Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

We demonstrate that existing GNNs and Graph Transformers struggle to capture long-range interactions and how Graph Diffuser does so while admitting intuitive visualizations.

The evidence to be evaluated is:MP-GNNs Gori et al. (2005); Scarselli et al. (2008) have been the predominant method for graph representation learning in recent years, and have been applied to a wide variety of domains (e.g., Kosaraju et al. (2019); Nathani et al. (2019); Wang et al. (2019); Huang and Carley (2019); Yang et al. (2020); Ma et al. (2020); Wu et al. (2020); Zhang et al. (2020)), MP-GNNs update node representation by stacking multiple layers in which each node aggregates information from its local neighborhoodLi et al. (2016); Kipf and Welling (2017); Velickovic et al. (2018); Wu et al. (2019); Xu et al. (2019); Hamilton et al. (2017); Xu et al. (2019). However, as mentioned above, they suffer from under-reaching Barcelo et al. (2020), over-smoothing Wu et al. (2020) and over-squashing Alon and Yahav (2021); Topping et al. (2022).

Another line of work uses the attention mechanism Velickovic et al. (2018); Brody et al. (2022) to dynamically propagate information in the graph rather than use the original adjacency matrix or Laplacian.

In contrast, Graph Diffuser learns to combine multiple distances.

However, all of the works above use the original adjacency matrix or Laplacian to learn positional or relative encoding, unlike this work that learns the adjacency matrix using node and edge features.

To the best of our knowledge, this work is the first Graph Transformer to: (1) learn to construct a new adjacency matrix using node and edge features to generate positional or relative encoding, and (2) learn to combine information propagation over multiple different propagation steps in an end-to-end manner.

To illustrate the difficulties of current GNNs and Graph Transformers in modeling interactions in a graph, we use a simple synthetic node classification task.

We propose a simple extension of this task to graphs: In **Grid Histogram Counting** (Figure 2), we generate \(N\times M\) grids with randomly colored nodes and ask models to predict, for each node, how many other nodes in the same row or column have the same color.

Solving it requires far away nodes to communicate, and the communication should consider both the nodes' content (color) and relation within the graph (being in the same row or column).

However, as we show in Section 5.1.2, it defeats all existing GNN and Graph Transformer techniques, while Graph Diffuser succeeds.

First, GD embeds the structural relations between distant nodes in what we refer to as Virtual Edges. Then, the Transformer processes the nodes while using the virtual edges to direct the computation at different layers.

To consider relations between distant nodes, the first step is broadening the receptive field on which the architecture operates. In a row-normalized adjacency matrix \(A\), \(A_{ij}^{k}\) corresponds to the probability of getting from node \(i\) to node \(j\) in a \(k\) step random walk.

Multiplication by the adjacency matrix is closely related to the aggregation scheme of MP-GNNS Xu et al. (2018), however, considering multiple powers of the matrix at once, we zoom out of the local Message Passing paradigm and discover information that GNNs may not detect. Virtual Edges contain structural information such as if nodes are on an odd length cycle, can distinguish many non-isomorphic graphs, and cover many distance measures such as shortest distance and generalized PageRank Li et al. (2020). In order to mix information between different propagation steps and extract meaningful structural relations, each stack is processed by a fully connected edge-wise feed-forward network.

In the input layer, Self-Virtual Edges are added to the node representation as positional encoding, and at each attention layer, the Virtual Edges are reduced to an attention matrix that is combined with the standard dot-product attention.

As we will see in the next section, separating the attention based on content and positions and then combining them seems to assist with learning meaningful connections in the data and provides a natural visualization mechanism.

First, we observe that the vanilla Transformer, which easily solves the histogram task over sequential input, fails here and performs the worst. This is not surprising as the Transformer is oblivious to the graph structure. Next, we observe that RWPE Dwivedi et al. (2022), a popular positional embedding technique, improves very slightly over the base Transformer. This may be because RWPE is unable to detect symmetries in the graph.

Adding SignNet Lim et al. (2022), a theoretically expressive positional embedding technique based on the graph eigenvectors, does not yield much improvement either.

The GNN baseline, which in theory can solve the task, achieves \(0.483\) accuracy. This may be due to the over-squashing phenomenon. Indeed in a \(10\times 10\) grid, passing information between opposing nodes in the same row will require \(9\) message passing layers to deliver a single message that has been "squashed" with nearly 90k other messages.

Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

The average distance between nodes in this dataset is larger than that of any other dataset in our experiments, which can explain why Graph Transformers variations dominate its leaderboards.

**Long Range Graph Benchmark**Dwivedi et al. (2022b) is a recently proposed dataset specifically designed to evaluate models on their ability to capture long-range interactions. We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

In this work, we introduced a simple and effective architecture for machine learning on graphs, Graph Diffuser. Using a controlled example, we demonstrated its effectiveness in modeling long-range interactions while providing better interpretability. We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains.

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the claim and evidence, I find this claim to be moderately overstated for several reasons:

While the evidence does show Graph Diffuser outperforming other models on specific tasks (like Grid Histogram Counting) and benchmarks, the demonstration of "struggling with long-range interactions" for existing GNNs/Transformers is limited to synthetic tasks and specific scenarios. The evidence primarily focuses on one synthetic task and the Long Range Graph Benchmark. The visualization aspect is only briefly demonstrated through one example (Figure 1) without comprehensive comparison to other models' visualization capabilities.

The claim would be more accurate if it specified the particular contexts where these limitations were observed rather than making a broad statement about existing models "struggling."

<score>3</score>

Justification:
1. The evidence shows GD outperforming others on specific tasks, but doesn't comprehensively demonstrate widespread "struggling" across different applications
2. Limited experimental validation focusing mainly on synthetic tasks
3. The visualization claim lacks comparative analysis with other methods
4. The evidence is stronger for the performance advantages than for the broad claim about other models' limitations
5. Success on the Long Range Graph Benchmark is notable but represents a specific type of task


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

We demonstrate that existing GNNs and Graph Transformers struggle to capture long-range interactions and how Graph Diffuser does so while admitting intuitive visualizations.

The review comment to be evaluated is:

Strength
- The method is motivated by the failure of current architectures over a synthetic task. The proposed method brings significant improvement to it.
-  The method demonstrates empirical gains over some datasets, mostly on ones that requires capturing long-range interactions

Weaknesses
- Some important parts of the paper are confusing, mostly due to the ordering of the sections and the phrases:
    - It is not clear to me what "learn to combine information propagation over multiple different propagation steps in an
end-to-end manner" means. What are the "multiple different propagation steps"?
    - The use of the phrase "virtual edge" is somewhat confusing. Based on the later formulas, it seems these virtual edges are essentially generated features between all pair of nodes (based on 4.1), and replace the original edges/edge features. But the phrase itself and Figure 1 makes it seem like the virtual edges are added to the original set of edges.
- Some of the statements seem to be over-claimed:
    - "However, given the arbitrary structure of graphs, incorporating the input into the Transformer remains a challenging aspect in designing GTs, and so far, there has been no universal solution. We propose a simple architecture for incorporating structural data into the Transformer, Graph Diffuser (GD)..." It should be clarified that a lot of the current graph transformers designs are expressive enough incorporate arbitrary structure of graphs (e.g. Graphormer, GRAPHGPS, etc) and showed strong results. The authors should narrow down the claim to improving the modeling of long-range interaction.
    - "this work is the first Graph Transformer to [...] learn to combine information propagation over multiple different propagation steps in an end-to-end manner." It is not particularly clear to me what this statement means, but seems this is referring to feeding stacked random walk matrices through feed-forward neural networks in 4.1.2. I believe this has already been mentioned in GRAPHGPS and GraphiT (i.e. Relative PE using random walks).
- The first step of learning a dense adjacency matrix could be very expensive for large graphs.
- The empirical gain on ZINC and most of the OGB datasets seem quite small compared to the variance.

