A symbolic-connectionist theory of relational inference and generalization

Abstract thematic roles in infants' representation of social events

Infants' thoughts are classically characterized as iconic, perceptual-like representations.1,2,3 Less clear is whether preverbal infants also possess a propositional language of thought, where mental symbols are combined according to syntactic rules, very much like words in sentences.4,5,6,7,8,9,10,11,12,13,14,15,16,17 Because it is rich, productive, and abstract, a language of thought would provide a key to explaining impressive achievements in early infancy, from logical inference to representation of false beliefs.18,19,20,21,22,23,24,25,26,27,28,29,30,31 A propositional language-including a language of thought5-implies thematic roles that, in a sentence, indicate the relation between noun and verb phrases, defining who acts on whom; i.e., who is the agent and who is the patient.32,33,34,35,36,37,38,39 Agent and patient roles are abstract in that they generally apply to different situations: whether A kicks, helps, or kisses B, A is the agent and B is the patient. Do preverbal infants represent abstract agent and patient roles? We presented 7-month-olds (n = 143) with sequences of scenes where the posture or relative positioning of two individuals indicated that, across different interactions, A acted on B. Results from habituation (experiment 1) and pupillometry paradigms (experiments 2 and 3) demonstrated that infants showed surprise when roles eventually switched (B acted on A). Thus, while encoding social interactions, infants fill in an abstract relational structure that marks the roles of agent and patient and that can be accessed via different event scenes and properties of the event participants (body postures or positioning). This mental process implies a combinatorial capacity that lays the foundations for productivity and compositionality in language and cognition.

From integers to fractions: The role of analogy in transfer and long-term learning

Fractions are the gatekeepers to advanced mathematics but are difficult to learn. One powerful learning mechanism is analogy, which builds fraction understanding on a pre-existing foundation of integer knowledge. Indeed, a short intervention that aligned fractions and integers on number lines improved children's estimates of fractions (Yu et al., 2022). The breadth and durability of such gains, however, are unknown, and analogies to other sources (such as percentages) may be equally powerful. To investigate this issue, we randomly assigned 109 fourth and fifth graders to one of three experimental conditions with different analogical sources (integers, percentages, or fractions) or a control condition. During training, children in the experimental conditions solved pairs of aligned fraction number line problems and proportionally-equivalent problems expressed in integers, percentages, or fractions (e.g., 3/8 on a 0-1 number line aligned with 3 on a 0-8 number line). Children in the control group solved fraction number-line problems sequentially. At pretest and a two-week delayed posttest, children completed a broad fraction knowledge battery, including estimation, comparison, categorization, ordering, and arithmetic. Results showed that aligning integers and fractions on number lines facilitated better estimation of fractional magnitudes, and the training effect transferred to novel fraction problems after two weeks. Similar gains were not observed for analogies using percentages. These findings highlight the importance of building new mathematical knowledge through analogies to familiar, similar sources.

Prior experience of variability influences generalisation of unspecified categories

Category variability or diversity is an important factor influencing generalisation. However, expectations of category variability may not only depend on the variability of encountered category members, but may also be shaped by prior experiences with similar categories. In this study, we investigated whether we could influence category generalisation by inducing different category representations in an A/Non-A categorisation task: Participants either learned about a homogeneous category Non-A or a diverse category Non-A during a priming phase. To better understand the transfer process, we varied the nature of the learning phase from implicit transfer to explicit instructions that actively requested participants to use their prior experiences. We found that while with a homogeneous Non-A representation, generalisation of the A and Non-A categories was equal, the generalisation of category Non-A widened after a priming phase with a diverse representation. In a second experiment, we found that the widening of generalisation of category Non-A occurred when the exemplars in this category were themselves diverse (feature-diverse condition) but not when the category contained distinct exemplars (exemplar-diverse condition). These results suggests that categorisation is influenced by previous categorisation experiences possibly altering the representation of a category. Furthermore, the study gives a hint what kind of heterogeneity is needed to observe the commonly reported broader generalisation of diverse categories. The finding has implications not only to understand the influence of prior experiences on category learning, but any cognitive process that hinges on generalisation.

A Phone in a Basket Looks Like a Knife in a Cup: Role-Filler Independence in Visual Processing

When a piece of fruit is in a bowl, and the bowl is on a table, we appreciate not only the individual objects and their features, but also the relations containment and support, which abstract away from the particular objects involved. Independent representation of roles (e.g., containers vs. supporters) and "fillers" of those roles (e.g., bowls vs. cups, tables vs. chairs) is a core principle of language and higher-level reasoning. But does such role-filler independence also arise in automatic visual processing? Here, we show that it does, by exploring a surprising error that such independence can produce. In four experiments, participants saw a stream of images containing different objects arranged in force-dynamic relations-e.g., a phone contained in a basket, a marker resting on a garbage can, or a knife sitting in a cup. Participants had to respond to a single target image (e.g., a phone in a basket) within a stream of distractors presented under time constraints. Surprisingly, even though participants completed this task quickly and accurately, they false-alarmed more often to images matching the target's relational category than to those that did not-even when those images involved completely different objects. In other words, participants searching for a phone in a basket were more likely to mistakenly respond to a knife in a cup than to a marker on a garbage can. Follow-up experiments ruled out strategic responses and also controlled for various confounding image features. We suggest that visual processing represents relations abstractly, in ways that separate roles from fillers.

Neural Correlates of Analogical Reasoning on Syntactic Patterns

Analogical reasoning is central to thought and learning. However, previous neuroscience studies have focused mainly on neural substrates for visuospatial and semantic analogies. There has not yet been research on the neural correlates of analogical reasoning on syntactic patterns generated by the syntactic rules, a key feature of human language faculty. The present investigation took an initial step to address this paucity. Twenty-four participants, whose brain activity was monitored by fMRI, engaged in first-order and second-order relational judgments of syntactic patterns as well as simple and complex working memory tasks. After scanning, participants rated the difficulty of each step during analogical reasoning; these ratings were related to signal intensities in activated regions of interest using Spearman correlation analyses. After prior research, differences in activation levels during second-order and first-order relational judgments were taken as evidence of analogical reasoning. These analyses showed that analogical reasoning on syntactic patterns recruited brain regions consistent with those supporting visuospatial and semantic analogies, including the anterior and posterior parts of the left middle frontal gyrus, anatomically corresponding to the left rostrolateral pFC and the left dorsolateral pFC. The correlation results further revealed that the posterior middle frontal gyrus might be involved in analogical access and mapping with syntactic patterns. Our study is the first to investigate the process of analogical reasoning on syntactic patterns at the neurobiological level and provide evidence of the specific functional roles of related regions during subprocesses of analogical reasoning.

