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This paper introduces a framework for tunable soft equivariance in neural networks by projecting model weights into a designed subspace, allowing for controlled deviations from strict equivariance. Theoretical bounds on the induced equivariance error are derived, providing guarantees on the degree of equivariance achieved. Experiments across image classification, semantic segmentation, and trajectory prediction demonstrate improved performance and reduced equivariance error on ImageNet and other benchmarks when applying this soft equivariance technique to pre-trained ViT and ResNet models.
Trade strict equivariance for a performance boost: this weight-space projection method lets you dial in the right amount of symmetry for your task, even on ImageNet.
Equivariance is a fundamental property in computer vision models, yet strict equivariance is rarely satisfied in real-world data, which can limit a model's performance. Controlling the degree of equivariance is therefore desirable. We propose a general framework for constructing soft equivariant models by projecting the model weights into a designed subspace. The method applies to any pre-trained architecture and provides theoretical bounds on the induced equivariance error. Empirically, we demonstrate the effectiveness of our method on multiple pre-trained backbones, including ViT and ResNet, across image classification, semantic segmentation, and human-trajectory prediction tasks. Notably, our approach improves the performance while simultaneously reducing equivariance error on the competitive ImageNet benchmark.
