Diversified Node Sampling based Hierarchical Transformer Pooling for Graph Representation Learning

Graph pooling methods have been widely used on downsampling graphs, achieving impressive results on multiple graph-level tasks like graph classification and graph generation. An important line called node dropping pooling aims at exploiting learnable scoring functions to drop nodes with comparatively lower significance scores. However, existing node dropping methods suffer from two limitations: (1) for each pooled node, these models struggle to capture long-range dependencies since they mainly take GNNs as the backbones; (2) pooling only the highest-scoring nodes tends to preserve similar nodes, thus discarding the affluent information of low-scoring nodes. To address these issues, we propose a Graph Transformer Pooling method termed GTPool, which introduces Transformer to node dropping pooling to efficiently capture long-range pairwise interactions and meanwhile sample nodes diversely. Specifically, we design a scoring module based on the self-attention mechanism that takes both global context and local context into consideration, measuring the importance of nodes more comprehensively. GTPool further utilizes a diversified sampling method named Roulette Wheel Sampling (RWS) that is able to flexibly preserve nodes across different scoring intervals instead of only higher scoring nodes. In this way, GTPool could effectively obtain long-range information and select more representative nodes. Extensive experiments on 11 benchmark datasets demonstrate the superiority of GTPool over existing popular graph pooling methods.

SignGT: Signed Attention-based Graph Transformer for Graph Representation Learning

The emerging graph Transformers have achieved impressive performance for graph representation learning over graph neural networks (GNNs). In this work, we regard the self-attention mechanism, the core module of graph Transformers, as a two-step aggregation operation on a fully connected graph. Due to the property of generating positive attention values, the self-attention mechanism is equal to conducting a smooth operation on all nodes, preserving the low-frequency information. However, only capturing the low-frequency information is inefficient in learning complex relations of nodes on diverse graphs, such as heterophily graphs where the high-frequency information is crucial. To this end, we propose a Signed Attention-based Graph Transformer (SignGT) to adaptively capture various frequency information from the graphs. Specifically, SignGT develops a new signed self-attention mechanism (SignSA) that produces signed attention values according to the semantic relevance of node pairs. Hence, the diverse frequency information between different node pairs could be carefully preserved. Besides, SignGT proposes a structure-aware feed-forward network (SFFN) that introduces the neighborhood bias to preserve the local topology information. In this way, SignGT could learn informative node representations from both long-range dependencies and local topology information. Extensive empirical results on both node-level and graph-level tasks indicate the superiority of SignGT against state-of-the-art graph Transformers as well as advanced GNNs.

PIAT: Parameter Interpolation based Adversarial Training for Image Classification

Adversarial training has been demonstrated to be the most effective approach to defend against adversarial attacks. However, existing adversarial training methods show apparent oscillations and overfitting issue in the training process, degrading the defense efficacy. In this work, we propose a novel framework, termed Parameter Interpolation based Adversarial Training (PIAT), that makes full use of the historical information during training. Specifically, at the end of each epoch, PIAT tunes the model parameters as the interpolation of the parameters of the previous and current epochs. Besides, we suggest to use the Normalized Mean Square Error (NMSE) to further improve the robustness by aligning the clean and adversarial examples. Compared with other regularization methods, NMSE focuses more on the relative magnitude of the logits rather than the absolute magnitude. Extensive experiments on several benchmark datasets and various networks show that our method could prominently improve the model robustness and reduce the generalization error. Moreover, our framework is general and could further boost the robust accuracy when combined with other adversarial training methods.

