Transitive inference in humans (Homo sapiens) and rhesus macaques (Macaca mulatta) after massed training of the last two list items

Transitive inference as probabilistic preference learning

Transitive inference (TI) is a cognitive task that assesses an organism's ability to infer novel relations between items based on previously acquired knowledge. TI is known for exhibiting various behavioral and neural signatures, such as the serial position effect (SPE), symbolic distance effect (SDE), and the brain's capacity to maintain and merge separate ranking models. We propose a novel framework that casts TI as a probabilistic preference learning task, using one-parameter Mallows models. We present a series of simulations that highlight the effectiveness of our novel approach. We show that the Mallows ranking model natively reproduces SDE and SPE. Furthermore, extending the model using Bayesian selection showcases its capacity to generate and merge ranking hypotheses as pairs with connecting symbols. Finally, we employ neural networks to replicate Mallows models, demonstrating how this framework aligns with observed prefrontal neural activity during TI. Our innovative approach sheds new light on the nature of TI, emphasizing the potential of probabilistic preference learning for unraveling its underlying neural mechanisms.

Honey bees rely on associative stimulus strength after training on an olfactory transitive inference task

Transitive inference, the ability to establish hierarchical relationships between stimuli, is typically tested by training with premise pairs (e.g., A + B-, B + C-, C + D-, D + E-), which establishes a stimulus hierarchy (A > B > C > D > E). When subjects are tested with non-adjacent stimuli (e.g., B vs. D), a preference for B indicates transitive inference, while no preference indicates decisions based on stimulus associative strength, as B and D are equally reinforced. Previous studies with bees and wasps, conducted in an operant context, have shown conflicting results. However, this context allows free movement and the possibility to avoid non-reinforced options, thus reducing the number of non-reinforced trials. To address this, we examined whether honey bees could perform transitive inference using a Pavlovian protocol that fully controls reinforcement. We conditioned bees with five odorants, either forward-or backward-paired with a sucrose solution, across four discrimination tasks. In all experiments, bees showed no preference for B over D, choosing equally between them, regardless of the training schedule. Our results show that bees' choices were primarily influenced by stimulus associative strength and a recency effect, with greater weight given to the most recent reinforced or non-reinforced stimulus. We discuss these findings in the context of honey bee memory, suggesting that memory constraints may limit cognitive solutions to transitive inference tasks in bees.

Transitive inference in a clinical childhood sample with a focus on autism spectrum disorder

Transitive inference (TI) has a long history in the study of human development. There have, however, few pediatric studies that report clinical diagnoses have tested trial-and-error TI learning, in which participants infer item relations, rather than evaluate them explicitly from verbal descriptions. Children aged 8-10 underwent a battery of clinical assessments and received a range of diagnoses, potentially including autism spectrum disorder (ASD), attention-deficit hyperactive disorder (ADHD), anxiety disorders (AD), specific learning disorders (SLD), and/or communication disorders (CD). Participants also performed a trial-and-error learning task that tested for TI. Response accuracy and reaction time were assessed using a statistical model that controlled for diagnostic comorbidity at the group level. Participants in all diagnostic categories showed evidence of TI. However, a model comparison analysis suggested that those diagnosed with ASD succeeded in a qualitatively different way, responding more slowly to each choice and improving faster across trials than their non-ASD counterparts. Additionally, TI performance was not associated with IQ. Overall, our data suggest that superficially similar performance levels between ASD and non-ASD participants may have resulted from a difference in the speed-accuracy tradeoff made by each group. Our work provides a preliminary profile of the impact of various clinical diagnoses on TI performance in young children. Of these, an ASD diagnosis resulted in the largest difference in task strategy.

A geometrical solution underlies general neural principle for serial ordering

A general mathematical description of how the brain sequentially encodes knowledge remains elusive. We propose a linear solution for serial learning tasks, based on the concept of mixed selectivity in high-dimensional neural state spaces. In our framework, neural representations of items in a sequence are projected along a "geometric" mental line learned through classical conditioning. The model successfully solves serial position tasks and explains behaviors observed in humans and animals during transitive inference tasks amidst noisy sensory input and stochastic neural activity. This approach extends to recurrent neural networks performing motor decision tasks, where the same geometric mental line correlates with motor plans and modulates network activity according to the symbolic distance between items. Serial ordering is thus predicted to emerge as a monotonic mapping between sensory input and behavioral output, highlighting a possible pivotal role for motor-related associative cortices in transitive inference tasks.

