Learned Representation of Implied Serial Order in Posterior Parietal Cortex

A mathematical theory of relational generalization in transitive inference

Humans and animals routinely infer relations between different items or events and generalize these relations to novel combinations of items. This allows them to respond appropriately to radically novel circumstances and is fundamental to advanced cognition. However, how learning systems (including the brain) can implement the necessary inductive biases has been unclear. Here we investigated transitive inference (TI), a classic relational task paradigm in which subjects must learn a relation (A > B and B > C) and generalize it to new combinations of items (A > C). Through mathematical analysis, we found that a broad range of biologically relevant learning models (e.g. gradient flow or ridge regression) perform TI successfully and recapitulate signature behavioral patterns long observed in living subjects. First, we found that models with item-wise additive representations automatically encode transitive relations. Second, for more general representations, a single scalar "conjunctivity factor" determines model behavior on TI and, further, the principle of norm minimization (a standard statistical inductive bias) enables models with fixed, partly conjunctive representations to generalize transitively. Finally, neural networks in the "rich regime," which enables representation learning and has been found to improve generalization, unexpectedly show poor generalization and anomalous behavior. We find that such networks implement a form of norm minimization (over hidden weights) that yields a local encoding mechanism lacking transitivity. Our findings show how minimal statistical learning principles give rise to a classical relational inductive bias (transitivity), explain empirically observed behaviors, and establish a formal approach to understanding the neural basis of relational abstraction.

The transitive inference task to study the neuronal correlates of memory-driven decision making: A monkey neurophysiology perspective

A vast amount of literature agrees that rank-ordered information as A>B>C>D>E>F is mentally represented in spatially organized schemas after learning. This organization significantly influences the process of decision-making, using the acquired premises, i.e. deciding if B is higher than D is equivalent to comparing their position in this space. The implementation of non-verbal versions of the transitive inference task has provided the basis for ascertaining that different animal species explore a mental space when deciding among hierarchically organized memories. In the present work, we reviewed several studies of transitive inference that highlighted this ability in animals and, consequently, the animal models developed to study the underlying cognitive processes and the main neural structures supporting this ability. Further, we present the literature investigating which are the underlying neuronal mechanisms. Then we discuss how non-human primates represent an excellent model for future studies, providing ideal resources for better understanding the neuronal correlates of decision-making through transitive inference tasks.

Sleep-related benefits to transitive inference are modulated by encoding strength and joint rank

Transitive inference is a measure of relational learning that has been shown to improve across sleep. Here, we examine this phenomenon further by studying the impact of encoding strength and joint rank. In experiment 1, participants learned adjacent premise pairs and were then tested on inferential problems derived from those pairs. In line with prior work, we found improved transitive inference performance after retention across a night of sleep compared with wake alone. Experiment 2 extended these findings using a within-subject design and found superior transitive inference performance on a hierarchy, consolidated across 27 h including sleep compared with just 3 h of wake. In both experiments, consolidation-related improvement was enhanced when presleep learning (i.e., encoding strength) was stronger. We also explored the interaction of these effects with the joint rank effect, in which items were scored according to their rank in the hierarchy, with more dominant item pairs having the lowest scores. Interestingly, the consolidation-related benefit was greatest for more dominant inference pairs (i.e., those with low joint rank scores). Overall, our findings provide further support for the improvement of transitive inference across a consolidation period that includes sleep. We additionally show that encoding strength and joint rank strongly modulate this effect.

Cortical Grey Matter Mediates Increases in Model-Based Control and Learning from Positive Feedback from Adolescence to Adulthood

Cognition and brain structure undergo significant maturation from adolescence into adulthood. Model-based (MB) control is known to increase across development, which is mediated by cognitive abilities. Here, we asked two questions unaddressed in previous developmental studies. First, what are the brain structural correlates of age-related increases in MB control? Second, how are age-related increases in MB control from adolescence to adulthood influenced by motivational context? A human developmental sample (n = 103; age, 12-50, male/female, 55:48) completed structural MRI and an established task to capture MB control. The task was modified with respect to outcome valence by including (1) reward and punishment blocks to manipulate the motivational context and (2) an additional choice test to assess learning from positive versus negative feedback. After replicating that an age-dependent increase in MB control is mediated by cognitive abilities, we demonstrate first-time evidence that gray matter density (GMD) in the parietal cortex mediates the increase of MB control with age. Although motivational context did not relate to age-related changes in MB control, learning from positive feedback improved with age. Meanwhile, negative feedback learning showed no age effects. We present a first report that an age-related increase in positive feedback learning was mediated by reduced GMD in the parietal, medial, and dorsolateral prefrontal cortex. Our findings indicate that brain maturation, putatively reflected in lower GMD, in distinct and partially overlapping brain regions could lead to a more efficient brain organization and might thus be a key developmental step toward age-related increases in planning and value-based choice.SIGNIFICANCE STATEMENT Changes in model-based decision-making are paralleled by extensive maturation in cognition and brain structure across development. Still, to date the neuroanatomical underpinnings of these changes remain unclear. Here, we demonstrate for the first time that parietal GMD mediates age-dependent increases in model-based control. Age-related increases in positive feedback learning were mediated by reduced GMD in the parietal, medial, and dorsolateral prefrontal cortex. A manipulation of motivational context did not have an impact on age-related changes in model-based control. These findings highlight that brain maturation in distinct and overlapping cortical regions constitutes a key developmental step toward improved value-based choices.

Neural correlates of transitive inference: An SDM meta-analysis on 32 fMRI studies

Transitive inference (TI) is a critical capacity involving the integration of relevant information into prior knowledge structure for drawing novel inferences on unobserved relationships. To date, the neural correlates of TI remain unclear due to the small sample size and heterogeneity of various experimental tasks from individual studies. Here, the meta-analysis on 32 fMRI studies was performed to detect brain activation patterns of TI and its three paradigms (spatial inference, hierarchical inference, and associative inference). We found the hippocampus, prefrontal cortex (PFC), putamen, posterior parietal cortex (PPC), retrosplenial cortex (RSC), supplementary motor area (SMA), precentral gyrus (PreCG), and median cingulate cortex (MCC) were engaged in TI. Specifically, the RSC was implicated in the associative inference, whereas PPC, SMA, PreCG, and MCC were implicated in the hierarchical inference. In addition, the hierarchical inference and associative inference both evoked activation in the hippocampus, medial PFC, and PCC. Although the meta-analysis on spatial inference did not generate a reliable result due to insufficient amount of investigations, the present work still offers a new insight for better understanding the neural basis underlying TI.

Category learning in a transitive inference paradigm

The implied order of a ranked set of visual images can be learned without reliance on information that explicitly signals their order. Such learning is difficult to explain by associative mechanisms, but can be accounted for by cognitive representations and processes such as transitive inference. Our study sought to determine if those processes also apply to learning categories of images. We asked whether participants can (a) infer that stimulus images belonged to familiar categories, even when the images for each trial were unique, and (b) sort those categories into an ordering that obeys transitivity. Participants received minimal verbal instruction and a single session of training. Despite this, they learned the implied order of lists of fixed stimuli and lists of ordered categories, using trial-unique exemplars. We trained two groups, one for which stimuli were constant throughout training and testing (n = 60), and one for which exemplars of each category were trial-unique (n = 50). Our findings suggest that differing cognitive processes may underpin serial learning when learning about specific stimuli as opposed to stimulus categories.