LieConv continuous-data group convolutions

What changed

Lifts continuous coordinates into a Lie group and parameterizes convolution kernels through its Lie algebra, enabling local learned convolutions on irregularly sampled data.

Scientific scope

Lifts continuous coordinates into a Lie group and parameterizes convolution kernels through its Lie algebra, enabling local learned convolutions on irregularly sampled data. Original construction restricts to groups with surjective exponential maps and appropriate lifting/sampling. Monte Carlo convolution is equivariant in distribution, not every finite random realization exactly equivariant. No unrestricted all-Lie-group or integrator-level energy conservation claim; inherits group convolution and efficient PointConv.

Evidence

The linked original sources describe the stated contribution and its evidence limits. WRS has not independently rerun the experiments or certified a proof. Original construction restricts to groups with surjective exponential maps and appropriate lifting/sampling. Monte Carlo convolution is equivariant in distribution, not every finite random realization exactly equivariant. No unrestricted all-Lie-group or integrator-level energy conservation claim; inherits group convolution and efficient PointConv.

Contributors

• Source-listed authors and technical contributors · SCIENCE: Source-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.

• Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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