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This paper introduces a framework linking sheaf cohomology with E(3)-equivariant neural networks for predicting molecular Hamiltonians, proposing Equivariant Cellular Sheaf Networks that generalize existing methods and provide topological insights.
This controlled study compares geometric algebra (Cl(3,0)) layers against a minimal scalarization baseline for SO(3)-equivariant vector learning, finding that geometric algebra adds no benefit for single-stage tasks but significantly beats scalarization in low-data regimes for deeply composed group operations.
This paper shows that the geometric symmetry visible from neural network weights depends on the positional encoding and readout observable, and validates this using MLPs trained on 2D signed distance functions with multiple symmetry groups.
This paper proposes Equivariant Poincaré ResNets, combining hyperbolic geometry with discrete symmetry groups to improve efficiency in learning visual representations by treating rotated features as symmetric rather than distinct hierarchical concepts.