Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new behavior of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information -- the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.

Discovering governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in a variety of areas of science and engineering. Current methods require either some prior knowledge (e.g., candidate PDE terms) to discover the PDE form, or a large dataset to learn a surrogate model of the PDE solution operator. Here, we propose the first solution operator learning method that only needs one PDE solution, i.e., one-shot learning. We first decompose the entire computational domain into small domains, where we learn a local solution operator, and then we find the coupled solution via either mesh-based fixed-point iteration or meshfree local-solution-operator informed neural networks. We demonstrate the effectiveness of our method on different PDEs, and our method exhibits a strong generalization property.

Embedding words in vector space is a fundamental first step in state-of-the-art natural language processing (NLP). Typical NLP solutions employ pre-defined vector representations to improve generalization by co-locating similar words in vector space. For instance, Word2Vec is a self-supervised predictive model that captures the context of words using a neural network. Similarly, GLoVe is a popular unsupervised model incorporating corpus-wide word co-occurrence statistics. Such word embedding has significantly boosted important NLP tasks, including sentiment analysis, document classification, and machine translation. However, the embeddings are dense floating-point vectors, making them expensive to compute and difficult to interpret. In this paper, we instead propose to represent the semantics of words with a few defining words that are related using propositional logic. To produce such logical embeddings, we introduce a Tsetlin Machine-based autoencoder that learns logical clauses self-supervised. The clauses consist of contextual words like "black," "cup," and "hot" to define other words like "coffee," thus being human-understandable. We evaluate our embedding approach on several intrinsic and extrinsic benchmarks, outperforming GLoVe on six classification tasks. Furthermore, we investigate the interpretability of our embedding using the logical representations acquired during training. We also visualize word clusters in vector space, demonstrating how our logical embedding co-locate similar words.

Model bias triggered by long-tailed data has been widely studied. However, measure based on the number of samples cannot explicate three phenomena simultaneously: (1) Given enough data, the classification performance gain is marginal with additional samples. (2) Classification performance decays precipitously as the number of training samples decreases when there is insufficient data. (3) Model trained on sample-balanced datasets still has different biases for different classes. In this work, we define and quantify the semantic scale of classes, which is used to measure the feature diversity of classes. It is exciting to find experimentally that there is a marginal effect of semantic scale, which perfectly describes the first two phenomena. Further, the quantitative measurement of semantic scale imbalance is proposed, which can accurately reflect model bias on multiple datasets, even on sample-balanced data, revealing a novel perspective for the study of class imbalance. Due to the prevalence of semantic scale imbalance, we propose semantic-scale-balanced learning, including a general loss improvement scheme and a dynamic re-weighting training framework that overcomes the challenge of calculating semantic scales in real-time during iterations. Comprehensive experiments show that dynamic semantic-scale-balanced learning consistently enables the model to perform superiorly on large-scale long-tailed and non-long-tailed natural and medical datasets, which is a good starting point for mitigating the prevalent but unnoticed model bias.

Tsetlin Machine (TM) has been gaining popularity as an inherently interpretable machine leaning method that is able to achieve promising performance with low computational complexity on a variety of applications. The interpretability and the low computational complexity of the TM are inherited from the Boolean expressions for representing various sub-patterns. Although possessing favorable properties, TM has not been the go-to method for AI applications, mainly due to its conceptual and theoretical differences compared with perceptrons and neural networks, which are more widely known and well understood. In this paper, we provide detailed insights for the operational concept of the TM, and try to bridge the gap in the theoretical understanding between the perceptron and the TM. More specifically, we study the operational concept of the TM following the analytical structure of perceptrons, showing the resemblance between the perceptrons and the TM. Through the analysis, we indicated that the TM's weight update can be considered as a special case of the gradient weight update. We also perform an empirical analysis of TM by showing the flexibility in determining the clause length, visualization of decision boundaries and obtaining interpretable boolean expressions from TM. In addition, we also discuss the advantages of TM in terms of its structure and its ability to solve more complex problems.

The stock market prediction has been a traditional yet complex problem researched within diverse research areas and application domains due to its non-linear, highly volatile and complex nature. Existing surveys on stock market prediction often focus on traditional machine learning methods instead of deep learning methods. Deep learning has dominated many domains, gained much success and popularity in recent years in stock market prediction. This motivates us to provide a structured and comprehensive overview of the research on stock market prediction focusing on deep learning techniques. We present four elaborated subtasks of stock market prediction and propose a novel taxonomy to summarize the state-of-the-art models based on deep neural networks from 2011 to 2022. In addition, we also provide detailed statistics on the datasets and evaluation metrics commonly used in the stock market. Finally, we highlight some open issues and point out several future directions by sharing some new perspectives on stock market prediction.