How children generalize novel nouns: An eye-tracking analysis of their generalization strategies

Recent research has shown that comparisons of multiple learning stimuli which are associated with the same novel noun favor taxonomic generalization of this noun. These findings contrast with single-stimulus learning in which children follow so-called lexical biases. However, little is known about the underlying search strategies. The present experiment provides an eye-tracking analysis of search strategies during novel word learning in a comparison design. We manipulated both the conceptual distance between the two learning items, i.e., children saw examples which were associated with a noun (e.g., the two learning items were either two bracelets in a "close" comparison condition or a bracelet and a watch in a "far" comparison condition), and the conceptual distance between the learning items and the taxonomically related items in the generalization options (e.g., the taxonomic generalization answer; a pendant, a near generalization item; versus a bow tie, a distant generalization item). We tested 5-, 6- and 8-year-old children's taxonomic (versus perceptual and thematic) generalization of novel names for objects. The search patterns showed that participants first focused on the learning items and then compared them with each of the possible choices. They also spent less time comparing the various options with one another; this search profile remained stable across age groups. Data also revealed that early comparisons, (i.e., reflecting alignment strategies) predicted generalization performance. We discuss four search strategies as well as the effect of age and conceptual distance on these strategies.

Neural dynamic foundations of a theory of higher cognition: the case of grounding nested phrases

Because cognitive competences emerge in evolution and development from the sensory-motor domain, we seek a neural process account for higher cognition in which all representations are necessarily grounded in perception and action. The challenge is to understand how hallmarks of higher cognition, productivity, systematicity, and compositionality, may emerge from such a bottom-up approach. To address this challenge, we present key ideas from Dynamic Field Theory which postulates that neural populations are organized by recurrent connectivity to create stable localist representations. Dynamic instabilities enable the autonomous generation of sequences of mental states. The capacity to apply neural circuitry across broad sets of inputs that emulates the function call postulated in symbolic computation emerges through coordinate transforms implemented in neural gain fields. We show how binding localist neural representations through a shared index dimension enables conceptual structure, in which the interdependence among components of a representation is flexibly expressed. We demonstrate these principles in a neural dynamic architecture that represents and perceptually grounds nested relational and action phrases. Sequences of neural processing steps are generated autonomously to attentionally select the referenced objects and events in a manner that is sensitive to their interdependencies. This solves the problem of 2 and the massive binding problem in expressions such as "the small tree that is to the left of the lake which is to the left of the large tree". We extend earlier work by incorporating new types of grammatical constructions and a larger vocabulary. We discuss the DFT framework relative to other neural process accounts of higher cognition and assess the scope and challenges of such neural theories.

Emergent neural dynamics and geometry for generalization in a transitive inference task

Relational cognition-the ability to infer relationships that generalize to novel combinations of objects-is fundamental to human and animal intelligence. Despite this importance, it remains unclear how relational cognition is implemented in the brain due in part to a lack of hypotheses and predictions at the levels of collective neural activity and behavior. Here we discovered, analyzed, and experimentally tested neural networks (NNs) that perform transitive inference (TI), a classic relational task (if A > B and B > C, then A > C). We found NNs that (i) generalized perfectly, despite lacking overt transitive structure prior to training, (ii) generalized when the task required working memory (WM), a capacity thought to be essential to inference in the brain, (iii) emergently expressed behaviors long observed in living subjects, in addition to a novel order-dependent behavior, and (iv) expressed different task solutions yielding alternative behavioral and neural predictions. Further, in a large-scale experiment, we found that human subjects performing WM-based TI showed behavior inconsistent with a class of NNs that characteristically expressed an intuitive task solution. These findings provide neural insights into a classical relational ability, with wider implications for how the brain realizes relational cognition.

Electrophysiological hallmarks for event relations and event roles in working memory

The ability to maintain events (i.e., interactions between/among objects) in working memory is crucial for our everyday cognition, yet the format of this representation is poorly understood. The current ERP study was designed to answer two questions: How is maintaining events (e.g., the tiger hit the lion) neurally different from maintaining item coordinations (e.g., the tiger and the lion)? That is, how is the event relation (present in events but not coordinations) represented? And how is the agent, or initiator of the event encoded differently from the patient, or receiver of the event during maintenance? We used a novel picture-sentence match-across-delay approach in which the working memory representation was "pinged" during the delay, replicated across two ERP experiments with Chinese and English materials. We found that maintenance of events elicited a long-lasting late sustained difference in posterior-occipital electrodes relative to non-events. This effect resembled the negative slow wave reported in previous studies of working memory, suggesting that the maintenance of events in working memory may impose a higher cost compared to coordinations. Although we did not observe significant ERP differences associated with pinging the agent vs. the patient during the delay, we did find that the ping appeared to dampen the ongoing sustained difference, suggesting a shift from sustained activity to activity silent mechanisms. These results suggest a new method by which ERPs can be used to elucidate the format of neural representation for events in working memory.

Toward a General Framework of Biased Reasoning: Coherence-Based Reasoning

A considerable amount of experimental research has been devoted to uncovering biased forms of reasoning. Notwithstanding the richness and overall empirical soundness of the bias research, the field can be described as disjointed, incomplete, and undertheorized. In this article, we seek to address this disconnect by offering "coherence-based reasoning" as a parsimonious theoretical framework that explains a sizable number of important deviations from normative forms of reasoning. Represented in connectionist networks and processed through constraint-satisfaction processing, coherence-based reasoning serves as a ubiquitous, essential, and overwhelmingly adaptive apparatus in people's mental toolbox. This adaptive process, however, can readily be overrun by bias when the network is dominated by nodes or links that are incorrect, overweighted, or otherwise nonnormative. We apply this framework to explain a variety of well-established biased forms of reasoning, including confirmation bias, the halo effect, stereotype spillovers, hindsight bias, motivated reasoning, emotion-driven reasoning, ideological reasoning, and more.

