Learning the mapping between two function spaces has garnered considerable research attention. However, learning the solution operator of partial differential equations (PDEs) remains a challenge in scientific computing. Fourier neural operator (FNO) was recently proposed to learn solution operators, and it achieved an excellent performance. In this study, we propose a novel \textit{pseudo-differential integral operator} (PDIO) to analyze and generalize the Fourier integral operator in FNO. PDIO is inspired by a pseudo-differential operator, which is a generalized differential operator characterized by a certain symbol. We parameterize this symbol using a neural network and demonstrate that the neural network-based symbol is contained in a smooth symbol class. Subsequently, we verify that the PDIO is a bounded linear operator, and thus is continuous in the Sobolev space. We combine the PDIO with the neural operator to develop a \textit{pseudo-differential neural operator} (PDNO) and learn the nonlinear solution operator of PDEs. We experimentally validate the effectiveness of the proposed model by utilizing Darcy flow and the Navier-Stokes equation. The obtained results indicate that the proposed PDNO outperforms the existing neural operator approaches in most experiments.
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Multivariate Time Series (MTS) anomaly detection focuses on pinpointing samples that diverge from standard operational patterns, which is crucial for ensuring the safety and security of industrial applications. The primary challenge in this domain is to develop representations capable of discerning anomalies effectively. The prevalent methods for anomaly detection in the literature are predominantly reconstruction-based and predictive in nature. However, they typically concentrate on a single-dimensional instance level, thereby not fully harnessing the complex associations inherent in industrial MTS. To address this issue, we propose a novel self-supervised hierarchical contrastive consistency learning method for detecting anomalies in MTS, named HCL-MTSAD. It innovatively leverages data consistency at multiple levels inherent in industrial MTS, systematically capturing consistent associations across four latent levels-measurement, sample, channel, and process. By developing a multi-layer contrastive loss, HCL-MTSAD can extensively mine data consistency and spatio-temporal association, resulting in more informative representations. Subsequently, an anomaly discrimination module, grounded in self-supervised hierarchical contrastive learning, is designed to detect timestamp-level anomalies by calculating multi-scale data consistency. Extensive experiments conducted on six diverse MTS datasets retrieved from real cyber-physical systems and server machines, in comparison with 20 baselines, indicate that HCL-MTSAD's anomaly detection capability outperforms the state-of-the-art benchmark models by an average of 1.8\% in terms of F1 score.
To characterize the function space explored by neural networks (NNs) is an important aspect of learning theory. In this work, noticing that a multi-layer NN generates implicitly a hierarchy of reproducing kernel Hilbert spaces (RKHSs) - named a neural Hilbert ladder (NHL) - we define the function space as an infinite union of RKHSs, which generalizes the existing Barron space theory of two-layer NNs. We then establish several theoretical properties of the new space. First, we prove a correspondence between functions expressed by L-layer NNs and those belonging to L-level NHLs. Second, we prove generalization guarantees for learning an NHL with a controlled complexity measure. Third, we derive a non-Markovian dynamics of random fields that governs the evolution of the NHL which is induced by the training of multi-layer NNs in an infinite-width mean-field limit. Fourth, we show examples of depth separation in NHLs under the ReLU activation function. Finally, we perform numerical experiments to illustrate the feature learning aspect of NN training through the lens of NHLs.
In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness compared to Convolutional Neural Networks (CNNs). This paper presents clear empirical evidence through spectral analysis to elucidate the superiority of FNO over CNNs: FNO is significantly more capable of learning low-frequencies. This empirical evidence also unveils FNO's distinct low-frequency bias, which limits FNO's effectiveness in learning high-frequency information from PDE data. To tackle this challenge, we introduce SpecBoost, an ensemble learning framework that employs multiple FNOs to better capture high-frequency information. Specifically, a secondary FNO is utilized to learn the overlooked high-frequency information from the prediction residual of the initial FNO. Experiments demonstrate that SpecBoost noticeably enhances FNO's prediction accuracy on diverse PDE applications, achieving an up to 71% improvement.
Automated data labeling techniques are crucial for accelerating the development of deep learning models, particularly in complex medical imaging applications. However, ensuring accuracy and efficiency remains challenging. This paper presents iterative refinement strategies for automated data labeling in facial landmark diagnosis to enhance accuracy and efficiency for deep learning models in medical applications, including dermatology, plastic surgery, and ophthalmology. Leveraging feedback mechanisms and advanced algorithms, our approach iteratively refines initial labels, reducing reliance on manual intervention while improving label quality. Through empirical evaluation and case studies, we demonstrate the effectiveness of our proposed strategies in deep learning tasks across medical imaging domains. Our results highlight the importance of iterative refinement in automated data labeling to enhance the capabilities of deep learning systems in medical imaging applications.
Unsupervised (a.k.a. Self-supervised) representation learning (URL) has emerged as a new paradigm for time series analysis, because it has the ability to learn generalizable time series representation beneficial for many downstream tasks without using labels that are usually difficult to obtain. Considering that existing approaches have limitations in the design of the representation encoder and the learning objective, we have proposed Contrastive Shapelet Learning (CSL), the first URL method that learns the general-purpose shapelet-based representation through unsupervised contrastive learning, and shown its superior performance in several analysis tasks, such as time series classification, clustering, and anomaly detection. In this paper, we develop TimeCSL, an end-to-end system that makes full use of the general and interpretable shapelets learned by CSL to achieve explorable time series analysis in a unified pipeline. We introduce the system components and demonstrate how users interact with TimeCSL to solve different analysis tasks in the unified pipeline, and gain insight into their time series by exploring the learned shapelets and representation.
