An O(L^3) algorithm computes contracted Clebsch-Gordan tensor products for equivariant ML potentials using a structured angular grid and spherical Poisson bracket to handle parity-odd terms at fixed CP rank.
Spherical CNNs
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective. In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.
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Mapped convolutions generalize standard convolutions by decoupling sampling and weighting, enabling direct convolution on spherical and mesh data with a 17% improvement in spherical depth estimation.
SurReal architecture applies weighted Fréchet mean convolution and distance-based FC layers to complex data, improving accuracy on MSTAR (94% to 98%) and RadioML with 8-10% of baseline model size.
GSNO uses position-dependent spherical Green's functions to create flexible neural operators that adapt to non-equivariant systems on spheres while keeping spectral efficiency and grid invariance.
TetraSphere integrates a TetraTransform based on steerable spherical neurons into VN-DGCNN to produce an O(3)-equivariant descriptor that reports new SOTA results on rotated ScanObjectNN, ModelNet40 classification, and ShapeNet segmentation.
Spherical CNNs with deformation-augmented training data achieve faster and more accurate cortical parcellation than multi-atlas or naive U-Net methods on 427 adult brains.
Sphere-Depth benchmark shows substantial performance degradation in both general and spherical-aware depth estimation models under simulated camera pose variations.
Geometric deep learning provides a unified mathematical framework based on grids, groups, graphs, geodesics, and gauges to explain and extend neural network architectures by incorporating physical regularities.
citing papers explorer
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Fast contracted Clebsch--Gordan tensor products for equivariant graph neural networks
An O(L^3) algorithm computes contracted Clebsch-Gordan tensor products for equivariant ML potentials using a structured angular grid and spherical Poisson bracket to handle parity-odd terms at fixed CP rank.
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Mapped Convolutions
Mapped convolutions generalize standard convolutions by decoupling sampling and weighting, enabling direct convolution on spherical and mesh data with a 17% improvement in spherical depth estimation.
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SurReal: Fr\'echet Mean and Distance Transform for Complex-Valued Deep Learning
SurReal architecture applies weighted Fréchet mean convolution and distance-based FC layers to complex data, improving accuracy on MSTAR (94% to 98%) and RadioML with 8-10% of baseline model size.
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Generalized Spherical Neural Operators: Green's Function Formulation
GSNO uses position-dependent spherical Green's functions to create flexible neural operators that adapt to non-equivariant systems on spheres while keeping spectral efficiency and grid invariance.
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TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis
TetraSphere integrates a TetraTransform based on steerable spherical neurons into VN-DGCNN to produce an O(3)-equivariant descriptor that reports new SOTA results on rotated ScanObjectNN, ModelNet40 classification, and ShapeNet segmentation.
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Cortical Surface Parcellation using Spherical Convolutional Neural Networks
Spherical CNNs with deformation-augmented training data achieve faster and more accurate cortical parcellation than multi-atlas or naive U-Net methods on 427 adult brains.
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Sphere-Depth: A Benchmark for Depth Estimation Methods with Varying Spherical Camera Orientations
Sphere-Depth benchmark shows substantial performance degradation in both general and spherical-aware depth estimation models under simulated camera pose variations.
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Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
Geometric deep learning provides a unified mathematical framework based on grids, groups, graphs, geodesics, and gauges to explain and extend neural network architectures by incorporating physical regularities.