In this work, we present an analysis of the generalization of Neural Operators (NOs) and derived architectures. We proposed a family of networks, which we name (${\textit{s}}{\text{NO}}+\varepsilon$), where we modify the layout of NOs towards an architecture resembling a Transformer; mainly, we substitute the Attention module with the Integral Operator part of NOs. The resulting network preserves universality, has a better generalization to unseen data, and similar number of parameters as NOs. On the one hand, we study numerically the generalization by gradually transforming NOs into ${\textit{s}}{\text{NO}}+\varepsilon$ and verifying a reduction of the test loss considering a time-harmonic wave dataset with different frequencies. We perform the following changes in NOs: (a) we split the Integral Operator (non-local) and the (local) feed-forward network (MLP) into different layers, generating a {\it sequential} structure which we call sequential Neural Operator (${\textit{s}}{\text{NO}}$), (b) we add the skip connection, and layer normalization in ${\textit{s}}{\text{NO}}$, and (c) we incorporate dropout and stochastic depth that allows us to generate deep networks. In each case, we observe a decrease in the test loss in a wide variety of initialization, indicating that our changes outperform the NO. On the other hand, building on infinite-dimensional Statistics, and in particular the Dudley Theorem, we provide bounds of the Rademacher complexity of NOs and ${\textit{s}}{\text{NO}}$, and we find the following relationship: the upper bound of the Rademacher complexity of the ${\textit{s}}{\text{NO}}$ is a lower-bound of the NOs, thereby, the generalization error bound of ${\textit{s}}{\text{NO}}$ is smaller than NO, which further strengthens our numerical results.
Tiny object detection has become an active area of research because images with tiny targets are common in several important real-world scenarios. However, existing tiny object detection methods use standard deep neural networks as their backbone architecture. We argue that such backbones are inappropriate for detecting tiny objects as they are designed for the classification of larger objects, and do not have the spatial resolution to identify small targets. Specifically, such backbones use max-pooling or a large stride at early stages in the architecture. This produces lower resolution feature-maps that can be efficiently processed by subsequent layers. However, such low-resolution feature-maps do not contain information that can reliably discriminate tiny objects. To solve this problem we design 'bottom-heavy' versions of backbones that allocate more resources to processing higher-resolution features without introducing any additional computational burden overall. We also investigate if pre-training these backbones on images of appropriate size, using CIFAR100 and ImageNet32, can further improve performance on tiny object detection. Results on TinyPerson and WiderFace show that detectors with our proposed backbones achieve better results than the current state-of-the-art methods.
Recent years have seen the ever-increasing importance of pre-trained models and their downstream training in deep learning research and applications. At the same time, the defense for adversarial examples has been mainly investigated in the context of training from random initialization on simple classification tasks. To better exploit the potential of pre-trained models in adversarial robustness, this paper focuses on the fine-tuning of an adversarially pre-trained model in various classification tasks. Existing research has shown that since the robust pre-trained model has already learned a robust feature extractor, the crucial question is how to maintain the robustness in the pre-trained model when learning the downstream task. We study the model-based and data-based approaches for this goal and find that the two common approaches cannot achieve the objective of improving both generalization and adversarial robustness. Thus, we propose a novel statistics-based approach, Two-WIng NormliSation (TWINS) fine-tuning framework, which consists of two neural networks where one of them keeps the population means and variances of pre-training data in the batch normalization layers. Besides the robust information transfer, TWINS increases the effective learning rate without hurting the training stability since the relationship between a weight norm and its gradient norm in standard batch normalization layer is broken, resulting in a faster escape from the sub-optimal initialization and alleviating the robust overfitting. Finally, TWINS is shown to be effective on a wide range of image classification datasets in terms of both generalization and robustness. Our code is available at //github.com/ziquanliu/CVPR2023-TWINS.
Out-of-distribution (OOD) detection aims at enhancing standard deep neural networks to distinguish anomalous inputs from original training data. Previous progress has introduced various approaches where the in-distribution training data and even several OOD examples are prerequisites. However, due to privacy and security, auxiliary data tends to be impractical in a real-world scenario. In this paper, we propose a data-free method without training on natural data, called Class-Conditional Impressions Reappearing (C2IR), which utilizes image impressions from the fixed model to recover class-conditional feature statistics. Based on that, we introduce Integral Probability Metrics to estimate layer-wise class-conditional deviations and obtain layer weights by Measuring Gradient-based Importance (MGI). The experiments verify the effectiveness of our method and indicate that C2IR outperforms other post-hoc methods and reaches comparable performance to the full access (ID and OOD) detection method, especially in the far-OOD dataset (SVHN).
