arXiv:2510.14007v2 Announce Type: replace-cross Abstract: We introduce Conditional Clifford-Steerable CNNs (C-CSCNNs), a unified framework that incorporates equivariance to arbitrary pseudo-Euclidean groups and significantly improves the expressivity of standard CSCNNs. We show that the kernel basis of the standard formulation is incomplete, limiting model capacity. To address this, we augment the kernels with equivariant representations of the input feature field. We derive the equivariance constraint for these input-dependent kernels and show how it can be solved efficiently via implicit par
The continuous evolution of AI research pushes for more robust and efficient architectures, making improvements in CNNs for complex tasks like PDE modeling a natural progression.
Improving CNNs for tasks like PDE modeling could unlock significant advancements in scientific simulations, engineering design, and potentially, the development of more generalizable AI agents.
The proposed C-CSCNNs offer a more expressive and complete framework for equivariant CNNs, potentially leading to more accurate and efficient models for physical phenomena.
- · AI researchers
- · Scientific computing sector
- · Engineering and simulation industries
- · Drug discovery and materials science
- · Traditional non-equivariant CNN approaches
- · Inefficient PDE solving methods
More accurate and faster simulations of complex physical systems will become possible.
This could accelerate R&D cycles in fields currently bottlenecked by computational modeling.
Reduced time and cost in design and discovery could lead to entirely new products and industries.
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Read at arXiv cs.AI