Analogical Minds

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.

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.

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.

Recent advances in deep learning have produced models that far outstrip human performance in a number of domains. However, where machine learning approaches still fall far short of human-level performance is in the capacity to transfer knowledge across domains. While a human learner will happily apply knowledge acquired in one domain (e.g., mathematics) to a different domain (e.g., cooking; a vinaigrette is really just a ratio between edible fat and acid), machine learning models still struggle profoundly at such tasks. I will present a case that human intelligence might be (at least partially) usefully characterised by our ability to transfer knowledge widely, and a framework that we have developed for learning representations that support such transfer. The model is compared to current machine learning approaches.

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.

A key component of humans' striking creativity in solving problems is our ability to construct novel descriptions to help us characterize novel categories. Bongard problems, which challenge the problem solver to come up with a rule for distinguishing visual scenes that fall into two categories, provide an elegant test of this ability. Bongard problems are challenging for both human and machine category learners because only a handful of example scenes are presented for each category, and they often require the open-ended creation of new descriptions. A new sub-type of Bongard problem called Physical Bongard Problems (PBPs) is introduced, which require solvers to perceive and predict the physical spatial dynamics implicit in the depicted scenes. The PATHS (Perceiving And Testing Hypotheses on Structures) computational model which can solve many PBPs is presented, and compared to human performance on the same problems. PATHS and humans are similarly affected by the ordering of scenes within a PBP, with spatially and temporally juxtaposed scenes promoting category learning when they are similar and belong to different categories, or dissimilar and belong to the same category. The core theoretical commitments of PATHS which we believe to also exemplify human open-ended category learning are a) the continual perception of new scene descriptions over the course of category learning; b) the context-dependent nature of that perceptual process, in which the scenes establish the context for one another; c) hypothesis construction by combining descriptions into logical expressions; and d) bi-directional interactions between perceiving new aspects of scenes and constructing hypotheses for the rule that distinguishes categories.

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.

People from cultures around the world tend to borrow from the domain of space to represent abstract concepts. For example, in the domain on time, we use spatial metaphors (e.g., describing the future as being in front and the past behind), accompany our speech with spatial gestures (e.g., gesturing to the left to refer to a past event), and use external tools that project time onto a spatial reference frame (e.g., calendars). Importantly, these associations are also present in the way we think and reason about time, suggesting that space and time are also linked in the mind. In this talk, I will explore the developmental origins and functional implications of these types of cross-dimensional associations. To start, I will discuss the roles that language and culture play in shaping how children in the US and India represent time. Next, I will use word learning and memory as test cases for exploring why cross-dimensional associations may be cognitively advantageous. Finally, I will talk about future directions and the practical implications for this line of work, with a focus on how encouraging spatial representations of abstract concepts could improve learning outcomes.

Humans are incredible learners, a talent supported by our ability to detect and transfer relational similarities between items and events. Spotting these common relations despite perceptual differences is challenging, yet there’s evidence that this ability begins early, with infants as young as 3 months discriminating same and different (Anderson et al., 2018; Ferry et al., 2015). How? To understand the underlying mechanisms, I examine how learning outcomes in the first year correspond with changes in input and in infant age. I discuss the commonalities in this process with that seen in older children and adults, as well as differences due to interactions with other maturing processes like language and visual attention.

Existing accounts of analogical transfer highlight the importance of comparison-based schema abstraction in aiding retrieval of relevant prior knowledge from memory. In this talk, we discuss an alternative view, the category status hypothesis—which states that if knowledge of a target principle is represented as a relational category, it is easier to activate as a result of categorizing (as opposed to cue-based reminding)—and briefly review supporting evidence. We then further investigate this hypothesis by designing study tasks that promote different facets of category-level representations and assess their impact on spontaneous analogical transfer. A Baseline group compared two analogous cases; the remaining groups experienced comparison plus another task intended to impact the category status of the knowledge representation. The Intension group read an abstract statement of the principle with a supporting task of generating a new case. The Extension group read two more positive cases with the task of judging whether each exemplified the target principle. The Mapping group read a contrast case with the task of revising it into a positive example of the target principle (thereby providing practice moving in both directions between type and token, i.e., evaluating a given case relative to knowledge and using knowledge to generate a revised case). The results demonstrated that both Intension and Extension groups led to transfer improvements over Baseline (with the former demonstrating both improved accessibility of prior knowledge and ability to apply relational concepts). Implications for theories of analogical transfer are discussed.

