Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that jointly perform computations on $n$-node graphs. The graph is assumed to be partitioned in a balanced fashion among the $k$ machines, a common implementation in many real-world systems. Communication is point-to-point via bandwidth-constrained links, and the goal is to minimize the round complexity, i.e., the number of communication rounds required to finish a computation. We present a generic methodology that allows to obtain efficient algorithms in the $k$-machine model using distributed algorithms for the classical CONGEST model of distributed computing. Using this methodology, we obtain algorithms for various fundamental graph problems such as connectivity, minimum spanning trees, shortest paths, maximal independent sets, and finding subgraphs, showing that many of these problems can be solved in $\tilde{O}(n/k)$ rounds; this shows that one can achieve speedup nearly linear in $k$. To complement our upper bounds, we present lower bounds on the round complexity that quantify the fundamental limitations of solving graph problems distributively. We first show a lower bound of $\Omega(n/k)$ rounds for computing a spanning tree of the input graph. This result implies the same bound for other fundamental problems such as computing a minimum spanning tree, breadth-first tree, or shortest paths tree. We also show a $\tilde \Omega(n/k^2)$ lower bound for connectivity, spanning tree verification and other related problems. The latter lower bounds follow from the development and application of novel results in a random-partition variant of the classical communication complexity model.
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Large language models have demonstrated surprising ability to perform in-context learning, i.e., these models can be directly applied to solve numerous downstream tasks by conditioning on a prompt constructed by a few input-output examples. However, prior research has shown that in-context learning can suffer from high instability due to variations in training examples, example order, and prompt formats. Therefore, the construction of an appropriate prompt is essential for improving the performance of in-context learning. In this paper, we revisit this problem from the view of predictive bias. Specifically, we introduce a metric to evaluate the predictive bias of a fixed prompt against labels or a given attributes. Then we empirically show that prompts with higher bias always lead to unsatisfactory predictive quality. Based on this observation, we propose a novel search strategy based on the greedy search to identify the near-optimal prompt for improving the performance of in-context learning. We perform comprehensive experiments with state-of-the-art mainstream models such as GPT-3 on various downstream tasks. Our results indicate that our method can enhance the model's in-context learning performance in an effective and interpretable manner.
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output changes can result in costly decisions, reduced user trust, potential security concerns, and lack of replicability. In this study, we consider the Lipschitz continuity of algorithms as a stability measure and initiate a systematic study of the Lipschitz continuity of algorithms for (weighted) graph problems. Depending on how we embed the output solution to a metric space, we can think of several Lipschitzness notions. We mainly consider the one that is invariant under scaling of weights, and we provide Lipschitz continuous algorithms and lower bounds for the minimum spanning tree problem, the shortest path problem, and the maximum weight matching problem. In particular, our shortest path algorithm is obtained by first designing an algorithm for unweighted graphs that are robust against edge contractions and then applying it to the unweighted graph constructed from the original weighted graph. Then, we consider another Lipschitzness notion induced by a natural mapping that maps the output solution to its characteristic vector. It turns out that no Lipschitz continuous algorithm exists for this Lipschitz notion, and we instead design algorithms with bounded pointwise Lipschitz constants for the minimum spanning tree problem and the maximum weight bipartite matching problem. Our algorithm for the latter problem is based on an LP relaxation with entropy regularization.
Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most promising solution is distributed training which distributes the workload of training across multiple computing nodes. However, the workflows, computational patterns, communication patterns, and optimization techniques of distributed GNN training remain preliminarily understood. In this paper, we provide a comprehensive survey of distributed GNN training by investigating various optimization techniques used in distributed GNN training. First, distributed GNN training is classified into several categories according to their workflows. In addition, their computational patterns and communication patterns, as well as the optimization techniques proposed by recent work are introduced. Second, the software frameworks and hardware platforms of distributed GNN training are also introduced for a deeper understanding. Third, distributed GNN training is compared with distributed training of deep neural networks, emphasizing the uniqueness of distributed GNN training. Finally, interesting issues and opportunities in this field are discussed.
Graph neural networks (GNNs) are a type of deep learning models that learning over graphs, and have been successfully applied in many domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to large graphs. As a remedy, distributed computing becomes a promising solution of training large-scale GNNs, since it is able to provide abundant computing resources. However, the dependency of graph structure increases the difficulty of achieving high-efficiency distributed GNN training, which suffers from the massive communication and workload imbalance. In recent years, many efforts have been made on distributed GNN training, and an array of training algorithms and systems have been proposed. Yet, there is a lack of systematic review on the optimization techniques from graph processing to distributed execution. In this survey, we analyze three major challenges in distributed GNN training that are massive feature communication, the loss of model accuracy and workload imbalance. Then we introduce a new taxonomy for the optimization techniques in distributed GNN training that address the above challenges. The new taxonomy classifies existing techniques into four categories that are GNN data partition, GNN batch generation, GNN execution model, and GNN communication protocol.We carefully discuss the techniques in each category. In the end, we summarize existing distributed GNN systems for multi-GPUs, GPU-clusters and CPU-clusters, respectively, and give a discussion about the future direction on scalable GNNs.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
Data in Knowledge Graphs often represents part of the current state of the real world. Thus, to stay up-to-date the graph data needs to be updated frequently. To utilize information from Knowledge Graphs, many state-of-the-art machine learning approaches use embedding techniques. These techniques typically compute an embedding, i.e., vector representations of the nodes as input for the main machine learning algorithm. If a graph update occurs later on -- specifically when nodes are added or removed -- the training has to be done all over again. This is undesirable, because of the time it takes and also because downstream models which were trained with these embeddings have to be retrained if they change significantly. In this paper, we investigate embedding updates that do not require full retraining and evaluate them in combination with various embedding models on real dynamic Knowledge Graphs covering multiple use cases. We study approaches that place newly appearing nodes optimally according to local information, but notice that this does not work well. However, we find that if we continue the training of the old embedding, interleaved with epochs during which we only optimize for the added and removed parts, we obtain good results in terms of typical metrics used in link prediction. This performance is obtained much faster than with a complete retraining and hence makes it possible to maintain embeddings for dynamic Knowledge Graphs.
This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.
While existing work in robust deep learning has focused on small pixel-level $\ell_p$ norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations -- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
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.
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