The discovery and comparison of symbolic magnitudes

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.

Large as being on top of the world and small as hitting the roof: a common magnitude representation for the comparison of emotions and numbers

Previous work on the direct speed-intensity association (SIA) on comparative judgement tasks involved spatially distributed responses over spatially distributed stimuli with high motivational significance like facial expressions of emotions. This raises the possibility that the inferred stimulus-driven regulation of lateralized motor reactivity described by SIA, which was against the one expected on the basis of a valence-specific lateral bias, was entirely due to attentional capture from motivational significance (beyond numerical cognition). In order to establish the relevance of numerical cognition on the regulation of attentional capture we ran two complementary experiments. These involved the same direct comparison task on stimulus pairs that were fully comparable in terms of their analog representation of intensity but with different representational domain and motivational significance: symbolic magnitudes with low motivational significance in experiment 1 vs. emotions with rather high motivational significance in experiment 2. The results reveal a general SIA and point to a general mechanism regulating comparative judgements. This is based on the way spatial attention is captured toward locations that contain the stimulus which is closest in term of relative intensity to the extremal values of the series, regardless from its representational domain being it symbolic or emotional.

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.

Factors and processes in children's transitive deductions

Transitive tasks are important for understanding how children develop socio-cognitively. However, developmental research has been restricted largely to questions surrounding maturation. We asked 6-, 7- and 8-year-olds (N = 117) to solve a composite of five different transitive tasks. Tasks included conditions asking about item-C (associated with the marked relation) in addition to the usual case of asking only about item-A (associated with the unmarked relation). Here, children found resolving item-C much easier than resolving item-A, a finding running counter to long-standing assumptions about transitive reasoning. Considering gender perhaps for the first time, boys exhibited higher transitive scores than girls overall. Finally, analysing in the context of one recent and well-specified theory of spatial transitive reasoning, we generated the prediction that reporting the full series should be easier than deducing any one item from that series. This prediction was not upheld. We discuss amendments necessary to accommodate all our earlier findings.

Dimensional interaction in distance judgment

Participants decided under speed stress whether or not the horizontal distances between pairs of frontal locations exceeded a criterion distance. The error rate reflected parallel effects of the horizontal and vertical distance between the locations. Whereas dimensional interaction in perceptual judgment has previously been attributed either to the perception of the stimulus or to the response decision concerning the stimulus, here dimensional interaction was attributed to the process of distance assessment regarding the test locations. Under the proposed account, the horizontal distance between the locations could not be assessed independently of the vertical distance. Only the overall distance between the locations could be assessed. However, because the horizontal and vertical positions of the locations could be independently assessed, the horizontal distance between the locations was available to the extent that the vertical positions of the locations were weighted so as to minimize vertical distance prior to the assessment of overall distance. In support of this account, parallel effects of horizontal and vertical distance were not observed when participants decided whether or not pairs of locations had the same horizontal position.