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.

Self-derivation through memory integration: a longitudinal examination of performance and relations with academic achievements in elementary classrooms

Self-derivation through memory integration is the cognitive process of generating new knowledge by integrating individual facts. Across two studies, we longitudinally examined developmental change, individual stability, and relations with academic performance in a diverse agricultural community. We documented children's self-derivation in their classrooms and examined the relation with self-derivation and academic performance a year later. In Study 1, we examined self-derivation (n = 94; Mage= 6.67; initially grades K and 1) using the same paradigm at both time points. We found evidence of developmental change from Time 1 to Time 2. However, self-derivation accounted for a small portion of the variance in self-derivation (reflecting individual stability) and academic performance measured one year later. In Study 2, we examined self-derivation across two different paradigms with children beginning in Grades 2 and 3 (n = 82; Mage= 8.60). Even across paradigms, we found evidence for individual stability. Year 1 self-derivation also predicted Year 2 academic performance. We posit that self-derivation through integration is a domain-general construct related to academic performance.

Transitive inference and the testing effect: Retrieval practice impairs transitive inference

There is substantial interest in the extent to which the testing effect (the finding that retrieval practice enhances memory) extends to more complex forms of learning, especially those entailing greater element interactivity. Transitive inference (TI) requires just such interactivity, in which information must be combined across multiple learning elements or premises to extract an underlying structure. Picklesimer et al. provided preliminary evidence that retrieval practice fails to enhance, and actually disrupts, TI. This study assessed the generality of that result. The current experiments employed a seven- or eight-element TI paradigm in which participants initially learned a set of premise pairs (e.g., A > B, B > C, and C > D) and then engaged in either restudy or retrieval practice of the premise pairs before taking a final test that assessed memory for the original premise pairs and one's ability to make TIs (e.g., to infer that B > D). Experiments 1 and 2 used pictorial materials and simultaneous presentation of premises during learning, a form of presentation that has induced testing effects on other forms of inference. For TI, the results were unchanged from Picklesimer et al.-TI was worse for retrieval practice than restudy. Experiment 3 used verbal materials and likewise found worse TI for retrieval practice. A small-scale meta-analysis combining the current experiments with those of Picklesimer et al. revealed a significant negative testing effect on TI (d = -0.37). Although retrieval practice enhances many aspects of memory, this fundamental aspect of human reasoning may be impaired by retrieval practice.

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.

In the absence of extensive initial training, cleaner wrasse Labroides dimidiatus fail a transitive inference task

Transitive inference (TI) is a reasoning capacity that allows individuals to deduce unknown pair relationships from previous knowledge of other pair relationships. Its occurrence in a wide range of animals, including insects, has been linked to their ecological needs. Thus, TI should be absent in species that do not rely on such inferences in their natural lives. We hypothesized that the latter applies to the cleaner wrasse Labroides dimidiatus and tested this with 19 individuals using a five-term series (A > B > C > D > E) experiment. Cleaners first learned to prefer a food-rewarding plate (+) over a non-rewarding plate (-) in four plate pairs that imply a hierarchy from plate A to plate E (A+B-, B+C-, C+D-, D+E-), with the learning order counterbalanced between subjects. We then tested for spontaneous preferences in the unknown pairs BD (transitive inference task) and AE (as a control for anchors), interspersed between trials involving a mix of all known adjacent pairs. The cleaners systematically preferred A over E and showed good performance for A+B- and D+E- trials. Conversely, cleaners did not prefer B over D. These results were unaffected by the reinforcement history, but the order of learning of the different pairs of plates had a main impact on the remembrance of the initial training pairs. Overall, cleaners performed randomly in B+C- and C+D- trials. Thus, a memory constraint may have prevented subjects from applying TI. Indeed, a parallel study on cleaner wrasse provided positive evidence for TI but was achieved following extensive training on the non-adjacent pairs which may have over-ridden the ecological relevance of the task.

