Mathematical learning disabilities (MLD) affect up to 14% of school-age children, yet the underlying neurocognitive mechanisms remain elusive. We developed drift diffusion model with dynamic performance monitoring (DDM-DPM), an innovative cognitive model that captures both external and internal sources of structural variability in task performance. Combining DDM-DPM with functional brain imaging, we examined symbolic and nonsymbolic quantity discrimination in female and male children with MLD and typically developing children matched on age, gender, and IQ. Children with MLD showed format-dependent alterations in response caution and posterror adjustment, despite similar observed performance measures between groups. The latent cognitive processes during symbolic quantity discrimination predicted broader mathematical abilities better than those during nonsymbolic quantity discrimination. Neuroimaging results revealed that reduced activity in middle frontal gyrus mediated deficits in response caution in symbolic format, while reduced activity in the anterior cingulate cortex mediated deficits in posterror adjustment in symbolic format in children with MLD. These findings provide novel support for a multidimensional deficit view of MLD that extends beyond basic number processing to include metacognitive processes. Our findings also provide novel support for and extend the access deficit model, which posits that individuals with MLD may have relatively intact quantity representations but struggle with numerical representations in symbolic formats. Our study highlights the value of integrating latent cognitive modeling with neuroimaging to reveal subtle mechanisms underlying learning disabilities and identify potential targets for intervention.

Nonergodicity and Simpson's paradox present significant, yet underappreciated challenges in cognitive neuroscience. Leveraging brain imaging and behavioral data from over 4000 individuals and a Bayesian computational model of cognitive dynamics, we investigated brain-behavior relationships underlying cognitive control at both between-subjects and within-subjects levels. Strikingly, brain-behavior associations reversed across levels of analysis, revealing pervasive nonergodicity. Within-subjects analysis uncovered dissociated neural representations of reactive and proactive control and revealed that individuals who adaptively versus maladaptively regulated cognitive control exhibited distinct brain-behavior associations. Our findings demonstrate that between-subjects analyses can fundamentally mischaracterize within-individuals mechanisms, as group-level patterns not only disagreed with individual-level patterns but often reversed them. This work highlights the necessity of distinguishing between-subjects and within-subjects inferences in neuroscience, with implications for understanding cognitive mechanisms and designing personalized interventions.

Learning disabilities affect a substantial proportion of children worldwide, with far-reaching consequences for their academic, professional, and personal lives. Here we develop digital twins—biologically plausible personalized deep neural networks (pDNNs)—to investigate the neurophysiological mechanisms underlying learning disabilities in children. Our pDNN reproduces behavioral and neural activity patterns observed in affected children, including lower performance accuracy, slower learning rates, neural hyperexcitability, and reduced neural differentiation of numerical problems. Crucially, pDNN models reveal aberrancies in the geometry of manifold structure, providing a comprehensive view of how neural excitability influences both learning performance and the internal structure of neural representations. Our findings not only advance knowledge of the neurophysiological underpinnings of learning differences but also open avenues for targeted, personalized strategies designed to bridge cognitive gaps in affected children. This work reveals the power of digital twins integrating artificial intelligence and neuroscience to uncover mechanisms underlying neurodevelopmental disorders.

Children exhibit remarkable variability in their mathematical problem-solving abilities, yet the cognitive, metacognitive and affective mechanisms underlying these individual differences remain poorly understood. We developed a novel Bayesian model of arithmetic problem-solving (BMAPS) to uncover the latent processes governing children's arithmetic strategy choice and efficiency. BMAPS inferred cognitive parameters related to strategy execution and metacognitive parameters related to strategy selection, revealing key mechanisms of adaptive problem solving. BMAPS parameters collectively explained individual differences in problem-solving performance, predicted longitudinal gains in arithmetic fluency and mathematical reasoning, and mediated the effects of anxiety and attitudes on performance. Clustering analyses using BMAPS parameters revealed distinct profiles of strategy use, metacognitive efficiency, and developmental change. By quantifying the fine-grained dynamics of strategy selection and execution and their relation to affective factors and academic outcomes, BMAPS provides new insights into the cognitive and metacognitive underpinnings of children's mathematical learning. This work advances powerful computational methods for uncovering latent mechanisms of complex cognition in children.

The brain's ability to detect behaviorally relevant stimuli from sensory inputs is fundamental to cognition, yet the neural mechanisms linking synaptic processes to event-related potential (ERP) signatures remain unclear. Here, we develop recurrent neural network (RNN) models of ERP responses demonstrating that short-term synaptic depression - a ubiquitous plasticity mechanism - provides a unified computational framework for mismatch negativity (MMN) and P300 responses across passive and active oddball paradigms. Our models reveal that neural populations spontaneously organize stimulus representations into probability-dependent geometric manifolds, where rare events occupy expanded state space. Hierarchical connectivity creates 9-fold signal amplification with enhanced noise robustness, explaining P300's functional advantages over sensory responses. Critically, the same synaptic mechanism accounts for attentional modulation of behaviorally relevant stimuli, providing the first unified explanation bridging automatic and controlled attention. This framework offers quantitative predictions for how synaptic and connectivity disruptions manifest as altered MMN and P300 characteristics in neuropsychiatric disorders including schizophrenia and autism.

The mapping between nonsymbolic quantities and symbolic numbers lays the foundation for mathematical development in children. However, the neural mechanisms underlying this crucial cognitive bridge remain unclear. Here, we investigate the computational principles governing symbolic-nonsymbolic integration using a biologically inspired neural network trained through developmentally inspired stages. Our investigation reveals that generalization from nonsymbolic to symbolic numerical processing emerges specifically when representational alignment forms between these numerical formats. Notably, this alignment appears to be stronger in cross-format comparison-based mapping compared to direct-label-based mapping. Furthermore, we demonstrate that subsequent symbolic specialization creates a representational divergence that impairs nonsymbolic performance while maintaining the ordinal structure of the mapping. These findings highlight representational alignment as a fundamental mechanism in numerical cognition and suggest that targeted cross-format comparison tasks may be particularly effective in improving mathematical learning in children with numerical processing difficulties.

We developed a novel Proactive Reactive and Attentional Dynamics (PRAD) computational model designed to dissect the latent mechanisms of inhibitory control in human cognition. Leveraging data from over 7,500 participants in the NIH Adolescent Brain Cognitive Development study, we demonstrate that PRAD surpasses traditional models by integrating proactive, reactive, and attentional components of inhibitory control. Employing a hierarchical Bayesian framework, PRAD offers a granular view of the dynamics underpinning action execution and inhibition, provides debiased estimates of stop-signal reaction times, and elucidates individual and temporal variability in cognitive control processes. Our findings reveal significant intra-individual variability, challenging conventional assumptions of random variability across trials. By addressing nonergodicity and systematically accounting for the multi-componential nature of cognitive control, PRAD advances our understanding of the cognitive mechanisms driving individual differences in cognitive control and provides a sophisticated computational framework for dissecting dynamic cognitive processes across diverse populations. ### Competing Interest Statement The authors have declared no competing interest.

The default mode network (DMN) is a large-scale brain network known to be suppressed during a wide range of cognitive tasks. However, our comprehension of its role in naturalistic and unconstrained behaviors has remained elusive because most research on the DMN has been conducted within the restrictive confines of MRI scanners. Here, we use multisite GCaMP (a genetically encoded calcium indicator) fiber photometry with simultaneous videography to probe DMN function in awake, freely exploring rats. We examined neural dynamics in three core DMN nodes—the retrosplenial cortex, cingulate cortex, and prelimbic cortex—as well as the anterior insula node of the salience network, and their association with the rats’ spatial exploration behaviors. We found that DMN nodes displayed a hierarchical functional organization during spatial exploration, characterized by stronger coupling with each other than with the anterior insula. Crucially, these DMN nodes encoded the kinematics of spatial exploration, including linear and angular velocity. Additionally, we identified latent brain states that encoded distinct patterns of time-varying exploration behaviors and found that higher linear velocity was associated with enhanced DMN activity, heightened synchronization among DMN nodes, and increased anticorrelation between the DMN and anterior insula. Our findings highlight the involvement of the DMN in collectively and dynamically encoding spatial exploration in a real-world setting. Our findings challenge the notion that the DMN is primarily a “task-negative” network disengaged from the external world. By illuminating the DMN’s role in naturalistic behaviors, our study underscores the importance of investigating brain network function in ecologically valid contexts.

Nonergodicity and Simpson’s paradox pose significant and underappreciated challenges for neuroscience. Using stop signal task data from over 4,000 children and a Bayesian computational model of cognitive dynamics, we investigated brain-behavior relationships underlying inhibitory control at both between-subjects and within-subjects levels. Strikingly, between-subjects associations of inhibitory control activations with stop signal reaction times, probabilities of proactivity, and proactive delays were reversed within subjects, revealing the nonergodic nature of these processes. Nonergodicity was observed throughout the brain but was most pronounced in the salience network. Furthermore, within-subjects analysis revealed dissociated brain representations of reactive and proactive processing, and distinct brain-behavior associations for subjects who adaptively and who maladaptively regulated inhibitory control. This work advances our knowledge of the dynamic neural mechanisms of inhibitory control during a critical developmental period and has implications for personalized interventions in cognitive disorders. Embracing nonergodicity is crucial for understanding brain-behavior relationships and developing effective interventions. ### Competing Interest Statement The authors have declared no competing interest.

Learning disabilities affect a significant proportion of children worldwide, with far-reaching consequences for their academic, professional, and personal lives. Here we develop digital twins - biologically plausible personalized Deep Neural Networks (pDNNs) - to investigate the neurophysiological mechanisms underlying learning disabilities in children. Our pDNN reproduces behavioral and neural activity patterns observed in affected children, including lower performance accuracy, slower learning rates, neural hyper-excitability, and reduced neural differentiation of numerical problems. Crucially, pDNN models reveal aberrancies in the geometry of manifold structure, providing a comprehensive view of how neural excitability influences both learning performance and the internal structure of neural representations. Our findings not only advance knowledge of the neurophysiological underpinnings of learning differences but also open avenues for targeted, personalized strategies designed to bridge cognitive gaps in affected children. This work reveals the power of digital twins integrating AI and neuroscience to uncover mechanisms underlying neurodevelopmental disorders.

Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.

The circular drift-diffusion model (CDDM) is a sequential sampling model designed to account for decisions and response times in decision-making tasks with a circular set of choice alternatives. We present and demonstrate a fully Bayesian implementation and extension of the CDDM. This development allows researchers to apply the CDDM to data from complex experiments and draw conclusions about targeted hypotheses. The Bayesian implementation relies on a custom JAGS module. We describe the module and demonstrate its adequacy through a simulation study. We then illustrate the advantages of the implementation by revisiting data from a continuous orientation judgment task. We develop a graphical model for the analysis that is based on the CDDM, but extends it with hierarchical and latent-mixture structures.We then demonstrate how these extensions are used to accommodate the design of the experiment and to implement psychological assumptions about individual differences, the difficulty of different stimulus conditions, and the impact of cues on decision making. Finally, we demonstrate how the computational Bayesian inference enabled by JAGS allows these assumptions to be tested and addresses psychological research questions about people's decision making.

The n-back task is a widely used behavioral task for measuring working memory and the ability to inhibit interfering information. We develop a novel model of the commonly used 2-back task using the cognitive psychometric framework provided by Multinomial Processing Trees. Our model involves three parameters: a memory parameter, corresponding to how well an individual encodes and updates sequence information about presented stimuli; a decision parameter corresponding to how well participants execute choices based on information stored in memory; and a base-rate parameter corresponding to bias for responding “yes” or “no”. We test the parameter recovery properties of the model using existing 2-back experimental designs, and demonstrate the application of the model to two previous data sets: one from social psychology involving faces corresponding to different races (Stelter and Degner, British Journal of Psychology 109:777–798, 2018), and one from cognitive neuroscience involving more than 1000 participants from the Human Connectome Project (Van Essen et al., Neuroimage 80:62–79, 2013). We demonstrate that the model can be used to infer interpretable individual-level parameters. We develop a hierarchical extension of the model to test differences between stimulus conditions, comparing faces of different races, and comparing face to non-face stimuli. We also develop a multivariate regression extension to examine the relationship between the model parameters and individual performance on standardized cognitive measures including the List Sorting and Flanker tasks. We conclude by discussing how our model can be used to dissociate underlying cognitive processes such as encoding failures, inhibition failures, and binding failures.

