Analogical Minds

Vocabulary learning applications like Duolingo have millions of users around the world, but yet are based on very simple heuristics to choose teaching material to provide to their users. In this presentation, we will discuss the possibility to develop more advanced artificial teachers, which would be based on modeling of the learner’s inner characteristics. In the case of teaching vocabulary, understanding how the learner memorizes is enough. When it comes to picking grammar exercises, it becomes essential to assess how the learner reasons, in particular by analogy. This second application will illustrate how analogical and case-based reasoning can be employed in an alternative way in education: not as the teaching algorithm, but as a part of the learner’s model.

Theory of mind, which consists of reasoning about the knowledge, belief, desire, and similar mental states of others, is a key component of social reasoning and social interaction. While it has been studied by cognitive scientists for decades, none of the prevailing theories of the processes that underlie theory of mind reasoning and development explain the breadth of experimental findings. I propose that this is because theory of mind is, like much of human reasoning, inherently analogical. In this talk, I will discuss several theory of mind findings from the psychology literature, the challenges they pose for our understanding of theory of mind, and bring in evidence from the Analogical Theory of Mind (AToM) cognitive model that demonstrates how these findings fit into an analogical understanding of theory of mind reasoning.

Space is the universal donor for relations" (Gentner, 2014). This quote is the foundation of my talk. I will explore how and why visual representations and analogies are related, and why. I will also explore how considering the relation between analogy and spatial reasoning can shed light on why and how spatial thinking is correlated with learning in STEM fields. For example, I will consider children’s numbers sense and learning of the number line from the perspective of analogical reasoning.

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.

How and why are analogies spontaneously generated? Despite the prominence of analogy in learning and reasoning, there is little research on whether and how analogy is spontaneously generated in everyday settings. Here we fill this gap by gathering parents' answers to children's real questions, and examining analogy use in parental explanations. Study 1 found that parents used analogy spontaneously in their explanations, despite no prompt nor mention of analogy in the instruction. Study 2 found that these analogical explanations were rated highly by parents, schoolteachers, and university students alike. In Study 3, six-year-olds also rated good analogical explanations highly, but unlike their parents, did not rate them higher than causal, non-analogical explanations. We discuss what makes an analogy a good explanation, and how theories from both explanation and analogy research explain one’s motivation for spontaneously generating analogies.

Engineering designers practice design-by-analogy (DbA) during concept generation to retrieve knowledge from external sources or memory as inspiration to solve design problems. DbA is a tool for innovation that involves retrieving analogies from a source domain and transferring the knowledge to a target domain. While DbA produces innovative results, designers often come up with analogies by themselves or through serendipitous, random encounters. Computational support systems for searching analogies have been developed to facilitate DbA in systematic design practice. However, many systems have focused on a query-based approach, in which a designer inputs a keyword or a query function and is returned a set of algorithmically determined stimuli. In this presentation, a new analogical retrieval process that leverages a visual interaction technique is introduced. It enables designers to explore a space of analogies, rather than be constrained by what’s retrieved by a query-based algorithm. With an exploration-based DbA tool, designers have the potential to uncover more useful and unexpected inspiration for innovative design solutions.

A core question in human development is how we bring meaning to conventional symbols. This question is deeply connected to understanding how children learn mathematics—a symbol system with unique vocabularies, syntaxes, and written forms. In this talk, I will present findings from a program of research focused on children’s acquisition of place value symbols (i.e., multidigit number meanings). The base-10 symbol system presents a variety of obstacles to children, particularly in English. Children who cannot overcome these obstacles face years of struggle as they progress through the mathematics curriculum of the upper elementary and middle school grades. Through a combination of longitudinal, cross-sectional, and pretest-training-posttest approaches, I aim to illuminate relational learning mechanisms by which children sometimes succeed in mastering the place value system, as well as instructional techniques we might use to help those who do not.

Prior studies of A:B::C:D verbal analogies have identified several factors that affect performance, including the semantic similarity between source and target domains (semantic distance), the semantic association between the C-term and incorrect answers (distracter salience), and the type of relations between word pairs (e.g., categorical, compositional, and causal). However, it is unclear how these stimulus properties affect performance when utilized together. Moreover, how do these item factors interact with individual differences such as crystallized intelligence and creative thinking? Several studies reveal interactions among these item and individual difference factors impacting verbal analogy performance. For example, a three-way interaction demonstrated that the effects of semantic distance and distracter salience had a greater impact on performance for compositional and causal relations than for categorical ones (Jones, Kmiecik, Irwin, & Morrison, 2022). Implications for analogy theories and future directions are discussed.

