Constant Time Graph Neural Networks
The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods to huge graphs such as social network graphs and web graphs still remains a challenge. In particular, the existing methods for accelerating GNNs are either not theoretically guaranteed in terms of approximation error, or they require at least a linear time computation cost. In this study, we analyze the neighbor sampling technique to obtain a constant time approximation algorithm for GraphSAGE, the graph attention networks (GAT), and the graph convolutional networks (GCN). The proposed approximation algorithm can theoretically guarantee the precision of approximation. The key advantage of the proposed approximation algorithm is that the complexity is completely independent of the numbers of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability. To the best of our knowledge, this is the first constant time approximation algorithm for GNNs with a theoretical guarantee. Through experiments using synthetic and real-world datasets, we demonstrate the speed and precision of the proposed approximation algorithm and validate our theoretical results.
In this paper, the authors provide a theoretical framework for characterizing the approximation guarantees provided by node sampling to estimate embeddings in various GNN architectures. In particular, they prove several PAC learning-style bounds on the embedding and gradient estimation when using node sampling approaches. They also observe that since the number of nodes selected for sampling is not dependent on the size of the graph, this amounts to a constant time operation for determining embedding and gradient estimates. Importantly, a variety of existing works have already proposed node sampling (“constant-time GNNs”), so the contribution of this work lies in the theoretical bounds. A moderate set of experiments suggests the empirical behavior follows the theoretical expectations. Overall (and described in the comments below), I believe this paper provides some interesting theoretical results for an approach that is widely-used in practice. However, I believe the title and abstract are misleading; this paper does not suggest some new sampling strategy; it only gives a theoretical approximation error for existing approaches and network architectures. Comments While the authors do make this clear later in the paper, the contributions of this work are only the theoretical bounds; the node sampling algorithms have been proposed in existing work. Both the title and abstract are misleading. Still, the theoretical bounds do provide an interesting understanding of an approach which is commonly used in practice. It would be helpful to give the intuition behind the assumptions and proofs. Currently, it is difficult for a non-expert to follow the reasoning and practical implications of much of this work. Currently, it is not clear if these results are “constructive”, in the sense that they do not obviously suggest some new sampling strategy, etc. Of course, it is still interesting to characterize commonly-used practices, but one does wish the theory suggested, say, a better sampling strategy, etc. Typos, etc. “r”, the number of sampled nodes, is not defined in the main body of the paper. The text in Footnote 1 is a little confusing, in that the text refers to approximating the embedding, while the text in the footnote describes a prediction problem. A reader could easily interpret this to mean that the error on the downstream prediction problem will be bounded (which is not what this work shows). The text mentions that O_G (v,i) refers to the i^th “neighborhood” of v. Presumably, this should be “neighbor”. “we take” -> “We take”
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Constant Time Graph Neural Networks
The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods to huge graphs such as social network graphs and web graphs still remains a challenge. In particular, the existing methods for accelerating GNNs are either not theoretically guaranteed in terms of approximation error, or they require at least a linear time computation cost. In this study, we analyze the neighbor sampling technique to obtain a constant time approximation algorithm for GraphSAGE, the graph attention networks (GAT), and the graph convolutional networks (GCN). The proposed approximation algorithm can theoretically guarantee the precision of approximation. The key advantage of the proposed approximation algorithm is that the complexity is completely independent of the numbers of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability. To the best of our knowledge, this is the first constant time approximation algorithm for GNNs with a theoretical guarantee. Through experiments using synthetic and real-world datasets, we demonstrate the speed and precision of the proposed approximation algorithm and validate our theoretical results.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



In this paper, the authors provide a theoretical framework for characterizing the approximation guarantees provided by node sampling to estimate embeddings in various GNN architectures. In particular, they prove several PAC learning-style bounds on the embedding and gradient estimation when using node sampling approaches. They also observe that since the number of nodes selected for sampling is not dependent on the size of the graph, this amounts to a constant time operation for determining embedding and gradient estimates. Importantly, a variety of existing works have already proposed node sampling (“constant-time GNNs”), so the contribution of this work lies in the theoretical bounds. A moderate set of experiments suggests the empirical behavior follows the theoretical expectations. Overall (and described in the comments below), I believe this paper provides some interesting theoretical results for an approach that is widely-used in practice. However, I believe the title and abstract are misleading; this paper does not suggest some new sampling strategy; it only gives a theoretical approximation error for existing approaches and network architectures. Comments While the authors do make this clear later in the paper, the contributions of this work are only the theoretical bounds; the node sampling algorithms have been proposed in existing work. Both the title and abstract are misleading. Still, the theoretical bounds do provide an interesting understanding of an approach which is commonly used in practice. It would be helpful to give the intuition behind the assumptions and proofs. Currently, it is difficult for a non-expert to follow the reasoning and practical implications of much of this work. Currently, it is not clear if these results are “constructive”, in the sense that they do not obviously suggest some new sampling strategy, etc. Of course, it is still interesting to characterize commonly-used practices, but one does wish the theory suggested, say, a better sampling strategy, etc. Typos, etc. “r”, the number of sampled nodes, is not defined in the main body of the paper. The text in Footnote 1 is a little confusing, in that the text refers to approximating the embedding, while the text in the footnote describes a prediction problem. A reader could easily interpret this to mean that the error on the downstream prediction problem will be bounded (which is not what this work shows). The text mentions that O_G (v,i) refers to the i^th “neighborhood” of v. Presumably, this should be “neighbor”. “we take” -> “We take”
assistant
In this paper, the authors provide a theoretical framework for characterizing the approximation guarantees provided by node sampling to estimate embeddings in various GNN architectures. In particular, they prove several PAC learning-style bounds on the embedding and gradient estimation when using node sampling approaches. They also observe that since the number of nodes selected for sampling is not dependent on the size of the graph, this amounts to a constant time operation for determining embedding and gradient estimates. Importantly, a variety of existing works have already proposed node sampling (“constant-time GNNs”), so the contribution of this work lies in the theoretical bounds. A moderate set of experiments suggests the empirical behavior follows the theoretical expectations. Overall (and described in the comments below), I believe this paper provides some interesting theoretical results for an approach that is widely-used in practice. However, I believe the title and abstract are misleading; this paper does not suggest some new sampling strategy; it only gives a theoretical approximation error for existing approaches and network architectures. Comments While the authors do make this clear later in the paper, the contributions of this work are only the theoretical bounds; the node sampling algorithms have been proposed in existing work. Both the title and abstract are misleading. Still, the theoretical bounds do provide an interesting understanding of an approach which is commonly used in practice. It would be helpful to give the intuition behind the assumptions and proofs. Currently, it is difficult for a non-expert to follow the reasoning and practical implications of much of this work. Currently, it is not clear if these results are “constructive”, in the sense that they do not obviously suggest some new sampling strategy, etc. Of course, it is still interesting to characterize commonly-used practices, but one does wish the theory suggested, say, a better sampling strategy, etc. Typos, etc. “r”, the number of sampled nodes, is not defined in the main body of the paper. The text in Footnote 1 is a little confusing, in that the text refers to approximating the embedding, while the text in the footnote describes a prediction problem. A reader could easily interpret this to mean that the error on the downstream prediction problem will be bounded (which is not what this work shows). The text mentions that O_G (v,i) refers to the i^th “neighborhood” of v. Presumably, this should be “neighbor”. “we take” -> “We take”