GNOT: A General Neural Operator Transformer for Operator Learning

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular mesh. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods.

A Comprehensive Study on Robustness of Image Classification Models: Benchmarking and Rethinking

The robustness of deep neural networks is usually lacking under adversarial examples, common corruptions, and distribution shifts, which becomes an important research problem in the development of deep learning. Although new deep learning methods and robustness improvement techniques have been constantly proposed, the robustness evaluations of existing methods are often inadequate due to their rapid development, diverse noise patterns, and simple evaluation metrics. Without thorough robustness evaluations, it is hard to understand the advances in the field and identify the effective methods. In this paper, we establish a comprehensive robustness benchmark called \textbf{ARES-Bench} on the image classification task. In our benchmark, we evaluate the robustness of 55 typical deep learning models on ImageNet with diverse architectures (e.g., CNNs, Transformers) and learning algorithms (e.g., normal supervised training, pre-training, adversarial training) under numerous adversarial attacks and out-of-distribution (OOD) datasets. Using robustness curves as the major evaluation criteria, we conduct large-scale experiments and draw several important findings, including: 1) there is an inherent trade-off between adversarial and natural robustness for the same model architecture; 2) adversarial training effectively improves adversarial robustness, especially when performed on Transformer architectures; 3) pre-training significantly improves natural robustness based on more training data or self-supervised learning. Based on ARES-Bench, we further analyze the training tricks in large-scale adversarial training on ImageNet. By designing the training settings accordingly, we achieve the new state-of-the-art adversarial robustness. We have made the benchmarking results and code platform publicly available.

Diffusion Models and Semi-Supervised Learners Benefit Mutually with Few Labels

We propose a three-stage training strategy called dual pseudo training (DPT) for conditional image generation and classification in semi-supervised learning. First, a classifier is trained on partially labeled data and predicts pseudo labels for all data. Second, a conditional generative model is trained on all data with pseudo labels and generates pseudo images given labels. Finally, the classifier is trained on real data augmented by pseudo images with labels. We demonstrate large-scale diffusion models and semi-supervised learners benefit mutually with a few labels via DPT. In particular, on the ImageNet 256x256 generation benchmark, DPT can generate realistic, diverse, and semantically correct images with very few labels. With two (i.e., < 0.2%) and five (i.e., < 0.4%) labels per class, DPT achieves an FID of 3.44 and 3.37 respectively, outperforming strong diffusion models with full labels, such as IDDPM, CDM, ADM, and LDM. Besides, DPT outperforms competitive semi-supervised baselines substantially on ImageNet classification benchmarks with one, two, and five labels per class, achieving state-of-the-art top-1 accuracies of 59.0 (+2.8), 69.5 (+3.0), and 73.6 (+1.2) respectively.

Confidence-based Reliable Learning under Dual Noises

Deep neural networks (DNNs) have achieved remarkable success in a variety of computer vision tasks, where massive labeled images are routinely required for model optimization. Yet, the data collected from the open world are unavoidably polluted by noise, which may significantly undermine the efficacy of the learned models. Various attempts have been made to reliably train DNNs under data noise, but they separately account for either the noise existing in the labels or that existing in the images. A naive combination of the two lines of works would suffer from the limitations in both sides, and miss the opportunities to handle the two kinds of noise in parallel. This work provides a first, unified framework for reliable learning under the joint (image, label)-noise. Technically, we develop a confidence-based sample filter to progressively filter out noisy data without the need of pre-specifying noise ratio. Then, we penalize the model uncertainty of the detected noisy data instead of letting the model continue over-fitting the misleading information in them. Experimental results on various challenging synthetic and real-world noisy datasets verify that the proposed method can outperform competing baselines in the aspect of classification performance.

Revisiting Discriminative vs. Generative Classifiers: Theory and Implications

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires $O(\log n)$ samples to approach its asymptotic error while the corresponding multiclass logistic regression requires $O(n)$ samples, where $n$ is the feature dimension. To establish it, we present a multiclass $\mathcal{H}$-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the ``two regimes'' phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

A Comprehensive Survey of Continual Learning: Theory, Method and Application

To cope with real-world dynamics, an intelligent agent needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance drop of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative strategies address continual learning, and how they are adapted to particular challenges in various applications. Through an in-depth discussion of continual learning in terms of the current trends, cross-directional prospects and interdisciplinary connections with neuroscience, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

Semiparametric Regression for Spatial Data via Deep Learning

In this work, we propose a deep learning-based method to perform semiparametric regression analysis for spatially dependent data. To be specific, we use a sparsely connected deep neural network with rectified linear unit (ReLU) activation function to estimate the unknown regression function that describes the relationship between response and covariates in the presence of spatial dependence. Under some mild conditions, the estimator is proven to be consistent, and the rate of convergence is determined by three factors: (1) the architecture of neural network class, (2) the smoothness and (intrinsic) dimension of true mean function, and (3) the magnitude of spatial dependence. Our method can handle well large data set owing to the stochastic gradient descent optimization algorithm. Simulation studies on synthetic data are conducted to assess the finite sample performance, the results of which indicate that the proposed method is capable of picking up the intricate relationship between response and covariates. Finally, a real data analysis is provided to demonstrate the validity and effectiveness of the proposed method.

Why Are Conditional Generative Models Better Than Unconditional Ones?

Extensive empirical evidence demonstrates that conditional generative models are easier to train and perform better than unconditional ones by exploiting the labels of data. So do score-based diffusion models. In this paper, we analyze the phenomenon formally and identify that the key of conditional learning is to partition the data properly. Inspired by the analyses, we propose self-conditioned diffusion models (SCDM), which is trained conditioned on indices clustered by the k-means algorithm on the features extracted by a model pre-trained in a self-supervised manner. SCDM significantly improves the unconditional model across various datasets and achieves a record-breaking FID of 3.94 on ImageNet 64x64 without labels. Besides, SCDM achieves a slightly better FID than the corresponding conditional model on CIFAR10.

DQ-DETR: Dual Query Detection Transformer for Phrase Extraction and Grounding

In this paper, we study the problem of visual grounding by considering both phrase extraction and grounding (PEG). In contrast to the previous phrase-known-at-test setting, PEG requires a model to extract phrases from text and locate objects from images simultaneously, which is a more practical setting in real applications. As phrase extraction can be regarded as a $1$D text segmentation problem, we formulate PEG as a dual detection problem and propose a novel DQ-DETR model, which introduces dual queries to probe different features from image and text for object prediction and phrase mask prediction. Each pair of dual queries is designed to have shared positional parts but different content parts. Such a design effectively alleviates the difficulty of modality alignment between image and text (in contrast to a single query design) and empowers Transformer decoder to leverage phrase mask-guided attention to improve performance. To evaluate the performance of PEG, we also propose a new metric CMAP (cross-modal average precision), analogous to the AP metric in object detection. The new metric overcomes the ambiguity of Recall@1 in many-box-to-one-phrase cases in phrase grounding. As a result, our PEG pre-trained DQ-DETR establishes new state-of-the-art results on all visual grounding benchmarks with a ResNet-101 backbone. For example, it achieves $91.04\%$ and $83.51\%$ in terms of recall rate on RefCOCO testA and testB with a ResNet-101 backbone. Code will be availabl at \url{https://github.com/IDEA-Research/DQ-DETR}.

Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from fully being explored in the field of physics-informed machine learning. We believe that this study will encourage researchers in the machine learning community to actively participate in the interdisciplinary research of physics-informed machine learning.