Xinping Yi

Gaojie Jin, Xinping Yi, Wei Huang et al.

Adversarial training has been shown to be one of the most effective approaches to improve the robustness of deep neural networks. It is formalized as a min-max optimization over model weights and adversarial perturbations, where the weights can be optimized through gradient descent methods like SGD. In this paper, we show that treating model weights as random variables allows for enhancing adversarial training through \textbf{S}econd-Order \textbf{S}tatistics \textbf{O}ptimization (S$^2$O) with respect to the weights. By relaxing a common (but unrealistic) assumption of previous PAC-Bayesian frameworks that all weights are statistically independent, we derive an improved PAC-Bayesian adversarial generalization bound, which suggests that optimizing second-order statistics of weights can effectively tighten the bound. In addition to this theoretical insight, we conduct an extensive set of experiments, which show that S$^2$O not only improves the robustness and generalization of the trained neural networks when used in isolation, but also integrates easily in state-of-the-art adversarial training techniques like TRADES, AWP, MART, and AVMixup, leading to a measurable improvement of these techniques. The code is available at \url{https://github.com/Alexkael/S2O}.

Gaojie Jin, Xinping Yi, Dengyu Wu et al.

In recent years, there has been an explosion of research into developing more robust deep neural networks against adversarial examples. Adversarial training appears as one of the most successful methods. To deal with both the robustness against adversarial examples and the accuracy over clean examples, many works develop enhanced adversarial training methods to achieve various trade-offs between them. Leveraging over the studies that smoothed update on weights during training may help find flat minima and improve generalization, we suggest reconciling the robustness-accuracy trade-off from another perspective, i.e., by adding random noise into deterministic weights. The randomized weights enable our design of a novel adversarial training method via Taylor expansion of a small Gaussian noise, and we show that the new adversarial training method can flatten loss landscape and find flat minima. With PGD, CW, and Auto Attacks, an extensive set of experiments demonstrate that our method enhances the state-of-the-art adversarial training methods, boosting both robustness and clean accuracy. The code is available at https://github.com/Alexkael/Randomized-Adversarial-Training.

Dengyu Wu, Gaojie Jin, Han Yu et al.

Spiking neural network (SNN), as the next generation of artificial neural network (ANN), offer a closer mimicry of natural neural networks and hold promise for significant improvements in computational efficiency. However, the current SNN is trained to infer over a fixed duration, overlooking the potential of dynamic inference in SNN. In this paper, we strengthen the marriage between SNN and event-driven processing with a proposal to consider a cutoff in SNN, which can terminate SNN anytime during inference to achieve efficient inference. Two novel optimisation techniques are presented to achieve inference efficient SNN: a Top-K cutoff and a regularisation.The proposed regularisation influences the training process, optimising SNN for the cutoff, while the Top-K cutoff technique optimises the inference phase. We conduct an extensive set of experiments on multiple benchmark frame-based datasets, such asCIFAR10/100, Tiny-ImageNet, and event-based datasets, including CIFAR10-DVS, N-Caltech101 and DVS128 Gesture. The experimental results demonstrate the effectiveness of our techniques in both ANN-to-SNN conversion and direct training, enabling SNNs to require 1.76 to 2.76x fewer timesteps for CIFAR-10, while achieving 1.64 to 1.95x fewer timesteps across all event-based datasets, with near-zero accuracy loss. These findings affirms the compatibility and potential benefits of our techniques in enhancing accuracy and reducing inference latency when integrated with existing methods. Code available: https://github.com/Dengyu-Wu/SNNCutoff

Jingwei Guo, Kaizhu Huang, Rui Zhang et al.

