RESUMO
Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the axes effectively shrinks their radii, revealing a duality between correlations and geometry with respect to the problem of classification. We then apply our results to accurately estimate the capacity of deep network data.
RESUMO
BACKGROUND: Prenatal exposure to persistent organic pollutants (POPs), widespread in North America, is associated with increased Attention Deficit/Hyperactivity Disorder (ADHD) symptoms and may be a modifiable risk for ADHD phenotypes. However, the effects of moderate exposure to POPs on task-based inhibitory control performance, related brain function, and ADHD-related symptoms remain unknown, limiting our ability to develop interventions targeting the neural impact of common levels of exposure. OBJECTIVES: The goal of this study was to examine the association between prenatal POP exposure and inhibitory control performance, neural correlates of inhibitory control and ADHD-related symptoms. METHODS: Prospective data was gathered in an observational study of Canadian mother-child dyads, with moderate exposure to POPs, including polychlorinated biphenyls (PCBs) and polybrominated diphenyl ethers (PBDEs), as part of the GESTation and the Environment (GESTE) cohort in Sherbrooke, Quebec, Canada. The sample included 87 eligible children, 46 with maternal plasma samples, functional magnetic resonance imaging (fMRI) data of Simon task performance at 9-11 years, and parental report of clinical symptoms via the Behavioral Assessment System for Children 3 (BASC-3). Simon task performance was probed via drift diffusion modeling, and parameter estimates were related to POP exposure. Simon task-based fMRI data was modeled to examine the difference in incongruent vs congruent trials in regions of interest (ROIs) identified by meta analysis. RESULTS: Of the 46 participants with complete data, 29 were male, and mean age was 10.42 ± 0.55 years. Increased POP exposure was associated with reduced accuracy (e.g. PCB molar sum rate ratio = 0.95; 95% CI [0.90, 0.99]), drift rate (e.g. for PCB molar sum ß = -0.42; 95% CI [-0.77, -0.07]), and task-related brain activity (e.g. in inferior frontal cortex for PCB molar sum ß = -0.35; 95% CI [-0.69, -0.02]), and increased ADHD symptoms (e.g. hyperactivity PCB molar sum ß = 2.35; 95%CI [0.17, 4.53]), supporting the possibility that prenatal exposure to POPs is a modifiable risk for ADHD phenotypes. DISCUSSION: We showed that exposure to POPs is related to task-based changes in neural activity in brain regions important for inhibitory control, suggesting a biological mechanism underlying previously documented associations between POPs and neurobehavioral deficits found in ADHD phenotypes.