An experimental and simulation study of the impact of emotional information on analogical reasoning

We investigated whether and how emotional information would affect analogical reasoning. We hypothesized that task-irrelevant emotional information would impair performance whereas task-relevant emotional information would enhance it. In Study 1, 233 undergraduates completed a novel version of the People Pieces Task (Emotional Faces People Task), an analogical reasoning task in which the task characters displayed emotional or neutral facial expressions (within-participants). The emotional faces were relevant or irrelevant to the task (between-participants). We simulated the behavioral results using the Learning and Inference with Schemas and Analogies (LISA) model of relational reasoning. LISA is a neurally plausible, symbolic-connectionist computational model of analogical reasoning. In comparison to neutral trials, participants were slower but more accurate on emotion-relevant trials, and were faster but less accurate on emotion-irrelevant trials. Simulations using the LISA model demonstrated that it is possible to account for the effects of emotional information on reasoning in terms of how emotional stimuli attract attention during a reasoning task. In Study 2, 255 undergraduates completed the Emotional Faces People Task at either a high- or low-working memory load. The high working memory load condition of Study 2 replicated the findings of Study 1, showing that participants were more accurate on emotion-relevant trials than on emotion-irrelevant trials; in Study 2, this increased accuracy could not be accounted for by a speed-accuracy tradeoff. The working memory manipulation influenced the manner in which the congruence (with the correct answer) of emotion-irrelevant emotion influenced performance. Simulations using the LISA model showed that manipulating the salience of emotion, the error penalty, as well as vigilance (which determines the likelihood that LISA will notice it has attended to an irrelevant relation), could reasonably reproduce the behavioral results of both low and high working memory load conditions of Study 2.

Promoting Complex Problem Solving by Introducing Schema-Governed Categories of Key Causal Models

The ability to recognize key causal models across situations is associated with expertise. The acquisition of schema-governed category knowledge of key causal models may underlie this ability. In an experimental study (n = 183), we investigated the effects of promoting the construction of schema-governed categories and how an enhanced ability to recognize the key causal models relates to performance in complex problem-solving tasks that are based on the key causal models. In a 2 × 2 design, we tested the effects of an adapted version of an intervention designed to build abstract mental representations of the key causal models and a tutorial designed to convey conceptual understanding of the key causal models and procedural knowledge. Participants who were enabled to recognize the underlying key causal models across situations as a result of the intervention and the tutorial (i.e., causal sorters) outperformed non-causal sorters in the subsequent complex problem-solving task. Causal sorters outperformed the control group, except for the subtask knowledge application in the experimental group that did not receive the tutorial and, hence, did not have the opportunity to elaborate their conceptual understanding of the key causal models. The findings highlight that being able to categorize novel situations according to their underlying key causal model alone is insufficient for enhancing the transfer of the according concept. Instead, for successful application, conceptual and procedural knowledge also seem to be necessary. By using a complex problem-solving task as the dependent variable for transfer, we extended the scope of the results to dynamic tasks that reflect some of the typical challenges of the 21st century.

The Effect of Alcohol and Sexual Arousal on Explicit and Implicit Condom Attitudes and Intentions to Use a Condom

Alcohol and sexual arousal are contextual determinants of condomless sex. Dual-process theory postulates that two types of cognitive processing contribute to the regulation of behavior: one that is fast, intuitive and automatic, and another that is slower and deliberative. This study applied a dual-process model to investigate condomless sexual behavior, highlighting the potential importance of implicit attitudes in condomless sex. We investigated whether the impact of alcohol and sexual arousal on condom use-related attitudes and intentions was explained by diminished working memory capacity, as dual-process models suggest. We also investigated whether this effect could be explained by implicit and explicit attitudes toward condom use. Male participants (N = 30) were randomized using a 2 × 2 within-subjects design that manipulated alcohol intoxication (placebo vs. alcohol beverages) and sexual arousal (neutral vs. erotic movie clips). We measured participants' working memory capacity, intentions to use a condom, and explicit and implicit attitudes toward condom use. Significant main effects of alcohol intoxication and sexual arousal on working memory capacity were found. No significant interaction was found for the combined effect of alcohol intoxication and sexual arousal on intentions to use a condom. There was no significant effect of implicit attitudes on intentions to use a condom, although a trend toward significance (p = 0.06) was found for the effect of implicit attitudes on intentions to use a condom when participants were in a state of alcohol intoxication. Theoretical and practical implications of this study are discussed.

Analogical inferences mediated by relational categories

The standard approach posits that analogical inferences are generated by copying unmapped base relations, substituting mapped target entities for source entities, and generating slots for base entities that have not found a correspondence in the target. In the present study we argue that this mechanism does not adequately explain the generation of inferences mediated by relational categories. Experiment 1 revealed that for analogies in which the gist of the information to be transferred is better captured by relational categories than by explicit relations, inferences are more concerned with reinstantiating the base relational category than with ensuring that the relation of the inference resembles that of the base. Experiment 2 replicated this finding with analogies between situations maintaining a higher degree of semantic and contextual distance. The following experiments addressed whether there are further restrictions that guide a more fine-grained selection of exemplars. Experiment 3 revealed that when no relevant differences exist between compared situations, the exemplars included in analogical inferences tend to match the base exemplars along salient dimensions of the relational category to which both exemplars belong. In turn, Experiment 4 replicated this finding with analogies between situations maintaining some degree of semantic and contextual distance. The study adds to a growing literature recognizing the role of categorization in analogical reasoning. The challenges posed by the present results to the traditional view of analogical inference are discussed, as well as the prospects of the categorial mechanism for explaining other types of analogies not included in the present study.

Promoting learning transfer in science through a complexity approach and computational modeling

This article concerns the synergy between science learning, understanding complexity, and computational thinking (CT), and their impact on near and far learning transfer. The potential relationship between computer-based model construction and knowledge transfer has yet to be explored. We studied middle school students who modeled systemic phenomena using the Much.Matter.in.Motion (MMM) platform. A distinct innovation of this work is the complexity-based visual epistemic structure underpinning the Much.Matter.in.Motion (MMM) platform, which guided students' modeling of complex systems. This epistemic structure suggests that a complex system can be described and modeled by defining entities and assigning them (1) properties, (2) actions, and (3) interactions with each other and with their environment. In this study, we investigated students' conceptual understanding of science, systems understanding, and CT. We also explored whether the complexity-based structure is transferable across different domains. The study employs a quasi-experimental, pretest-intervention-posttest-control comparison-group design, with 26 seventh-grade students in an experimental group, and 24 in a comparison group. Findings reveal that students who constructed computational models significantly improved their science conceptual knowledge, systems understanding, and CT. They also showed relatively high degrees of transfer-both near and far-with a medium effect size for the far transfer of learning. For the far-transfer items, their explanations included entities' properties and interactions at the micro level. Finally, we found that learning CT and learning how to think complexly contribute independently to learning transfer, and that conceptual understanding in science impacts transfer only through the micro-level behaviors of entities in the system. A central theoretical contribution of this work is to offer a method for promoting far transfer. This method suggests using visual epistemic scaffolds of the general thinking processes we would like to support, as shown in the complexity-based structure on the MMM interface, and incorporating these visual structures into the core problem-solving activities.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11251-023-09624-w.

