Solving partial differential equations (PDEs) using a data-driven approach has become increasingly common. The recent development of the operator learning paradigm has enabled the solution of a broader range of PDE-related problems. We propose an operator learning method to solve time-dependent PDEs continuously in time without needing any temporal discretization. The proposed approach, named DiTTO, is inspired by latent diffusion models. While diffusion models are usually used in generative artificial intelligence tasks, their time-conditioning mechanism is extremely useful for PDEs. The diffusion-inspired framework is combined with elements from the Transformer architecture to improve its capabilities. We demonstrate the effectiveness of the new approach on a wide variety of PDEs in multiple dimensions, namely the 1-D Burgers' equation, 2-D Navier-Stokes equations, and the acoustic wave equation in 2-D and 3-D. DiTTO achieves state-of-the-art results in terms of accuracy for these problems. We also present a method to improve the performance of DiTTO by using fast sampling concepts from diffusion models. Finally, we show that DiTTO can accurately perform zero-shot super-resolution in time.
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Computing gradients of an expectation with respect to the distributional parameters of a discrete distribution is a problem arising in many fields of science and engineering. Typically, this problem is tackled using Reinforce, which frames the problem of gradient estimation as a Monte Carlo simulation. Unfortunately, the Reinforce estimator is especially sensitive to discrepancies between the true probability distribution and the drawn samples, a common issue in low sampling regimes that results in inaccurate gradient estimates. In this paper, we introduce DBsurf, a reinforce-based estimator for discrete distributions that uses a novel sampling procedure to reduce the discrepancy between the samples and the actual distribution. To assess the performance of our estimator, we subject it to a diverse set of tasks. Among existing estimators, DBsurf attains the lowest variance in a least squares problem commonly used in the literature for benchmarking. Furthermore, DBsurf achieves the best results for training variational auto-encoders (VAE) across different datasets and sampling setups. Finally, we apply DBsurf to build a simple and efficient Neural Architecture Search (NAS) algorithm with state-of-the-art performance.
Developers introduce code clones to improve programming productivity. Many existing studies have achieved impressive performance in monolingual code clone detection. However, during software development, more and more developers write semantically equivalent programs with different languages to support different platforms and help developers translate projects from one language to another. Considering that collecting cross-language parallel data, especially for low-resource languages, is expensive and time-consuming, how designing an effective cross-language model that does not rely on any parallel data is a significant problem. In this paper, we propose a novel method named ZC3 for Zero-shot Cross-language Code Clone detection. ZC3 designs the contrastive snippet prediction to form an isomorphic representation space among different programming languages. Based on this, ZC3 exploits domain-aware learning and cycle consistency learning to further constrain the model to generate representations that are aligned among different languages meanwhile are diacritical for different types of clones. To evaluate our approach, we conduct extensive experiments on four representative cross-language clone detection datasets. Experimental results show that ZC3 outperforms the state-of-the-art baselines by 67.12%, 51.39%, 14.85%, and 53.01% on the MAP score, respectively. We further investigate the representational distribution of different languages and discuss the effectiveness of our method.
Deep Neural Networks (DNNs) have shown unparalleled achievements in numerous applications, reflecting their proficiency in managing vast data sets. Yet, their static structure limits their adaptability in ever-changing environments. This research presents a new algorithm that allows the convolutional layer of a Convolutional Neural Network (CNN) to dynamically evolve based on data input, while still being seamlessly integrated into existing DNNs. Instead of a rigid architecture, our approach iteratively introduces kernels to the convolutional layer, gauging its real-time response to varying data. This process is refined by evaluating the layer's capacity to discern image features, guiding its growth. Remarkably, our unsupervised method has outstripped its supervised counterparts across diverse datasets like MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100. It also showcases enhanced adaptability in transfer learning scenarios. By introducing a data-driven model scalability strategy, we are filling a void in deep learning, leading to more flexible and efficient DNNs suited for dynamic settings. Code:(//github.com/YunjieZhu/Extensible-Convolutional-Layer-git-version).
Ensemble methods are commonly used in classification due to their remarkable performance. Achieving high accuracy in a data stream environment is a challenging task considering disruptive changes in the data distribution, also known as concept drift. A greater diversity of ensemble components is known to enhance prediction accuracy in such settings. Despite the diversity of components within an ensemble, not all contribute as expected to its overall performance. This necessitates a method for selecting components that exhibit high performance and diversity. We present a novel ensemble construction and maintenance approach based on MMR (Maximal Marginal Relevance) that dynamically combines the diversity and prediction accuracy of components during the process of structuring an ensemble. The experimental results on both four real and 11 synthetic datasets demonstrate that the proposed approach (DynED) provides a higher average mean accuracy compared to the five state-of-the-art baselines.