The social worlds of young children primarily revolve around parents and caregivers, who play a key role in guiding children's social and cognitive development. However, a hallmark of adolescence is a shift in orientation toward nonfamilial social targets, an adaptive process that prepares adolescents for their independence. Little is known regarding neurobiological signatures underlying changes in adolescents' social orientation. Using functional brain imaging of human voice processing in children and adolescents (ages 7-16), we demonstrate distinct neural signatures for mother's voice and nonfamilial voices across child and adolescent development in reward and social valuation systems, instantiated in nucleus accumbens and ventromedial prefrontal cortex. While younger children showed greater activity in these brain systems for mother's voice compared with nonfamilial voices, older adolescents showed the opposite effect with increased activity for nonfamilial compared with mother's voice. Findings uncover a critical role for reward and social valuative brain systems in the pronounced changes in adolescents' orientation toward nonfamilial social targets. Our approach provides a template for examining developmental shifts in social reward and motivation in individuals with pronounced social impairments, including adolescents with autism. SIGNIFICANCE STATEMENT Children's social worlds undergo a transformation during adolescence. While socialization in young children revolves around parents and caregivers, adolescence is characterized by a shift in social orientation toward nonfamilial social partners. Here we show that this shift is reflected in neural activity measured from reward processing regions in response to brief vocal samples. When younger children hear their mother's voice, reward processing regions show greater activity compared with when they hear nonfamilial, unfamiliar voices. Strikingly, older adolescents show the opposite effect, with increased activity for nonfamilial compared with mother's voice. Findings identify the brain basis of adolescents' switch in social orientation toward nonfamilial social partners and provides a template for understanding neurodevelopment in clinical populations with social and communication difficulties.

Restricted and repetitive behaviors (RRBs) are a defining clinical feature of autism spectrum disorders (ASD). RRBs are highly heterogeneous with variable expression of circumscribed interests (CI), insistence of sameness (IS) and repetitive motor actions (RM), which are major impediments to effective functioning in individuals with ASD; yet, the neurobiological basis of CI, IS and RM is unknown. Here we evaluate a unified functional brain circuit model of RRBs and test the hypothesis that CI and IS are associated with aberrant cognitive control circuit dynamics, whereas RM is associated with aberrant motor circuit dynamics. Using task-free fMRI data from 96 children, we first demonstrate that time-varying cross-network interactions in cognitive control circuit are significantly reduced and inflexible in children with ASD, and predict CI and IS symptoms, but not RM symptoms. Furthermore, we show that time-varying cross-network interactions in motor circuit are significantly greater in children with ASD, and predict RM symptoms, but not CI or IS symptoms. We confirmed these results using cross-validation analyses. Moreover, we show that brain-clinical symptom relations are not detected with time-averaged functional connectivity analysis. Our findings provide neurobiological support for the validity of RRB subtypes and identify dissociable brain circuit dynamics as a candidate biomarker for a key clinical feature of ASD.

Mathematical knowledge is constructed hierarchically during development from a basic understanding of addition and subtraction, two foundational and inter-related, but semantically distinct, numerical operations. Early in development, children show remarkable variability in their numerical problem-solving skills and difficulties in solving even simple addition and subtraction problems are a hallmark of math learning difficulties. Here, we use novel quantitative analyses to investigate whether less distinct representations are associated with poor problem-solving abilities in children during the early stages of math-skill acquisition. Crucially, we leverage dimensional and categorical analyses to identify linear and nonlinear neurobehavioral profiles of individual differences in math skills. Behaviorally, performance on the two different numerical operations was less differentiated in children with low math abilities, and lower problem-solving efficiency stemmed from weak evidence-accumulation during problem-solving. Children with low numerical abilities also showed less differentiated neural representations between addition and subtraction operations in multiple cortical areas, including the fusiform gyrus, intraparietal sulcus, anterior temporal cortex and insula. Furthermore, analysis of multi-regional neural representation patterns revealed significantly higher network similarity and aberrant integration of representations within a fusiform gyrus-intraparietal sulcus pathway important for manipulation of numerical quantity. These findings identify the lack of distinct neural representations as a novel neurobiological feature of individual differences in children's numerical problem-solving abilities, and an early developmental biomarker of low math skills. More generally, our approach combining dimensional and categorical analyses overcomes pitfalls associated with the use of arbitrary cutoffs for probing neurobehavioral profiles of individual differences in math abilities.

