Deep Extrinsic Manifold Representation for Vision Tasks

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick named Deep Extrinsic Manifold Representation (DEMR) for visual tasks in this context. DEMR incorporates extrinsic manifold embedding into deep neural networks, which helps generate manifold representations. The DEMR approach does not directly optimize the complex geodesic loss. Instead, it focuses on optimizing the computation graph within the embedded Euclidean space, allowing for adaptability to various architectural requirements. We provide empirical evidence supporting the proposed concept on two types of manifolds, $SE(3)$ and its associated quotient manifolds. This evidence offers theoretical assurances regarding feasibility, asymptotic properties, and generalization capability. The experimental results show that DEMR effectively adapts to point cloud alignment, producing outputs in $ SE(3) $, as well as in illumination subspace learning with outputs on the Grassmann manifold.

WaveAttack: Asymmetric Frequency Obfuscation-based Backdoor Attacks Against Deep Neural Networks

Due to the popularity of Artificial Intelligence (AI) technology, numerous backdoor attacks are designed by adversaries to mislead deep neural network predictions by manipulating training samples and training processes. Although backdoor attacks are effective in various real scenarios, they still suffer from the problems of both low fidelity of poisoned samples and non-negligible transfer in latent space, which make them easily detectable by existing backdoor detection algorithms. To overcome the weakness, this paper proposes a novel frequency-based backdoor attack method named WaveAttack, which obtains image high-frequency features through Discrete Wavelet Transform (DWT) to generate backdoor triggers. Furthermore, we introduce an asymmetric frequency obfuscation method, which can add an adaptive residual in the training and inference stage to improve the impact of triggers and further enhance the effectiveness of WaveAttack. Comprehensive experimental results show that WaveAttack not only achieves higher stealthiness and effectiveness, but also outperforms state-of-the-art (SOTA) backdoor attack methods in the fidelity of images by up to 28.27\% improvement in PSNR, 1.61\% improvement in SSIM, and 70.59\% reduction in IS.

Continual Learning via Manifold Expansion Replay

In continual learning, the learner learns multiple tasks in sequence, with data being acquired only once for each task. Catastrophic forgetting is a major challenge to continual learning. To reduce forgetting, some existing rehearsal-based methods use episodic memory to replay samples of previous tasks. However, in the process of knowledge integration when learning a new task, this strategy also suffers from catastrophic forgetting due to an imbalance between old and new knowledge. To address this problem, we propose a novel replay strategy called Manifold Expansion Replay (MaER). We argue that expanding the implicit manifold of the knowledge representation in the episodic memory helps to improve the robustness and expressiveness of the model. To this end, we propose a greedy strategy to keep increasing the diameter of the implicit manifold represented by the knowledge in the buffer during memory management. In addition, we introduce Wasserstein distance instead of cross entropy as distillation loss to preserve previous knowledge. With extensive experimental validation on MNIST, CIFAR10, CIFAR100, and TinyImageNet, we show that the proposed method significantly improves the accuracy in continual learning setup, outperforming the state of the arts.

EqGAN: Feature Equalization Fusion for Few-shot Image Generation

Due to the absence of fine structure and texture information, existing fusion-based few-shot image generation methods suffer from unsatisfactory generation quality and diversity. To address this problem, we propose a novel feature Equalization fusion Generative Adversarial Network (EqGAN) for few-shot image generation. Unlike existing fusion strategies that rely on either deep features or local representations, we design two separate branches to fuse structures and textures by disentangling encoded features into shallow and deep contents. To refine image contents at all feature levels, we equalize the fused structure and texture semantics at different scales and supplement the decoder with richer information by skip connections. Since the fused structures and textures may be inconsistent with each other, we devise a consistent equalization loss between the equalized features and the intermediate output of the decoder to further align the semantics. Comprehensive experiments on three public datasets demonstrate that, EqGAN not only significantly improves generation performance with FID score (by up to 32.7%) and LPIPS score (by up to 4.19%), but also outperforms the state-of-the-arts in terms of accuracy (by up to 1.97%) for downstream classification tasks.

Curvature-based Transformer for Molecular Property Prediction

The prediction of molecular properties is one of the most important and challenging tasks in the field of artificial intelligence-based drug design. Among the current mainstream methods, the most commonly used feature representation for training DNN models is based on SMILES and molecular graphs, although these methods are concise and effective, they also limit the ability to capture spatial information. In this work, we propose Curvature-based Transformer to improve the ability of Graph Transformer neural network models to extract structural information on molecular graph data by introducing Discretization of Ricci Curvature. To embed the curvature in the model, we add the curvature information of the graph as positional Encoding to the node features during the attention-score calculation. This method can introduce curvature information from graph data without changing the original network architecture, and it has the potential to be extended to other models. We performed experiments on chemical molecular datasets including PCQM4M-LST, MoleculeNet and compared with models such as Uni-Mol, Graphormer, and the results show that this method can achieve the state-of-the-art results. It is proved that the discretized Ricci curvature also reflects the structural and functional relationship while describing the local geometry of the graph molecular data.