Replay and compositional computation

Replay in the brain has been viewed as rehearsal or, more recently, as sampling from a transition model. Here, we propose a new hypothesis: that replay is able to implement a form of compositional computation where entities are assembled into relationally bound structures to derive qualitatively new knowledge. This idea builds on recent advances in neuroscience, which indicate that the hippocampus flexibly binds objects to generalizable roles and that replay strings these role-bound objects into compound statements. We suggest experiments to test our hypothesis, and we end by noting the implications for AI systems which lack the human ability to radically generalize past experience to solve new problems.

The Binding Problem 2.0: Beyond Perceptual Features

The "binding problem" has been a central question in vision science for some 30 years: When encoding multiple objects or maintaining them in working memory, how are we able to represent the correspondence between a specific feature and its corresponding object correctly? In this letter we argue that the boundaries of this research program in fact extend far beyond vision, and we call for coordinated pursuit across the broader cognitive science community of this central question for cognition, which we dub "Binding Problem 2.0".

Graph Mapping: A novel and simple test to validly assess fluid reasoning

We present Graph Mapping - a simple and effective computerized test of fluid intelligence (reasoning ability). The test requires structure mapping - a key component of the reasoning process. Participants are asked to map a pair of corresponding nodes across two mathematically isomorphic but visually different graphs. The test difficulty can be easily manipulated - the more complex structurally and dissimilar visually the graphs, the higher response error rate. Graph Mapping offers high flexibility in item generation, ranging from trivial to extremally difficult items, supporting progressive item sequences suitable for correlational studies. It also allows multiple item instances (clones) at a fixed difficulty level as well as full item randomization, both particularly suitable for within-subject experimental designs, longitudinal studies, and adaptive testing. The test has short administration times and is unfamiliar to participants, yielding practical advantages. Graph Mapping has excellent psychometric properties: Its convergent validity and reliability is comparable to the three leading traditional fluid reasoning tests. The convenient software allows a researcher to design the optimal test variant for a given study and sample. Graph Mapping can be downloaded from: https://osf.io/wh7zv/.

Computational Investigations of Learning and Synchronization in Cognitive Control

Complex cognition requires binding together of stimulus, action, and other features, across different time scales. Several implementations of such binding have been proposed in the literature, most prominently synaptic binding (learning) and synchronization. Biologically plausible accounts of how these different types of binding interact in the human brain are still lacking. To this end, we adopt a computational approach to investigate the impact of learning and synchronization on both behavioral (reaction time, error rate) and neural (θ power) measures. We train four models varying in their ability to learn and synchronize for an extended period of time on three seminal action control paradigms varying in difficulty. Learning, but not synchronization, proved essential for behavioral improvement. Synchronization however boosts performance of difficult tasks, avoiding the computational pitfalls of catastrophic interference. At the neural level, θ power decreases with practice but increases with task difficulty. Our simulation results bring new insights in how different types of binding interact in different types of tasks, and how this is translated in both behavioral and neural metrics.

Fluid Intelligence Emerges from Representing Relations

Based on recent findings in cognitive neuroscience and psychology as well as computational models of working memory and reasoning, I argue that fluid intelligence (fluid reasoning) can amount to representing in the mind the key relation(s) for the task at hand. Effective representation of relations allows for enormous flexibility of thinking but depends on the validity and robustness of the dynamic patterns of argument-object (role-filler) bindings, which encode relations in the brain. Such a reconceptualization of the fluid intelligence construct allows for the simplification and purification of its models, tests, and potential brain mechanisms.

Analogical mapping across sensory modalities and evidence for a general analogy factor

Analogy is a central component of human cognition. Analogical "mapping" of similarities between pieces of information present in our experiences supports cognitive and social development, classroom learning, and creative insights and innovation. To date, analogical mapping has primarily been studied within separate modalities of information (e.g., verbal analogies between words, visuo-spatial analogies between objects). However, human experience, in development and adulthood, includes highly variegated information (e.g., words, sounds, objects) received via multiple sensory and information-processing pathways (e.g., visual vs. auditory pathways). Whereas cross-modal correspondences (e.g., between pitch and height) have been observed, the correspondences were between individual items, rather than between relations. Thus, analogical mapping (characterized by second-order relations between relations) has not been directly tested as a basis for cross-modal correspondence. Here, we devised novel cross-modality analogical stimuli (lines-to-sounds, lines-to-words, words-to-sounds) that explicated second-order comparisons between relations. In four samples across three studies-participants demonstrated well-above-chance identification of cross-modal second-order relations, providing robust evidence of analogy across modalities. Further, performance across all analogy types was explained by a single factor, indicating a modality-general analogical ability (i.e., an "analo-g" factor). Analo-g explained performance over-and-above fluid intelligence as well as verbal and spatial abilities, though a stronger relationship to verbal than visuo-spatial ability emerged, consistent with verbal/semantic contributions to analogy. The present data suggests novel questions about our ability to find/learn second-order relations among the diverse information sources that populate human experience, and about cross-modal human and AI analogical mapping in developmental, educational, and creative contexts.

Uncovering the course of analogical mapping using eye tracking

Analogical mapping - the core component of analogical reasoning - consists of establishing the relational structure shared by two analogous situations and inferring the missing elements in a less familiar situation from a more familiar one. Several existing models of analogy predicted that the complete relational structure can be considered in parallel. Other models postulated that mapping can be less or more incremental - it can access only a relatively small part of the structure, and needs to move to its other parts in steps in order to construct the final relational correspondence. However, the precise time course of analogical mapping, especially in sufficiently complex analogies, to date was rarely studied empirically. In two studies, eye tracking was used to assess in a rigorous way the extent to which mapping can be incremental. In a newly designed geometric A:B::C:D task, pattern D was generated from C according to the same shape transformations that generated pattern B from A. The six possible response options differed systematically in the number of correct transformations, from no transformation matching, via partial relational match, up to the full match. In Study 1, the relational match of options fixated on by participants was initially low but increased monotonically over the course of analogy. The number of corresponding eye fixations predicted 68% variance in relational match of the final response. The correct option was chosen only if fixated on for a sufficiently long time. Study 2 replicated the findings using a more ecologically valid and less demanding task variant that required to map the changes in people's appearance. The results support these theoretical models of analogy which postulate strictly incremental mapping.