Class-aware Information for Logit-based Knowledge Distillation

Knowledge distillation aims to transfer knowledge to the student model by utilizing the predictions/features of the teacher model, and feature-based distillation has recently shown its superiority over logit-based distillation. However, due to the cumbersome computation and storage of extra feature transformation, the training overhead of feature-based methods is much higher than that of logit-based distillation. In this work, we revisit the logit-based knowledge distillation, and observe that the existing logit-based distillation methods treat the prediction logits only in the instance level, while many other useful semantic information is overlooked. To address this issue, we propose a Class-aware Logit Knowledge Distillation (CLKD) method, that extents the logit distillation in both instance-level and class-level. CLKD enables the student model mimic higher semantic information from the teacher model, hence improving the distillation performance. We further introduce a novel loss called Class Correlation Loss to force the student learn the inherent class-level correlation of the teacher. Empirical comparisons demonstrate the superiority of the proposed method over several prevailing logit-based methods and feature-based methods, in which CLKD achieves compelling results on various visual classification tasks and outperforms the state-of-the-art baselines.

On the Complexity of Bayesian Generalization

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the $complexity$ of concepts becomes diverse. Specifically, at the $representational \ level$, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the $computational \ level$, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

Local Magnification for Data and Feature Augmentation

In recent years, many data augmentation techniques have been proposed to increase the diversity of input data and reduce the risk of overfitting on deep neural networks. In this work, we propose an easy-to-implement and model-free data augmentation method called Local Magnification (LOMA). Different from other geometric data augmentation methods that perform global transformations on images, LOMA generates additional training data by randomly magnifying a local area of the image. This local magnification results in geometric changes that significantly broaden the range of augmentations while maintaining the recognizability of objects. Moreover, we extend the idea of LOMA and random cropping to the feature space to augment the feature map, which further boosts the classification accuracy considerably. Experiments show that our proposed LOMA, though straightforward, can be combined with standard data augmentation to significantly improve the performance on image classification and object detection. And further combination with our feature augmentation techniques, termed LOMA_IF&FO, can continue to strengthen the model and outperform advanced intensity transformation methods for data augmentation.

Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power

It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust training error can be near zero via some methods, all existing algorithms lead to a high robust generalization error. In this paper, we provide a theoretical understanding of this puzzling phenomenon from the perspective of expressive power for deep neural networks. Specifically, for binary classification problems with well-separated data, we show that, for ReLU networks, while mild over-parameterization is sufficient for high robust training accuracy, there exists a constant robust generalization gap unless the size of the neural network is exponential in the data dimension $d$. Even if the data is linear separable, which means achieving low clean generalization error is easy, we can still prove an $\exp({\Omega}(d))$ lower bound for robust generalization. Moreover, we establish an improved upper bound of $\exp({\mathcal{O}}(k))$ for the network size to achieve low robust generalization error when the data lies on a manifold with intrinsic dimension $k$ ($k \ll d$). Nonetheless, we also have a lower bound that grows exponentially with respect to $k$ -- the curse of dimensionality is inevitable. By demonstrating an exponential separation between the network size for achieving low robust training and generalization error, our results reveal that the hardness of robust generalization may stem from the expressive power of practical models.

Uncovering the Local Hidden Community Structure in Social Networks

Hidden community is a useful concept proposed recently for social network analysis. To handle the rapid growth of network scale, in this work, we explore the detection of hidden communities from the local perspective, and propose a new method that detects and boosts each layer iteratively on a subgraph sampled from the original network. We first expand the seed set from a single seed node based on our modified local spectral method and detect an initial dominant local community. Then we temporarily remove the members of this community as well as their connections to other nodes, and detect all the neighborhood communities in the remaining subgraph, including some "broken communities" that only contain a fraction of members in the original network. The local community and neighborhood communities form a dominant layer, and by reducing the edge weights inside these communities, we weaken this layer's structure to reveal the hidden layers. Eventually, we repeat the whole process and all communities containing the seed node can be detected and boosted iteratively. We theoretically show that our method can avoid some situations that a broken community and the local community are regarded as one community in the subgraph, leading to the inaccuracy on detection which can be caused by global hidden community detection methods. Extensive experiments show that our method could significantly outperform the state-of-the-art baselines designed for either global hidden community detection or multiple local community detection.