Spherical Harmonics
A set of orthogonal basis functions defined on the sphere, characterized by degree l representing angular momentum features. They are a core mathematical tool for constructing SO(3)-equivariant neural networks such as Tensor Field Networks.
Timeline (last 90 days)
The heat semigroup of spherical Brownian motion is generated by the Laplace-Beltrami operator, and its kernel can be expanded in spherical harmonics to give an analytical transition density.
DaFISH is a lighting disentanglement method that can be plugged into any novel view synthesis pipeline, representing lighting via spherical harmonics and decomposing each point's emitted color into surface albedo and an SH lighting factor.
The choice of SH order may affect the ability to capture lighting detail and requires a trade-off in practice.
Spherical harmonics are a set of orthogonal basis functions defined on the sphere, analogous to a generalization of Fourier series on the circle, and are commonly used to efficiently represent low-frequency directional lighting.
Complete-class certificates can distinguish SH0, SH1 and SH2 fits on a learned density.
For a set of residual isotropic spatial sources at fixed density, positive gain can be achieved on every fixed finite-order spherical harmonic.
Spherical harmonics characterize angular momentum by order l, where l=0 corresponds to scalars, l=1 corresponds to vectors, and higher orders correspond to tensor representations.
Legendre polynomials are a set of orthogonal polynomials defined on the interval [-1, 1], which generalize to spherical harmonics when extended to spherical coordinates.
When the activation function is ReLU, the target function is a pure spherical harmonic, and under Gaussian universality assumptions, the student's error scales approximately as the square of the teacher's error
The paper analyzes two extended settings: more general stopping times and target functions supported on multiple spherical harmonic orders
All Facts (10)
The heat semigroup of spherical Brownian motion is generated by the Laplace-Beltrami operator, and its kernel can be expanded in spherical harmonics to give an analytical transition density.
50%UnverifiedDaFISH is a lighting disentanglement method that can be plugged into any novel view synthesis pipeline, representing lighting via spherical harmonics and decomposing each point's emitted color into surface albedo and an SH lighting factor.
50%UnverifiedThe choice of SH order may affect the ability to capture lighting detail and requires a trade-off in practice.
50%UnverifiedSpherical harmonics are a set of orthogonal basis functions defined on the sphere, analogous to a generalization of Fourier series on the circle, and are commonly used to efficiently represent low-frequency directional lighting.
50%UnverifiedComplete-class certificates can distinguish SH0, SH1 and SH2 fits on a learned density.
50%UnverifiedFor a set of residual isotropic spatial sources at fixed density, positive gain can be achieved on every fixed finite-order spherical harmonic.
50%UnverifiedSpherical harmonics characterize angular momentum by order l, where l=0 corresponds to scalars, l=1 corresponds to vectors, and higher orders correspond to tensor representations.
50%UnverifiedLegendre polynomials are a set of orthogonal polynomials defined on the interval [-1, 1], which generalize to spherical harmonics when extended to spherical coordinates.
50%UnverifiedWhen the activation function is ReLU, the target function is a pure spherical harmonic, and under Gaussian universality assumptions, the student's error scales approximately as the square of the teacher's error
50%UnverifiedThe paper analyzes two extended settings: more general stopping times and target functions supported on multiple spherical harmonic orders
50%