Using generated data to improve the performance of downstream discriminative models has recently gained popularity due to the great development of pre-trained language models. In most previous studies, generative models and discriminative models are trained separately and thus could not adapt to any changes in each other. As a result, the generated samples can easily deviate from the real data distribution, while the improvement of the discriminative model quickly reaches saturation. Generative adversarial networks (GANs) train generative models via an adversarial process with discriminative models to achieve joint training. However, the training of standard GANs is notoriously unstable and often falls short of convergence. In this paper, to address these issues, we propose a $\textit{self-consistent learning}$ framework, in which a discriminator and a generator are cooperatively trained in a closed-loop form. The discriminator and the generator enhance each other during multiple rounds of alternating training until a scoring consensus is reached. This framework proves to be easy to train and free from instabilities such as mode collapse and non-convergence. Extensive experiments on sentence semantic matching demonstrate the effectiveness of the proposed framework: the discriminator achieves 10+ AP of improvement on the zero-shot setting and new state-of-the-art performance on the full-data setting.
In this work, we leverage visual prompting (VP) to improve adversarial robustness of a fixed, pre-trained model at testing time. Compared to conventional adversarial defenses, VP allows us to design universal (i.e., data-agnostic) input prompting templates, which have plug-and-play capabilities at testing time to achieve desired model performance without introducing much computation overhead. Although VP has been successfully applied to improving model generalization, it remains elusive whether and how it can be used to defend against adversarial attacks. We investigate this problem and show that the vanilla VP approach is not effective in adversarial defense since a universal input prompt lacks the capacity for robust learning against sample-specific adversarial perturbations. To circumvent it, we propose a new VP method, termed Class-wise Adversarial Visual Prompting (C-AVP), to generate class-wise visual prompts so as to not only leverage the strengths of ensemble prompts but also optimize their interrelations to improve model robustness. Our experiments show that C-AVP outperforms the conventional VP method, with 2.1X standard accuracy gain and 2X robust accuracy gain. Compared to classical test-time defenses, C-AVP also yields a 42X inference time speedup.
We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a multiple-index model, i.e., $y=g(\langle\boldsymbol{u_1},\boldsymbol{x}\rangle,...,\langle\boldsymbol{u_k},\boldsymbol{x}\rangle)$ with a noisy link function $g$. We prove that the first-layer weights of the NN converge to the $k$-dimensional principal subspace spanned by the vectors $\boldsymbol{u_1},...,\boldsymbol{u_k}$ of the true model, when online SGD with weight decay is used for training. This phenomenon has several important consequences when $k \ll d$. First, by employing uniform convergence on this smaller subspace, we establish a generalization error bound of $O(\sqrt{{kd}/{T}})$ after $T$ iterations of SGD, which is independent of the width of the NN. We further demonstrate that, SGD-trained ReLU NNs can learn a single-index target of the form $y=f(\langle\boldsymbol{u},\boldsymbol{x}\rangle) + \epsilon$ by recovering the principal direction, with a sample complexity linear in $d$ (up to log factors), where $f$ is a monotonic function with at most polynomial growth, and $\epsilon$ is the noise. This is in contrast to the known $d^{\Omega(p)}$ sample requirement to learn any degree $p$ polynomial in the kernel regime, and it shows that NNs trained with SGD can outperform the neural tangent kernel at initialization. Finally, we also provide compressibility guarantees for NNs using the approximate low-rank structure produced by SGD.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, multi-layer architectures, which are required to propagate knowledge to distant nodes in the graph, dilute the knowledge by performing extensive Laplacian smoothing at each layer and thereby consequently decrease performance. In order to still enjoy the benefit brought by the graph structure while preventing dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node to improve information propagation in the graph. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches.
Adversarial attacks to image classification systems present challenges to convolutional networks and opportunities for understanding them. This study suggests that adversarial perturbations on images lead to noise in the features constructed by these networks. Motivated by this observation, we develop new network architectures that increase adversarial robustness by performing feature denoising. Specifically, our networks contain blocks that denoise the features using non-local means or other filters; the entire networks are trained end-to-end. When combined with adversarial training, our feature denoising networks substantially improve the state-of-the-art in adversarial robustness in both white-box and black-box attack settings. On ImageNet, under 10-iteration PGD white-box attacks where prior art has 27.9% accuracy, our method achieves 55.7%; even under extreme 2000-iteration PGD white-box attacks, our method secures 42.6% accuracy. A network based on our method was ranked first in Competition on Adversarial Attacks and Defenses (CAAD) 2018 --- it achieved 50.6% classification accuracy on a secret, ImageNet-like test dataset against 48 unknown attackers, surpassing the runner-up approach by ~10%. Code and models will be made publicly available.