten the motor learning process and induce insight and skill improvement in tasks that usually demand many hours of practice. The experiment included a drawing task, in which subjects were asked to connect four dots into a closed shape, and a mirror game, in which subjects tracked an oval that moved across the screen. After establishing a baseline, subjects were given an analogy, explicit instructions, or no further instruction. We compared their improvement in overall skill, accuracy, and speed. Subjects in the analogy and explicit groups improved their performance in the drawing task, while significant differences were found in the mirror game only for slow movements between analogy and controls. In conclusion, analogies are an important tool for teachers and coaches, and more research is needed to understand how to apply them for maximum results. They can rapidly change motor control and strategy but may also affect only some aspects of a movement and not others. Careful thought is needed to construct an effective analogy that encompasses relevant movement facets, as well as the practitioner’s personal background and experience.

Comparison is a powerful learning process that improves learning in many domains. For over 10 years, my colleagues and I have researched how we can use comparison to support better learning of school mathematics within classroom settings. In 5 short-term experimental, classroom-based studies, we evaluated comparison of solution methods for supporting mathematics knowledge and tested whether prior knowledge impacted effectiveness. We next developed supplemental Algebra I curriculum and professional development for teachers to integrate Comparison and Explanation of Multiple Strategies (CEMS) in their classrooms and tested the promise of the approach when implemented by teachers in two studies. Benefits and challenges emerged in these studies. I will conclude with evidence-based guidelines for effectively supporting comparison and explanation in the classroom. Overall, this program of research illustrates how cognitive science research can guide the design of effective educational materials as well as challenges that occur when bridging from cognitive science research to classroom instruction.