We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient Discretisation Method, we show that the algorithm is long-term stable for a broad class of particular Gradient Discretisations. Building on the long-term stability and the derived continuity of the algorithm's solution operator, we construct two sequences of approximate invariant measures. At the moment, each sequence lacks one important feature: either the existence of a limit measure, or the invariance with respect to the discrete semigroup. We derive an abstract condition that merges both properties, recovering the existence of an invariant measure. We provide an example for which invariance and existence hold simultaneously, and characterise the invariant measure completely. We close the article by conducting two numerical experiments that show the influence of transport noise on the dynamics of power-law fluids; in particular, we find that transport noise enhances the dissipation of kinetic energy, the mixing of particles, as well as the size of vortices.
The rapid development of deep learning has made a great progress in segmentation, one of the fundamental tasks of computer vision. However, the current segmentation algorithms mostly rely on the availability of pixel-level annotations, which are often expensive, tedious, and laborious. To alleviate this burden, the past years have witnessed an increasing attention in building label-efficient, deep-learning-based segmentation algorithms. This paper offers a comprehensive review on label-efficient segmentation methods. To this end, we first develop a taxonomy to organize these methods according to the supervision provided by different types of weak labels (including no supervision, coarse supervision, incomplete supervision and noisy supervision) and supplemented by the types of segmentation problems (including semantic segmentation, instance segmentation and panoptic segmentation). Next, we summarize the existing label-efficient segmentation methods from a unified perspective that discusses an important question: how to bridge the gap between weak supervision and dense prediction -- the current methods are mostly based on heuristic priors, such as cross-pixel similarity, cross-label constraint, cross-view consistency, cross-image relation, etc. Finally, we share our opinions about the future research directions for label-efficient deep segmentation.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.
Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.
While deep learning strategies achieve outstanding results in computer vision tasks, one issue remains. The current strategies rely heavily on a huge amount of labeled data. In many real-world problems it is not feasible to create such an amount of labeled training data. Therefore, researchers try to incorporate unlabeled data into the training process to reach equal results with fewer labels. Due to a lot of concurrent research, it is difficult to keep track of recent developments. In this survey we provide an overview of often used techniques and methods in image classification with fewer labels. We compare 21 methods. In our analysis we identify three major trends. 1. State-of-the-art methods are scaleable to real world applications based on their accuracy. 2. The degree of supervision which is needed to achieve comparable results to the usage of all labels is decreasing. 3. All methods share common techniques while only few methods combine these techniques to achieve better performance. Based on all of these three trends we discover future research opportunities.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.
Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks' Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.