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.

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.

Figure 1: The illustrative examples for two proposed techniques: Back-imagination and Back-speech. Tiny ImageNet [Le and Y ang, 2015] serves as a compact version of the comprehensive ImageNet dataset. The Stanford Sentiment Treebank-2 (SST -2) [Socher et al., 2013] is a sentiment classification dataset Given the scarcity of datasets for understanding natural language in visual scenes, we introduce a novel textual entailment dataset, named Textual Natural Contextual Classification (TNCC). This dataset is formulated on the foundation of Crisscrossed Captions [Parekh et al., 2020], an image In this work, we employ a uniform experimental configuration for both textual entailment and sentiment classification tasks. For the image classification task, we employ the ResNet18 [He et al., 2015] model, which is considered more suitable for small datasets.

In this section, we provide proof for the disentanglement identifiability of the inferred exogenous variable. Our proof consists of three main components. Then we have ( f, T, λ) ( f, T, λ) . The conditional V AE, in this case, inherits all the properties of maximum likelihood estimation. The following proof is based on the reduction to absurdity.

In this paper, we propose an efficient search method of augmentation policies, called Fast AutoAugment,motivatedbyBayesianDA[36].

Directional features As in previous work [3, 6, 10], we apply a 128-dimensional directional encoding byreplicating(cosθi,sinθi,cosφi,sinφi)by32times torepresent theorientation ofeach single-viewiwith respect to the agent's current orientation, whereθi andφi are the angles of the heading and elevation to that single-view. Replicating the encoding by 32 times does not enrich its information but makes its gradient 32 times larger during back-propagation. We suspect that this benefits the agent to learn about the action-related terms (e.g.