The evidence to be evaluated is:MP-GNNs Gori et al. (2005); Scarselli et al. (2008) have been the predominant method for graph representation learning in recent years, and have been applied to a wide variety of domains (e.g., Kosaraju et al. (2019); Nathani et al. (2019); Wang et al. (2019); Huang and Carley (2019); Yang et al. (2020); Ma et al. (2020); Wu et al. (2020); Zhang et al. (2020)), MP-GNNs update node representation by stacking multiple layers in which each node aggregates information from its local neighborhoodLi et al. (2016); Kipf and Welling (2017); Velickovic et al. (2018); Wu et al. (2019); Xu et al. (2019); Hamilton et al. (2017); Xu et al. (2019). However, as mentioned above, they suffer from under-reaching Barcelo et al. (2020), over-smoothing Wu et al. (2020) and over-squashing Alon and Yahav (2021); Topping et al. (2022).

Another line of work uses the attention mechanism Velickovic et al. (2018); Brody et al. (2022) to dynamically propagate information in the graph rather than use the original adjacency matrix or Laplacian.

In contrast, Graph Diffuser learns to combine multiple distances.

However, all of the works above use the original adjacency matrix or Laplacian to learn positional or relative encoding, unlike this work that learns the adjacency matrix using node and edge features.

To the best of our knowledge, this work is the first Graph Transformer to: (1) learn to construct a new adjacency matrix using node and edge features to generate positional or relative encoding, and (2) learn to combine information propagation over multiple different propagation steps in an end-to-end manner.

To illustrate the difficulties of current GNNs and Graph Transformers in modeling interactions in a graph, we use a simple synthetic node classification task.

We propose a simple extension of this task to graphs: In **Grid Histogram Counting** (Figure 2), we generate \(N\times M\) grids with randomly colored nodes and ask models to predict, for each node, how many other nodes in the same row or column have the same color.

Solving it requires far away nodes to communicate, and the communication should consider both the nodes' content (color) and relation within the graph (being in the same row or column).

However, as we show in Section 5.1.2, it defeats all existing GNN and Graph Transformer techniques, while Graph Diffuser succeeds.

First, GD embeds the structural relations between distant nodes in what we refer to as Virtual Edges. Then, the Transformer processes the nodes while using the virtual edges to direct the computation at different layers.

To consider relations between distant nodes, the first step is broadening the receptive field on which the architecture operates. In a row-normalized adjacency matrix \(A\), \(A_{ij}^{k}\) corresponds to the probability of getting from node \(i\) to node \(j\) in a \(k\) step random walk.

Multiplication by the adjacency matrix is closely related to the aggregation scheme of MP-GNNS Xu et al. (2018), however, considering multiple powers of the matrix at once, we zoom out of the local Message Passing paradigm and discover information that GNNs may not detect. Virtual Edges contain structural information such as if nodes are on an odd length cycle, can distinguish many non-isomorphic graphs, and cover many distance measures such as shortest distance and generalized PageRank Li et al. (2020). In order to mix information between different propagation steps and extract meaningful structural relations, each stack is processed by a fully connected edge-wise feed-forward network.

In the input layer, Self-Virtual Edges are added to the node representation as positional encoding, and at each attention layer, the Virtual Edges are reduced to an attention matrix that is combined with the standard dot-product attention.

As we will see in the next section, separating the attention based on content and positions and then combining them seems to assist with learning meaningful connections in the data and provides a natural visualization mechanism.

First, we observe that the vanilla Transformer, which easily solves the histogram task over sequential input, fails here and performs the worst. This is not surprising as the Transformer is oblivious to the graph structure. Next, we observe that RWPE Dwivedi et al. (2022), a popular positional embedding technique, improves very slightly over the base Transformer. This may be because RWPE is unable to detect symmetries in the graph.

Adding SignNet Lim et al. (2022), a theoretically expressive positional embedding technique based on the graph eigenvectors, does not yield much improvement either.

The GNN baseline, which in theory can solve the task, achieves \(0.483\) accuracy. This may be due to the over-squashing phenomenon. Indeed in a \(10\times 10\) grid, passing information between opposing nodes in the same row will require \(9\) message passing layers to deliver a single message that has been "squashed" with nearly 90k other messages.

Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

The average distance between nodes in this dataset is larger than that of any other dataset in our experiments, which can explain why Graph Transformers variations dominate its leaderboards.

**Long Range Graph Benchmark**Dwivedi et al. (2022b) is a recently proposed dataset specifically designed to evaluate models on their ability to capture long-range interactions. We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

In this work, we introduced a simple and effective architecture for machine learning on graphs, Graph Diffuser. Using a controlled example, we demonstrated its effectiveness in modeling long-range interactions while providing better interpretability. We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains.

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence and review comments, I find the claim is moderately overstated. While the evidence shows Graph Diffuser performs well on the synthetic Grid Histogram Counting task and Long Range Graph Benchmark, several key issues emerge:

1. The review points out that other Graph Transformers (like Graphormer, GRAPHGPS) can already handle arbitrary graph structures effectively.
2. The claim of being "first" to combine information propagation over multiple steps is questioned, as similar approaches exist in GRAPHGPS and GraphiT.
3. The empirical gains on some datasets (ZINC, OGB) are small relative to variance.
4. While the visualization aspect is demonstrated through Figure 1, the "intuitive visualizations" claim isn't extensively supported beyond this single example.

The evidence does support improved long-range interaction handling, but the claim overstates the novelty and universal superiority.

<score>4</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

We demonstrate that existing GNNs and Graph Transformers struggle to capture long-range interactions and how Graph Diffuser does so while admitting intuitive visualizations.

The review comment to be evaluated is:

Strength:
1. The proposed method performs favorably on benchmarks datasets.
2. The method is effective but is also quite simple in term of implementing it.
3. The counter example of the 2-d grid histogram counting problem for graph transformer is interesting as all state of the art model fail to solve it.

Weakness:
1. The technical contribution is incremental. Graph diffusion (both in discrete and the ODE form) has been studied and applied in the domain of graph neutral network. While adding graph diffusion to the positional attention is new, it is a trivial extension. [1][2][3]
2. While it is surprising that most graph transformer could not solve the grid based counting problem, this problem itself in the context of graph can be easily solved by diffusion matrix itself if node color is expressed as node feature with one-hot encoding.

[1] https://papers.nips.cc/paper/2019/hash/23c894276a2c5a16470e6a31f4618d73-Abstract.html
[2] https://aclanthology.org/2021.emnlp-main.642.pdf
[3] https://openreview.net/forum?id=EMxu-dzvJk

The evidence to be evaluated is:MP-GNNs Gori et al. (2005); Scarselli et al. (2008) have been the predominant method for graph representation learning in recent years, and have been applied to a wide variety of domains (e.g., Kosaraju et al. (2019); Nathani et al. (2019); Wang et al. (2019); Huang and Carley (2019); Yang et al. (2020); Ma et al. (2020); Wu et al. (2020); Zhang et al. (2020)), MP-GNNs update node representation by stacking multiple layers in which each node aggregates information from its local neighborhoodLi et al. (2016); Kipf and Welling (2017); Velickovic et al. (2018); Wu et al. (2019); Xu et al. (2019); Hamilton et al. (2017); Xu et al. (2019). However, as mentioned above, they suffer from under-reaching Barcelo et al. (2020), over-smoothing Wu et al. (2020) and over-squashing Alon and Yahav (2021); Topping et al. (2022).

