Densely structured pruning methods utilizing simple pruning heuristics can deliver immediate compression and acceleration benefits with acceptable benign performances. However, empirical findings indicate such naïvely pruned networks are extremely fragile under simple adversarial attacks. Naturally, we would be interested in knowing if such a phenomenon also holds for carefully designed modern structured pruning methods. If so, then to what extent is the severity? And what kind of remedies are available? Unfortunately, both questions remain largely unaddressed: no prior art is able to provide a thorough investigation on the adversarial performance of modern structured pruning methods (spoiler: it is not good), yet the few works that attempt to provide mitigation often do so at various extra costs with only to-be-desired performance. In this work, we answer both questions by fairly and comprehensively investigating the adversarial performance of 10+ popular structured pruning methods. Solutionwise, we take advantage of Grouped Kernel Pruning (GKP)'s recent success in pushing densely structured pruning freedom to a more fine-grained level.

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve SE(3)-equivariance by design. From the graph spectrum view, our method can be interpreted as convolution on graphons (dense graphs with infinitely many nodes), which we term InfGCN. By leveraging both the continuous graphon structure and the discrete graph structure of the input data, our model can effectively capture the geometric information while preserving equivariance. Through extensive experiments on large-scale electron density datasets, we observed that our model significantly outperformed the current state-of-the-art architectures. Multiple ablation studies were also carried out to demonstrate the effectiveness of the proposed architecture.

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve SE(3)-equivariance by design. From the graph spectrum view, our method can be interpreted as convolution on graphons (dense graphs with infinitely many nodes), which we term InfGCN. By leveraging both the continuous graphon structure and the discrete graph structure of the input data, our model can effectively capture the geometric information while preserving equivariance. Through extensive experiments on large-scale electron density datasets, we observed that our model significantly outperformed the current state-of-the-art architectures. Multiple ablation studies were also carried out to demonstrate the effectiveness of the proposed architecture.

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have demonstrated impressive performance across various domains and applications such as protein and drug design. A prevalent intuition about such models is that the integration of relevant symmetry results in enhanced generalization. Moreover, it is posited that when the data and/or the model may only exhibit approximate or partial symmetry, the optimal or best-performing model is one where the model symmetry aligns with the data symmetry. In this paper, we conduct a formal unified investigation of these intuitions.

A.1 More on setup Settings and hyperparameters We train MultiMix and Dense MultiMix with mixed examples only. We use a mini-batch of size b = 128 examples in all experiments. Following Manifold Mixup [51], for every mini-batch, we apply MultiMix with probability 0.5 or input mixup otherwise. For multi-GPU experiments, all training hyperparameters including m and n are per GPU. For Dense MultiMix, the spatial resolution is r =4 4 = 16 on CIFAR-10/100 and r =7 7 = 49 on Imagenet by default.

Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or embedding) where it takes place, while the augmentation process itself is less studied. In most methods, the number of generated examples is limited to the mini-batch size and the number of examples being interpolated is limited to two (pairs), in the input space. We make progress in this direction by introducing MultiMix, which generates an arbitrarily large number of interpolated examples beyond the mini-batch size, and interpolates the entire mini-batch in the embedding space.

Interpreting the decisions of deep learning models has been actively studied since the explosion of deep neural networks. One of the most convincing interpretation approaches is salience-based visual interpretation, such as Grad-CAM, where the generation of attention maps depends merely on categorical labels. Although existing interpretation methods can provide explainable decision clues, they often yield partial correspondence between image and saliency maps due to the limited discriminative information from one-hot labels. This paper develops a Language-Image COnsistency model for explainable image classification, termed LICO, by correlating learnable linguistic prompts with corresponding visual features in a coarse-to-fine manner. Specifically, we first establish a coarse global manifold structure alignment by minimizing the distance between the distributions of image and language features. We then achieve fine-grained saliency maps by applying optimal transport (OT) theory to assign local feature maps with class-specific prompts. Extensive experimental results on eight benchmark datasets demonstrate that the proposed LICO achieves a significant improvement in generating more explainable attention maps in conjunction with existing interpretation methods such as Grad-CAM. Remarkably, LICO improves the classification performance of existing models without introducing any computational overhead during inference. Source code is made available at https://github.com/ymLeiFDU/LICO.