Why do children struggle on analogical reasoning tasks? Considering the role of problem format by measuring visual attention

Given the importance of analogical reasoning to bootstrapping children's understanding of the world, why is this ability so challenging for children? Two common sources of error have been implicated: 1) children's inability to prioritize relational information during initial problem solving; 2) children's inability to disengage from salient distractors. Here, we use eye tracking to examine children and adults' looking patterns when solving scene analogies, finding that children and adults attended differently to distractors, and that this attention predicted performance. These results provide the most direct evidence to date that feature based distraction is an important way children and adults differ during early analogical reasoning. In contrast to recent work using propositional analogies, we find no differences in children and adults' prioritization of relational information during problem solving, and while there are some differences in general attentional strategies across age groups, neither prioritization of relational information nor attentional strategy predict successful problem solving. Together, our results suggest that analogy problem format should be taken into account when considering developmental factors in children's analogical reasoning.

The Neural Correlates of Analogy Component Processes

Analogical reasoning is a core facet of higher cognition in humans. Creating analogies as we navigate the environment helps us learn. Analogies involve reframing novel encounters using knowledge of familiar, relationally similar contexts stored in memory. When an analogy links a novel encounter with a familiar context, it can aid in problem solving. Reasoning by analogy is a complex process that is mediated by multiple brain regions and mechanisms. Several advanced computational architectures have been developed to simulate how these brain processes give rise to analogical reasoning, like the "learning with inferences and schema abstraction" architecture and the Companion architecture. To obtain this power to simulate human reasoning, theses architectures assume that various computational "subprocesses" comprise analogical reasoning, such as analogical access, mapping, inference, and schema induction, consistent with the structure-mapping framework proposed decades ago. However, little is known about how these subprocesses relate to actual brain processes. While some work in neuroscience has linked analogical reasoning to regions of brain prefrontal cortex, more research is needed to investigate the wide array of specific neural hypotheses generated by the computational architectures. In the current article, we review the association between historically important computational architectures of analogy and empirical studies in neuroscience. In particular, we focus on evidence for a frontoparietal brain network underlying analogical reasoning and the degree to which brain mechanisms mirror the computational subprocesses. We also offer a general vantage on the current- and future-states of neuroscience research in this domain and provide some recommendations for future neuroimaging studies.

The Perception of Relations

The world contains not only objects and features (red apples, glass bowls, wooden tables), but also relations holding between them (apples contained in bowls, bowls supported by tables). Representations of these relations are often developmentally precocious and linguistically privileged; but how does the mind extract them in the first place? Although relations themselves cast no light onto our eyes, a growing body of work suggests that even very sophisticated relations display key signatures of automatic visual processing. Across physical, eventive, and social domains, relations such as support, fit, cause, chase, and even socially interact are extracted rapidly, are impossible to ignore, and influence other perceptual processes. Sophisticated and structured relations are not only judged and understood, but also seen - revealing surprisingly rich content in visual perception itself.

A Dissociative Framework for Understanding Same-Different Conceptualization

Cognitive, comparative, and developmental psychologists have long been interested in humans' and animals' ability to respond to abstract relations. Cross-species research has used relational matching-to-sample (RMTS) tasks in which participants try to find stimulus pairs that "match" because they express the same abstract relation (same or different). Researchers seek to understand the cognitive processes that underlie successful matching, and the cognitive constraints that create species differences in these tasks. Here we describe a dissociative framework drawn from cognitive neuroscience. It has strong potential to illuminate the area of same-different conceptualization. It has already influenced comparative research on categorization and metacognition. This dissociative framework also shows that species differences in same-different conceptualization have resonance with species differences in other comparative domains.

Conceptual anchoring dissociates implicit and explicit category learning

Categorization researchers have long debated the possibility of multiple category-learning systems. The need persists for paradigms that dissociate explicit-declarative category-learning processes (featuring verbalizable category rules) from implicit-procedural processes (featuring stimulus-response associations lying beneath declarative cognition). The authors contribute a new paradigm, using perfectly matched exclusive-or (XOR) category tasks differing only in the availability or absence of easily verbalizable conceptual content. This manipulation transformed learning. The conceptual task alone was learned suddenly, by insightful rule discovery, producing explicit-declarative XOR knowledge. The perceptual task was learned more gradually, consistent with associative-learning processes, producing impoverished declarative knowledge. We also tested participants under regimens of immediate and deferred reinforcement. The conceptual task alone was learned through processes that survive the loss of trial-by-trial reinforcement. All results support the idea that humans have perceptual-associative processes for implicit learning, but also an overlain conceptual system that under the right circumstances constitutes a parallel explicit-declarative category-learning system. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Individual differences in relational reasoning

Various forms of relational processing have been linked to cognitive capacity measures, such as working memory and fluid intelligence. However, previous work has not established the extent to which different forms of relational processing reflect common factors, nor whether individual differences in cognitive style also contribute to variations in relational reasoning. The current study took an individual-differences approach to investigate the prerequisites for relational processing. In two studies, college students completed a battery of standardized tests of individual differences related to fluid intelligence and cognitive style, as well as a series of experimental tasks that require relational reasoning. Moderate correlations were obtained between relational processing and measures of cognitive capacity. Questionnaire measures of cognitive style generally did not improve predictions of relational processing beyond the influence of measures of cognitive capacity.

How do people choose among rational number notations?

Three rational number notations -- fractions, decimals, and percentages -- have existed in their modern forms for over 300 years, suggesting that each notation serves a distinct function. However, it is unclear what these functions are and how people choose which notation to use in a given situation. In the present article, we propose quantification process theory to account for people's preferences among fractions, decimals, and percentages. According to this theory, the preferred notation for representing a ratio corresponding to a given situation depends on the processes used to quantify the ratio or its components. Quantification process theory predicts that if exact enumeration is used to generate a ratio, fractions will be preferred to decimals and percentages; in contrast, if estimation is used to generate the ratio, decimals and percentages will be preferred to fractions. Moreover, percentages will be preferred over decimals for representing ratios when approximation to the nearest percent is sufficiently precise, due to the lesser processing demands of using percentages. Experiments 1, 2, and 3 yielded empirical evidence regarding preferences that were consistent with quantification process theory. Experiment 4 indicated that the accuracy with which participants identified the numerical values of ratios when they used different notations generally paralleled their preferences. Educational implications of the findings are discussed.