While Graph Neural Networks (GNNs) have achieved enormous success in multiple graph analytical tasks, modern variants mostly rely on the strong inductive bias of homophily. However, real-world networks typically exhibit both homophilic and heterophilic linking patterns, wherein adjacent nodes may share dissimilar attributes and distinct labels. Therefore, GNNs smoothing node proximity holistically may aggregate both task-relevant and irrelevant (even harmful) information, limiting their ability to generalize to heterophilic graphs and potentially causing non-robustness. In this work, we propose a novel Edge Splitting GNN (ES-GNN) framework to adaptively distinguish between graph edges either relevant or irrelevant to learning tasks. This essentially transfers the original graph into two subgraphs with the same node set but complementary edge sets dynamically. Given that, information propagation separately on these subgraphs and edge splitting are alternatively conducted, thus disentangling the task-relevant and irrelevant features. Theoretically, we show that our ES-GNN can be regarded as a solution to a disentangled graph denoising problem, which further illustrates our motivations and interprets the improved generalization beyond homophily. Extensive experiments over 11 benchmark and 1 synthetic datasets not only demonstrate the effective performance of ES-GNN but also highlight its robustness to adversarial graphs and mitigation of the over-smoothing problem.

Gaojie Jin, Ronghui Mu, Xinping Yi et al.

The Invariant Risk Minimization (IRM) approach aims to address the challenge of domain generalization by training a feature representation that remains invariant across multiple environments. However, in noisy environments, IRM-related techniques such as IRMv1 and VREx may be unable to achieve the optimal IRM solution, primarily due to erroneous optimization directions. To address this issue, we introduce ICorr (an abbreviation for Invariant Correlation), a novel approach designed to surmount the above challenge in noisy settings. Additionally, we dig into a case study to analyze why previous methods may lose ground while ICorr can succeed. Through a theoretical lens, particularly from a causality perspective, we illustrate that the invariant correlation of representation with label is a necessary condition for the optimal invariant predictor in noisy environments, whereas the optimization motivations for other methods may not be. Furthermore, we empirically demonstrate the effectiveness of ICorr by comparing it with other domain generalization methods on various noisy datasets. The code is available at https://github.com/Alexkael/ICorr.

Jiaxu Liu, Xinping Yi, Tianle Zhang et al.

In traditional Graph Neural Networks (GNNs), the assumption of a fixed embedding manifold often limits their adaptability to diverse graph geometries. Recently, Hamiltonian system-inspired GNNs have been proposed to address the dynamic nature of such embeddings by incorporating physical laws into node feature updates. We present Symplectic Structure-Aware Hamiltonian GNN (SAH-GNN), a novel approach that generalizes Hamiltonian dynamics for more flexible node feature updates. Unlike existing Hamiltonian approaches, SAH-GNN employs Riemannian optimization on the symplectic Stiefel manifold to adaptively learn the underlying symplectic structure, circumventing the limitations of existing Hamiltonian GNNs that rely on a pre-defined form of standard symplectic structure. This innovation allows SAH-GNN to automatically adapt to various graph datasets without extensive hyperparameter tuning. Moreover, it conserves energy during training meaning the implicit Hamiltonian system is physically meaningful. Finally, we empirically validate SAH-GNN's superiority and adaptability in node classification tasks across multiple types of graph datasets.

Dengyu Wu, Yi Qi, Kaiwen Cai et al.

Spiking Neural Network (SNN) is acknowledged as the next generation of Artificial Neural Network (ANN) and hold great promise in effectively processing spatial-temporal information. However, the choice of timestep becomes crucial as it significantly impacts the accuracy of the neural network training. Specifically, a smaller timestep indicates better performance in efficient computing, resulting in reduced latency and operations. While, using a small timestep may lead to low accuracy due to insufficient information presentation with few spikes. This observation motivates us to develop an SNN that is more reliable for adaptive timestep by introducing a novel regularisation technique, namely Spatial-Temporal Regulariser (STR). Our approach regulates the ratio between the strength of spikes and membrane potential at each timestep. This effectively balances spatial and temporal performance during training, ultimately resulting in an Anytime Optimal Inference (AOI) SNN. Through extensive experiments on frame-based and event-based datasets, our method, in combination with cutoff based on softmax output, achieves state-of-the-art performance in terms of both latency and accuracy. Notably, with STR and cutoff, SNN achieves 2.14 to 2.89 faster in inference compared to the pre-configured timestep with near-zero accuracy drop of 0.50% to 0.64% over the event-based datasets. Code available: https://github.com/Dengyu-Wu/AOI-SNN-Regularisation

Ganlin Liu, Ziling Liang, Xiaowei Huang et al.

