Many data extraction tasks of practical relevance require not only syntactic pattern matching but also semantic reasoning about the content of the underlying text. While regular expressions are very well suited for tasks that require only syntactic pattern matching, they fall short for data extraction tasks that involve both a syntactic and semantic component. To address this issue, we introduce semantic regexes, a generalization of regular expressions that facilitates combined syntactic and semantic reasoning about textual data. We also propose a novel learning algorithm that can synthesize semantic regexes from a small number of positive and negative examples. Our proposed learning algorithm uses a combination of neural sketch generation and compositional type-directed synthesis for fast and effective generalization from a small number of examples. We have implemented these ideas in a new tool called Smore and evaluated it on representative data extraction tasks involving several textual datasets. Our evaluation shows that semantic regexes can better support complex data extraction tasks than standard regular expressions and that our learning algorithm significantly outperforms existing tools, including state-of-the-art neural networks and program synthesis tools.
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In continual learning, the learner learns multiple tasks in sequence, with data being acquired only once for each task. Catastrophic forgetting is a major challenge to continual learning. To reduce forgetting, some existing rehearsal-based methods use episodic memory to replay samples of previous tasks. However, in the process of knowledge integration when learning a new task, this strategy also suffers from catastrophic forgetting due to an imbalance between old and new knowledge. To address this problem, we propose a novel replay strategy called Manifold Expansion Replay (MaER). We argue that expanding the implicit manifold of the knowledge representation in the episodic memory helps to improve the robustness and expressiveness of the model. To this end, we propose a greedy strategy to keep increasing the diameter of the implicit manifold represented by the knowledge in the buffer during memory management. In addition, we introduce Wasserstein distance instead of cross entropy as distillation loss to preserve previous knowledge. With extensive experimental validation on MNIST, CIFAR10, CIFAR100, and TinyImageNet, we show that the proposed method significantly improves the accuracy in continual learning setup, outperforming the state of the arts.
Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic regression with nonconvex regularization term. In this paper, we propose a unified framework to solve $\ell_1$-regularized logistic regression, which can be naturally extended to nonconvex regularization term, as long as certain requirement is satisfied. In addition, we also utilize a different line search criteria to guarantee monotone convergence for various regularization terms. Empirical experiments on binary classification tasks with real-world datasets demonstrate our proposed algorithms are capable of performing classification and feature selection effectively at a lower computational cost.
We develop a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space of parameters and latent variables. In particular, we prove that the parameter marginal of the stationary measure of this diffusion has the form of a Gibbs measure where number of particles acts as the inverse temperature parameter in classical settings for global optimisation. Using a particular rescaling, we then prove geometric ergodicity of this system and bound the discretisation error in a manner that is uniform in time and does not increase with the number of particles. The discretisation results in an algorithm, termed Interacting Particle Langevin Algorithm (IPLA) which can be used for MMLE. We further prove nonasymptotic bounds for the optimisation error of our estimator in terms of key parameters of the problem, and also extend this result to the case of stochastic gradients covering practical scenarios. We provide numerical experiments to illustrate the empirical behaviour of our algorithm in the context of logistic regression with verifiable assumptions. Our setting provides a straightforward way to implement a diffusion-based optimisation routine compared to more classical approaches such as the Expectation Maximisation (EM) algorithm, and allows for especially explicit nonasymptotic bounds.
We propose a unified dynamic tracking algorithmic framework (PLAY-CS) to reconstruct signal sequences with their intrinsic structured dynamic sparsity. By capitalizing on specific statistical assumptions concerning the dynamic filter of the signal sequences, the proposed framework exhibits versatility by encompassing various existing dynamic compressive sensing (DCS) algorithms. This is achieved through the incorporation of a newly proposed Partial-Laplacian filtering sparsity model, tailored to capture a more sophisticated dynamic sparsity. In practical scenarios such as dynamic channel tracking in wireless communications, the framework demonstrates enhanced performance compared to existing DCS algorithms.
Recent work in scientific machine learning (SciML) has focused on incorporating partial differential equation (PDE) information into the learning process. Much of this work has focused on relatively "easy" PDE operators (e.g., elliptic and parabolic), with less emphasis on relatively "hard" PDE operators (e.g., hyperbolic). Within numerical PDEs, the latter problem class requires control of a type of volume element or conservation constraint, which is known to be challenging. Delivering on the promise of SciML requires seamlessly incorporating both types of problems into the learning process. To address this issue, we propose ProbConserv, a framework for incorporating conservation constraints into a generic SciML architecture. To do so, ProbConserv combines the integral form of a conservation law with a Bayesian update. We provide a detailed analysis of ProbConserv on learning with the Generalized Porous Medium Equation (GPME), a widely-applicable parameterized family of PDEs that illustrates the qualitative properties of both easier and harder PDEs. ProbConserv is effective for easy GPME variants, performing well with state-of-the-art competitors; and for harder GPME variants it outperforms other approaches that do not guarantee volume conservation. ProbConserv seamlessly enforces physical conservation constraints, maintains probabilistic uncertainty quantification (UQ), and deals well with shocks and heteroscedasticities. In each case, it achieves superior predictive performance on downstream tasks.
We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of $k$-out-of-$n$ systems and with stress-strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions.
Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as $d$-logics. Unlike logics based on the topological closure operator, $d$-logics have not previously been studied in the framework of dynamical systems, which are pairs $(X,f)$ consisting of a topological space $X$ equipped with a continuous function $f\colon X\to X$. We introduce the logics $\bf{wK4C}$, $\bf{K4C}$ and $\bf{GLC}$ and show that they all have the finite Kripke model property and are sound and complete with respect to the $d$-semantics in this dynamical setting. In particular, we prove that $\bf{wK4C}$ is the $d$-logic of all dynamic topological systems, $\bf{K4C}$ is the $d$-logic of all $T_D$ dynamic topological systems, and $\bf{GLC}$ is the $d$-logic of all dynamic topological systems based on a scattered space. We also prove a general result for the case where $f$ is a homeomorphism, which in particular yields soundness and completeness for the corresponding systems $\bf{wK4H}$, $\bf{K4H}$ and $\bf{GLH}$. The main contribution of this work is the foundation of a general proof method for finite model property and completeness of dynamic topological $d$-logics. Furthermore, our result for $\bf{GLC}$ constitutes the first step towards a proof of completeness for the trimodal topo-temporal language with respect to a finite axiomatisation -- something known to be impossible over the class of all spaces.
2D-based Industrial Anomaly Detection has been widely discussed, however, multimodal industrial anomaly detection based on 3D point clouds and RGB images still has many untouched fields. Existing multimodal industrial anomaly detection methods directly concatenate the multimodal features, which leads to a strong disturbance between features and harms the detection performance. In this paper, we propose Multi-3D-Memory (M3DM), a novel multimodal anomaly detection method with hybrid fusion scheme: firstly, we design an unsupervised feature fusion with patch-wise contrastive learning to encourage the interaction of different modal features; secondly, we use a decision layer fusion with multiple memory banks to avoid loss of information and additional novelty classifiers to make the final decision. We further propose a point feature alignment operation to better align the point cloud and RGB features. Extensive experiments show that our multimodal industrial anomaly detection model outperforms the state-of-the-art (SOTA) methods on both detection and segmentation precision on MVTec-3D AD dataset. Code is available at //github.com/nomewang/M3DM.
Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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