Efficient memory-based problem-solving strategies are a cardinal feature of expertise across a wide range of cognitive domains in childhood. However, little is known about the neurocognitive mechanisms that underlie the acquisition of efficient memory-based problem-solving strategies. Here we develop, to the best of our knowledge, a novel neurocognitive process model of latent memory processes to investigate how cognitive training designed to improve children’s problem-solving skills alters brain network organization and leads to increased use and efficiency of memory retrieval-based strategies. We found that training increased both the use and efficiency of memory retrieval. Functional brain network analysis revealed training-induced changes in modular network organization, characterized by increase in network modules and reorganization of hippocampal-cortical circuits. Critically, training-related changes in modular network organization predicted performance gains, with emergent hippocampal, rather than parietal cortex, circuitry driving gains in efficiency of memory retrieval. Our findings elucidate a neurocognitive process model of brain network mechanisms that drive learning and gains in children’s efficient problem-solving strategies.

BACKGROUND:Anxiety and stress reactivity are risk factors for the development of affective disorders. However, the behavioral and neurocircuit mechanisms that potentiate maladaptive emotion regulation are poorly understood. Neuroimaging studies have implicated the amygdala and dorsolateral prefrontal cortex (DLPFC) in emotion regulation, but how anxiety and stress alter their context-specific causal circuit interactions is not known. Here, we use computational modeling to inform affective pathophysiology, etiology, and neurocircuit targets for early intervention.METHODS:Forty-five children (10-11 years of age; 25 boys) reappraised aversive stimuli during functional magnetic resonance imaging scanning. Clinical measures of anxiety and stress were acquired for each child. Drift-diffusion modeling of behavioral data and causal circuit analysis of functional magnetic resonance imaging data, with a National Institute of Mental Health Research Domain Criteria approach, were used to characterize latent behavioral and neurocircuit decision-making dynamics driving emotion regulation.RESULTS:Children successfully reappraised negative responses to aversive stimuli. Drift-diffusion modeling revealed that emotion regulation was characterized by increased initial bias toward positive reactivity during viewing of aversive stimuli and increased drift rate, which captured evidence accumulation during emotion evaluation. Crucially, anxiety and stress reactivity impaired latent behavioral dynamics associated with reappraisal and decision making. Anxiety and stress increased dynamic casual influences from the right amygdala to DLPFC. In contrast, DLPFC, but not amygdala, reactivity was correlated with evidence accumulation and decision making during emotion reappraisal.CONCLUSIONS:Our findings provide new insights into how anxiety and stress in children impact decision making and amygdala-DLPFC signaling during emotion regulation, and uncover latent behavioral and neurocircuit mechanisms of early risk for psychopathology.

Jeliazkov and Poirier (2008) analyze the daily incidence of violence during the Second Intifada in a statistical way using an analytical Bayesian implementation of a second-order discrete Markov process. We tackle the same data and modeling problem from our perspective as cognitive scientists. First, we propose a psychological model of violence, based on a latent psychological construct we call “build up” that controls the retaliatory and repetitive violent behavior by both sides in the conflict. Build up is based on a social memory of recent violence and generates the probability and intensity of current violence. Our psychological model is implemented as a generative probabilistic graphical model, which allows for fully Bayesian inference using computational methods. We show that our model is both descriptively adequate, based on posterior predictive checks, and has good predictive performance. We then present a series of results that show how inferences based on the model can provide insight into the nature of the conflict. These inferences consider the base rates of violence in different periods of the Second Intifada, the nature of the social memory for recent violence, and the way repetitive versus retaliatory violent behavior affects each side in the conflict. Finally, we discuss possible extensions of our model and draw conclusions about the potential theoretical and methodological advantages of treating societal conflict as a cognitive modeling problem.