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Recognition of geometrical patterns seems to be an important aspect of human intelligence. Geometric pattern recognition is used in many intelligence tests, including Dehaene’s odd-one-out test of Core Geometry (CG)) based on intuitive geometrical concepts (Dehaene et al., 2006). Earlier work has developed a symmetry-based cognitive model of Dehaene’s test and demonstrated performance comparable to that of humans. In this work, we further investigate the role of symmetry in geometrical intuition and build a cognitive model for the 2-Alternative Forced Choice (2-AFC) variation of the CG test (Marupudi &amp; Varma 2021). In contrast to Dehaene’s test, 2-AFC leaves almost no space for cognitive models based on generalization over multiple examples. Our symmetry-based model achieves an accuracy comparable to the human average on the 2-AFC test and appears to capture an essential part of intuitive geometry.

CogSci 2022

Symmetry as a Representation for Intuitive Geometry?

Recognition of geometrical patterns seems to be an important aspect of human intelligence. Geometric pattern recognition is used in many intelligence tests, including Dehaene’s odd-one-out test of Core Geometry (CG)) based on intuitive geometrical concepts (Dehaene et al., 2006). Earlier work has developed a symmetry-based cognitive model of Dehaene’s test and demonstrated performance comparable to that of humans. In this work, we further investigate the role of symmetry in geometrical intuition and build a cognitive model for the 2-Alternative Forced Choice (2-AFC) variation of the CG test (Marupudi & Varma 2021). In contrast to Dehaene’s test, 2-AFC leaves almost no space for cognitive models based on generalization over multiple examples. Our symmetry-based model achieves an accuracy comparable to the human average on the 2-AFC test and appears to capture an essential part of intuitive geometry.

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Join us for CogSci2022! Our 44th Annual Conference will be centered around the theme of diversity, with an accompanying range of keynotes and invited speakers who themselves highlight the diversity of our field. Our three symposia are Cognition across Diverse Populations, Cognition within Diverse Societies, and Global Challenges for Cognitive Science. The conference is being offered in a fully hybrid environment for onsite and online attendees.
 
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The 44th Annual Meeting of the Cognitive Science Society highlighted research on the theme Cognitive Diversity in addition to the full breadth and diversity of research topics offered by the society’s membership. 





Within-species variability is a fundamental biological concept, essential in understanding advanced concepts like evolution. Students formally encounter variability in their study of genetics in 4th grade; however, children’s cognitive biases can constrain their learning of variability. Diagrams are often used to facilitate learning of biological concepts, so it is important to understand how genetic inheritance diagrams depict variability. We analyzed 647 diagrams collected from textbooks and websites to examine how much variation diagrams present. We coded (1) depictions of within-species variability, and (2) other perceptual features implicated in learning (e.g., concreteness, richness). Preliminary findings indicate that many diagrams depict some within-species variability. Additionally, most diagrams used abstract representations of organisms and traits, which research suggests may be less optimal for younger students’ learning but may encourage transfer in older students. We will discuss how diagram features may reinforce children’s cognitive biases and may influence students’ learning of inheritance and variability.

Perceptual Features in Visual Representations: A Content Analysis of Inheritance Diagrams

Path integration, the ability to maintain an estimate of one's location by continuously integrating self-motion cues, is a vital component of the brain's navigation system. We present a spiking neural network model of path integration derived from a starting assumption that the brain represents continuous variables, such as spatial coordinates, using Spatial Semantic Pointers (SSPs). SSPs are a representation for encoding continuous variables as high-dimensional vectors, and can also be used to create structured, hierarchical representations for neural cognitive modelling. Path integration can be performed by a recurrently-connected neural network using SSP representations. Unlike past work, we show that our model can be used to continuously update variables of any dimensionality. We demonstrate that symbol-like object representations can be bound to continuous SSP representations. Specifically, we incorporate a simple model of working memory to remember environment maps with such symbol-like representations situated in 2D space.

A model of path integration that connects neural and symbolic representation

A recent sampling-based model of causal cognition, the Mutation Sampler, can explain the average responses of participants on a wide variety of tasks (Davis & Rehder, 2020). Careful analysis, however, shows that the predicted response distributions do not match empirical data. As an explanation for the observed response distributions, we propose that people engage in mutation sampling when confronted with a causal query and subsequently integrate this information with a prior. Several theoretical arguments can be made for the notion that people use priors in causal judgements; it is rational and matches the phenomenology of making such judgements. We have modelled this process with a new model called the Bayesian Mutation Sampler (BMS). We fit the BMS to experimental data and find that, in addition to average responses, the BMS explains multiple ‘distributional phenomena’, such as the moderate conservatism of the bulk of responses and the lack of extreme responses.