Despite the recent increase in research activity, deep-learning models have not yet been widely accepted in several real-world settings, such as medicine. The shortage of high-quality annotated data often hinders the development of robust and generalizable models, which do not suffer from degraded effectiveness when presented with out-of-distribution (OOD) datasets. Contrastive Self-Supervised Learning (SSL) offers a potential solution to labeled data scarcity, as it takes advantage of unlabeled data to increase model effectiveness and robustness. However, the selection of appropriate transformations during the learning process is not a trivial task and even breaks down the ability of the network to extract meaningful information. In this research, we propose uncovering the optimal augmentations for applying contrastive learning in 1D phonocardiogram (PCG) classification. We perform an extensive comparative evaluation of a wide range of audio-based augmentations, evaluate models on multiple datasets across downstream tasks, and report on the impact of each augmentation. We demonstrate that depending on its training distribution, the effectiveness of a fully-supervised model can degrade up to 32%, while SSL models only lose up to 10% or even improve in some cases. We argue and experimentally demonstrate that, contrastive SSL pretraining can assist in providing robust classifiers which can generalize to unseen, OOD data, without relying on time- and labor-intensive annotation processes by medical experts. Furthermore, the proposed evaluation protocol sheds light on the most promising and appropriate augmentations for robust PCG signal processing, by calculating their effect size on model training. Finally, we provide researchers and practitioners with a roadmap towards producing robust models for PCG classification, in addition to an open-source codebase for developing novel approaches.
Deep Learning (DL) has advanced various fields by extracting complex patterns from large datasets. However, the computational demands of DL models pose environmental and resource challenges. Deep shift neural networks (DSNNs) offer a solution by leveraging shift operations to reduce computational complexity at inference. Following the insights from standard DNNs, we are interested in leveraging the full potential of DSNNs by means of AutoML techniques. We study the impact of hyperparameter optimization (HPO) to maximize DSNN performance while minimizing resource consumption. Since this combines multi-objective (MO) optimization with accuracy and energy consumption as potentially complementary objectives, we propose to combine state-of-the-art multi-fidelity (MF) HPO with multi-objective optimization. Experimental results demonstrate the effectiveness of our approach, resulting in models with over 80\% in accuracy and low computational cost. Overall, our method accelerates efficient model development while enabling sustainable AI applications.
Human activity recognition (HAR) will be an essential function of various emerging applications. However, HAR typically encounters challenges related to modality limitations and label scarcity, leading to an application gap between current solutions and real-world requirements. In this work, we propose MESEN, a multimodal-empowered unimodal sensing framework, to utilize unlabeled multimodal data available during the HAR model design phase for unimodal HAR enhancement during the deployment phase. From a study on the impact of supervised multimodal fusion on unimodal feature extraction, MESEN is designed to feature a multi-task mechanism during the multimodal-aided pre-training stage. With the proposed mechanism integrating cross-modal feature contrastive learning and multimodal pseudo-classification aligning, MESEN exploits unlabeled multimodal data to extract effective unimodal features for each modality. Subsequently, MESEN can adapt to downstream unimodal HAR with only a few labeled samples. Extensive experiments on eight public multimodal datasets demonstrate that MESEN achieves significant performance improvements over state-of-the-art baselines in enhancing unimodal HAR by exploiting multimodal data.
Denoising diffusion probabilistic models for image inpainting aim to add the noise to the texture of image during the forward process and recover masked regions with unmasked ones of the texture via the reverse denoising process. Despite the meaningful semantics generation, the existing arts suffer from the semantic discrepancy between masked and unmasked regions, since the semantically dense unmasked texture fails to be completely degraded while the masked regions turn to the pure noise in diffusion process, leading to the large discrepancy between them. In this paper, we aim to answer how unmasked semantics guide texture denoising process;together with how to tackle the semantic discrepancy, to facilitate the consistent and meaningful semantics generation. To this end, we propose a novel structure-guided diffusion model named StrDiffusion, to reformulate the conventional texture denoising process under structure guidance to derive a simplified denoising objective for image inpainting, while revealing: 1) the semantically sparse structure is beneficial to tackle semantic discrepancy in early stage, while dense texture generates reasonable semantics in late stage; 2) the semantics from unmasked regions essentially offer the time-dependent structure guidance for the texture denoising process, benefiting from the time-dependent sparsity of the structure semantics. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective by exploiting the consistency of the denoised structure between masked and unmasked regions. Besides, we devise an adaptive resampling strategy as a formal criterion as whether structure is competent to guide the texture denoising process, while regulate their semantic correlations. Extensive experiments validate the merits of StrDiffusion over the state-of-the-arts. Our code is available at //github.com/htyjers/StrDiffusion.
Data augmentation is one of the regularization strategies for the training of deep learning models, which enhances generalizability and prevents overfitting, leading to performance improvement. Although researchers have proposed various data augmentation techniques, they often lack consideration for the difficulty of augmented data. Recently, another line of research suggests incorporating the concept of curriculum learning with data augmentation in the field of natural language processing. In this study, we adopt curriculum data augmentation for image data augmentation and propose colorful cutout, which gradually increases the noise and difficulty introduced in the augmented image. Our experimental results highlight the possibility of curriculum data augmentation for image data. We publicly released our source code to improve the reproducibility of our study.
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