Implications of Vector-space models of Relational Concepts
Vector-space models are used frequently to compare similarity and dimensionality among entity concepts. What happens when we apply these models to relational concepts? What is the evidence that such models do apply to relational concepts? If we use such a model, then one implication is that maximizing surface feature variation should improve relational concept learning. For example, in STEM instruction, the effectiveness of teaching by analogy is often limited by students’ focus on superficial features of the source and target exemplars. However, in contrast to the prediction of the vector-space computational model, the strategy of progressive alignment (moving from perceptually similar to different targets) has been suggested to address this issue (Gentner & Hoyos, 2017), and human behavioral evidence has shown benefits from progressive alignment. Here I will present some preliminary data that supports the computational approach. Participants were explicitly instructed to match stimuli based on relations while perceptual similarity of stimuli varied parametrically. We found that lower perceptual similarity reduced accurate relational matching. This finding demonstrates that perceptual similarity may interfere with relational judgements, but also hints at why progressive alignment maybe effective. These are preliminary, exploratory data and I to hope receive feedback on the framework and to start a discussion in a group on the utility of vector-space models for relational concepts in general.
Roots of Analogy
Can nonhuman animals perceive the relation-between-relations? This intriguing question has been studied over the last 40 years; nonetheless, the extent to which nonhuman species can do so remains controversial. Here, I review empirical evidence suggesting that pigeons, parrots, crows, and baboons join humans in reliably acquiring and transferring relational matching-to-sample (RMTS). Many theorists consider that RMTS captures the essence of analogy, because basic to analogy is appreciating the ‘relation between relations.’ Factors affecting RMTS performance include: prior training experience, the entropy of the sample stimulus, and whether the items that serve as sample stimuli can also serve as choice stimuli.
Analogies between exemplars of schema-governed categories
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.
Modelling metaphor comprehension as a form of analogizing
What do people do when they comprehend language in discourse? According to many psychologists, they build and maintain cognitive representations of utterances in four complementary mental models for discourse that interact with each other: the surface text, the text base, the situation model, and the context model. When people encounter metaphors in these utterances, they need to incorporate them into each of these mental representations for the discourse. Since influential metaphor theories define metaphor as a form of (figurative) analogy, involving cross-domain mapping of a smaller or greater extent, the general expectation has been that metaphor comprehension is also based on analogizing. This expectation, however, has been partly borne out by the data, but not completely. There is no one-to-one relationship between metaphor as (conceptual) structure (analogy) and metaphor as (psychological) process (analogizing). According to Deliberate Metaphor Theory (DMT), only some metaphors are handled by analogy. Instead, most metaphors are presumably handled by lexical disambiguation. This is a hypothesis that brings together most metaphor research in a provocatively new way: it means that most metaphors are not processed metaphorically, which produces a paradox of metaphor. In this talk I will sketch out how this paradox arises and how it can be resolved by a new version of DMT, which I have described in my forthcoming book Slowing metaphor down: Updating Deliberate Metaphor Theory (currently under review). In this theory, the distinction between, but also the relation between, analogy in metaphorical structure versus analogy in metaphorical process is of central importance.
Learning by Analogy in Mathematics
Analogies between old and new concepts are common during classroom instruction. While previous studies of transfer focus on how features of initial learning guide later transfer to new problem solving, less is known about how to best support analogical transfer from previous learning while children are engaged in new learning episodes. Such research may have important implications for teaching and learning in mathematics, which often includes analogies between old and new information. Some existing research promotes supporting learners' explicit connections across old and new information within an analogy. In this talk, I will present evidence that instructors can invite implicit analogical reasoning through warm-up activities designed to activate relevant prior knowledge. Warm-up activities "close the transfer space" between old and new learning without additional direct instruction.
Analogy and Spatial Cognition: How and Why they matter for STEM learning
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.
Analogy Use in Parental Explanation
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.
From the Didactic to the Heuristic Use of Analogies in Science Teaching
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.
A new experimental paradigm to study analogy transfer
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.
Differences between beginning and advanced students using specific analogical stimuli during design-by-analogy
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.
Analogy and ethics: opportunities at the intersection
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.
Analogical encodings and recodings
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.
Zero-shot visual reasoning with probabilistic analogical mapping
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.
Probabilistic Analogical Mapping with Semantic Relation Networks
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
Representations of abstract relations in infancy
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 in motor learning - acquisition and refinement of movement skills
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.
Transforming task representations
Humans can adapt to a novel task on our first try. By contrast, artificial intelligence systems often require immense amounts of data to adapt. In this talk, I will discuss my recent work (https://www.pnas.org/content/117/52/32970) on creating deep learning systems that can adapt on their first try by exploiting relationships between tasks. Specifically, the approach is based on transforming a representation for a known task to produce a representation for the novel task, by inferring and then using a higher order function that captures a relationship between the tasks. This approach can be interpreted as a type of analogical reasoning. I will show that task transformation can allow systems to adapt to novel tasks on their first try in domains ranging from card games, to mathematical objects, to image classification and reinforcement learning. I will discuss the analogical interpretation of this approach, an analogy between levels of abstraction within the model architecture that I refer to as homoiconicity, and what this work might suggest about using deep-learning models to infer analogies more generally.
