Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations, while entorhinal cortex compresses these predictive representations with spectral methods that support smooth generalization among related states. I will also cover recent work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design.

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.

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.

According to the concreteness fading approach, instruction should start with concrete representations and progress stepwise to representations that are more idealized. Various researchers have suggested that concreteness fading is a broadly applicable instructional approach. In this talk, we conceptually analyze examples of concreteness fading in mathematics and various science domains. In this analysis, we draw on theories of analogical and relational reasoning and on the literature about learning with multiple representations. Furthermore, we report on an experimental study in which we employed concreteness fading in advanced physics education. The results of the conceptual analysis and the experimental study indicate that concreteness fading may not be as generalizable as has been suggested. The reasons for this limited generalizability are twofold. First, the types of representations and the relations between them differ across different domains. Second, the instructional goals between domains and the subsequent roles of the representations vary.

Previous work suggests that children’s ability to understand metaphors emerges late in development. Researchers argue that children’s initial failure to understand metaphors is due to an inability to reason about shared relational structures between concepts. However, recent work demonstrates that preschoolers, toddlers, and even infants are already capable of relational reasoning. Might preschoolers also be capable of understanding metaphors, given more sensitive experimental paradigms? I explore whether preschoolers (N = 200, ages 4-5) understand functional metaphors, namely metaphors based on functional similarities. In Experiment 1a, preschoolers rated functional metaphors (e.g. “Roofs are hats”; “Clouds are sponges”) as “smarter” than nonsense statements. In Experiment 1b, adults (N = 48) also rated functional metaphors as “smarter” than nonsense statements (e.g. “Dogs are scissors”; “Boats are skirts”). In Experiment 2, preschoolers preferred functional explanations (e.g. “Both hold water”) over perceptual explanations (e.g. “Both are fluffy”) when interpreting a functional metaphor (e.g. “Clouds are sponges”). In Experiment 3, preschoolers preferred functional metaphors over nonsense statements in a dichotomous-choice task. Overall, this work demonstrates preschoolers’ early-emerging ability to understand functional metaphors.

It is a truth universally acknowledged that relational reasoning is important for learning in Science, Technology, Engineering, and Mathematics (STEM) disciplines. However, much research on relational reasoning uses examples unrelated to STEM concepts (understandably, to control for prior knowledge in many cases). In this talk I will discuss how real STEM concepts can be profitably used in relational reasoning research, using fraction concepts in mathematics as an example.