Relational Integration in the Human Brain: A Review and Synthesis

Relational integration is required when multiple explicit representations of relations between entities must be jointly considered to make inferences. We provide an overview of the neural substrate of relational integration in humans and the processes that support it, focusing on work on analogical and deductive reasoning. In addition to neural evidence, we consider behavioral and computational work that has informed neural investigations of the representations of individual relations and of relational integration. In very general terms, evidence from neuroimaging, neuropsychological, and neuromodulatory studies points to a small set of regions (generally left lateralized) that appear to constitute key substrates for component processes of relational integration. These include posterior parietal cortex, implicated in the representation of first-order relations (e.g., A:B); rostrolateral pFC, apparently central in integrating first-order relations so as to generate and/or evaluate higher-order relations (e.g., A:B::C:D); dorsolateral pFC, involved in maintaining relations in working memory; and ventrolateral pFC, implicated in interference control (e.g., inhibiting salient information that competes with relevant relations). Recent work has begun to link computational models of relational representation and reasoning with patterns of neural activity within these brain areas.

A Compositional Neural Architecture for Language

Hierarchical structure and compositionality imbue human language with unparalleled expressive power and set it apart from other perception–action systems. However, neither formal nor neurobiological models account for how these defining computational properties might arise in a physiological system. I attempt to reconcile hierarchy and compositionality with principles from cell assembly computation in neuroscience; the result is an emerging theory of how the brain could convert distributed perceptual representations into hierarchical structures across multiple timescales while representing interpretable incremental stages of (de)compositional meaning. The model's architecture—a multidimensional coordinate system based on neurophysiological models of sensory processing—proposes that a manifold of neural trajectories encodes sensory, motor, and abstract linguistic states. Gain modulation, including inhibition, tunes the path in the manifold in accordance with behavior and is how latent structure is inferred. As a consequence, predictive information about upcoming sensory input during production and comprehension is available without a separate operation. The proposed processing mechanism is synthesized from current models of neural entrainment to speech, concepts from systems neuroscience and category theory, and a symbolic-connectionist computational model that uses time and rhythm to structure information. I build on evidence from cognitive neuroscience and computational modeling that suggests a formal and mechanistic alignment between structure building and neural oscillations, and moves toward unifying basic insights from linguistics and psycholinguistics with the currency of neural computation.

Taking the Relational Structure of Fractions Seriously: Relational Reasoning Predicts Fraction Knowledge in Elementary School Children

Understanding and using symbolic fractions in mathematics is critical for access to advanced STEM concepts. However, children and adults consistently struggle with fractions. Here, we take a novel perspective on symbolic fractions, considering them within the framework of relational structures in cognitive psychology, such as those studied in analogy research. We tested the hypothesis that relational reasoning ability is important for reasoning about fractions by examining the relation between scores on a domain-general test of relational reasoning (TORR Jr.) and a test of fraction knowledge consisting of various types of fraction problems in 194 second grade and 145 fifth grade students. We found that relational reasoning was a significant predictor of fractions knowledge, even when controlling for non-verbal IQ and fractions magnitude processing for both grades. The effects of relational reasoning also remained significant when controlling for overall mathematics knowledge and skill for second graders but was attenuated for fifth graders. These findings suggest that this important subdomain of mathematical cognition is integrally tied to relational reasoning and opens the possibility that instruction targeting relational reasoning may prove to be a viable avenue for improving children's fractions skills.

Network architectures supporting learnability

Human learners acquire complex interconnected networks of relational knowledge. The capacity for such learning naturally depends on two factors: the architecture (or informational structure) of the knowledge network itself and the architecture of the computational unit-the brain-that encodes and processes the information. That is, learning is reliant on integrated network architectures at two levels: the epistemic and the computational, or the conceptual and the neural. Motivated by a wish to understand conventional human knowledge, here, we discuss emerging work assessing network constraints on the learnability of relational knowledge, and theories from statistical physics that instantiate the principles of thermodynamics and information theory to offer an explanatory model for such constraints. We then highlight similarities between those constraints on the learnability of relational networks, at one level, and the physical constraints on the development of interconnected patterns in neural systems, at another level, both leading to hierarchically modular networks. To support our discussion of these similarities, we employ an operational distinction between the modeller (e.g. the human brain), the model (e.g. a single human's knowledge) and the modelled (e.g. the information present in our experiences). We then turn to a philosophical discussion of whether and how we can extend our observations to a claim regarding explanation and mechanism for knowledge acquisition. What relation between hierarchical networks, at the conceptual and neural levels, best facilitate learning? Are the architectures of optimally learnable networks a topological reflection of the architectures of comparably developed neural networks? Finally, we contribute to a unified approach to hierarchies and levels in biological networks by proposing several epistemological norms for analysing the computational brain and social epistemes, and for developing pedagogical principles conducive to curious thought. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Two Ways to Build a Thought: Distinct Forms of Compositional Semantic Representation across Brain Regions

To understand a simple sentence such as "the woman chased the dog", the human mind must dynamically organize the relevant concepts to represent who did what to whom. This structured recombination of concepts (woman, dog, chased) enables the representation of novel events, and is thus a central feature of intelligence. Here, we use functional magnetic resonance (fMRI) and encoding models to delineate the contributions of three brain regions to the representation of relational combinations. We identify a region of anterior-medial prefrontal cortex (amPFC) that shares representations of noun-verb conjunctions across sentences: for example, a combination of "woman" and "chased" to encode woman-as-chaser, distinct from woman-as-chasee. This PFC region differs from the left-mid superior temporal cortex (lmSTC) and hippocampus, two regions previously implicated in representing relations. lmSTC represents broad role combinations that are shared across verbs (e.g., woman-as-agent), rather than narrow roles, limited to specific actions (woman-as-chaser). By contrast, a hippocampal sub-region represents events sharing narrow conjunctions as dissimilar. The success of the hippocampal conjunctive encoding model is anti-correlated with generalization performance in amPFC on a trial-by-trial basis, consistent with a pattern separation mechanism. Thus, these three regions appear to play distinct, but complementary, roles in encoding compositional event structure.