Hyperbolic Graph Diffusion Model for Molecule Generation

Recently, diffusion models have achieved remarkable performance in data generation, e.g., generating high-quality images. Nevertheless, chemistry molecules often have complex non-Euclidean spatial structures, with the behavior changing dynamically and unpredictably. Most existing diffusion models highly rely on computing the probability distribution, i.e., Gaussian distribution, in Euclidean space, which cannot capture internal non-Euclidean structures of molecules, especially the hierarchical structures of the implicit manifold surface represented by molecules. It has been observed that the complex hierarchical structures in hyperbolic embedding space become more prominent and easier to be captured. In order to leverage both the data generation power of diffusion models and the strong capability to extract complex geometric features of hyperbolic embedding, we propose to extend the diffusion model to hyperbolic manifolds for molecule generation, namely, Hyperbolic Graph Diffusion Model (HGDM). The proposed HGDM employs a hyperbolic variational autoencoder to generate the hyperbolic hidden representation of nodes and then a score-based hyperbolic graph neural network is used to learn the distribution in hyperbolic space. Numerical experimental results show that the proposed HGDM achieves higher performance on several molecular datasets, compared with state-of-the-art methods.

FedMR: Federated Learning via Model Recombination

Although Federated Learning (FL) enables global model training across clients without compromising their raw data, existing Federated Averaging (FedAvg)-based methods suffer from the problem of low inference performance, especially for unevenly distributed data among clients. This is mainly because i) FedAvg initializes client models with the same global models, which makes the local training hard to escape from the local search for optimal solutions; and ii) by averaging model parameters in a coarse manner, FedAvg eclipses the individual characteristics of local models. To address such issues that strongly limit the inference capability of FL, we propose a novel and effective FL paradigm named FedMR (Federated Model Recombination). Unlike conventional FedAvg-based methods, the cloud server of FedMR shuffles each layer of collected local models and recombines them to achieve new models for local training on clients. Due to the diversified initialization models for clients coupled with fine-grained model recombination, FedMR can converge to a well-generalized global model for all the clients, leading to a superior inference performance. Experimental results show that, compared with state-of-the-art FL methods, FedMR can significantly improve inference accuracy in a quicker manner without exposing client privacy.

Group Equivariant BEV for 3D Object Detection

Recently, 3D object detection has attracted significant attention and achieved continuous improvement in real road scenarios. The environmental information is collected from a single sensor or multi-sensor fusion to detect interested objects. However, most of the current 3D object detection approaches focus on developing advanced network architectures to improve the detection precision of the object rather than considering the dynamic driving scenes, where data collected from sensors equipped in the vehicle contain various perturbation features. As a result, existing work cannot still tackle the perturbation issue. In order to solve this problem, we propose a group equivariant bird's eye view network (GeqBevNet) based on the group equivariant theory, which introduces the concept of group equivariant into the BEV fusion object detection network. The group equivariant network is embedded into the fused BEV feature map to facilitate the BEV-level rotational equivariant feature extraction, thus leading to lower average orientation error. In order to demonstrate the effectiveness of the GeqBevNet, the network is verified on the nuScenes validation dataset in which mAOE can be decreased to 0.325. Experimental results demonstrate that GeqBevNet can extract more rotational equivariant features in the 3D object detection of the actual road scene and improve the performance of object orientation prediction.

Autoencoders with Intrinsic Dimension Constraints for Learning Low Dimensional Image Representations

Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly focus on the minimizing the reconstruction error on pixel level of image, while ignoring the preservation of Intrinsic Dimension (ID), which is a fundamental geometric property of data representations in Deep Neural Networks (DNNs). Motivated by the important role of ID, in this paper, we propose a novel deep representation learning approach with autoencoder, which incorporates regularization of the global and local ID constraints into the reconstruction of data representations. This approach not only preserves the global manifold structure of the whole dataset, but also maintains the local manifold structure of the feature maps of each point, which makes the learned low-dimensional features more discriminant and improves the performance of the downstream algorithms. To our best knowledge, existing works are rare and limited on exploiting both global and local ID invariant properties on the regularization of autoencoders. Numerical experimental results on benchmark datasets (Extended Yale B, Caltech101 and ImageNet) show that the resulting regularized learning models achieve better discriminative representations for downstream tasks including image classification and clustering.

Multi-scale Geometry-aware Transformer for 3D Point Cloud Classification

Self-attention modules have demonstrated remarkable capabilities in capturing long-range relationships and improving the performance of point cloud tasks. However, point cloud objects are typically characterized by complex, disordered, and non-Euclidean spatial structures with multiple scales, and their behavior is often dynamic and unpredictable. The current self-attention modules mostly rely on dot product multiplication and dimension alignment among query-key-value features, which cannot adequately capture the multi-scale non-Euclidean structures of point cloud objects. To address these problems, this paper proposes a self-attention plug-in module with its variants, Multi-scale Geometry-aware Transformer (MGT). MGT processes point cloud data with multi-scale local and global geometric information in the following three aspects. At first, the MGT divides point cloud data into patches with multiple scales. Secondly, a local feature extractor based on sphere mapping is proposed to explore the geometry inner each patch and generate a fixed-length representation for each patch. Thirdly, the fixed-length representations are fed into a novel geodesic-based self-attention to capture the global non-Euclidean geometry between patches. Finally, all the modules are integrated into the framework of MGT with an end-to-end training scheme. Experimental results demonstrate that the MGT vastly increases the capability of capturing multi-scale geometry using the self-attention mechanism and achieves strong competitive performance on mainstream point cloud benchmarks.