Paper: Less is More: One-shot Subgraph Reasoning on Large-scale Knowledge Graphs (ICLR-2024)

Reviewer comment (Writing):
In sections 4.4, a significant number of symbols, abbreviations, and technical terms are employed. Some symbols are not adequately explained, which may potentially cause difficulties for readers during their reading. For example, the supp() in 4.4 Theorem 1 does not provide an explanation.

Author response:
Thanks for your kind suggestions. **We have made several modifications to our draft. Please refer to our latest draft, where the modified contents are highlighted in blue.** Specifically,

- **Word use.** We update the words used in our draft, e.g., "paradigm" -> "manner", "KG reasoning" -> "link prediction", and "reasoning" -> "prediction". The keyword of our method is fine-tuned to "one-shot subgraph link prediction" and formally defined in Def. 1. We delete those repeated claims, e.g., the two-step prediction pipeline with sampling and predicting.
- **Technical details.** We move some technical details from the appendix to the main contents. Please refer to Sec. 4.2, where the implementation details of search space, search problem, and search algorithm are elaborated on. Besides, for a better understanding, we also add Fig. 2 to illustrate the technical details.
- **Experimental intuitions.** The intuitions of the experiments are further explained and highlighted in Sec. 5. For example, in Fig. 5, the below distributions of degree and distance show the statistical properties of each subgraph. More importantly, the visualization of Fig. 5 shows that the local structure of query entity $u$ is well preserved, while the true answers $v$ are also covered in the subgraphs, which contributes to the model's performance. 
- **Mathematical symbols and equations.** We add more introduction to the used variables in Sec. 4.3 and leave the detailed proof in Appendix A.3. We also label the formulas in Secs. 4.2 and 4.3 with numbers.

We thoroughly considered the concerns the reviewer pointed out and tried our best to improve the contents. Let us know if some content needs to be further modified, and we will modify it as soon as possible.

Reviewer comment (Presentation):
The formulas in sections 4.3 and 4.4 are not labeled, such as (6) and (7).

Author response:
Thanks for your kind suggestions. **We have made several modifications to our draft. Please refer to our latest draft, where the modified contents are highlighted in blue.** Specifically,

- **Word use.** We update the words used in our draft, e.g., "paradigm" -> "manner", "KG reasoning" -> "link prediction", and "reasoning" -> "prediction". The keyword of our method is fine-tuned to "one-shot subgraph link prediction" and formally defined in Def. 1. We delete those repeated claims, e.g., the two-step prediction pipeline with sampling and predicting.
- **Technical details.** We move some technical details from the appendix to the main contents. Please refer to Sec. 4.2, where the implementation details of search space, search problem, and search algorithm are elaborated on. Besides, for a better understanding, we also add Fig. 2 to illustrate the technical details.
- **Experimental intuitions.** The intuitions of the experiments are further explained and highlighted in Sec. 5. For example, in Fig. 5, the below distributions of degree and distance show the statistical properties of each subgraph. More importantly, the visualization of Fig. 5 shows that the local structure of query entity $u$ is well preserved, while the true answers $v$ are also covered in the subgraphs, which contributes to the model's performance. 
- **Mathematical symbols and equations.** We add more introduction to the used variables in Sec. 4.3 and leave the detailed proof in Appendix A.3. We also label the formulas in Secs. 4.2 and 4.3 with numbers.

We thoroughly considered the concerns the reviewer pointed out and tried our best to improve the contents. Let us know if some content needs to be further modified, and we will modify it as soon as possible.

Reviewer comment (Evaluation):
Given that the proposed method relies on a non-parametric heuristic (PPR) for sampling, how interpretable are the final predictions and reasoning steps? Can the method provide insights into why a certain answer was chosen for a given query?

Author response:
Thanks for the valuable feedback. If a certain answer is chosen for a given query by our method, it should **(1) remain in the subgraph by the sampler** and **(2) get a high score with a relatively high rank by the predictor**. 

Speficically, for **(1)**, 

- Our experiments in Tab. 3 and Fig. 3 reveal that PPR gets a much higher Coverage Ratio (CR) and notably outperforms other heuristics (BFS, PR, RW, RAND) in identifying potential answers.
- The reason is that PPR is query-dependent and local-structure-preserving for its single-source scoring that starts from $u$. Previous studies also show that $v$ is generally near to $u$, and the relational paths connecting $u$ and $v$ that support the query also lie close to $u$. 

