Nonnegative Matrix Factorization is an important tool in unsupervised machine learning to decompose a data matrix into a product of parts that are often interpretable. Many algorithms have been proposed during the last three decades. A well-known method is the Multiplicative Updates algorithm proposed by Lee and Seung in 2002. Multiplicative updates have many interesting features: they are simple to implement and can be adapted to popular variants such as sparse Nonnegative Matrix Factorization, and, according to recent benchmarks, is state-of-the-art for many problems where the loss function is not the Frobenius norm. In this manuscript, we propose to improve the Multiplicative Updates algorithm seen as an alternating majorization minimization algorithm by crafting a tighter upper bound of the Hessian matrix for each alternate subproblem. Convergence is still ensured and we observe in practice on both synthetic and real world dataset that the proposed fastMU algorithm is often several orders of magnitude faster than the regular Multiplicative Updates algorithm, and can even be competitive with state-of-the-art methods for the Frobenius loss.
相關內容
Satellite image time series in the optical and infrared spectrum suffer from frequent data gaps due to cloud cover, cloud shadows, and temporary sensor outages. It has been a long-standing problem of remote sensing research how to best reconstruct the missing pixel values and obtain complete, cloud-free image sequences. We approach that problem from the perspective of representation learning and develop U-TILISE, an efficient neural model that is able to implicitly capture spatio-temporal patterns of the spectral intensities, and that can therefore be trained to map a cloud-masked input sequence to a cloud-free output sequence. The model consists of a convolutional spatial encoder that maps each individual frame of the input sequence to a latent encoding; an attention-based temporal encoder that captures dependencies between those per-frame encodings and lets them exchange information along the time dimension; and a convolutional spatial decoder that decodes the latent embeddings back into multi-spectral images. We experimentally evaluate the proposed model on EarthNet2021, a dataset of Sentinel-2 time series acquired all over Europe, and demonstrate its superior ability to reconstruct the missing pixels. Compared to a standard interpolation baseline, it increases the PSNR by 1.8 dB at previously seen locations and by 1.3 dB at unseen locations.
Logic synthesis is the first and most vital step in chip design. This steps converts a chip specification written in a hardware description language (such as Verilog) into an optimized implementation using Boolean logic gates. State-of-the-art logic synthesis algorithms have a large number of logic minimization heuristics, typically applied sequentially based on human experience and intuition. The choice of the order greatly impacts the quality (e.g., area and delay) of the synthesized circuit. In this paper, we propose INVICTUS, a model-based offline reinforcement learning (RL) solution that automatically generates a sequence of logic minimization heuristics ("synthesis recipe") based on a training dataset of previously seen designs. A key challenge is that new designs can range from being very similar to past designs (e.g., adders and multipliers) to being completely novel (e.g., new processor instructions). %Compared to prior work, INVICTUS is the first solution that uses a mix of RL and search methods joint with an online out-of-distribution detector to generate synthesis recipes over a wide range of benchmarks. Our results demonstrate significant improvement in area-delay product (ADP) of synthesized circuits with up to 30\% improvement over state-of-the-art techniques. Moreover, INVICTUS achieves up to $6.3\times$ runtime reduction (iso-ADP) compared to the state-of-the-art.
Cographs are a class of (undirected) graphs, characterized by the absence of induced subgraphs isomorphic to the four-vertices path, showing an intuitive one-to-one correspondence with classical propositional formulas. In this paper we study sequent calculi operating on graphs, as a generalization of sequent calculi operating on formulas, therefore on cographs. We mostly focus on sequent systems with multiplicative rules (in the sense of linear logic, that is, linear and context-free rules) extending multiplicative linear logic with connectives allowing us to represent modular decomposition of graphs by formulas, therefore obtaining a representation of a graph with linear size with respect to the number of its vertices. We show that these proof systems satisfy basic proof theoretical properties such as initial coherence, cut-elimination and analyticity of proof search. We prove that the system conservatively extend multiplicative linear logic with and without mix, and that the system extending the former derives the same graphs which are derivable in the deep inference system GS from the literature. We provide a syntax for proof nets for our systems by extending the syntax of Retor\'e's RB-structures to represent graphical connectives. A topological characterization of those structures encoding correct proofs is given, as well as a sequentialization procedure to construct a derivation from a correct structure. We conclude the paper by discussing how to extend those linear systems with the structural rules of weakening and contraction, providing a sequent system for an extension of classical propositional logic beyond cographs.