Traditional brain-style (connectionist) approaches basically hit a wall when it comes to relational cognition. As an alternative to the well-known approaches of structured connectionism and deep learning, I present an engine for relational pattern recognition based on minimalist reinterpretations of first principles of connectionism. Results of computational experiments will be discussed on problems testing relational learning and universal generalization.

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.

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.

Research on analogical processing and reasoning has provided strong evidence that the use of adequate educational analogies has strong and positive effects on the learning of mathematics. In this talk I will show some experimental results suggesting that analogies based on spatial representations might be particularly effective to improve mathematics learning. Since fostering mathematics learning also involves addressing psychosocial factors such as the development of mathematical anxiety, providing social incentives to learn, and fostering engagement and motivation, I will argue that one area to explore with great potential to improve math learning is applying analogical research in the development of learning games aimed to improve math learning. Finally, I will show some early prototypes of an educational project devoted to developing games designed to foster the learning of early mathematics in kindergarten children.

Analogical reasoning is a complex ‘high-level’ cognitive process characterised by making inferences based on analogical comparisons. As with other high-level processes, development takes place over a protracted time period and believed to result from changes in multiple ‘lower-level’ systems. In the case of analogical reasoning, changes in systems responsible for conceptual knowledge, task knowledge, inhibition, and working memory have all been causally implicated in development. Whilst there is evidence that each of these systems contributes to development, what the relative contribution of each across development is, and how they interact with each, remain largely unanswered questions. In this presentation, I will describe how cross-sectional trajectory analysis can be used as a complementary method to shed light on these questions.

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.

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.

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.

Humans’ ability to perceive and abstract relational structure is fundamental to our learning. It allows us to acquire knowledge all the way from linguistic grammar to spatial knowledge to social structures. How does a learner begin to perceive structure in the world? Why do we sometimes fail to see structural commonalities across events? To begin to answer these questions, I attempt to bridge two large, yet somewhat separate research traditions in understanding human’s structural abstraction: rule learning (Marcus et al., 1999) and analogical learning (Gentner, 1989). On the one hand, rule learning research has shown humans’ domain-general ability and ease—as early as 7-month-olds—to abstract structure from a limited experience. On the other hand, analogical learning works have shown robust constraints in structural abstraction: young learners prefer object similarity over relational similarity. To understand this seeming paradox between ease and difficulty, we conducted a series of studies using the classic rule learning paradigm (Marcus et al., 1999) but with an analogical (object vs. relation) twist. Adults were presented with 2-minute sentences or events (syllables or shapes) containing a rule. At test, they had to choose between rule abstraction and object matches—the same syllable or shape they saw before. Surprisingly, while in the absence of object matches adults were perfectly capable of abstracting the rule, their ability to do so declined sharply when object matches were present. Our initial results suggest that rule learning ability may be subject to the usual constraints and signatures of analogical learning: preference to object similarity can dampen rule generalization. Humans’ abstraction is also concrete at the same time.

From a developmental standpoint, it has been argued that two major complementary factors contribute to the development of analogy comprehension: world knowledge and executive functions. Here I will provide evidence in support of the second view. Beyond paradigms that manipulate task difficulty (e.g., number and types of distractors and semantic distance between domains) we will provide eye-tracking data that describes differences in the way children and adults compare the base and target domains in analogy problems. We will follow the same approach with ageing people. This latter population provides a unique opportunity to disentangle the contribution of knowledge and executive processes in analogy making since knowledge is (more than) preserved and executive control is decreasing. Using this paradigm, I will show the extent to which world knowledge (assessed through vocabulary) compensates for decreasing executive control in older populations. Our eye-tracking data suggests that, to a certain extent, differences between younger and older adults are analogous to the differences between younger adults and children in the way they compare the base and the target domains in analogy problems.