Despite impressive capability in learning over graph-structured data, graph neural networks (GNN) suffer from adversarial topology perturbation in both training and inference phases. While adversarial training has demonstrated remarkable effectiveness in image classification tasks, its suitability for GNN models has been doubted until a recent advance that shifts the focus from transductive to inductive learning. Still, GNN robustness in the inductive setting is under-explored, and it calls for deeper understanding of GNN adversarial training. To this end, we propose a new concept of graph subspace energy (GSE) -- a generalization of graph energy that measures graph stability -- of the adjacency matrix, as an indicator of GNN robustness against topology perturbations. To further demonstrate the effectiveness of such concept, we propose an adversarial training method with the perturbed graphs generated by maximizing the GSE regularization term, referred to as AT-GSE. To deal with the local and global topology perturbations raised respectively by LRBCD and PRBCD, we employ randomized SVD (RndSVD) and Nystrom low-rank approximation to favor the different aspects of the GSE terms. An extensive set of experiments shows that AT-GSE outperforms consistently the state-of-the-art GNN adversarial training methods over different homophily and heterophily datasets in terms of adversarial accuracy, whilst more surprisingly achieving a superior clean accuracy on non-perturbed graphs.

Jiaxu Liu, Xinping Yi, Sihao Wu et al.

While Hyperbolic Graph Neural Network (HGNN) has recently emerged as a powerful tool dealing with hierarchical graph data, the limitations of scalability and efficiency hinder itself from generalizing to deep models. In this paper, by envisioning depth as a continuous-time embedding evolution, we decouple the HGNN and reframe the information propagation as a partial differential equation, letting node-wise attention undertake the role of diffusivity within the Hyperbolic Neural PDE (HPDE). By introducing theoretical principles \textit{e.g.,} field and flow, gradient, divergence, and diffusivity on a non-Euclidean manifold for HPDE integration, we discuss both implicit and explicit discretization schemes to formulate numerical HPDE solvers. Further, we propose the Hyperbolic Graph Diffusion Equation (HGDE) -- a flexible vector flow function that can be integrated to obtain expressive hyperbolic node embeddings. By analyzing potential energy decay of embeddings, we demonstrate that HGDE is capable of modeling both low- and high-order proximity with the benefit of local-global diffusivity functions. Experiments on node classification and link prediction and image-text classification tasks verify the superiority of the proposed method, which consistently outperforms various competitive models by a significant margin.

Gaojie Jin, Xinping Yi, Pengfei Yang et al.

While dropout is known to be a successful regularization technique, insights into the mechanisms that lead to this success are still lacking. We introduce the concept of \emph{weight expansion}, an increase in the signed volume of a parallelotope spanned by the column or row vectors of the weight covariance matrix, and show that weight expansion is an effective means of increasing the generalization in a PAC-Bayesian setting. We provide a theoretical argument that dropout leads to weight expansion and extensive empirical support for the correlation between dropout and weight expansion. To support our hypothesis that weight expansion can be regarded as an \emph{indicator} of the enhanced generalization capability endowed by dropout, and not just as a mere by-product, we have studied other methods that achieve weight expansion (resp.\ contraction), and found that they generally lead to an increased (resp.\ decreased) generalization ability. This suggests that dropout is an attractive regularizer, because it is a computationally cheap method for obtaining weight expansion. This insight justifies the role of dropout as a regularizer, while paving the way for identifying regularizers that promise improved generalization through weight expansion.

Gaojie Jin, Xinping Yi, Xiaowei Huang

This paper proposes to study neural networks through neuronal correlation, a statistical measure of correlated neuronal activity on the penultimate layer. We show that neuronal correlation can be efficiently estimated via weight matrix, can be effectively enforced through layer structure, and is a strong indicator of generalisation ability of the network. More importantly, we show that neuronal correlation significantly impacts on the accuracy of entropy estimation in high-dimensional hidden spaces. While previous estimation methods may be subject to significant inaccuracy due to implicit assumption on neuronal independence, we present a novel computational method to have an efficient and authentic computation of entropy, by taking into consideration the neuronal correlation. In doing so, we install neuronal correlation as a central concept of neural network.