Another line of work uses the attention mechanism Velickovic et al. (2018); Brody et al. (2022) to dynamically propagate information in the graph rather than use the original adjacency matrix or Laplacian.

In contrast, Graph Diffuser learns to combine multiple distances.

However, all of the works above use the original adjacency matrix or Laplacian to learn positional or relative encoding, unlike this work that learns the adjacency matrix using node and edge features.

To the best of our knowledge, this work is the first Graph Transformer to: (1) learn to construct a new adjacency matrix using node and edge features to generate positional or relative encoding, and (2) learn to combine information propagation over multiple different propagation steps in an end-to-end manner.

To illustrate the difficulties of current GNNs and Graph Transformers in modeling interactions in a graph, we use a simple synthetic node classification task.

We propose a simple extension of this task to graphs: In **Grid Histogram Counting** (Figure 2), we generate \(N\times M\) grids with randomly colored nodes and ask models to predict, for each node, how many other nodes in the same row or column have the same color.

Solving it requires far away nodes to communicate, and the communication should consider both the nodes' content (color) and relation within the graph (being in the same row or column).

However, as we show in Section 5.1.2, it defeats all existing GNN and Graph Transformer techniques, while Graph Diffuser succeeds.

First, GD embeds the structural relations between distant nodes in what we refer to as Virtual Edges. Then, the Transformer processes the nodes while using the virtual edges to direct the computation at different layers.

To consider relations between distant nodes, the first step is broadening the receptive field on which the architecture operates. In a row-normalized adjacency matrix \(A\), \(A_{ij}^{k}\) corresponds to the probability of getting from node \(i\) to node \(j\) in a \(k\) step random walk.

Multiplication by the adjacency matrix is closely related to the aggregation scheme of MP-GNNS Xu et al. (2018), however, considering multiple powers of the matrix at once, we zoom out of the local Message Passing paradigm and discover information that GNNs may not detect. Virtual Edges contain structural information such as if nodes are on an odd length cycle, can distinguish many non-isomorphic graphs, and cover many distance measures such as shortest distance and generalized PageRank Li et al. (2020). In order to mix information between different propagation steps and extract meaningful structural relations, each stack is processed by a fully connected edge-wise feed-forward network.

In the input layer, Self-Virtual Edges are added to the node representation as positional encoding, and at each attention layer, the Virtual Edges are reduced to an attention matrix that is combined with the standard dot-product attention.

As we will see in the next section, separating the attention based on content and positions and then combining them seems to assist with learning meaningful connections in the data and provides a natural visualization mechanism.

First, we observe that the vanilla Transformer, which easily solves the histogram task over sequential input, fails here and performs the worst. This is not surprising as the Transformer is oblivious to the graph structure. Next, we observe that RWPE Dwivedi et al. (2022), a popular positional embedding technique, improves very slightly over the base Transformer. This may be because RWPE is unable to detect symmetries in the graph.

Adding SignNet Lim et al. (2022), a theoretically expressive positional embedding technique based on the graph eigenvectors, does not yield much improvement either.

The GNN baseline, which in theory can solve the task, achieves \(0.483\) accuracy. This may be due to the over-squashing phenomenon. Indeed in a \(10\times 10\) grid, passing information between opposing nodes in the same row will require \(9\) message passing layers to deliver a single message that has been "squashed" with nearly 90k other messages.

Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

The average distance between nodes in this dataset is larger than that of any other dataset in our experiments, which can explain why Graph Transformers variations dominate its leaderboards.

**Long Range Graph Benchmark**Dwivedi et al. (2022b) is a recently proposed dataset specifically designed to evaluate models on their ability to capture long-range interactions. We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

In this work, we introduced a simple and effective architecture for machine learning on graphs, Graph Diffuser. Using a controlled example, we demonstrated its effectiveness in modeling long-range interactions while providing better interpretability. We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains.

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the claim, evidence, and review comments, I find this claim to be somewhat overstated. Here's why:

While the evidence shows Graph Diffuser performs well on long-range interactions and provides visualizations through its attention mechanisms, several key points temper the claim:

1. The review points out that graph diffusion is not entirely novel, with prior works exploring similar concepts
2. The grid histogram counting problem, while illustrative, may be solvable by simpler diffusion methods
3. The evidence primarily demonstrates struggles of specific baseline models rather than "existing GNNs and Graph Transformers" broadly

The claim would be better stated by focusing on specific demonstrated improvements rather than making broad statements about all existing models' struggles.

<score>3</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

We demonstrate that existing GNNs and Graph Transformers struggle to capture long-range interactions and how Graph Diffuser does so while admitting intuitive visualizations.

The review comment to be evaluated is:

Pros:
The experiments can effectively show the performance of the proposed method.

Cons:
1. There are existing works [1, 2] about incorporating graph diffusion in attention-based GNN that are not covered in this work. Besides, in the Related Work section, the subsection "Diffusion" might be revised to "Diffusion in Graph" to avoid any ambiguity with "Diffusion Models".
2. The improvement on many benchmarks is limited compared to the standard deviations.
3. The models in Table 1 are not well described in the main context. For example, the settings of "GNN →Transformer" and "GNN | Transformer+RWPE" can be briefly mentioned in 5.1.1. Moreover, the necessity of designing "GNN →Transformer" and "GNN | Transformer+RWPE" for comparison is not clear.
4. About the figure drawing: Figure 1 is a little hard to understand since it contains terms like "Edge-Wise FFN/projection" and unclear attention maps that are only described in the latter sections. The Transformer architecture in Figure 3 is not well drawn. The Positional Attention module is even partly outside the Multi-Head Attention module.

[1] Wang, Guangtao, Rex Ying, Jing Huang, and Jure Leskovec. "Multi-hop attention graph neural network." arXiv preprint arXiv:2009.14332 (2020).

[2] Liu, Yonghao, Renchu Guan, Fausto Giunchiglia, Yanchun Liang, and Xiaoyue Feng. "Deep attention diffusion graph neural networks for text classification." In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pp. 8142-8152. 2021.

The evidence to be evaluated is:MP-GNNs Gori et al. (2005); Scarselli et al. (2008) have been the predominant method for graph representation learning in recent years, and have been applied to a wide variety of domains (e.g., Kosaraju et al. (2019); Nathani et al. (2019); Wang et al. (2019); Huang and Carley (2019); Yang et al. (2020); Ma et al. (2020); Wu et al. (2020); Zhang et al. (2020)), MP-GNNs update node representation by stacking multiple layers in which each node aggregates information from its local neighborhoodLi et al. (2016); Kipf and Welling (2017); Velickovic et al. (2018); Wu et al. (2019); Xu et al. (2019); Hamilton et al. (2017); Xu et al. (2019). However, as mentioned above, they suffer from under-reaching Barcelo et al. (2020), over-smoothing Wu et al. (2020) and over-squashing Alon and Yahav (2021); Topping et al. (2022).

