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Supervised learning problems may become ill-posed when there is a lack of information, resulting in unstable and non-unique solutions. However, instead of solely relying on regularization, initializing an informative ill-posed operator is akin to posing better questions to achieve more accurate answers. The Fredholm integral equation of the first kind (FIFK) is a reliable ill-posed operator that can integrate distributions and prior knowledge as input information. By incorporating input distributions and prior knowledge, the FIFK operator can address the limitations of using high-dimensional input distributions by semi-supervised assumptions, leading to more precise approximations of the integral operator. Additionally, the FIFK's incorporation of probabilistic principles can further enhance the accuracy and effectiveness of solutions. In cases of noisy operator equations and limited data, the FIFK's flexibility in defining problems using prior information or cross-validation with various kernel designs is especially advantageous. This capability allows for detailed problem definitions and facilitates achieving high levels of accuracy and stability in solutions. In our study, we examined the FIFK through two different approaches. Firstly, we implemented a semi-supervised assumption by using the same Fredholm operator kernel and data function kernel and incorporating unlabeled information. Secondly, we used the MSDF method, which involves selecting different kernels on both sides of the equation to define when the mapping kernel is different from the data function kernel. To assess the effectiveness of the FIFK and the proposed methods in solving ill-posed problems, we conducted experiments on a real-world dataset. Our goal was to compare the performance of these methods against the widely used least-squares method and other comparable methods.

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The success of deep learning is frequently described as the ability to train all parameters of a network on a specific application in an end-to-end fashion. Yet, several design choices on the camera level, including the pixel layout of the sensor, are considered as pre-defined and fixed, and high resolution, regular pixel layouts are considered to be the most generic ones in computer vision and graphics, treating all regions of an image as equally important. While several works have considered non-uniform, \eg, hexagonal or foveated, pixel layouts in hardware and image processing, the layout has not been integrated into the end-to-end learning paradigm so far. In this work, we present the first truly end-to-end trained imaging pipeline that optimizes the size and distribution of pixels on the imaging sensor jointly with the parameters of a given neural network on a specific task. We derive an analytic, differentiable approach for the sensor layout parameterization that allows for task-specific, local varying pixel resolutions. We present two pixel layout parameterization functions: rectangular and curvilinear grid shapes that retain a regular topology. We provide a drop-in module that approximates sensor simulation given existing high-resolution images to directly connect our method with existing deep learning models. We show that network predictions benefit from learnable pixel layouts for two different downstream tasks, classification and semantic segmentation.

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.

Neural architecture-based recommender systems have achieved tremendous success in recent years. However, when dealing with highly sparse data, they still fall short of expectation. Self-supervised learning (SSL), as an emerging technique to learn with unlabeled data, recently has drawn considerable attention in many fields. There is also a growing body of research proceeding towards applying SSL to recommendation for mitigating the data sparsity issue. In this survey, a timely and systematical review of the research efforts on self-supervised recommendation (SSR) is presented. Specifically, we propose an exclusive definition of SSR, on top of which we build a comprehensive taxonomy to divide existing SSR methods into four categories: contrastive, generative, predictive, and hybrid. For each category, the narrative unfolds along its concept and formulation, the involved methods, and its pros and cons. Meanwhile, to facilitate the development and evaluation of SSR models, we release an open-source library SELFRec, which incorporates multiple benchmark datasets and evaluation metrics, and has implemented a number of state-of-the-art SSR models for empirical comparison. Finally, we shed light on the limitations in the current research and outline the future research directions.

Image-level weakly supervised semantic segmentation (WSSS) is a fundamental yet challenging computer vision task facilitating scene understanding and automatic driving. Most existing methods resort to classification-based Class Activation Maps (CAMs) to play as the initial pseudo labels, which tend to focus on the discriminative image regions and lack customized characteristics for the segmentation task. To alleviate this issue, we propose a novel activation modulation and recalibration (AMR) scheme, which leverages a spotlight branch and a compensation branch to obtain weighted CAMs that can provide recalibration supervision and task-specific concepts. Specifically, an attention modulation module (AMM) is employed to rearrange the distribution of feature importance from the channel-spatial sequential perspective, which helps to explicitly model channel-wise interdependencies and spatial encodings to adaptively modulate segmentation-oriented activation responses. Furthermore, we introduce a cross pseudo supervision for dual branches, which can be regarded as a semantic similar regularization to mutually refine two branches. Extensive experiments show that AMR establishes a new state-of-the-art performance on the PASCAL VOC 2012 dataset, surpassing not only current methods trained with the image-level of supervision but also some methods relying on stronger supervision, such as saliency label. Experiments also reveal that our scheme is plug-and-play and can be incorporated with other approaches to boost their performance.

Deep learning on graphs has attracted significant interests recently. However, most of the works have focused on (semi-) supervised learning, resulting in shortcomings including heavy label reliance, poor generalization, and weak robustness. To address these issues, self-supervised learning (SSL), which extracts informative knowledge through well-designed pretext tasks without relying on manual labels, has become a promising and trending learning paradigm for graph data. Different from SSL on other domains like computer vision and natural language processing, SSL on graphs has an exclusive background, design ideas, and taxonomies. Under the umbrella of graph self-supervised learning, we present a timely and comprehensive review of the existing approaches which employ SSL techniques for graph data. We construct a unified framework that mathematically formalizes the paradigm of graph SSL. According to the objectives of pretext tasks, we divide these approaches into four categories: generation-based, auxiliary property-based, contrast-based, and hybrid approaches. We further conclude the applications of graph SSL across various research fields and summarize the commonly used datasets, evaluation benchmark, performance comparison and open-source codes of graph SSL. Finally, we discuss the remaining challenges and potential future directions in this research field.

The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.

Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

We propose a novel attention gate (AG) model for medical imaging that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting salient features useful for a specific task. This enables us to eliminate the necessity of using explicit external tissue/organ localisation modules of cascaded convolutional neural networks (CNNs). AGs can be easily integrated into standard CNN architectures such as the U-Net model with minimal computational overhead while increasing the model sensitivity and prediction accuracy. The proposed Attention U-Net architecture is evaluated on two large CT abdominal datasets for multi-class image segmentation. Experimental results show that AGs consistently improve the prediction performance of U-Net across different datasets and training sizes while preserving computational efficiency. The code for the proposed architecture is publicly available.

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