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Obtaining the solutions of partial differential equations based on various machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine (called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gauss, sine, and trigonometric (sin+cos) functions are introduced to assess our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing approaches for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equation in both regular and irregular domains.

Path reasoning methods over knowledge graphs have gained popularity for their potential to improve transparency in recommender systems. However, the resulting models still rely on pre-trained knowledge graph embeddings, fail to fully exploit the interdependence between entities and relations in the KG for recommendation, and may generate inaccurate explanations. In this paper, we introduce PEARLM, a novel approach that efficiently captures user behaviour and product-side knowledge through language modelling. With our approach, knowledge graph embeddings are directly learned from paths over the KG by the language model, which also unifies entities and relations in the same optimisation space. Constraints on the sequence decoding additionally guarantee path faithfulness with respect to the KG. Experiments on two datasets show the effectiveness of our approach compared to state-of-the-art baselines. Source code and datasets: AVAILABLE AFTER GETTING ACCEPTED.

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

While deep reinforcement learning (RL) has been demonstrated effective in solving complex control tasks, sample efficiency remains a key challenge due to the large amounts of data required for remarkable performance. Existing research explores the application of representation learning for data-efficient RL, e.g., learning predictive representations by predicting long-term future states. However, many existing methods do not fully exploit the structural information inherent in sequential state signals, which can potentially improve the quality of long-term decision-making but is difficult to discern in the time domain. To tackle this problem, we propose State Sequences Prediction via Fourier Transform (SPF), a novel method that exploits the frequency domain of state sequences to extract the underlying patterns in time series data for learning expressive representations efficiently. Specifically, we theoretically analyze the existence of structural information in state sequences, which is closely related to policy performance and signal regularity, and then propose to predict the Fourier transform of infinite-step future state sequences to extract such information. One of the appealing features of SPF is that it is simple to implement while not requiring storage of infinite-step future states as prediction targets. Experiments demonstrate that the proposed method outperforms several state-of-the-art algorithms in terms of both sample efficiency and performance.

Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word ambiguity, (2) word synonymity, and (3) dynamic contextual dependency. To address these challenges, we propose a novel GNN-based sparse structure learning model for inductive document classification. Specifically, a document-level graph is initially generated by a disjoint union of sentence-level word co-occurrence graphs. Our model collects a set of trainable edges connecting disjoint words between sentences and employs structure learning to sparsely select edges with dynamic contextual dependencies. Graphs with sparse structures can jointly exploit local and global contextual information in documents through GNNs. For inductive learning, the refined document graph is further fed into a general readout function for graph-level classification and optimization in an end-to-end manner. Extensive experiments on several real-world datasets demonstrate that the proposed model outperforms most state-of-the-art results, and reveal the necessity to learn sparse structures for each document.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

Aspect based sentiment analysis (ABSA) can provide more detailed information than general sentiment analysis, because it aims to predict the sentiment polarities of the given aspects or entities in text. We summarize previous approaches into two subtasks: aspect-category sentiment analysis (ACSA) and aspect-term sentiment analysis (ATSA). Most previous approaches employ long short-term memory and attention mechanisms to predict the sentiment polarity of the concerned targets, which are often complicated and need more training time. We propose a model based on convolutional neural networks and gating mechanisms, which is more accurate and efficient. First, the novel Gated Tanh-ReLU Units can selectively output the sentiment features according to the given aspect or entity. The architecture is much simpler than attention layer used in the existing models. Second, the computations of our model could be easily parallelized during training, because convolutional layers do not have time dependency as in LSTM layers, and gating units also work independently. The experiments on SemEval datasets demonstrate the efficiency and effectiveness of our models.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.