Explaining Full Response Distributions in Causal Reasoning Tasks: The Bayesian Mutation Sampler

Many of the real world phenomena that cognizers must grapple with are continuous, not only in the values they can take, but also in how these values change over time. The mind must somehow abstract from these inputs to extract useful discrete concepts such as objects, events and causal relationships. We investigate several factors that affect basic inferences about causal relationships between continuous variables based on observations in continuous time. In a novel experiment, we explore the ways in which causal judgments are sensitive to factors that relate to causal inductive biases (e.g. causal lags, the direction of variation) and causal perception (e.g. the range and rapidity of variation). We argue standard statistical time-series models have limited utility in accounting for human sensitivity to these factors. We suggest further work is needed to fully understand the cognitive processes that underlie causal induction from time-series information.

Intuitions and Perceptual Constraints on Causal Learning from Dynamics

When assessing the quality of a machine, people might consider the machine’s outputs—how well it serves its function. Alternatively, people might also consider the efficiency of the machine. We investigated this possibility in two experiments (N = 392). In each experiment, participants saw pairs of machines, one with simple inside parts and one with more complex inside parts. Machines either had the same output or unknown outputs, and people judged which of the two machines was better. When the machines had the same output, participants in both experiments judged that machines with simpler inside parts were better than ones with more complex insides. However, when machines’ functions were unknown, people predominantly judged that machines with complex insides were better. Together, our work shows that people consider both parts and functions of machines when inferring quality.

Using efficiency to infer the quality of machines

Human learning and generalization benefit from bootstrapping: we arrive at complex concepts by starting small and building upon past successes. In this paper, we examine a computational account of causal conceptual bootstrapping, and describe a novel experiment in which the sequence of training data results in a dramatic order effect: participants succeed in identifying a compound concept only after experiencing training data in a “helpful” order. Our computational model represents causal relations as reusable, modular programs, which can themselves be “chunked” and flexibly reused to tackle more complex tasks. Our specific approach is based in combinatory logic and adaptor grammars, building on previous theories that posit a “language of thought” for concept representation, but making the learning process more sensitive to a learner’s experiences than any particular choice of conceptual primitives. Crucially, we demonstrate that a caching mechanism like that used in adaptor grammars is key to explain human-like bootstrapping patterns in causal generalization.

Powering up causal generalization: A model of human conceptual bootstrapping with adaptor grammars

How do people make causal judgments about other's decisions? Prior work has argued that judging causation requires going beyond what actually happened and simulating what would have happened in a relevant counterfactual situation. Here, we extend the counterfactual simulation model of causal judgments for physical events, to explain judgments about other agents' decisions. In our experiments, an agent chooses what path to take to reach a goal. In Experiment 1, participants either made hypothetical judgments about whether the agent would succeed were it to take a certain path, or counterfactual judgments about whether the agent would have succeeded had it taken a different path. In Experiment 2, participants made causal judgments about whether the agent succeeded or failed because of the path that it took. Our computational model accurately captured participants' judgments in both experiments and we find that causal judgments are better explained by counterfactuals rather than hypotheticals.

That was close! A counterfactual simulation model of causal judgments about decisions

One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We developed an approach to eliciting self-explanations in which the ITS guided students to select explanations that were conceptually rich in nature. Students who used the ITS with self-explanations scored higher on a posttest that included items tapping both conceptual and procedural knowledge than did students who used a version of the ITS that included only traditional problem-solving practice. This study replicates previous findings that self-explanation and worked examples in an ITS can foster algebra learning (Booth et al., 2013). Further, this study extends prior work to show that guiding students towards conceptual explanations is beneficial.

Self-Explanation of Worked Examples Integrated in an Intelligent Tutoring System Enhances Problem Solving and Efficiency in Algebra

Research about explanation processes is gaining relevance because of the increased popularity of artificial systems required to explain their function or outcome. Following an interactive approach, not only explainers but also explainees contribute to successful interactions. However, little is known about how explainees actively guide explanation processes and how their involvement relates to learning. We explored the occurrence and type of explainees’ questions in 20 adult–adult explanation dialogues about unknown present and absent objects. Crucially, we related the question types to the explainees’ subsequent recall of the unknown object labels. We found that explainees asked different types of questions, especially about the object’s label and facts. Questions about the object’s function were asked more when objects were present. In addition, requests for labeling were linked to better recall. The results contribute to designing explainable AI that aim to provide relevant explanations and to further experimental approaches to study explanations.

Explain with, rather than explain to: How explainees shape their learning

Recent work suggests that perceptual decoupling (i.e., eye behavior becoming less determined by the sensory environment) is responsible for eye behaviour changes between externally and internally directed cognition. In the current study we investigated perceptual decoupling effects on smooth pursuit eye movements elicited by simultaneous engagement in internal visual and arithmetic task under two workload conditions. The results of multilevel modelling showed that effects of perceptual decoupling were moderated by task type (higher for visual internal activity), workload (higher for high internal demands) and follow a characteristic time course relative to internal operations. The findings indicate that perceptual decoupling is a central mechanism underlying differences in eye behaviour between internally and externally directed cognition and shed light on relevant conditions of this effect.

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Symmetry as a Representation for Intuitive Geometry?

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