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Implicit Bias of Linear Equivariant Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train a full-width linear G-CNN with gradient descent | Linear G-CNN · Linearly separable binary classification over finite groups | Fourier 2/L-Schatten norm | Helped |
| Use a band-limited linear G-CNN | Linear G-CNN · Linearly separable classification over compact Lie groups | Fourier 2/L-Schatten norm | Helped |
| Use equivariant group-convolution architecture rather than a fully connected network | G-CNN · Synthetic classification over D8 and D60; MNIST digits 1 and 5 | Fourier-space Schatten norm | Helped |
| Use a G-CNN rather than a standard CNN | G-CNN · Synthetic classification over D8 and D60; MNIST digits 1 and 5 | Fourier-space Schatten norm | Helped |
| Add ReLU nonlinearities between hidden layers | G-CNN · Synthetic classification, D60 | Local-linearization Fourier Schatten norm | Mixed |
| Use a nonlinear spherical CNN | Spherical CNN · Rotated spherical MNIST, SO(3) | Local-linearization Fourier Schatten norm | Mixed |
Closest papers by meaning
- Group Equivariant Convolutional Networks (ICML 2016 · similarity 0.92)
- Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts (ICML 2024 · similarity 0.91)
- Group Downsampling with Equivariant Anti-aliasing (ICLR 2025 · similarity 0.89)
- Lie Group Decompositions for Equivariant Neural Networks (ICLR 2024 · similarity 0.88)
- Equivariant Neural Tangent Kernels (ICML 2025 · similarity 0.88)
- Learning symmetries via weight-sharing with doubly stochastic tensors (NeurIPS 2024 · similarity 0.88)
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