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Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Measure capacity using the dimension of the group-fixed subspace | Equivariant representations with group-invariant linear readout · G-invariant binary classification | fraction of separable dichotomies | Helped |
| Use one trivial dimension per output filter | Standard periodic convolution · Standard periodic CNN layer | capacity scaling: P ∼ 2N | Helped |
| Replace the regular representation with a direct-sum representation contributing two trivial irreps per output channel | Equivariant convolution · Direct-sum equivariant convolution | capacity scaling: P ∼ 4N | Helped |
| Add local average pooling | Standard CNN · Local average pooling | fraction of separable dichotomies | No clear effect |
| Add local nonlinear pooling | Equivariant code · G-invariant classification after local nonlinear pooling | fraction of separable dichotomies: at least f(P, floor(N_0 / k)); at most f(P,N_0) | Hurt |
| Apply 2x2 max pooling | Random periodic convolutional layer after ReLU · Random convolutional layer | fraction of separable dichotomies: between 1/4 and 1 | Hurt |
| Apply 2x2 max pooling | VGG-11 pretrained on CIFAR-10 · CIFAR-10 | fraction of separable dichotomies | Hurt |
| Replace classification over the full group with classification invariant only to subgroup H | Pooled code with regular representation of H · H-invariant classification after local nonlinear pooling | fraction of separable dichotomies | Helped |
| Apply global average pooling | Equivariant representation · Global average pooling | linear separability | No clear effect |
| Use a non-periodic convolution instead of a periodic convolution | Convolutional layer · Non-periodic convolution | fraction of separable dichotomies | Helped |
| Append trivial irreps to the cyclic rotation representation | Cyclic-group rotation representation · Cyclic-group classification | fraction of separable dichotomies: f(P, N-2) | Helped |
Closest papers by meaning
- Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions (NeurIPS 2025 · similarity 0.90)
- Probing Equivariance and Symmetry Breaking in Convolutional Networks (NeurIPS 2025 · similarity 0.89)
- On Making $SE(2)$-Invariant Networks Optimal (NeurIPS 2026 · similarity 0.89)
- REVISITING MULTI-PERMUTATION EQUIVARIANCE THROUGH THE LENS OF IRREDUCIBLE REPRESENTATIONS (ICLR 2025 · similarity 0.88)
- Lie Group Decompositions for Equivariant Neural Networks (ICLR 2024 · similarity 0.88)
- A Tale of Two Symmetries: Exploring the Loss Landscape of Equivariant Models (NeurIPS 2025 · similarity 0.88)
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