Active transitive inference: When learner control facilitates integrative encoding

A growing body of research indicates that active control of learning improves episodic memory for material experienced during study. It is less clear how active learning impacts the integration of those experiences into flexible, generalizable knowledge. This study uses a novel active transitive inference task to investigate how people learn a relational hierarchy through active selection of premise pairs. Active control improved memory for studied premises as well as transitive inferences involving items that were never experienced together during study. Active learners also exhibited a systematic search preference, generating sequences of overlapping premises that may facilitate relational integration. Critically, however, advantages from active control were not universal: Only participants with higher working memory capacity benefited from the opportunity to select premise pairs during learning. These findings suggest that active control enhances integrative encoding of studied material, but only among individuals with sufficient cognitive resources.

Structured sequence processing and combinatorial binding: neurobiologically and computationally informed hypotheses

Understanding how the brain forms representations of structured information distributed in time is a challenging endeavour for the neuroscientific community, requiring computationally and neurobiologically informed approaches. The neural mechanisms for segmenting continuous streams of sensory input and establishing representations of dependencies remain largely unknown, as do the transformations and computations occurring between the brain regions involved in these aspects of sequence processing. We propose a blueprint for a neurobiologically informed and informing computational model of sequence processing (entitled: Vector-symbolic Sequencing of Binding INstantiating Dependencies, or VS-BIND). This model is designed to support the transformation of serially ordered elements in sensory sequences into structured representations of bound dependencies, readily operates on multiple timescales, and encodes or decodes sequences with respect to chunked items wherever dependencies occur in time. The model integrates established vector symbolic additive and conjunctive binding operators with neurobiologically plausible oscillatory dynamics, and is compatible with modern spiking neural network simulation methods. We show that the model is capable of simulating previous findings from structured sequence processing tasks that engage fronto-temporal regions, specifying mechanistic roles for regions such as prefrontal areas 44/45 and the frontal operculum during interactions with sensory representations in temporal cortex. Finally, we are able to make predictions based on the configuration of the model alone that underscore the importance of serial position information, which requires input from time-sensitive cells, known to reside in the hippocampus and dorsolateral prefrontal cortex. This article is part of the theme issue 'Towards mechanistic models of meaning composition'.

Tensors and compositionality in neural systems

Neither neurobiological nor process models of meaning composition specify the operator through which constituent parts are bound together into compositional structures. In this paper, we argue that a neurophysiological computation system cannot achieve the compositionality exhibited in human thought and language if it were to rely on a multiplicative operator to perform binding, as the tensor product (TP)-based systems that have been widely adopted in cognitive science, neuroscience and artificial intelligence do. We show via simulation and two behavioural experiments that TPs violate variable-value independence, but human behaviour does not. Specifically, TPs fail to capture that in the statements fuzzy cactus and fuzzy penguin, both cactus and penguin are predicated by fuzzy(x) and belong to the set of fuzzy things, rendering these arguments similar to each other. Consistent with that thesis, people judged arguments that shared the same role to be similar, even when those arguments themselves (e.g., cacti and penguins) were judged to be dissimilar when in isolation. By contrast, the similarity of the TPs representing fuzzy(cactus) and fuzzy(penguin) was determined by the similarity of the arguments, which in this case approaches zero. Based on these results, we argue that neural systems that use TPs for binding cannot approximate how the human mind and brain represent compositional information during processing. We describe a contrasting binding mechanism that any physiological or artificial neural system could use to maintain independence between a role and its argument, a prerequisite for compositionality and, thus, for instantiating the expressive power of human thought and language in a neural system. This article is part of the theme issue 'Towards mechanistic models of meaning composition'.

Cross-Situational Statistical Learning of New Words Despite Bilateral Hippocampal Damage and Severe Amnesia

Word learning requires learners to bind together arbitrarily-related phonological, visual, and conceptual information. Prior work suggests that this binding can be robustly achieved via incidental cross-situational statistical exposure to words and referents. When cross-situational statistical learning (CSSL) is tested in the laboratory, there is no information on any given trial to identify the referent of a novel word. However, by tracking which objects co-occur with each word across trials, learners may acquire mappings through statistical association. While CSSL behavior is well-characterized, its brain correlates are not. The arbitrary nature of CSSL mappings suggests hippocampal involvement, but the incremental, statistical nature of the learning raises the possibility of neocortical or procedural learning systems. Prior studies have shown that neurological patients with hippocampal pathology have word-learning impairments, but this has not been tested in a statistical learning paradigm. Here, we used a neuropsychological approach to test whether patients with bilateral hippocampal pathology (N = 3) could learn new words in a CSSL paradigm. In the task, patients and healthy comparison participants completed a CSSL word-learning task in which they acquired eight word/object mappings. During each trial of the CSSL task, participants saw two objects on a computer display, heard one novel word, and selected the most likely referent. Across trials, words were 100% likely to co-occur with their referent, but only 14.3% likely with non-referents. Two of three amnesic patients learned the associations between objects and word forms, although performance was impaired relative to healthy comparison participants. Our findings show that the hippocampus is not strictly necessary for CSSL for words, although it may facilitate such learning. This is consistent with a hybrid account of CSSL supported by implicit and explicit memory systems, and may have translational applications for remediation of (word-) learning deficits in neurological populations with hippocampal pathology.

Training neural networks to encode symbols enables combinatorial generalization

Combinatorial generalization-the ability to understand and produce novel combinations of already familiar elements-is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body of research suggests that conventional neural networks cannot solve this problem unless they are endowed with mechanisms specifically engineered for the purpose of representing symbols. In this paper, we introduce a novel way of representing symbolic structures in connectionist terms-the vectors approach to representing symbols (VARS), which allows training standard neural architectures to encode symbolic knowledge explicitly at their output layers. In two simulations, we show that neural networks not only can learn to produce VARS representations, but in doing so they achieve combinatorial generalization in their symbolic and non-symbolic output. This adds to other recent work that has shown improved combinatorial generalization under some training conditions, and raises the question of whether specific mechanisms or training routines are needed to support symbolic processing. This article is part of the theme issue 'Towards mechanistic models of meaning composition'.