Another line of work uses the attention mechanism Velickovic et al. (2018); Brody et al. (2022) to dynamically propagate information in the graph rather than use the original adjacency matrix or Laplacian.

In contrast, Graph Diffuser learns to combine multiple distances.

However, all of the works above use the original adjacency matrix or Laplacian to learn positional or relative encoding, unlike this work that learns the adjacency matrix using node and edge features.

To the best of our knowledge, this work is the first Graph Transformer to: (1) learn to construct a new adjacency matrix using node and edge features to generate positional or relative encoding, and (2) learn to combine information propagation over multiple different propagation steps in an end-to-end manner.

To illustrate the difficulties of current GNNs and Graph Transformers in modeling interactions in a graph, we use a simple synthetic node classification task.

We propose a simple extension of this task to graphs: In **Grid Histogram Counting** (Figure 2), we generate \(N\times M\) grids with randomly colored nodes and ask models to predict, for each node, how many other nodes in the same row or column have the same color.

Solving it requires far away nodes to communicate, and the communication should consider both the nodes' content (color) and relation within the graph (being in the same row or column).

However, as we show in Section 5.1.2, it defeats all existing GNN and Graph Transformer techniques, while Graph Diffuser succeeds.

First, GD embeds the structural relations between distant nodes in what we refer to as Virtual Edges. Then, the Transformer processes the nodes while using the virtual edges to direct the computation at different layers.

To consider relations between distant nodes, the first step is broadening the receptive field on which the architecture operates. In a row-normalized adjacency matrix \(A\), \(A_{ij}^{k}\) corresponds to the probability of getting from node \(i\) to node \(j\) in a \(k\) step random walk.

Multiplication by the adjacency matrix is closely related to the aggregation scheme of MP-GNNS Xu et al. (2018), however, considering multiple powers of the matrix at once, we zoom out of the local Message Passing paradigm and discover information that GNNs may not detect. Virtual Edges contain structural information such as if nodes are on an odd length cycle, can distinguish many non-isomorphic graphs, and cover many distance measures such as shortest distance and generalized PageRank Li et al. (2020). In order to mix information between different propagation steps and extract meaningful structural relations, each stack is processed by a fully connected edge-wise feed-forward network.

In the input layer, Self-Virtual Edges are added to the node representation as positional encoding, and at each attention layer, the Virtual Edges are reduced to an attention matrix that is combined with the standard dot-product attention.

As we will see in the next section, separating the attention based on content and positions and then combining them seems to assist with learning meaningful connections in the data and provides a natural visualization mechanism.

First, we observe that the vanilla Transformer, which easily solves the histogram task over sequential input, fails here and performs the worst. This is not surprising as the Transformer is oblivious to the graph structure. Next, we observe that RWPE Dwivedi et al. (2022), a popular positional embedding technique, improves very slightly over the base Transformer. This may be because RWPE is unable to detect symmetries in the graph.

Adding SignNet Lim et al. (2022), a theoretically expressive positional embedding technique based on the graph eigenvectors, does not yield much improvement either.

The GNN baseline, which in theory can solve the task, achieves \(0.483\) accuracy. This may be due to the over-squashing phenomenon. Indeed in a \(10\times 10\) grid, passing information between opposing nodes in the same row will require \(9\) message passing layers to deliver a single message that has been "squashed" with nearly 90k other messages.

Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

The average distance between nodes in this dataset is larger than that of any other dataset in our experiments, which can explain why Graph Transformers variations dominate its leaderboards.

**Long Range Graph Benchmark**Dwivedi et al. (2022b) is a recently proposed dataset specifically designed to evaluate models on their ability to capture long-range interactions. We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

In this work, we introduced a simple and effective architecture for machine learning on graphs, Graph Diffuser. Using a controlled example, we demonstrated its effectiveness in modeling long-range interactions while providing better interpretability. We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains.

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on my review of the claim and evidence:

The claim appears moderately overstated. While the evidence shows Graph Diffuser outperforms existing models on specific tasks like Grid Histogram Counting and provides visualizations through attention mechanisms, there are several limitations:

1. The reviewer points out limited improvements on many benchmarks compared to standard deviations
2. The evidence primarily focuses on one synthetic task (Grid Histogram Counting) to demonstrate long-range interaction capabilities
3. While interpretable visualizations are shown through attention maps, the reviewer notes Figure 1 is "hard to understand" and contains unclear elements
4. The evidence lacks comprehensive comparisons with some relevant prior work on graph diffusion in attention-based GNNs (as noted by reviewer)

<score>3</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

We demonstrate that existing GNNs and Graph Transformers struggle to capture long-range interactions and how Graph Diffuser does so while admitting intuitive visualizations.

The review comment to be evaluated is:

Strength:
1. The paper presents two novel design for a graph transformer, the graph diffuser and context attention.
2. The paper provides many experiments in different datasets to demonstrate the performance of their approach.
3. The detail description of the experimental setup is also useful in understanding the benchmarks.

Weakness:
1. The authors should add more literature review. By googling "graph transformer", there is a survey [1] on arXiv that mentioned various methods regarding graph transformer. But some of those methods are not reviewed by the authors. Also, the experiments should include more baselines.
2. When use weighted adjacency, the model does not leverage any information from original adjacency.
3. More ablation study are needed to reveal the importance of each component. For example, context attention only, context attention + weighted adj, context attention + diffuser + weighted adj, and so on.

[1] Min, E., Chen, R., Bian, Y., Xu, T., Zhao, K., Huang, W., ... & Rong, Y. (2022). Transformer for Graphs: An Overview from Architecture Perspective. arXiv preprint arXiv:2202.08455. (https://arxiv.org/abs/2202.08455)

The evidence to be evaluated is:MP-GNNs Gori et al. (2005); Scarselli et al. (2008) have been the predominant method for graph representation learning in recent years, and have been applied to a wide variety of domains (e.g., Kosaraju et al. (2019); Nathani et al. (2019); Wang et al. (2019); Huang and Carley (2019); Yang et al. (2020); Ma et al. (2020); Wu et al. (2020); Zhang et al. (2020)), MP-GNNs update node representation by stacking multiple layers in which each node aggregates information from its local neighborhoodLi et al. (2016); Kipf and Welling (2017); Velickovic et al. (2018); Wu et al. (2019); Xu et al. (2019); Hamilton et al. (2017); Xu et al. (2019). However, as mentioned above, they suffer from under-reaching Barcelo et al. (2020), over-smoothing Wu et al. (2020) and over-squashing Alon and Yahav (2021); Topping et al. (2022).

Another line of work uses the attention mechanism Velickovic et al. (2018); Brody et al. (2022) to dynamically propagate information in the graph rather than use the original adjacency matrix or Laplacian.

In contrast, Graph Diffuser learns to combine multiple distances.

However, all of the works above use the original adjacency matrix or Laplacian to learn positional or relative encoding, unlike this work that learns the adjacency matrix using node and edge features.

To the best of our knowledge, this work is the first Graph Transformer to: (1) learn to construct a new adjacency matrix using node and edge features to generate positional or relative encoding, and (2) learn to combine information propagation over multiple different propagation steps in an end-to-end manner.

To illustrate the difficulties of current GNNs and Graph Transformers in modeling interactions in a graph, we use a simple synthetic node classification task.

We propose a simple extension of this task to graphs: In **Grid Histogram Counting** (Figure 2), we generate \(N\times M\) grids with randomly colored nodes and ask models to predict, for each node, how many other nodes in the same row or column have the same color.

