arXiv:2511.18417v2 Announce Type: replace-cross
Abstract: We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a topological category with Radon measures. Formulating linear and nonlinear layers in the categorical setup, we prove the equivariant universal approximation theorem in the general setting: the class of finite-depth CENNs is dense in the space of continuous equivariant transformations. We instantiate the framework for groups/groupoids, posets/lattices, graphs and cellular sheaves, deriving universal approximation theorems for them in a systematic manner. Categorical equivariant deep learning thus allows us to expand the horizons of equivariant deep learning beyond group actions, encompassing not only geometric symmetries but also contextual and compositional symmetries.
Just-In-Time Adaptive Interventions for Weight Management Among Adults With Excess Body Weight: Scoping Review
Background: Just-in-time adaptive interventions (JITAIs) use real-time monitoring to deliver personalized support at optimal moments, demonstrating potential for improving lifestyle behaviors in weight management. Objective: