We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.

翻译：我们研究了群不变二分类中线性等变可操控网络的梯度流隐式偏差。研究结果表明，参数化预测器的方向收敛于由输入群作用定义的最大间隔唯一群不变分类器。在输入表示满足酉假设的条件下，我们建立了可操控网络与数据增强之间的等价性。此外，我们证明了可操控网络相较于非不变网络具有更优的间隔（margin）与泛化界。