Solving it requires far away nodes to communicate, and the communication should consider both the nodes' content (color) and relation within the graph (being in the same row or column).

However, as we show in Section 5.1.2, it defeats all existing GNN and Graph Transformer techniques, while Graph Diffuser succeeds.

First, GD embeds the structural relations between distant nodes in what we refer to as Virtual Edges. Then, the Transformer processes the nodes while using the virtual edges to direct the computation at different layers.

To consider relations between distant nodes, the first step is broadening the receptive field on which the architecture operates. In a row-normalized adjacency matrix \(A\), \(A_{ij}^{k}\) corresponds to the probability of getting from node \(i\) to node \(j\) in a \(k\) step random walk.

Multiplication by the adjacency matrix is closely related to the aggregation scheme of MP-GNNS Xu et al. (2018), however, considering multiple powers of the matrix at once, we zoom out of the local Message Passing paradigm and discover information that GNNs may not detect. Virtual Edges contain structural information such as if nodes are on an odd length cycle, can distinguish many non-isomorphic graphs, and cover many distance measures such as shortest distance and generalized PageRank Li et al. (2020). In order to mix information between different propagation steps and extract meaningful structural relations, each stack is processed by a fully connected edge-wise feed-forward network.

In the input layer, Self-Virtual Edges are added to the node representation as positional encoding, and at each attention layer, the Virtual Edges are reduced to an attention matrix that is combined with the standard dot-product attention.

As we will see in the next section, separating the attention based on content and positions and then combining them seems to assist with learning meaningful connections in the data and provides a natural visualization mechanism.

First, we observe that the vanilla Transformer, which easily solves the histogram task over sequential input, fails here and performs the worst. This is not surprising as the Transformer is oblivious to the graph structure. Next, we observe that RWPE Dwivedi et al. (2022), a popular positional embedding technique, improves very slightly over the base Transformer. This may be because RWPE is unable to detect symmetries in the graph.

Adding SignNet Lim et al. (2022), a theoretically expressive positional embedding technique based on the graph eigenvectors, does not yield much improvement either.

The GNN baseline, which in theory can solve the task, achieves \(0.483\) accuracy. This may be due to the over-squashing phenomenon. Indeed in a \(10\times 10\) grid, passing information between opposing nodes in the same row will require \(9\) message passing layers to deliver a single message that has been "squashed" with nearly 90k other messages.

Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

The average distance between nodes in this dataset is larger than that of any other dataset in our experiments, which can explain why Graph Transformers variations dominate its leaderboards.

**Long Range Graph Benchmark**Dwivedi et al. (2022b) is a recently proposed dataset specifically designed to evaluate models on their ability to capture long-range interactions. We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

In this work, we introduced a simple and effective architecture for machine learning on graphs, Graph Diffuser. Using a controlled example, we demonstrated its effectiveness in modeling long-range interactions while providing better interpretability. We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains.

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, the claim appears to be well-supported but slightly overstated. While the evidence demonstrates that Graph Diffuser outperforms existing GNNs and Graph Transformers on the Grid Histogram Counting task and Long Range Graph Benchmark, showing better handling of long-range interactions, the visualization aspect is less thoroughly substantiated. The paper shows one example of intuitive visualization in Figure 1, but more comprehensive visualization analysis would be needed to fully support that part of the claim.

<score>2</score>

Justification:
1. Strengths supporting the claim:
- Clear experimental evidence showing Graph Diffuser outperforming baselines on Grid Histogram Counting task
- Strong performance on Long Range Graph Benchmark datasets
- Demonstration of how Virtual Edges help capture long-range dependencies
- Figure 1 provides a visual example of the attention mechanism

2. Limitations/overstatements:
- The visualization aspect is mentioned but not extensively demonstrated beyond one example
- Some reviewer comments point out the need for more ablation studies to fully understand component contributions
- The reviewer notes that when using weighted adjacency, the model doesn't leverage original adjacency information

3. The claim would be better stated if it focused more specifically on the demonstrated performance advantages and presented the visualization capabilities more modestly as an additional feature rather than a key differentiator.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Experiments on eight benchmarks show Graph Diffuser to be a highly competitive model, outperforming the state-of-the-art in a diverse set of domains.

The evidence to be evaluated is:Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

For 5 of the datasets, ZINC, OGBG-{molpcba, ppa,code2}, PCQM-Contact and PCQM4Mv2, we use the very competitive GPS Rampasek et al. (2022) as the Transformer model. For the LRGB benchmarks, Peptides-func and Peptides-struct, there are no official GPS hyperparameters, and we use a Transformer with the authors' baseline hyperparameters and a CLS token added to the input.

We evaluate our model on \(8\) datasets overall and compare our results with those of popular MPGNNs, Graph Transformers and other recent state-of-the-art models. Graph Diffuser exceeds SOTA in 6 of them and achieves very competitive results in the rest.

Table 2 shows the results, where we exceed SOTA results by a substitutional margin.

We evaluate GD on three graph-level prediction tasks from different domains and report the results at Table 3 **OGBG-MOLPCBA** is a multi-task binary classification dataset containing 438k molecules, and the task is to predict the activity/inactivity of 128 properties. Here we rank the second highest and the first among all GNN or Transformer architectures.

The previously highest-ranking model is GPS, and adding our positional attention and encoding to it proves to be an efficient strategy that reaches a new state-of-the-art.

Since positional encoding was not found to be significant by the previous three highest ranking models in this dataset, and considering the large improvement of our model over GPS, it seems that positional attention brings significant benefits in this benchmark, which allows us to reach a new state-of-the-art.

Here, our results are similar to GPS, which ranks highest among Graph Transformers variations. Our results lag behind only GEM-2 Liu et al. (2022), which was designed specifically for modeling molecular interactions.

We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains. With minimal hyperparameter tuning, Graph Diffuser achieves a new state-of-the-art on most datasets and reaches very competitive results on the rest. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **MAE \(\downarrow\)** \\ \hline GCN Kipf \& Welling (2017) & 0.367 \(\pm\) 0.011 \\ GIN Xu et al. (2019a) & 0.526 \(\pm\) 0.051 \\ GAT Velicković et al. (2018) & 0.384 \(\pm\) 0.007 \\ GatedGCN Bresson \& Laurent (2017); Dwivedi et al. (2020) & 0.282 \(\pm\) 0.015 \\ GatedGCN-LSP Dwivedi et al. (2022a) & 0.090 \(\pm\) 0.001 \\ CRaWI Toenshoff et al. (2021) & 0.085 \(\pm\) 0.004 \\ GIN-Ak Zhao et al. (2022) & 0.080 \(\pm\) 0.001 \\ SAN Kreuzer et al. (2021) & 0.139 \(\pm\) 0.006 \\ Graphormer Ying et al. (2021) & 0.122 \(\pm\) 0.006 \\ K-Sunggraph SAT Chen et al. (2022) & 0.094 \(\pm\) 0.008 \\ GPS Rampásek et al. (2022) & 0.070 \(\pm\) 0.004 \\ \hline Graph Diffuser(ours) & **0.0683 \(\pm\) 0.002** \\ \hline \hline \end{tabular}
\end{table}
Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input: Table 3: Test results in OGB graph-level benchmarks Hu et al. (2020). Pre-trained or ensemble models are not included. Bold:first, Underlined:Second.

