We show, in one dimension, that an $hp$-Finite Element Method ($hp$-FEM) discretisation can be solved in optimal complexity because the discretisation has a special sparsity structure that ensures that the \emph{reverse Cholesky factorisation} -- Cholesky starting from the bottom right instead of the top left -- remains sparse. Moreover, computing and inverting the factorisation almost entirely trivially parallelises across the different elements. By incorporating this approach into an Alternating Direction Implicit (ADI) method \`a la Fortunato and Townsend (2020) we can solve, within a prescribed tolerance, an $hp$-FEM discretisation of the (screened) Poisson equation on a rectangle, in parallel, with quasi-optimal complexity: $O(N^2 \log N)$ operations where $N$ is the maximal total degrees of freedom in each dimension. When combined with fast Legendre transforms we can also solve nonlinear time-evolution partial differential equations in a quasi-optimal complexity of $O(N^2 \log^2 N)$ operations, which we demonstrate on the (viscid) Burgers' equation.
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In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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.
Zero-shot Learning (ZSL), which aims to predict for those classes that have never appeared in the training data, has arisen hot research interests. The key of implementing ZSL is to leverage the prior knowledge of classes which builds the semantic relationship between classes and enables the transfer of the learned models (e.g., features) from training classes (i.e., seen classes) to unseen classes. However, the priors adopted by the existing methods are relatively limited with incomplete semantics. In this paper, we explore richer and more competitive prior knowledge to model the inter-class relationship for ZSL via ontology-based knowledge representation and semantic embedding. Meanwhile, to address the data imbalance between seen classes and unseen classes, we developed a generative ZSL framework with Generative Adversarial Networks (GANs). Our main findings include: (i) an ontology-enhanced ZSL framework that can be applied to different domains, such as image classification (IMGC) and knowledge graph completion (KGC); (ii) a comprehensive evaluation with multiple zero-shot datasets from different domains, where our method often achieves better performance than the state-of-the-art models. In particular, on four representative ZSL baselines of IMGC, the ontology-based class semantics outperform the previous priors e.g., the word embeddings of classes by an average of 12.4 accuracy points in the standard ZSL across two example datasets (see Figure 4).
Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.
Most object recognition approaches predominantly focus on learning discriminative visual patterns while overlooking the holistic object structure. Though important, structure modeling usually requires significant manual annotations and therefore is labor-intensive. In this paper, we propose to "look into object" (explicitly yet intrinsically model the object structure) through incorporating self-supervisions into the traditional framework. We show the recognition backbone can be substantially enhanced for more robust representation learning, without any cost of extra annotation and inference speed. Specifically, we first propose an object-extent learning module for localizing the object according to the visual patterns shared among the instances in the same category. We then design a spatial context learning module for modeling the internal structures of the object, through predicting the relative positions within the extent. These two modules can be easily plugged into any backbone networks during training and detached at inference time. Extensive experiments show that our look-into-object approach (LIO) achieves large performance gain on a number of benchmarks, including generic object recognition (ImageNet) and fine-grained object recognition tasks (CUB, Cars, Aircraft). We also show that this learning paradigm is highly generalizable to other tasks such as object detection and segmentation (MS COCO). Project page: //github.com/JDAI-CV/LIO.
Knowledge graphs capture structured information and relations between a set of entities or items. As such they represent an attractive source of information that could help improve recommender systems. However existing approaches in this domain rely on manual feature engineering and do not allow for end-to-end training. Here we propose knowledge-aware graph neural networks with label smoothness regularization to provide better recommendations. Conceptually, our approach computes user-specific item embeddings by first applying a trainable function that identifies important knowledge graph relationships for a given user. This way we transform the knowledge graph into a user-specific weighted graph and then applies a graph neural network to compute personalized item embeddings. To provide better inductive bias, we use label smoothness, which assumes that adjacent items in the knowledge graph are likely to have similar user relevance labels/scores. Label smoothness provides regularization over edge weights and we prove that it is equivalent to a label propagation scheme on a graph. Finally, we combine knowledge-aware graph neural networks and label smoothness and present the unified model. Experiment results show that our method outperforms strong baselines in four datasets. It also achieves strong performance in the scenario where user-item interactions are sparse.
Most deep learning-based models for speech enhancement have mainly focused on estimating the magnitude of spectrogram while reusing the phase from noisy speech for reconstruction. This is due to the difficulty of estimating the phase of clean speech. To improve speech enhancement performance, we tackle the phase estimation problem in three ways. First, we propose Deep Complex U-Net, an advanced U-Net structured model incorporating well-defined complex-valued building blocks to deal with complex-valued spectrograms. Second, we propose a polar coordinate-wise complex-valued masking method to reflect the distribution of complex ideal ratio masks. Third, we define a novel loss function, weighted source-to-distortion ratio (wSDR) loss, which is designed to directly correlate with a quantitative evaluation measure. Our model was evaluated on a mixture of the Voice Bank corpus and DEMAND database, which has been widely used by many deep learning models for speech enhancement. Ablation experiments were conducted on the mixed dataset showing that all three proposed approaches are empirically valid. Experimental results show that the proposed method achieves state-of-the-art performance in all metrics, outperforming previous approaches by a large margin.
In recent years, object detection has experienced impressive progress. Despite these improvements, there is still a significant gap in the performance between the detection of small and large objects. We analyze the current state-of-the-art model, Mask-RCNN, on a challenging dataset, MS COCO. We show that the overlap between small ground-truth objects and the predicted anchors is much lower than the expected IoU threshold. We conjecture this is due to two factors; (1) only a few images are containing small objects, and (2) small objects do not appear enough even within each image containing them. We thus propose to oversample those images with small objects and augment each of those images by copy-pasting small objects many times. It allows us to trade off the quality of the detector on large objects with that on small objects. We evaluate different pasting augmentation strategies, and ultimately, we achieve 9.7\% relative improvement on the instance segmentation and 7.1\% on the object detection of small objects, compared to the current state of the art method on MS COCO.
Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.
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.
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