To improve the performance of the dual-encoder retriever, one effective approach is knowledge distillation from the cross-encoder ranker. Existing works construct the candidate passages following the supervised learning setting where a query is paired with a positive passage and a batch of negatives. However, through empirical observation, we find that even the hard negatives from advanced methods are still too trivial for the teacher to distinguish, preventing the teacher from transferring abundant dark knowledge to the student through its soft label. To alleviate this issue, we propose ADAM, a knowledge distillation framework that can better transfer the dark knowledge held in the teacher with Adaptive Dark exAMples. Different from previous works that only rely on one positive and hard negatives as candidate passages, we create dark examples that all have moderate relevance to the query through mixing-up and masking in discrete space. Furthermore, as the quality of knowledge held in different training instances varies as measured by the teacher's confidence score, we propose a self-paced distillation strategy that adaptively concentrates on a subset of high-quality instances to conduct our dark-example-based knowledge distillation to help the student learn better. We conduct experiments on two widely-used benchmarks and verify the effectiveness of our method.

Bilevel optimization plays an essential role in many machine learning tasks, ranging from hyperparameter optimization to meta-learning. Existing studies on bilevel optimization, however, focus on either centralized or synchronous distributed setting. The centralized bilevel optimization approaches require collecting massive amount of data to a single server, which inevitably incur significant communication expenses and may give rise to data privacy risks. Synchronous distributed bilevel optimization algorithms, on the other hand, often face the straggler problem and will immediately stop working if a few workers fail to respond. As a remedy, we propose Asynchronous Distributed Bilevel Optimization (ADBO) algorithm. The proposed ADBO can tackle bilevel optimization problems with both nonconvex upper-level and lower-level objective functions, and its convergence is theoretically guaranteed. Furthermore, it is revealed through theoretic analysis that the iteration complexity of ADBO to obtain the $\epsilon$-stationary point is upper bounded by $\mathcal{O}(\frac{1}{{{\epsilon ^2}}})$. Thorough empirical studies on public datasets have been conducted to elucidate the effectiveness and efficiency of the proposed ADBO.

The dual-encoder has become the de facto architecture for dense retrieval. Typically, it computes the latent representations of the query and document independently, thus failing to fully capture the interactions between the query and document. To alleviate this, recent work expects to get query-informed representations of documents. During training, it expands the document with a real query, while replacing the real query with a generated pseudo query at inference. This discrepancy between training and inference makes the dense retrieval model pay more attention to the query information but ignore the document when computing the document representation. As a result, it even performs worse than the vanilla dense retrieval model, since its performance depends heavily on the relevance between the generated queries and the real query. In this paper, we propose a curriculum sampling strategy, which also resorts to the pseudo query at training and gradually increases the relevance of the generated query to the real query. In this way, the retrieval model can learn to extend its attention from the document only to both the document and query, hence getting high-quality query-informed document representations. Experimental results on several passage retrieval datasets show that our approach outperforms the previous dense retrieval methods1.

Camouflaged objects are seamlessly blended in with their surroundings, which brings a challenging detection task in computer vision. Optimizing a convolutional neural network (CNN) for camouflaged object detection (COD) tends to activate local discriminative regions while ignoring complete object extent, causing the partial activation issue which inevitably leads to missing or redundant regions of objects. In this paper, we argue that partial activation is caused by the intrinsic characteristics of CNN, where the convolution operations produce local receptive fields and experience difficulty to capture long-range feature dependency among image regions. In order to obtain feature maps that could activate full object extent, keeping the segmental results from being overwhelmed by noisy features, a novel framework termed Cross-Model Detail Querying network (DQnet) is proposed. It reasons the relations between long-range-aware representations and multi-scale local details to make the enhanced representation fully highlight the object regions and eliminate noise on non-object regions. Specifically, a vanilla ViT pretrained with self-supervised learning (SSL) is employed to model long-range dependencies among image regions. A ResNet is employed to enable learning fine-grained spatial local details in multiple scales. Then, to effectively retrieve object-related details, a Relation-Based Querying (RBQ) module is proposed to explore window-based interactions between the global representations and the multi-scale local details. Extensive experiments are conducted on the widely used COD datasets and show that our DQnet outperforms the current state-of-the-arts.