Hippocampal and medial prefrontal cortices encode structural task representations following progressive and interleaved training schedules

Memory generalisations may be underpinned by either encoding- or retrieval-based generalisation mechanisms and different training schedules may bias some learners to favour one of these mechanisms over the other. We used a transitive inference task to investigate whether generalisation is influenced by progressive vs randomly interleaved training, and overnight consolidation. On consecutive days, participants learnt pairwise discriminations from two transitive hierarchies before being tested during fMRI. Inference performance was consistently better following progressive training, and for pairs further apart in the transitive hierarchy. BOLD pattern similarity correlated with hierarchical distances in the left hippocampus (HIP) and medial prefrontal cortex (MPFC) following both training schedules. These results are consistent with the use of structural representations that directly encode hierarchical relationships between task features. However, such effects were only observed in the MPFC for recently learnt relationships. Furthermore, the MPFC appeared to maintain structural representations in participants who performed at chance on the inference task. We conclude that humans preferentially employ encoding-based mechanisms to store map-like relational codes that can be used for memory generalisation. These codes are expressed in the HIP and MPFC following both progressive and interleaved training but are not sufficient for accurate inference.

Superstitious learning of abstract order from random reinforcement

Humans and other animals often infer spurious associations among unrelated events. However, such superstitious learning is usually accounted for by conditioned associations, raising the question of whether an animal could develop more complex cognitive structures independent of reinforcement. Here, we tasked monkeys with discovering the serial order of two pictorial sets: a "learnable" set in which the stimuli were implicitly ordered and monkeys were rewarded for choosing the higher-rank stimulus and an "unlearnable" set in which stimuli were unordered and feedback was random regardless of the choice. We replicated prior results that monkeys reliably learned the implicit order of the learnable set. Surprisingly, the monkeys behaved as though some ordering also existed in the unlearnable set, showing consistent choice preference that transferred to novel untrained pairs in this set, even under a preference-discouraging reward schedule that gave rewards more frequently to the stimulus that was selected less often. In simulations, a model-free reinforcement learning algorithm (Q-learning) displayed a degree of consistent ordering among the unlearnable set but, unlike the monkeys, failed to do so under the preference-discouraging reward schedule. Our results suggest that monkeys infer abstract structures from objectively random events using heuristics that extend beyond stimulus-outcome conditional learning to more cognitive model-based learning mechanisms.

Determinants of elementary-school academic achievement: Component cognitive abilities and memory integration

Children are on a quest for knowledge. To achieve it, children must integrate separate but related episodes of learning. The theoretical model of memory integration posits that the process is supported by component cognitive abilities. In turn, memory integration predicts accumulation of a knowledge base. We tested this model in two studies (data collected in 2016-2018) with second (8-year-olds; n = 391; 196 female; 36% Black, 27% Hispanic/Latinx, 29% White, and 8% multiracial) and third (9-year-olds; n = 282; 148 female; 36% Black, 31% Hispanic/Latinx, 27% White, and 5% multiracial) graders. The results support the theoretical model and the role of verbal comprehension in learning new information, and also indicate that verbal comprehension alone is not sufficient to build knowledge.

Hierarchical development of dominance through the winner-loser effect and socio-spatial structure