Extensive research on science teaching has shown the effectiveness of analogies as a didactic tool which, when appropriately and effectively used, facilitates the learning process of abstract concepts. This seminar does not contradict the efficacy of such a didactic use of analogies in this seminar but switches attention and interest on their heuristic use in approaching and understanding of what previously unknown. Such a use of analogies derives from research with 10 to 17 year-olds, who, when asked to make predictions in novel situations and to then provide explanations about these predictions, they self-generated analogies and used them by reasoning on their basis. This heuristic use of analogies can be used in science teaching in revealing how students approach situations they have not considered before as well as the sources they draw upon in doing so.

The challenges of problem solving do not exclusively lie in how to perform heuristic search, but they begin with how we understand a given task: How to cognitively represent the task domain and its components can determine how quickly someone is able to progress towards a solution, whether advanced strategies can be discovered, or even whether a solution is found at all. While this challenge of constructing and changing representations has been acknowledged early on in problem solving research, for the most part it has been sidestepped by focussing on simple, well-defined problems whose representation is almost fully determined by the task instructions. Thus, the established theory of problem solving as heuristic search in problem spaces has little to say on this. In this talk, I will present a study designed to explore this issue, by virtue of finding and refining an adequate problem representation being its main challenge. In this exploratory case study, it was investigated how pairs of participants acquaint themselves with a complex spatial transformation task in the domain of iterated mental paper folding over the course of several days. Participants have to understand the geometry of edges which occurs when repeatedly mentally folding a sheet of paper in alternating directions without the use of external aids. Faced with the difficulty of handling increasingly complex folds in light of limited cognitive capacity, participants are forced to look for ways in which to represent folds more efficiently. In a qualitative analysis of video recordings of the participants' behaviour, the development of their conceptualisation of the task domain was traced over the course of the study, focussing especially on their use of gesture and the spontaneous occurrence and use of metaphors in the construction of new representations. Based on these observations, I will conclude the talk with several theoretical speculations regarding the roles of metaphor and cognitive capacity in representational change.

Individuals vary widely in how they categorize novel phenomena. This individual variation has led canonical theories in cognitive and social science to suggest that communication in large social networks leads populations to construct divergent category systems. Yet, anthropological data indicates that large, independent societies consistently arrive at similar categories across a range of topics. How is it possible for diverse populations, consisting of individuals with significant variation in how they view the world, to independently construct similar categories? Through a series of online experiments, I show how large communication networks within cultures can promote the formation of similar categories across cultures. For this investigation, I designed an online “Grouping Game” to observe how people construct categories in both small and large populations when tasked with grouping together the same novel and ambiguous images. I replicated this design for English-speaking subjects in the U.S. and Mandarin-speaking subjects in China. In both cultures, solitary individuals and small social groups produced highly divergent category systems. Yet, large social groups separately and consistently arrived at highly similar categories both within and across cultures. These findings are accurately predicted by a simple mathematical model of critical mass dynamics. Altogether, I show how large communication networks can filter lexical diversity among individuals to produce replicable society-level patterns, yielding unexpected implications for cultural evolution. In particular, I discuss how participants in both cultures readily harnessed analogies when categorizing novel stimuli, and I examine the role of communication networks in promoting cross-cultural similarities in analogy-making as the key engine of category formation.

Children need inference in order to learn the meanings of words. They must infer the referent from the situation in which a target word is said. Furthermore, to be able to use the word in other situations, they also need to infer what other referents the word can be generalized to. As verbs refer to relations between arguments, verb learning requires relational analogical inference, something which is challenging to young children. To overcome this difficulty, young children recruit a diverse range of cues in their inference of verb meanings, including, but not limited to, syntactic cues and social and pragmatic cues as well as statistical cues. They also utilize perceptual similarity (object similarity) in progressive alignment to extract relational verb meanings and further to gain insights about relational verb meanings. However, just having a list of these cues is not useful: the cues must be selected, combined, and coordinated to produce the optimal interpretation in a particular context. This process involves abductive reasoning, similar to what scientists do to form hypotheses from a range of facts or evidence. In this talk, I discuss how children use a chain of inferences to learn meanings of verbs. I consider not only the process of analogical mapping and progressive alignment, but also how children use abductive inference to find the source of analogy and gain insights into the general principles underlying verb learning. I also present recent findings from my laboratory that show that prelinguistic human infants use a rudimentary form of abductive reasoning, which enables the first step of word learning.

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.