Phase synchronization varies systematically with linguistic structure composition

Computation in neuronal assemblies is putatively reflected in the excitatory and inhibitory cycles of activation distributed throughout the brain. In speech and language processing, coordination of these cycles resulting in phase synchronization has been argued to reflect the integration of information on different timescales (e.g. segmenting acoustics signals to phonemic and syllabic representations; (Giraud and Poeppel 2012 Nat. Neurosci. 15, 511 (doi:10.1038/nn.3063)). A natural extension of this claim is that phase synchronization functions similarly to support the inference of more abstract higher-level linguistic structures (Martin 2016 Front. Psychol. 7, 120; Martin and Doumas 2017 PLoS Biol. 15, e2000663 (doi:10.1371/journal.pbio.2000663); Martin and Doumas. 2019 Curr. Opin. Behav. Sci. 29, 77-83 (doi:10.1016/j.cobeha.2019.04.008)). Hale et al. (Hale et al. 2018 Finding syntax in human encephalography with beam search. arXiv 1806.04127 (http://arxiv.org/abs/1806.04127)) showed that syntactically driven parsing decisions predict electroencephalography (EEG) responses in the time domain; here we ask whether phase synchronization in the form of either inter-trial phrase coherence or cross-frequency coupling (CFC) between high-frequency (i.e. gamma) bursts and lower-frequency carrier signals (i.e. delta, theta), changes as the linguistic structures of compositional meaning (viz., bracket completions, as denoted by the onset of words that complete phrases) accrue. We use a naturalistic story-listening EEG dataset from Hale et al. to assess the relationship between linguistic structure and phase alignment. We observe increased phase synchronization as a function of phrase counts in the delta, theta, and gamma bands, especially for function words. A more complex pattern emerged for CFC as phrase count changed, possibly related to the lack of a one-to-one mapping between 'size' of linguistic structure and frequency band-an assumption that is tacit in recent frameworks. These results emphasize the important role that phase synchronization, desynchronization, and thus, inhibition, play in the construction of compositional meaning by distributed neural networks in the brain. This article is part of the theme issue 'Towards mechanistic models of meaning composition'.

Breaking the perceptual-conceptual barrier: Relational matching and working memory

Cognitive, comparative, and developmental psychologists have long been interested in humans' and animals' ability to respond to abstract relations, as this ability may underlie important capacities like analogical reasoning. Cross-species research has used relational matching-to-sample (RMTS) tasks in which participants try to find stimulus pairs that "match" because they both express the same abstract relation (same or different). Researchers seek to understand the cognitive processes that underlie successful matching performance. In the present RMTS paradigm, the abstract-relational cue was made redundant with a first-order perceptual cue. Then the perceptual cue faded, requiring participants to transition from a perceptual to a conceptual approach by realizing the task's abstract-relational affordance. We studied participants' ability to make this transition with and without a working-memory load. The concurrent load caused participants to fail to break the perceptual-conceptual barrier unless the load was abandoned. We conclude that finding the conceptual solution depends on reconstruing the task using cognitive processes that are especially reliant on working memory. Our data provide the closest existing look at this cognitive reorganization. They raise important theoretical issues for cross-species comparisons of relational cognition, especially regarding animals' limitations in this domain.

Understanding associative vs. abstract pictorial relations: An ERP study

One of the most remarkable human abilities is extracting relations between objects, words or ideas - a process that underlies perception, learning and reasoning. Yet, perhaps due to its complexity, surprisingly little is known about the neural basis of this fundamental ability. Here, we examined EEG waveforms evoked by different types of relations, conveyed by pairs of images. Subjects were presented with the pairs, that were either associatively related, abstractly related or unrelated, and judged if they were related or not. Evidence for a gradual modulation of the amplitude of the N400 and late negativity was found, such that unrelated pairs elicited the most negative amplitude, followed by abstractly-related pairs and lastly associatively-related ones. However, this was confined to first encounter with the pairs, and a different, more dichotomous pattern was observed when the pairs were viewed for the second time. Then, no difference was found between associatively and abstractly related pairs, while both differed from unrelated pairs. Notably, when the pairs were sequentially presented, this pattern was found mostly in right electrodes, while it appeared both in left and right sites during simultaneous presentation of the pairs. This suggests that while two different mechanisms may be involved in generating predictions about an upcoming related/unrelated stimulus, online processing of associative and abstract semantic relations might be mediated by a single mechanism. Our results further support claims that the N400 component indexes multiple cognitive processes that overlap in time, yet not necessarily in neural generators.

Evidence of analogical re-representation from a change detection task

The flexibility to map similar, but non-identical relations, is a key characteristic of human analogical reasoning. Understanding how this flexibility is implemented is necessary for a complete accounting of analogical processes. The structure mapping theory of analogy addresses this issue by invoking re-representation-an online transformation of conceptually similar relational content that reveals potential partial identity matches between predicates. Despite the critical importance of re-representation to structure mapping, very little empirical work has validated the psychological reality of this mechanism, with the existing evidence being no more than suggestive. The present work investigates the likelihood of re-representation across two experiments using a novel change detection task. The resultant findings demonstrate precise evidence of representational change in relational content of analogs. Experiment 2 further explores the relationship between lower-order relational similarity and the likelihood of re-representation.

Emergence of analogy from relation learning

The ability to learn and make inferences based on relations is central to intelligence, underlying the distinctively human ability to reason by analogy across dissimilar situations. We have developed a computational model demonstrating that abstract relations, such as synonymy and antonymy, can be learned efficiently from semantic feature vectors for individual words and can be used to solve simple verbal analogy problems with close to human-level accuracy. The approach illustrates the potential synergy between deep learning from “big data” and supervised learning from “small data.” Core properties of high-level intelligence can emerge from relatively simple computations coupled with rich semantics. The model illustrates how operations on nonrelational inputs can give rise to protosymbolic relational representations.

By middle childhood, humans are able to learn abstract semantic relations (e.g., antonym, synonym, category membership) and use them to reason by analogy. A deep theoretical challenge is to show how such abstract relations can arise from nonrelational inputs, thereby providing key elements of a protosymbolic representation system. We have developed a computational model that exploits the potential synergy between deep learning from “big data” (to create semantic features for individual words) and supervised learning from “small data” (to create representations of semantic relations between words). Given as inputs labeled pairs of lexical representations extracted by deep learning, the model creates augmented representations by remapping features according to the rank of differences between values for the two words in each pair. These augmented representations aid in coping with the feature alignment problem (e.g., matching those features that make “love-hate” an antonym with the different features that make “rich-poor” an antonym). The model extracts weight distributions that are used to estimate the probabilities that new word pairs instantiate each relation, capturing the pattern of human typicality judgments for a broad range of abstract semantic relations. A measure of relational similarity can be derived and used to solve simple verbal analogies with human-level accuracy. Because each acquired relation has a modular representation, basic symbolic operations are enabled (notably, the converse of any learned relation can be formed without additional training). Abstract semantic relations can be induced by bootstrapping from nonrelational inputs, thereby enabling relational generalization and analogical reasoning.