Analogical reasoning and metaphor processing in autism - Similarities & differences
In this talk, I will present the results of two recent systematic reviews and meta-analyses related to analogical reasoning and metaphor processing in autism, together with the results of a study that investigated verbal analogical reasoning and metaphor processing in the same sample of participants. Both metaphors and analogies rely on exploiting similarities, and they necessitate contextual processing. Nevertheless, our findings relating to metaphor processing and analogical reasoning showed distinct patterns. Whereas analogical reasoning emerged as a relative strength in autism, metaphor processing was found to be a relative weakness. Additionally, both meta-analytic studies investigated the relations between the level of intelligence of participants included in the studies, and the effect size of group differences between the autistic and typically developing (TD) samples. These analyses suggested in the case of analogical reasoning that the relative advantage of ASD participants might only be present in the case of individuals with lower levels of intelligence. By contrast, impairments in metaphor processing appeared to be more pronounced in the case of individuals with relatively lower levels of (verbal) intelligence. In our experimental study, we administered both verbal analogies and metaphors to the same sample of high-functioning autistic participants and TD controls. The two groups were matched on age, verbal IQ, working memory and educational background. Our aim was to understand better the similarities and differences between processing analogies and metaphors, and to see whether the advantage in analogical reasoning and disadvantage in metaphor processing is universal in autism.
Analogy as a Catalyst for Cumulative Cultural Evolution
Analogies, broadly defined, map novel concepts onto familiar concepts, making them essential for perception, reasoning, and communication. We argue that analogy-building served a critical role in the evolution of cumulative culture, by allowing humans to learn and transmit complex behavioural sequences that would otherwise be too cognitively demanding or opaque to acquire. The emergence of a protolanguage consisting of simple labels would have provided early humans with the cognitive tools to build explicit analogies and to communicate them to others. This focus on analogy-building can shed new light on the coevolution of cognition and culture, and addresses recent calls for better integration of the field of cultural evolution with cognitive science. This talk will address what cumulative cultural evolution is, how we define analogy-building, how analogy-building applies to cumulative cultural evolution, how analogy-building fits into language evolution, and the implications of analogy-building for causal understanding and cognitive evolution.
The Structural Anchoring of Spontaneous Analogies
It is generally acknowledged that analogy is a core mechanism of human cognition, but paradoxically, analogies based on structural similarities would rarely be implemented spontaneously (e.g. without an explicit invitation to compare two representations). The scarcity of deep spontaneous analogies is at odds with the demonstration that familiar concepts from our daily-life are spontaneously used to encode the structure of our experiences. Based on this idea, we will present experimental works highlighting the predominant role of structural similarities in analogical retrieval. The educational stakes lurking behind the tendency to encode the problem’s structures through familiar concepts will also be addressed.
A Connectionist Account of Analogy-Making
Analogy-making is considered to be one of the cognitive processes which are hard to be accounted for in connectionist terms. A number of models have been proposed, but they are either tailed for specific analogical tasks or require complicated mechanisms which don’t fit into the mainstream connectionist modelling paradigm. In this talk I will present a new connectionist account of analogy-making based on the vector approach to representing symbols (VARS). This approach allows representing relational structures of varying complexity by numeric vectors with fixed dimensionality. I will also present a simple and computationally efficient mechanism of aligning VARS representations, which integrates both semantic similarity and structural constraints. The results of a series of simulations will demonstrate that VARS can account for basic analogical phenomena.
Abstraction and Analogy in Natural and Artificial Intelligence
In 1955, John McCarthy and colleagues proposed an AI summer research project with the following aim: “An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves.” More than six decades later, all of these research topics remain open and actively investigated in the AI community. While AI has made dramatic progress over the last decade in areas such as vision, natural language processing, and robotics, current AI systems still almost entirely lack the ability to form humanlike concepts and abstractions. Some cognitive scientists have proposed that analogy-making is a central mechanism for conceptual abstraction and understanding in humans. Douglas Hofstadter called analogy-making “the core of cognition”, and Hofstadter and co-author Emmanuel Sander noted, “Without concepts there can be no thought, and without analogies there can be no concepts.” In this talk I will reflect on the role played by analogy-making at all levels of intelligence, and on prospects for developing AI systems with humanlike abilities for abstraction and analogy.
Abstraction and Analogy in Natural and Artificial Intelligence
Learning by analogy is a powerful tool children’s developmental repertoire, as well as in educational contexts such as mathematics, where the key knowledge base involves building flexible schemas. However, noticing and learning from analogies develops over time and is cognitively resource intensive. I review studies that provide insight into the relationship between mechanisms driving children’s developing analogy skills, highlighting environmental inputs (parent talk and prior experiences priming attention to relations) and neuro-cognitive factors (Executive Functions and brain injury). I then note implications for mathematics learning, reviewing experimental findings that show analogy can improve learning, but also that both individual differences in EFs and environmental factors that reduce available EFs such as performance pressure can predict student learning.
Abstract Semantic Relations in Mind, Brain, and Machines
Abstract semantic relations (e.g., category membership, part-whole, antonymy, cause-effect) are central to human intelligence, underlying the distinctively human ability to reason by analogy. I will describe a computational project (Bayesian Analogy with Relational Transformations) that aims to extract explicit representations of abstract semantic relations from non-relational inputs automatically generated by machine learning. BART’s representations predict patterns of typicality and similarity for semantic relations, as well as similarity of neural signals triggered by semantic relations during analogical reasoning. In this approach, analogy emerges from the ability to learn and compare relations; mapping emerges later from the ability to compare patterns of relations.
Analogy in Cognitive Architecture
Cognitive architectures are attempts to build larger-scale models of minds. This talk will explore how structure-mapping models of analogical matching, retrieval, and generalization are used in the Companion cognitive architecture. Examples will include modeling conceptual change, learning by reading, and analogical Q/A training.