- According to the visualized subgraphs in Fig. 5, the local structure of query entity $u$ is well preserved, while the true answers $v$ are also covered in the subgraphs, which contributes to the model's performance. 

- Besides, the extracted subgraphs are interpretable to some extent, which shares the same manner of interpretable graph learning that aims to identify the key subgraphs for predictions [1, 2].

As for **(2)**,

- Our method with PPR achieves leading performances on all five large-scale benchmarks over all the baselines, especially on the largest YAGO3-10 and OGB datasets. If we replace the PPR with other heuristics, the final performance will also decrease significantly, as shown in Tab. 5.
- Importantly, we reveal that it is unnecessary to utilize the whole KG in link prediction; meanwhile, only a small proportion of entities and facts are essential for answering specific queries that can be quickly identified by the PPR heuristics.

Further, we provide a two-fold explanation regarding the better performance of the joint prediction, including the above two steps.

- **Data perspective: Extracting subgraphs can remove irrelevant information for link prediction.** Conventional structural models explicitly take all the entities and edges into prediction, while our one-shot-subgraph method discerns and excludes irrelevant entities while retaining the proper answers. This strategic refinement, in turn, contributes to simplifying the learning problem, thereby amplifying prediction performance. 
- Another supporting material is that only relying on a subgraph for prediction can also boost the test-time performance [2]. The method [2] extracts a subgraph $G_s$ as the interpretation of a GNN, wherein the integrated subgraph sampler can explicitly remove the spurious correlation or noisy information in the original $G$.
- **Model perspective: The higher learning efficiency on subgraphs can further boost hyper-parameter optimization.** Generally, hyperparameter optimization on large-scale datasets poses challenges due to the inherent inefficiencies in model training. However, the implementation of our subgraph-based method results in a substantial improvement in training efficiency. 
- Consequently, we can rapidly obtain evaluation feedback for configurations sampled from the hyperparameter space. The searched configuration usually leads to a deeper GNN (i.e., 8 layers, while previous studies are usually limited to 5 or 6 layers) that increases the expressiveness of prediction. These data-adaptive configurations also contribute to improved prediction performance.

[1] GNNExplainer: Generating Explanations for Graph Neural Networks. NeurIPS 2019.

[2] Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism. ICML 2022.

Reviewer comment (Theory):
How robust is the proposed method to noise or inaccuracies in the underlying knowledge graph? Are there any guarantees regarding the robustness of reasoning results in the presence of perturbations in the data?

Author response:
Thanks for the insightful comment about the noise aspect. Although noise robustness is not our focus, we conduct empirical studies with two kinds of input perturbations.

**Randomly adding noise**: We generate a noisy dataset by randomly adding noisy edges that are not observed from the dataset. Specifically, the entity set and relation set are kept the same. The noise ratio is computed as $\epsilon=\frac{|\mathcal{E}^{\text{noise}}|}{|\mathcal{E}^{\text{train}}|}$, and the $\mathcal{E}^{\text{val}}$ and $\mathcal{E}^{\text{test}}$ are clean to guarantee an accurate evaluation.

As the results (in MRR) shown below, such noise does not significantly influence the prediction performance. Even in the high-noise scenario ($\epsilon=50$%), the MRR result is nearly identical to that on the clean dataset. This result shows the preliminary robustness of the noise, and further investigation should be conducted with more complex noise patterns, e.g., by adopting adversarial techniques.

| Dataset / Noise ratio $\epsilon$ | 0% (clean) | 10%   | 20%   | 30%   | 40%   | 50%   |
| -------------------------------- | ---------- | ----- | ----- | ----- | ----- | ----- |
| WN18RR                           | 0.567      | 0.567 | 0.566 | 0.566 | 0.564 | 0.564 |
| NELL-995                         | 0.547      | 0.547 | 0.547 | 0.547 | 0.546 | 0.547 |
| YAGO3-10                         | 0.606      | 0.605 | 0.603 | 0.601 | 0.602 | 0.601 |

**Randomly deleting facts**: We create a more incomplete KG by randomly deleting the facts in the training set. The delete ratio is computed as $r=\frac{|\mathcal{E}^{\text{delete}}|}{|\mathcal{E}^{\text{train}}|}$, and the $\mathcal{E}^{\text{val}}$ and $\mathcal{E}^{\text{test}}$ are kept the same as the original dataset.