Knowledge graph completion (KGC) aims to discover missing relations of query entities. Current text-based models utilize the entity name and description to infer the tail entity given the head entity and a certain relation. Existing approaches also consider the neighborhood of the head entity. However, these methods tend to model the neighborhood using a flat structure and are only restricted to 1-hop neighbors. In this work, we propose a node neighborhood-enhanced framework for knowledge graph completion. It models the head entity neighborhood from multiple hops using graph neural networks to enrich the head node information. Moreover, we introduce an additional edge link prediction task to improve KGC. Evaluation on two public datasets shows that this framework is simple yet effective. The case study also shows that the model is able to predict explainable predictions.
Following unprecedented success on the natural language tasks, Transformers have been successfully applied to several computer vision problems, achieving state-of-the-art results and prompting researchers to reconsider the supremacy of convolutional neural networks (CNNs) as {de facto} operators. Capitalizing on these advances in computer vision, the medical imaging field has also witnessed growing interest for Transformers that can capture global context compared to CNNs with local receptive fields. Inspired from this transition, in this survey, we attempt to provide a comprehensive review of the applications of Transformers in medical imaging covering various aspects, ranging from recently proposed architectural designs to unsolved issues. Specifically, we survey the use of Transformers in medical image segmentation, detection, classification, reconstruction, synthesis, registration, clinical report generation, and other tasks. In particular, for each of these applications, we develop taxonomy, identify application-specific challenges as well as provide insights to solve them, and highlight recent trends. Further, we provide a critical discussion of the field's current state as a whole, including the identification of key challenges, open problems, and outlining promising future directions. We hope this survey will ignite further interest in the community and provide researchers with an up-to-date reference regarding applications of Transformer models in medical imaging. Finally, to cope with the rapid development in this field, we intend to regularly update the relevant latest papers and their open-source implementations at \url{//github.com/fahadshamshad/awesome-transformers-in-medical-imaging}.
Generalization to out-of-distribution (OOD) data is a capability natural to humans yet challenging for machines to reproduce. This is because most learning algorithms strongly rely on the i.i.d.~assumption on source/target data, which is often violated in practice due to domain shift. Domain generalization (DG) aims to achieve OOD generalization by using only source data for model learning. Since first introduced in 2011, research in DG has made great progresses. In particular, intensive research in this topic has led to a broad spectrum of methodologies, e.g., those based on domain alignment, meta-learning, data augmentation, or ensemble learning, just to name a few; and has covered various vision applications such as object recognition, segmentation, action recognition, and person re-identification. In this paper, for the first time a comprehensive literature review is provided to summarize the developments in DG for computer vision over the past decade. Specifically, we first cover the background by formally defining DG and relating it to other research fields like domain adaptation and transfer learning. Second, we conduct a thorough review into existing methods and present a categorization based on their methodologies and motivations. Finally, we conclude this survey with insights and discussions on future research directions.
Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.
With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation. Furthermore, XLNet integrates ideas from Transformer-XL, the state-of-the-art autoregressive model, into pretraining. Empirically, XLNet outperforms BERT on 20 tasks, often by a large margin, and achieves state-of-the-art results on 18 tasks including question answering, natural language inference, sentiment analysis, and document ranking.
Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a deep learning approach to spectral clustering that overcomes the above shortcomings. Our network, which we call SpectralNet, learns a map that embeds input data points into the eigenspace of their associated graph Laplacian matrix and subsequently clusters them. We train SpectralNet using a procedure that involves constrained stochastic optimization. Stochastic optimization allows it to scale to large datasets, while the constraints, which are implemented using a special-purpose output layer, allow us to keep the network output orthogonal. Moreover, the map learned by SpectralNet naturally generalizes the spectral embedding to unseen data points. To further improve the quality of the clustering, we replace the standard pairwise Gaussian affinities with affinities leaned from unlabeled data using a Siamese network. Additional improvement can be achieved by applying the network to code representations produced, e.g., by standard autoencoders. Our end-to-end learning procedure is fully unsupervised. In addition, we apply VC dimension theory to derive a lower bound on the size of SpectralNet. State-of-the-art clustering results are reported on the Reuters dataset. Our implementation is publicly available at //github.com/kstant0725/SpectralNet .
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