Latent Representations of Early Brain Development: A Multivariate Normative Model of Brian Structure and Behaviour

Individual variation in neurodevelopment plays a central role in shaping cognitive abilities and behavioural profiles, influencing both typical functioning and risk for neurodevelopmental conditions. While much research has focused on characterising trajectories of brain structure changes during development, this typically entails assessing brain regions individually, overlooking the multivariate nature of neuroimaging data. In this study, we trained an autoencoder to map latent representations of childrens brain development using T1-weighted MRI scans from a paediatric cohort (n = 564, 55% male, mean age 4.90 years, age range [0.11,15.38]). This approach enabled us to establish multivariate normative models of brain structure, providing a more comprehensive framework for understanding neurodevelopmental variation. The latent space representation from this model effectively captured demographic variables (age and sex), while preserving both global and local structural features. The model accurately reconstructed the data, having mean reconstruction of 0.04 {+/-} 0.01, whilst also capturing demographic features with classification accuracy for sex of 84% {+/-} 4%, and a mean absolute error of 0.79 {+/-} 0.06 years for age prediction, highlighting its sensitivity to developmental changes. Further, we validated the approach using correlation analysis to show that deviations from the latent norms were significantly associated with multiple cognitive and behavioural measures, suggesting that variations in brain structure may reflect individual differences in neurodevelopment. Finally, we generated reference brain images that represent typical development and used them to visualise structural differences in individuals who deviate from this normative pattern. Our findings demonstrate that semi-supervised autoencoders, combined with multivariate normative modelling, offer a framework for characterizing neurodevelopmental trajectories. This approach can identify meaningful deviations associated with cognition and behaviour and has potential future applications across the lifespan.