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We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem of linear poroelasticity with high contrast. Firstly, dominant basis functions generated by the CEM-GMsFEM approach are used to capture important degrees of freedom and it is known to give contrast-independent convergence that scales with the mesh size. In typical situation, one has very few degrees of freedom in dominant basis functions. This part is treated implicitly. Secondly, we design and introduce an additional space in the complement space and these degrees are treated explicitly. We also investigate the CFL-type stability restriction for this problem, and the restriction for the time step is contrast independent.

Math Word Problems (MWP) aims to automatically solve mathematical questions given in texts. Previous studies tend to design complex models to capture additional information in the original text so as to enable the model to gain more comprehensive features. In this paper, we turn our attention in the opposite direction, and work on how to discard redundant features containing spurious correlations for MWP. To this end, we design an Expression Syntax Information Bottleneck method for MWP (called ESIB) based on variational information bottleneck, which extracts essential features of expression syntax tree while filtering latent-specific redundancy containing syntax-irrelevant features. The key idea of ESIB is to encourage multiple models to predict the same expression syntax tree for different problem representations of the same problem by mutual learning so as to capture consistent information of expression syntax tree and discard latent-specific redundancy. To improve the generalization ability of the model and generate more diverse expressions, we design a self-distillation loss to encourage the model to rely more on the expression syntax information in the latent space. Experimental results on two large-scale benchmarks show that our model not only achieves state-of-the-art results but also generates more diverse solutions. The code is available.

We propose a novel interpretable deep neural network for text classification, called ProtoryNet, based on a new concept of prototype trajectories. Motivated by the prototype theory in modern linguistics, ProtoryNet makes a prediction by finding the most similar prototype for each sentence in a text sequence and feeding an RNN backbone with the proximity of each sentence to the corresponding active prototype. The RNN backbone then captures the temporal pattern of the prototypes, which we refer to as prototype trajectories. Prototype trajectories enable intuitive and fine-grained interpretation of the reasoning process of the RNN model, in resemblance to how humans analyze texts. We also design a prototype pruning procedure to reduce the total number of prototypes used by the model for better interpretability. Experiments on multiple public data sets show that ProtoryNet is more accurate than the baseline prototype-based deep neural net and reduces the performance gap compared to state-of-the-art black-box models. In addition, after prototype pruning, the resulting ProtoryNet models only need less than or around 20 prototypes for all datasets, which significantly benefits interpretability. Furthermore, we report a survey result indicating that human users find ProtoryNet more intuitive and easier to understand than other prototype-based methods.

We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(\sigma^{-1}_{\min} s_{\star} H \sqrt{N})$, where $\sigma_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound up to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.

Adversarial contrastive learning (ACL) is a technique that enhances standard contrastive learning (SCL) by incorporating adversarial data to learn a robust representation that can withstand adversarial attacks and common corruptions without requiring costly annotations. To improve transferability, the existing work introduced the standard invariant regularization (SIR) to impose style-independence property to SCL, which can exempt the impact of nuisance style factors in the standard representation. However, it is unclear how the style-independence property benefits ACL-learned robust representations. In this paper, we leverage the technique of causal reasoning to interpret the ACL and propose adversarial invariant regularization (AIR) to enforce independence from style factors. We regulate the ACL using both SIR and AIR to output the robust representation. Theoretically, we show that AIR implicitly encourages the representational distance between different views of natural data and their adversarial variants to be independent of style factors. Empirically, our experimental results show that invariant regularization significantly improves the performance of state-of-the-art ACL methods in terms of both standard generalization and robustness on downstream tasks. To the best of our knowledge, we are the first to apply causal reasoning to interpret ACL and develop AIR for enhancing ACL-learned robust representations. Our source code is at //github.com/GodXuxilie/Enhancing_ACL_via_AIR.

We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple tail-recursive programs in which the arguments of recursive calls can non-linearly refer to a variable that counts the number of recursive calls. The nomenclature is motivated by the fact that over a unary alphabet P-finite automata compute so-called P-finite sequences, that is, sequences that satisfy a linear recurrence with polynomial coefficients. Our main result shows that P-finite automata can be learned in polynomial time in Angluin's MAT exact learning model. This generalises the classical results that deterministic finite automata and weighted automata over a field are respectively polynomial-time learnable in the MAT model.

Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in recent years due to their improved approximation accuracy and better calibrated uncertainty estimates compared to Random Fourier Feature (RFF) methods. However, a key limitation of QFF is that its performance can suffer from well-known pathologies related to highly oscillatory quadrature, resulting in mediocre approximation with limited features. We address this critical issue via a new Trigonometric Quadrature Fourier Feature (TQFF) method, which uses a novel non-Gaussian quadrature rule specifically tailored for the desired Fourier transform. We derive an exact quadrature rule for TQFF, along with kernel approximation error bounds for the resulting feature map. We then demonstrate the improved performance of our method over RFF and Gaussian QFF in a suite of numerical experiments and applications, and show the TQFF enjoys accurate GP approximations over a broad range of length-scales using fewer features.

We propose a novel interpretable deep neural network for text classification, called ProtoryNet, based on a new concept of prototype trajectories. Motivated by the prototype theory in modern linguistics, ProtoryNet makes a prediction by finding the most similar prototype for each sentence in a text sequence and feeding an RNN backbone with the proximity of each sentence to the corresponding active prototype. The RNN backbone then captures the temporal pattern of the prototypes, which we refer to as prototype trajectories. Prototype trajectories enable intuitive and fine-grained interpretation of the reasoning process of the RNN model, in resemblance to how humans analyze texts. We also design a prototype pruning procedure to reduce the total number of prototypes used by the model for better interpretability. Experiments on multiple public data sets show that ProtoryNet is more accurate than the baseline prototype-based deep neural net and reduces the performance gap compared to state-of-the-art black-box models. In addition, after prototype pruning, the resulting ProtoryNet models only need less than or around 20 prototypes for all datasets, which significantly benefits interpretability. Furthermore, we report a survey result indicating that human users find ProtoryNet more intuitive and easier to understand than other prototype-based methods.

Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

We study the problem of textual relation embedding with distant supervision. To combat the wrong labeling problem of distant supervision, we propose to embed textual relations with global statistics of relations, i.e., the co-occurrence statistics of textual and knowledge base relations collected from the entire corpus. This approach turns out to be more robust to the training noise introduced by distant supervision. On a popular relation extraction dataset, we show that the learned textual relation embedding can be used to augment existing relation extraction models and significantly improve their performance. Most remarkably, for the top 1,000 relational facts discovered by the best existing model, the precision can be improved from 83.9% to 89.3%.