Volume parameterizations abound in recent literature, encompassing methods from classic voxel grids to implicit neural representations. While implicit representations offer impressive capacity and improved memory efficiency compared to voxel grids, they traditionally require training through nonconvex optimization, which can be slow and sensitive to initialization and hyperparameters. We introduce GA-Planes, a novel family of implicit neural volume representations inspired by Geometric Algebra that can be trained using convex optimization, addressing the limitations of nonconvex methods. GA-Planes models generalize many existing representations including any combination of features stored in tensor basis elements followed by a neural feature decoder, and can be adapted to convex or nonconvex training as needed for various inverse problems. In the 2D setting, we prove GA-Planes models are equivalent to a low-rank plus low-resolution matrix factorization that outperforms the classic low-rank plus sparse decomposition for fitting a natural image. In 3D, GA-Planes models exhibit competitive expressiveness, model size, and optimizability across tasks such as radiance field reconstruction, 3D segmentation, and video segmentation.

Learning-based methods offer performance leaps over traditional methods in classification analysis of high-dimensional functional MRI (fMRI) data. In this domain, deep-learning models that analyze functional connectivity (FC) features among brain regions have been particularly promising. However, many existing models receive as input temporally static FC features that summarize inter-regional interactions across an entire scan, reducing the temporal sensitivity of classifiers by limiting their ability to leverage information on dynamic FC features of brain activity. To improve the performance of baseline classification models without compromising efficiency, here we propose a novel plug-in based on a graph neural network, GraphCorr, to provide enhanced input features to baseline models. The proposed plug-in computes a set of latent FC features with enhanced temporal information while maintaining comparable dimensionality to static features. Taking brain regions as nodes and blood-oxygen-level-dependent (BOLD) signals as node inputs, GraphCorr leverages a node embedder module based on a transformer encoder to capture dynamic latent representations of BOLD signals. GraphCorr also leverages a lag filter module to account for delayed interactions across nodes by learning correlational features of windowed BOLD signals across time delays. These two feature groups are then fused via a message passing algorithm executed on the formulated graph. Comprehensive demonstrations on three public datasets indicate improved classification performance for several state-of-the-art graph and convolutional baseline models when they are augmented with GraphCorr.