Input: Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the claim and evidence, I find this claim to be slightly overstated. While Graph Diffuser does show strong performance, the evidence reveals:

- It outperforms SOTA in 6 out of 8 datasets, not all benchmarks
- For OGBG-MOLPCBA, it ranks second, not first overall
- For some benchmarks, it performs similarly to existing models like GPS
- The authors note they are "first to evaluate" on some datasets after baselines, suggesting limited competition
- Some improvements are marginal (e.g., ZINC dataset: 0.0683 vs GPS's 0.070)

While Graph Diffuser demonstrates competitive performance, the claim's wording suggests universal superiority across all benchmarks, which isn't fully supported by the detailed results.

<score>3</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Experiments on eight benchmarks show Graph Diffuser to be a highly competitive model, outperforming the state-of-the-art in a diverse set of domains.

The review comment to be evaluated is:

Strength
- The method is motivated by the failure of current architectures over a synthetic task. The proposed method brings significant improvement to it.
-  The method demonstrates empirical gains over some datasets, mostly on ones that requires capturing long-range interactions

Weaknesses
- Some important parts of the paper are confusing, mostly due to the ordering of the sections and the phrases:
    - It is not clear to me what "learn to combine information propagation over multiple different propagation steps in an
end-to-end manner" means. What are the "multiple different propagation steps"?
    - The use of the phrase "virtual edge" is somewhat confusing. Based on the later formulas, it seems these virtual edges are essentially generated features between all pair of nodes (based on 4.1), and replace the original edges/edge features. But the phrase itself and Figure 1 makes it seem like the virtual edges are added to the original set of edges.
- Some of the statements seem to be over-claimed:
    - "However, given the arbitrary structure of graphs, incorporating the input into the Transformer remains a challenging aspect in designing GTs, and so far, there has been no universal solution. We propose a simple architecture for incorporating structural data into the Transformer, Graph Diffuser (GD)..." It should be clarified that a lot of the current graph transformers designs are expressive enough incorporate arbitrary structure of graphs (e.g. Graphormer, GRAPHGPS, etc) and showed strong results. The authors should narrow down the claim to improving the modeling of long-range interaction.
    - "this work is the first Graph Transformer to [...] learn to combine information propagation over multiple different propagation steps in an end-to-end manner." It is not particularly clear to me what this statement means, but seems this is referring to feeding stacked random walk matrices through feed-forward neural networks in 4.1.2. I believe this has already been mentioned in GRAPHGPS and GraphiT (i.e. Relative PE using random walks).
- The first step of learning a dense adjacency matrix could be very expensive for large graphs.
- The empirical gain on ZINC and most of the OGB datasets seem quite small compared to the variance.

The evidence to be evaluated is:Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

For 5 of the datasets, ZINC, OGBG-{molpcba, ppa,code2}, PCQM-Contact and PCQM4Mv2, we use the very competitive GPS Rampasek et al. (2022) as the Transformer model. For the LRGB benchmarks, Peptides-func and Peptides-struct, there are no official GPS hyperparameters, and we use a Transformer with the authors' baseline hyperparameters and a CLS token added to the input.

We evaluate our model on \(8\) datasets overall and compare our results with those of popular MPGNNs, Graph Transformers and other recent state-of-the-art models. Graph Diffuser exceeds SOTA in 6 of them and achieves very competitive results in the rest.

Table 2 shows the results, where we exceed SOTA results by a substitutional margin.

We evaluate GD on three graph-level prediction tasks from different domains and report the results at Table 3 **OGBG-MOLPCBA** is a multi-task binary classification dataset containing 438k molecules, and the task is to predict the activity/inactivity of 128 properties. Here we rank the second highest and the first among all GNN or Transformer architectures.

The previously highest-ranking model is GPS, and adding our positional attention and encoding to it proves to be an efficient strategy that reaches a new state-of-the-art.

Since positional encoding was not found to be significant by the previous three highest ranking models in this dataset, and considering the large improvement of our model over GPS, it seems that positional attention brings significant benefits in this benchmark, which allows us to reach a new state-of-the-art.

Here, our results are similar to GPS, which ranks highest among Graph Transformers variations. Our results lag behind only GEM-2 Liu et al. (2022), which was designed specifically for modeling molecular interactions.

We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains. With minimal hyperparameter tuning, Graph Diffuser achieves a new state-of-the-art on most datasets and reaches very competitive results on the rest. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **MAE \(\downarrow\)** \\ \hline GCN Kipf \& Welling (2017) & 0.367 \(\pm\) 0.011 \\ GIN Xu et al. (2019a) & 0.526 \(\pm\) 0.051 \\ GAT Velicković et al. (2018) & 0.384 \(\pm\) 0.007 \\ GatedGCN Bresson \& Laurent (2017); Dwivedi et al. (2020) & 0.282 \(\pm\) 0.015 \\ GatedGCN-LSP Dwivedi et al. (2022a) & 0.090 \(\pm\) 0.001 \\ CRaWI Toenshoff et al. (2021) & 0.085 \(\pm\) 0.004 \\ GIN-Ak Zhao et al. (2022) & 0.080 \(\pm\) 0.001 \\ SAN Kreuzer et al. (2021) & 0.139 \(\pm\) 0.006 \\ Graphormer Ying et al. (2021) & 0.122 \(\pm\) 0.006 \\ K-Sunggraph SAT Chen et al. (2022) & 0.094 \(\pm\) 0.008 \\ GPS Rampásek et al. (2022) & 0.070 \(\pm\) 0.004 \\ \hline Graph Diffuser(ours) & **0.0683 \(\pm\) 0.002** \\ \hline \hline \end{tabular}
\end{table}
Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input: Table 3: Test results in OGB graph-level benchmarks Hu et al. (2020). Pre-trained or ensemble models are not included. Bold:first, Underlined:Second.

Input: Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on my analysis of the evidence and review comments, the claim that "Graph Diffuser is highly competitive and outperforms state-of-the-art across eight benchmarks" is somewhat overstated. While the model shows strong performance, several factors suggest the claim needs more nuance:

1. The improvements on some datasets (ZINC, OGB) are within variance margins, as noted in the review
2. For OGBG-molpcba, GD ranks second, not first
3. For some benchmarks, they are the first to evaluate besides baseline, limiting comparative claims
4. The review points out that other Graph Transformers can also handle arbitrary graph structures
5. The performance gains are more specifically related to long-range interactions rather than universal superiority

A more precise claim would acknowledge these limitations while highlighting the model's strengths in specific areas.

<score>4</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Experiments on eight benchmarks show Graph Diffuser to be a highly competitive model, outperforming the state-of-the-art in a diverse set of domains.

The review comment to be evaluated is:

Strength:
1. The proposed method performs favorably on benchmarks datasets.
2. The method is effective but is also quite simple in term of implementing it.
3. The counter example of the 2-d grid histogram counting problem for graph transformer is interesting as all state of the art model fail to solve it.

Weakness:
1. The technical contribution is incremental. Graph diffusion (both in discrete and the ODE form) has been studied and applied in the domain of graph neutral network. While adding graph diffusion to the positional attention is new, it is a trivial extension. [1][2][3]
2. While it is surprising that most graph transformer could not solve the grid based counting problem, this problem itself in the context of graph can be easily solved by diffusion matrix itself if node color is expressed as node feature with one-hot encoding.