In many groups of animals the dominance hierarchy is linear. What mechanisms underlie this linearity of the dominance hierarchy is under debate. Linearity is often attributed to cognitively sophisticated processes, such as transitive inference and eavesdropping. An alternative explanation is that it develops via the winner-loser effect. This effect implies that after a fight has been decided the winner is more likely to win again, and the loser is more likely to lose again. Although it has been shown that dominance hierarchies may develop via the winner-loser effect, the degree of linearity of such hierarchies is unknown. The aim of the present study is to investigate whether a similar degree of linearity, like in real animals, may emerge as a consequence of the winner-loser effect and the socio-spatial structure of group members. For this purpose, we use the model DomWorld, in which agents group and compete and the outcome of conflicts is self-reinforcing. Here dominance hierarchies are shown to emerge. We analyse the dominance hierarchy, behavioural dynamics and network triad motifs in the model using analytical methods from a previous study on dominance in real hens. We show that when one parameter, representing the intensity of aggression, was set high in the model DomWorld, it reproduced many patterns of hierarchical development typical of groups of hens, such as its high linearity. When omitting from the model the winner-loser effect or spatial location of individuals, this resemblance decreased markedly. We conclude that the combination of the spatial structure and the winner-loser effect provide a plausible alternative for hierarchical linearity to processes that are cognitively more sophisticated. Further research should determine whether the winner-loser effect and spatial structure of group members also explains the characteristics of hierarchical development in other species with a different dominance style than hens.

Positional inference in rhesus macaques

Understanding how organisms make transitive inferences is critical to understanding their general ability to learn serial relationships. In this context, transitive inference (TI) can be understood as a specific heuristic that applies broadly to many different serial learning tasks, which have been the focus of hundreds of studies involving dozens of species. In the present study, monkeys learned the order of 7-item lists of photographic stimuli by trial and error, and were then tested on "derived" lists. These derived test lists combined stimuli from multiple training lists in ambiguous ways, sometimes changing their order relative to training. We found that subjects displayed strong preferences when presented with novel test pairs, even when those pairs were drawn from different training lists. These preferences were helpful when test pairs had an ordering congruent with their ranks during training, but yielded consistently below-chance performance when pairs had an incongruent order relative to training. This behavior can be explained by the joint contributions of transitive inference and another heuristic that we refer to as "positional inference." Positional inferences play a complementary role to transitive inferences in facilitating choices between novel pairs of stimuli. The theoretical framework that best explains both transitive and positional inferences is a spatial model that represents both the position of each stimulus and its uncertainty. A computational implementation of this framework yields accurate predictions about both correct responses and errors on derived lists.

Associative models fail to characterize transitive inference performance in rhesus monkeys (Macaca mulatta)

It has been suggested that non-verbal transitive inference (if A > B and B > C, then A > C) can be accounted for by associative models. However, little is known about the applicability of such models to primate data. In Experiment 1, we tested the fit of two associative models to primate data from both sequential training, in which the training pairs were presented in a backward order, and simultaneous training, in which all training pairs are presented intermixed from the beginning. We found that the models provided an equally poor fit for both sequential and simultaneous training presentations, contrary to the case with data from pigeons. The models were also unable to predict the robust symbolic distance effects characteristic of primate transitive choices. In Experiment 2, we used the models to fit a list-linking design in which two seven-item transitive lists were first trained independently (A > B…. > F > G and H > I …. > M > N) then combined via a linking pair (G+ H-) into a single, 14-item list. The model produced accurate predictions for between-list pairs, but did not predict transitive responses for within-list pairs from list 2. Overall, our results support research indicating that associative strength does not adequately account for the behavior of primates in transitive inference tasks. The results also suggest that transitive choices may result from different processes, or different weighting of multiple processes, across species.

Learned Representation of Implied Serial Order in Posterior Parietal Cortex

Monkeys can learn the implied ranking of pairs of images drawn from an ordered set, despite never seeing all of the images simultaneously and without explicit spatial or temporal cues. We recorded the activity of posterior parietal cortex (including lateral intraparietal area LIP) neurons while monkeys learned 7-item transitive inference (TI) lists with 2 items presented on each trial. Behavior and neuronal activity were significantly influenced by the ordinal relationship of the stimulus pairs, specifically symbolic distance (the difference in rank) and joint rank (the sum of the ranks). Symbolic distance strongly predicted decision accuracy and learning rate. An effect of joint rank on performance was found nested within the symbolic distance effect. Across the population of neurons, there was significant modulation of firing correlated with the relative ranks of the two stimuli presented on each trial. Neurons exhibited selectivity for stimulus rank during learning, but not before or after. The observed behavior is poorly explained by associative or reward mechanisms, and appears more consistent with a mental workspace model in which implied serial order is mapped within a spatial framework. The neural data suggest that posterior parietal cortex supports serial learning by representing information about the ordinal relationship of the stimuli presented during a given trial.

