Relational Structure
relational structure
Perceiving relational structure
Mechanisms of relational structure mapping across analogy tasks
Following the seminal structure mapping theory by Dedre Gentner, the process of mapping the corresponding structures of relations defining two analogs has been understood as a key component of analogy making. However, not without a merit, in recent years some semantic, pragmatic, and perceptual aspects of analogy mapping attracted primary attention of analogy researchers. For almost a decade, our team have been re-focusing on relational structure mapping, investigating its potential mechanisms across various analogy tasks, both abstract (semantically-lean) and more concrete (semantically-rich), using diverse methods (behavioral, correlational, eye-tracking, EEG). I will present the overview of our main findings. They suggest that structure mapping (1) consists of an incremental construction of the ultimate mental representation, (2) which strongly depends on working memory resources and reasoning ability, (3) even if as little as a single trivial relation needs to be represented mentally. The effective mapping (4) is related to the slowest brain rhythm – the delta band (around 2-3 Hz) – suggesting its highly integrative nature. Finally, we have developed a new task – Graph Mapping – which involves pure mapping of two explicit relational structures. This task allows for precise investigation and manipulation of the mapping process in experiments, as well as is one of the best proxies of individual differences in reasoning ability. Structure mapping is as crucial to analogy as Gentner advocated, and perhaps it is crucial to cognition in general.
Navigating Increasing Levels of Relational Complexity: Perceptual, Analogical, and System Mappings
Relational thinking involves comparing abstract relationships between mental representations that vary in complexity; however, this complexity is rarely made explicit during everyday comparisons. This study explored how people naturally navigate relational complexity and interference using a novel relational match-to-sample (RMTS) task with both minimal and relationally directed instruction to observe changes in performance across three levels of relational complexity: perceptual, analogy, and system mappings. Individual working memory and relational abilities were examined to understand RMTS performance and susceptibility to interfering relational structures. Trials were presented without practice across four blocks and participants received feedback after each attempt to guide learning. Experiment 1 instructed participants to select the target that best matched the sample, while Experiment 2 additionally directed participants’ attention to same and different relations. Participants in Experiment 2 demonstrated improved performance when solving analogical mappings, suggesting that directing attention to relational characteristics affected behavior. Higher performing participants—those above chance performance on the final block of system mappings—solved more analogical RMTS problems and had greater visuospatial working memory, abstraction, verbal analogy, and scene analogy scores compared to lower performers. Lower performers were less dynamic in their performance across blocks and demonstrated negative relationships between analogy and system mapping accuracy, suggesting increased interference between these relational structures. Participant performance on RMTS problems did not change monotonically with relational complexity, suggesting that increases in relational complexity places nonlinear demands on working memory. We argue that competing relational information causes additional interference, especially in individuals with lower executive function abilities.
Analogical retrieval across disparate task domains
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.
Implementing structure mapping as a prior in deep learning models for abstract reasoning
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.
3 Reasons Why You Should Care About Category Theory
Category theory is a branch of mathematics which have been used to organize various regions of mathematics and related sciences from a radical “relation-first” point of view. Why consciousness researchers should care about category theory? " "There are (at least) 3 reasons:" "1 Everything is relational" "2 Everything is relation" "3 Relation is everything" "In this talk we explain the reasons above more concretely and introduce the ideas to utilize basic concepts in category theory for consciousness studies.
Preschoolers' Comprehension of Functional Metaphors
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.
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.
Is Rule Learning Like Analogy?
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.
Human single neurons in the medial temporal lobe encode inferred relational structures
FENS Forum 2024