[1] https://papers.nips.cc/paper/2019/hash/23c894276a2c5a16470e6a31f4618d73-Abstract.html
[2] https://aclanthology.org/2021.emnlp-main.642.pdf
[3] https://openreview.net/forum?id=EMxu-dzvJk

The evidence to be evaluated is:Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

For 5 of the datasets, ZINC, OGBG-{molpcba, ppa,code2}, PCQM-Contact and PCQM4Mv2, we use the very competitive GPS Rampasek et al. (2022) as the Transformer model. For the LRGB benchmarks, Peptides-func and Peptides-struct, there are no official GPS hyperparameters, and we use a Transformer with the authors' baseline hyperparameters and a CLS token added to the input.

We evaluate our model on \(8\) datasets overall and compare our results with those of popular MPGNNs, Graph Transformers and other recent state-of-the-art models. Graph Diffuser exceeds SOTA in 6 of them and achieves very competitive results in the rest.

Table 2 shows the results, where we exceed SOTA results by a substitutional margin.

We evaluate GD on three graph-level prediction tasks from different domains and report the results at Table 3 **OGBG-MOLPCBA** is a multi-task binary classification dataset containing 438k molecules, and the task is to predict the activity/inactivity of 128 properties. Here we rank the second highest and the first among all GNN or Transformer architectures.

The previously highest-ranking model is GPS, and adding our positional attention and encoding to it proves to be an efficient strategy that reaches a new state-of-the-art.

Since positional encoding was not found to be significant by the previous three highest ranking models in this dataset, and considering the large improvement of our model over GPS, it seems that positional attention brings significant benefits in this benchmark, which allows us to reach a new state-of-the-art.

Here, our results are similar to GPS, which ranks highest among Graph Transformers variations. Our results lag behind only GEM-2 Liu et al. (2022), which was designed specifically for modeling molecular interactions.

We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains. With minimal hyperparameter tuning, Graph Diffuser achieves a new state-of-the-art on most datasets and reaches very competitive results on the rest. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **MAE \(\downarrow\)** \\ \hline GCN Kipf \& Welling (2017) & 0.367 \(\pm\) 0.011 \\ GIN Xu et al. (2019a) & 0.526 \(\pm\) 0.051 \\ GAT Velicković et al. (2018) & 0.384 \(\pm\) 0.007 \\ GatedGCN Bresson \& Laurent (2017); Dwivedi et al. (2020) & 0.282 \(\pm\) 0.015 \\ GatedGCN-LSP Dwivedi et al. (2022a) & 0.090 \(\pm\) 0.001 \\ CRaWI Toenshoff et al. (2021) & 0.085 \(\pm\) 0.004 \\ GIN-Ak Zhao et al. (2022) & 0.080 \(\pm\) 0.001 \\ SAN Kreuzer et al. (2021) & 0.139 \(\pm\) 0.006 \\ Graphormer Ying et al. (2021) & 0.122 \(\pm\) 0.006 \\ K-Sunggraph SAT Chen et al. (2022) & 0.094 \(\pm\) 0.008 \\ GPS Rampásek et al. (2022) & 0.070 \(\pm\) 0.004 \\ \hline Graph Diffuser(ours) & **0.0683 \(\pm\) 0.002** \\ \hline \hline \end{tabular}
\end{table}
Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input: Table 3: Test results in OGB graph-level benchmarks Hu et al. (2020). Pre-trained or ensemble models are not included. Bold:first, Underlined:Second.

Input: Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence and review comments, here's my evaluation:

The claim appears moderately overstated. While Graph Diffuser shows strong performance across benchmarks, several nuances emerge:

1. The claim of "outperforming state-of-the-art" is only partially supported - it achieves best results in some but not all benchmarks:
- Ranks second in OGBG-MOLPCBA
- Lags behind GEM-2 in some cases
- Shows similar results to GPS in certain benchmarks

2. The review points out that the technical contribution is incremental, with graph diffusion being previously studied.

3. While the results are competitive, using phrases like "highly competitive" and broad claims of outperforming SOTA across "diverse domains" overstates the actual mixed performance shown in the evidence.

<score>3</score>

Justification:
- The evidence shows good but mixed performance across benchmarks
- The claim uses stronger language than warranted by the actual results
- Review comments highlight the incremental nature of the technical contribution
- Tables 2 and 3 show competitive but not uniformly superior performance
- Some improvements are marginal (e.g., ZINC: 0.0683 vs GPS: 0.070)


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Experiments on eight benchmarks show Graph Diffuser to be a highly competitive model, outperforming the state-of-the-art in a diverse set of domains.

The review comment to be evaluated is:

Pros:
The experiments can effectively show the performance of the proposed method.

Cons:
1. There are existing works [1, 2] about incorporating graph diffusion in attention-based GNN that are not covered in this work. Besides, in the Related Work section, the subsection "Diffusion" might be revised to "Diffusion in Graph" to avoid any ambiguity with "Diffusion Models".
2. The improvement on many benchmarks is limited compared to the standard deviations.
3. The models in Table 1 are not well described in the main context. For example, the settings of "GNN →Transformer" and "GNN | Transformer+RWPE" can be briefly mentioned in 5.1.1. Moreover, the necessity of designing "GNN →Transformer" and "GNN | Transformer+RWPE" for comparison is not clear.
4. About the figure drawing: Figure 1 is a little hard to understand since it contains terms like "Edge-Wise FFN/projection" and unclear attention maps that are only described in the latter sections. The Transformer architecture in Figure 3 is not well drawn. The Positional Attention module is even partly outside the Multi-Head Attention module.

[1] Wang, Guangtao, Rex Ying, Jing Huang, and Jure Leskovec. "Multi-hop attention graph neural network." arXiv preprint arXiv:2009.14332 (2020).

[2] Liu, Yonghao, Renchu Guan, Fausto Giunchiglia, Yanchun Liang, and Xiaoyue Feng. "Deep attention diffusion graph neural networks for text classification." In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pp. 8142-8152. 2021.

The evidence to be evaluated is:Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

For 5 of the datasets, ZINC, OGBG-{molpcba, ppa,code2}, PCQM-Contact and PCQM4Mv2, we use the very competitive GPS Rampasek et al. (2022) as the Transformer model. For the LRGB benchmarks, Peptides-func and Peptides-struct, there are no official GPS hyperparameters, and we use a Transformer with the authors' baseline hyperparameters and a CLS token added to the input.

We evaluate our model on \(8\) datasets overall and compare our results with those of popular MPGNNs, Graph Transformers and other recent state-of-the-art models. Graph Diffuser exceeds SOTA in 6 of them and achieves very competitive results in the rest.

Table 2 shows the results, where we exceed SOTA results by a substitutional margin.

We evaluate GD on three graph-level prediction tasks from different domains and report the results at Table 3 **OGBG-MOLPCBA** is a multi-task binary classification dataset containing 438k molecules, and the task is to predict the activity/inactivity of 128 properties. Here we rank the second highest and the first among all GNN or Transformer architectures.

The previously highest-ranking model is GPS, and adding our positional attention and encoding to it proves to be an efficient strategy that reaches a new state-of-the-art.

Since positional encoding was not found to be significant by the previous three highest ranking models in this dataset, and considering the large improvement of our model over GPS, it seems that positional attention brings significant benefits in this benchmark, which allows us to reach a new state-of-the-art.

Here, our results are similar to GPS, which ranks highest among Graph Transformers variations. Our results lag behind only GEM-2 Liu et al. (2022), which was designed specifically for modeling molecular interactions.