The Effect of Retrieval Practice on Transitive Inference

Abstract. Compared to restudying, retrieval practice has often been found to enhance memory (the testing effect). However, it has been proposed that materials with high element interactivity may not benefit from retrieval practice. Transitive inference (TI) requires just such interactivity, in which information must be combined across multiple learning elements or premises. The current study employed a 7-element TI paradigm in which participants initially learned a set of premises (e.g., A > B, B > C, C > D, etc.), then engaged in either restudy or retrieval practice with the premises, and then were given a final test that assessed memory for the original premises and one’s ability to make transitive inferences about them (e.g., to infer that B > D). Three experiments examined TI on final tests with retention intervals of a few minutes (Experiment 1), 2 days (Experiment 2), or up to a week (Experiment 3). Retrieval practice consistently failed to enhance transitive inference. Furthermore, retrieval practice significantly reduced TI in Experiment 1. Across experiments, TI was numerically worse in the retrieval-practice than restudy condition in 4 of 5 comparisons, and a small-scale meta-analysis revealed a significant negative effect of retrieval practice on TI.

Discovering Implied Serial Order Through Model-Free and Model-Based Learning

Humans and animals can learn to order a list of items without relying on explicit spatial or temporal cues. To do so, they appear to make use of transitivity, a property of all ordered sets. Here, we summarize relevant research on the transitive inference (TI) paradigm and its relationship to learning the underlying order of an arbitrary set of items. We compare six computational models of TI performance, three of which are model-free (Q-learning, Value Transfer, and REMERGE) and three of which are model-based (RL-Elo, Sequential Monte Carlo, and Betasort). Our goal is to assess the ability of these models to produce empirically observed features of TI behavior. Model-based approaches perform better under a wider range of scenarios, but no single model explains the full scope of behaviors reported in the TI literature.

Reward associations do not explain transitive inference performance in monkeys

Most accounts of behavior in nonhuman animals assume that they make choices to maximize expected reward value. However, model-free reinforcement learning based on reward associations cannot account for choice behavior in transitive inference paradigms. We manipulated the amount of reward associated with each item of an ordered list, so that maximizing expected reward value was always in conflict with decision rules based on the implicit list order. Under such a schedule, model-free reinforcement algorithms cannot achieve high levels of accuracy, even after extensive training. Monkeys nevertheless learned to make correct rule-based choices. These results show that monkeys' performance in transitive inference paradigms is not driven solely by expected reward and that appropriate inferences are made despite discordant reward incentives. We show that their choices can be explained by an abstract, model-based representation of list order, and we provide a method for inferring the contents of such representations from observed data.

Inferential Learning of Serial Order of Perceptual Categories by Rhesus Monkeys (Macaca mulatta)

Category learning in animals is typically trained explicitly, in most instances by varying the exemplars of a single category in a matching-to-sample task. Here, we show that male rhesus macaques can learn categories by a transitive inference paradigm in which novel exemplars of five categories were presented throughout training. Instead of requiring decisions about a constant set of repetitively presented stimuli, we studied the macaque's ability to determine the relative order of multiple exemplars of particular stimuli that were rarely repeated. Ordinal decisions generalized both to novel stimuli and, as a consequence, to novel pairings. Thus, we showed that rhesus monkeys could learn to categorize on the basis of implied ordinal position, without prior matching-to-sample training, and that they could then make inferences about category order. Our results challenge the plausibility of association models of category learning and broaden the scope of the transitive inference paradigm.SIGNIFICANCE STATEMENT The cognitive abilities of nonhuman animals are of enduring interest to scientists and the general public because they blur the dividing line between human and nonhuman intelligence. Categorization and sequence learning are highly abstract cognitive abilities each in their own right. This study is the first to provide evidence that visual categories can be ordered serially by macaque monkeys using a behavioral paradigm that provides no explicit feedback about category or serial order. These results strongly challenge accounts of learning based on stimulus-response associations.