Research map / Learning theory and algorithms / Kernels and regression theory
Provably Strict Generalisation Benefit for Equivariant Models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Enforce equivariance by projecting the minimum-norm least-squares predictor onto the equivariant subspace | Linear least-squares regression with an equivariant target · Invariant input distribution | test squared error | Helped |
| Enforce invariance by projecting the minimum-norm least-squares predictor onto the invariant subspace | Linear least-squares regression with an invariant target · Isotropic Gaussian inputs | test squared error | Helped |
| Orbit-average a learned predictor at test time | A predictor for an invariant target · Invariant input distribution | test squared error | Helped |
| Orbit-average the function class | A function class evaluated on a group-invariant distribution · Group-invariant data distribution | Rademacher complexity | Helped |
| Use a non-invariant input distribution | Orbit averaging as an orthogonal projection · General function space | orthogonality of symmetric and anti-symmetric components | Hurt |
| Use equivariant weight tying in place of unconstrained weights | ReLU neural networks · Invariant or equivariant prediction | VC dimension | Helped |
| Regularise the anti-symmetric component of each layer's weights | Neural network layers · Invariant or equivariant prediction | distance to the closest equivariant function | Helped |
Closest papers by meaning
- Equivariant Frames and the Impossibility of Continuous Canonicalization (ICML 2024 · similarity 0.87)
- A Canonicalization Perspective on Invariant and Equivariant Learning (NeurIPS 2024 · similarity 0.87)
- Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions (NeurIPS 2025 · similarity 0.87)
- On Universality Classes of Equivariant Networks (NeurIPS 2025 · similarity 0.86)
- Lie Group Decompositions for Equivariant Neural Networks (ICLR 2024 · similarity 0.85)
- Approximately Equivariant Neural Processes (NeurIPS 2024 · similarity 0.85)
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