We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains. With minimal hyperparameter tuning, Graph Diffuser achieves a new state-of-the-art on most datasets and reaches very competitive results on the rest. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **MAE \(\downarrow\)** \\ \hline GCN Kipf \& Welling (2017) & 0.367 \(\pm\) 0.011 \\ GIN Xu et al. (2019a) & 0.526 \(\pm\) 0.051 \\ GAT Velicković et al. (2018) & 0.384 \(\pm\) 0.007 \\ GatedGCN Bresson \& Laurent (2017); Dwivedi et al. (2020) & 0.282 \(\pm\) 0.015 \\ GatedGCN-LSP Dwivedi et al. (2022a) & 0.090 \(\pm\) 0.001 \\ CRaWI Toenshoff et al. (2021) & 0.085 \(\pm\) 0.004 \\ GIN-Ak Zhao et al. (2022) & 0.080 \(\pm\) 0.001 \\ SAN Kreuzer et al. (2021) & 0.139 \(\pm\) 0.006 \\ Graphormer Ying et al. (2021) & 0.122 \(\pm\) 0.006 \\ K-Sunggraph SAT Chen et al. (2022) & 0.094 \(\pm\) 0.008 \\ GPS Rampásek et al. (2022) & 0.070 \(\pm\) 0.004 \\ \hline Graph Diffuser(ours) & **0.0683 \(\pm\) 0.002** \\ \hline \hline \end{tabular}
\end{table}
Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input: Table 3: Test results in OGB graph-level benchmarks Hu et al. (2020). Pre-trained or ensemble models are not included. Bold:first, Underlined:Second.

Input: Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence and reviewer comments, I find this claim partially overstated. While Graph Diffuser does show strong performance across multiple benchmarks, several key points temper the claim:

1. The reviewer notes "improvement on many benchmarks is limited compared to standard deviations"
2. Evidence shows Graph Diffuser ranks second on OGBG-MOLPCBA, not first
3. For some benchmarks, they are "similar to GPS" rather than outperforming
4. On some datasets, they are "the first, other than author's baselines" to evaluate, making SOTA claims less meaningful
5. The claim of "outperforming state-of-the-art in diverse domains" is too strong given these limitations

While Graph Diffuser demonstrates competitive performance, the absolute claim of outperforming SOTA across diverse domains overstates the actual results shown in the evidence.

<score>4</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Experiments on eight benchmarks show Graph Diffuser to be a highly competitive model, outperforming the state-of-the-art in a diverse set of domains.

The review comment to be evaluated is:

Strength:
1. The paper presents two novel design for a graph transformer, the graph diffuser and context attention.
2. The paper provides many experiments in different datasets to demonstrate the performance of their approach.
3. The detail description of the experimental setup is also useful in understanding the benchmarks.

Weakness:
1. The authors should add more literature review. By googling "graph transformer", there is a survey [1] on arXiv that mentioned various methods regarding graph transformer. But some of those methods are not reviewed by the authors. Also, the experiments should include more baselines.
2. When use weighted adjacency, the model does not leverage any information from original adjacency.
3. More ablation study are needed to reveal the importance of each component. For example, context attention only, context attention + weighted adj, context attention + diffuser + weighted adj, and so on.

[1] Min, E., Chen, R., Bian, Y., Xu, T., Zhao, K., Huang, W., ... & Rong, Y. (2022). Transformer for Graphs: An Overview from Architecture Perspective. arXiv preprint arXiv:2202.08455. (https://arxiv.org/abs/2202.08455)

The evidence to be evaluated is:Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column.

For 5 of the datasets, ZINC, OGBG-{molpcba, ppa,code2}, PCQM-Contact and PCQM4Mv2, we use the very competitive GPS Rampasek et al. (2022) as the Transformer model. For the LRGB benchmarks, Peptides-func and Peptides-struct, there are no official GPS hyperparameters, and we use a Transformer with the authors' baseline hyperparameters and a CLS token added to the input.

We evaluate our model on \(8\) datasets overall and compare our results with those of popular MPGNNs, Graph Transformers and other recent state-of-the-art models. Graph Diffuser exceeds SOTA in 6 of them and achieves very competitive results in the rest.

Table 2 shows the results, where we exceed SOTA results by a substitutional margin.

We evaluate GD on three graph-level prediction tasks from different domains and report the results at Table 3 **OGBG-MOLPCBA** is a multi-task binary classification dataset containing 438k molecules, and the task is to predict the activity/inactivity of 128 properties. Here we rank the second highest and the first among all GNN or Transformer architectures.

The previously highest-ranking model is GPS, and adding our positional attention and encoding to it proves to be an efficient strategy that reaches a new state-of-the-art.

Since positional encoding was not found to be significant by the previous three highest ranking models in this dataset, and considering the large improvement of our model over GPS, it seems that positional attention brings significant benefits in this benchmark, which allows us to reach a new state-of-the-art.

Here, our results are similar to GPS, which ranks highest among Graph Transformers variations. Our results lag behind only GEM-2 Liu et al. (2022), which was designed specifically for modeling molecular interactions.

We are the first, other than the author's baselines, to evaluate our model on these datasets and currently rank first in all of them.

We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains. With minimal hyperparameter tuning, Graph Diffuser achieves a new state-of-the-art on most datasets and reaches very competitive results on the rest. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **MAE \(\downarrow\)** \\ \hline GCN Kipf \& Welling (2017) & 0.367 \(\pm\) 0.011 \\ GIN Xu et al. (2019a) & 0.526 \(\pm\) 0.051 \\ GAT Velicković et al. (2018) & 0.384 \(\pm\) 0.007 \\ GatedGCN Bresson \& Laurent (2017); Dwivedi et al. (2020) & 0.282 \(\pm\) 0.015 \\ GatedGCN-LSP Dwivedi et al. (2022a) & 0.090 \(\pm\) 0.001 \\ CRaWI Toenshoff et al. (2021) & 0.085 \(\pm\) 0.004 \\ GIN-Ak Zhao et al. (2022) & 0.080 \(\pm\) 0.001 \\ SAN Kreuzer et al. (2021) & 0.139 \(\pm\) 0.006 \\ Graphormer Ying et al. (2021) & 0.122 \(\pm\) 0.006 \\ K-Sunggraph SAT Chen et al. (2022) & 0.094 \(\pm\) 0.008 \\ GPS Rampásek et al. (2022) & 0.070 \(\pm\) 0.004 \\ \hline Graph Diffuser(ours) & **0.0683 \(\pm\) 0.002** \\ \hline \hline \end{tabular}
\end{table}
Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input: Table 3: Test results in OGB graph-level benchmarks Hu et al. (2020). Pre-trained or ensemble models are not included. Bold:first, Underlined:Second.

Input: Table 2: MAE for the ZINC dataset from Dwivedi et al. (2020b).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence and review comments, I find this claim requires careful evaluation.

The evidence shows Graph Diffuser (GD) performs very well but not universally better than all SOTA:
- Exceeds SOTA in 6 out of 8 datasets
- Ranks second on OGBG-MOLPCBA (behind non-GNN/Transformer models)
- Similar performance to GPS on some benchmarks
- Lags behind GEM-2 on molecular interactions

The claim's wording of "highly competitive" is justified, but "outperforming the state-of-the-art in a diverse set of domains" slightly overstates the results since it doesn't acknowledge where GD ranks second or matches existing SOTA. The reviewer also points out the need for more baselines and ablation studies.

<score>2</score>

While the claim has merit based on strong experimental results across multiple domains, it would be more precise to state that GD achieves SOTA on most benchmarks while remaining highly competitive on others.