Studies investigating neural information processing often implicitly ask both, which processing strategy out of several alternatives is used and how this strategy is implemented in neural dynamics. A prime example are studies on predictive coding. These often ask if confirmed predictions about inputs or predictions errors between internal predictions and inputs are passed on in a hierarchical neural system--while at the same time looking for the neural correlates of coding for errors and predictions. If we do not know exactly what a neural system predicts at any given moment, this results in a circular analysis--as has been criticized correctly. To circumvent such circular analysis, we propose to express information processing strategies (such as predictive coding) by local information-theoretic quantities, such that they can be estimated directly from neural data. We demonstrate our approach by investigating two opposing accounts of predictive coding-like processing strategies, where we quantify the building blocks of predictive coding, namely predictability of inputs and transfer of information, by local active information storage and local transfer entropy. We define testable hypotheses on the relationship of both quantities to identify which of the assumed strategies was used. We demonstrate our approach on spiking data from the retinogeniculate synapse of the cat. Applying our local information dynamics framework, we are able to show that the synapse codes for predictable rather than surprising input. To support our findings, we apply measures from partial information decomposition, which allow to differentiate if the transferred information is primarily bottom-up sensory input or information transferred conditionally on the current state of the synapse. Supporting our local information-theoretic results, we find that the synapse preferentially transfers bottom-up information.
Recent work on knowledge graph completion (KGC) focused on learning embeddings of entities and relations in knowledge graphs. These embedding methods require that all test entities are observed at training time, resulting in a time-consuming retraining process for out-of-knowledge-graph (OOKG) entities. To address this issue, current inductive knowledge embedding methods employ graph neural networks (GNNs) to represent unseen entities by aggregating information of known neighbors. They face three important challenges: (i) data sparsity, (ii) the presence of complex patterns in knowledge graphs (e.g., inter-rule correlations), and (iii) the presence of interactions among rule mining, rule inference, and embedding. In this paper, we propose a virtual neighbor network with inter-rule correlations (VNC) that consists of three stages: (i) rule mining, (ii) rule inference, and (iii) embedding. In the rule mining process, to identify complex patterns in knowledge graphs, both logic rules and inter-rule correlations are extracted from knowledge graphs based on operations over relation embeddings. To reduce data sparsity, virtual neighbors for OOKG entities are predicted and assigned soft labels by optimizing a rule-constrained problem. We also devise an iterative framework to capture the underlying relations between rule learning and embedding learning. In our experiments, results on both link prediction and triple classification tasks show that the proposed VNC framework achieves state-of-the-art performance on four widely-used knowledge graphs. Further analysis reveals that VNC is robust to the proportion of unseen entities and effectively mitigates data sparsity.
Graph mining tasks arise from many different application domains, ranging from social networks, transportation, E-commerce, etc., which have been receiving great attention from the theoretical and algorithm design communities in recent years, and there has been some pioneering work using the hotly researched reinforcement learning (RL) techniques to address graph data mining tasks. However, these graph mining algorithms and RL models are dispersed in different research areas, which makes it hard to compare different algorithms with each other. In this survey, we provide a comprehensive overview of RL models and graph mining and generalize these algorithms to Graph Reinforcement Learning (GRL) as a unified formulation. We further discuss the applications of GRL methods across various domains and summarize the method description, open-source codes, and benchmark datasets of GRL methods. Finally, we propose possible important directions and challenges to be solved in the future. This is the latest work on a comprehensive survey of GRL literature, and this work provides a global view for researchers as well as a learning resource for researchers outside the domain. In addition, we create an online open-source for both interested researchers who want to enter this rapidly developing domain and experts who would like to compare GRL methods.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at //github.com/google-research/google-research/tree/master/cluster_gcn.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
Deep learning has emerged as a powerful machine learning technique that learns multiple layers of representations or features of the data and produces state-of-the-art prediction results. Along with the success of deep learning in many other application domains, deep learning is also popularly used in sentiment analysis in recent years. This paper first gives an overview of deep learning and then provides a comprehensive survey of its current applications in sentiment analysis.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191