Steerable Neural ODEs on Homogeneous Spaces

• URL: http://arxiv.org/abs/2605.11133v1
• Date: Mon, 11 May 2026 18:41:11 GMT
• Title: Steerable Neural ODEs on Homogeneous Spaces
• Abstract summary: We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$.<n>We show that steerable NODEs are $G$-equivariant whenever the vector field generating the flow and the connection governing parallel transport are both $G$-invariant.
• Score: 1.611271868398988
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport associated feature vectors transforming under the local symmetry group $H$. We interpret features as sections of associated vector bundles over $M$, and describe their evolution as parallel transport. This results in a coupled system of ODEs consisting of a flow equation on $M$ and a steering equation acting on features. We show that steerable NODEs are $G$-equivariant whenever the vector field generating the flow and the connection governing parallel transport are both $G$-invariant. Furthermore, we demonstrate how steerable NODEs incorporate existing NODE models and continuous normalizing flows on Lie groups. Our framework provides the geometric foundation for learning continuous-time equivariant dynamics of general vector-valued features on homogeneous spaces.

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