Studies reported the effects of different types and different levels of abstraction of analogical stimuli on designers. However, specific, single visual analogical stimuli on the effects of designers have not been reported. We define this type of stimuli as specific analogical stimuli. We used the extended linkography method to analyze the facilitating and limiting effects of specific analogical stimuli and free association analogical stimuli (nonspecific analogical stimuli) on the students' creativity at different design levels. Through an empirical study, we explored the differences in the effects of specific analogy stimuli on the students at different design levels. It clarifies the use of analogical stimuli in design and the teaching of analogical design methods in design education.

Analogical reasoning is related to everyday learning and scholastic learning and is a robust predictor of g. Therefore, children's ability to reason by analogy is often measured in a school context to gain insight into children's cognitive and intellectual functioning. Often, the ability to reason by analogy is measured by means of conventional, static instruments. Static tests are criticised by researchers and practitioners to provide an overview of what individuals have learned in the past and for this reason are assumed not to tap into the potential for learning, based on Vygotsky's zone of proximal development. This seminar will focus on children's potential for reasoning by analogy, as measured by means of a dynamic test, which has a test-training-test design. In so doing, the potential relationship between dynamic test outcomes and executive functioning will be explored.

Abstracts: https://www.sites.google.com/site/analogylist/cross-cultural-symposium

Abstract concepts are a powerful tool to store information efficiently and to make wide-ranging predictions in new situations based on sparse data. Whereas looking-time studies point towards an early emergence of this ability in human infancy, other paradigms like the relational match to sample task often show a failure to detect abstract concepts like same and different until the late preschool years. Similarly, non-human animals have difficulties solving those tasks and often succeed only after long training regimes. Given the huge influence of small task modifications, there is an ongoing debate about the conclusiveness of these findings for the development and phylogenetic distribution of abstract reasoning abilities. Here, we applied the concept of “overhypotheses” which is well known in the infant and cognitive modeling literature to study the capabilities of 3 to 5-year-old children, chimpanzees, and capuchin monkeys in a unified and more ecologically valid task design. In a series of studies, participants themselves sampled reward items from multiple containers or witnessed the sampling process. Only when they detected the abstract pattern governing the reward distributions within and across containers, they could optimally guide their behavior and maximize the reward outcome in a novel test situation. We compared each species’ performance to the predictions of a probabilistic hierarchical Bayesian model capable of forming overhypotheses at a first and second level of abstraction and adapted to their species-specific reward preferences.

Building conceptual abstractions from sensory information and then reasoning about them is central to human intelligence. Abstract reasoning both relies on, and is facilitated by, our ability to make analogies about concepts from known domains to novel domains. Structure Mapping Theory of human analogical reasoning posits that analogical mappings rely on (higher-order) relations and not on the sensory content of the domain. This enables humans to reason systematically about novel domains, a problem with which machine learning (ML) models tend to struggle. We introduce a two-stage neural net framework, which we label Neural Structure Mapping (NSM), to learn visual analogies from Raven's Progressive Matrices, an abstract visual reasoning test of fluid intelligence. Our framework uses (1) a multi-task visual relationship encoder to extract constituent concepts from raw visual input in the source domain, and (2) a neural module net analogy inference engine to reason compositionally about the inferred relation in the target domain. Our NSM approach (a) isolates the relational structure from the source domain with high accuracy, and (b) successfully utilizes this structure for analogical reasoning in the target domain.

Knowledge discovery with computers requires a huge amount of search. Analogical reasoning is effective for efficient knowledge discovery. Therefore, we proposed analogical reasoning systems based on first-order predicate logic using Neuro-Symbolic AI. Neuro-Symbolic AI is a combination of Symbolic AI and artificial neural networks and has features that are easy for human interpretation and robust against data ambiguity and errors. We have implemented analogical reasoning systems by Neuro-symbolic AI models with word embedding which can represent similarity between words. Using the proposed systems, we efficiently extracted unknown rules from knowledge bases described in Prolog. The proposed method is the first case of analogical reasoning based on the first-order predicate logic using deep learning.

Affectively charged analogies are commonly used in literature and art, but also in politics and argumentation. There are reasons to think we may process these analogies differently. Notably, analogical reasoning is a complex process that requires the use of cognitive resources, which are limited. In the presence of affectively charged content, some of these resources might be directed towards affective processing and away from analogical reasoning. To investigate this idea, I investigated effects of affective charge on differences in brain activity evoked by sound versus unsound analogies. The presentation will detail the methods and results for two such experiments, one in which participants saw analogies formed of neutral and negative words and one in which they were created by combining conditioned symbols. I will also briefly discuss future research aiming to investigate the effects of analogical reasoning on brain activity related to affective processing.