As shown below, this kind of input perturbation greatly degenerates the performance, as the link prediction could rely heavily on the correct edges in the original dataset. Here, a sparser graph with more deleted edges cannot sufficiently support the prediction, and the message propagation from the query entity is also hindered. Hence, combating the graph's incompleteness would be a valuable direction.

| Dataset / Delete ratio $r$ | 0% (full) | 10%   | 20%   | 30%   | 40%   | 50%   |
| -------------------------- | --------- | ----- | ----- | ----- | ----- | ----- |
| WN18RR                     | 0.567     | 0.507 | 0.451 | 0.394 | 0.338 | 0.278 |
| NELL-995                   | 0.547     | 0.515 | 0.483 | 0.446 | 0.412 | 0.365 |
| YAGO3-10                   | 0.606     | 0.553 | 0.489 | 0.434 | 0.385 | 0.329 |

Reviewer comment (Novelty):
Although the problem is interesting, the proposed methodology is not surprising. The main idea is to use PPR to calculate probability and select the top of entities and relations. The reasoning on the subgraph is following the existing methods.

Author response:
We thank reviewer RRjT for the valuable feedback. We addressed all the comments you provided. Please find the point-to-point responses below. Any further comments and discussions are welcome!

**Q1.** About the novelty and contribution.

> Although the problem is interesting, the proposed methodology is not surprising. The main idea is to use PPR to calculate probability and select the top of entities and relations. The reasoning on the subgraph is following the existing methods.

**Reply:** Thanks for the feedback. We would like to kindly argue that it is **non-trivial** to achieve efficient and adaptive link prediction on large-scale KGs like YAGO3-10 and OGBL-WIKIKG2. Existing methods can easily get **out of memory** on these benchmarks, and searching for adaptive configuration is also **infeasible**. The proposed method in this work is **general** to existing methods for KG link prediction and can be integrated with more heuristic indicators for sampling.

Here, we would further explain the novelty and contributions in the following three folds:

- **A valuable research problem.** Our investigation delves into the limitations of structural models, which confront a pronounced scalability challenge. These models rely on prediction over the entire knowledge graph, encompassing all entities and edges, with the additional burden of scoring all entities as potential answers. This approach proves to be highly inefficient, impeding their optimization when applied to large-scale KGs. As a consequence, we present an open question, pondering how to conduct prediction on knowledge graphs efficiently and effectively, and seeking avenues to overcome this hindrance.

- **A conceptual framework with several practical instantiations.** In response to the prevalent scalability challenges faced by existing KG methods, we present a conceptual solution, i.e., the one-shot-subgraph manner for link prediction. This approach owns the enhanced flexibility and efficacy in design. Specifically, instead of conducting direct prediction on the complete original KG, we advocate a two-step prediction process involving subgraph sampling and subgraph-based prediction. In this regard, our proposed prediction manner comprises a sampler and a predictor. Leveraging the efficiency gains derived from subgraph-based prediction, we introduce an optimization technique for subgraph-based searching, incorporating several well-crafted technical designs. These innovations aim to strike a balance between prediction efficiency and the complexity associated with identifying optimal configurations within both data and model spaces.

- **Several important discoveries from experiments.** Through comprehensive experimentation on five prevalent KGs, we demonstrate that our framework achieves state-of-the-art performance. Particularly noteworthy are the substantial advancements we achieve in both efficiency and effectiveness, a trend that is particularly evident in the case of the largest YAGO3-10 and OGB datasets. Our quest for optimal configurations leads us to the intriguing revelation that utilizing the entire KG for prediction is unnecessary. Instead, simple heuristics can efficiently identify a small proportion of entities and facts essential for answering specific queries without the need for additional learning. These compelling findings hold significant meaning and are poised to pique the interest of the KG community.

Reviewer comment (Experiments):
The paper emphasizes improved efficiency, but I did not find a comparison of efficiency between the proposed method and the existing ones.

Author response:
**Q2.** The comparison of efficiency.

> The paper emphasizes improved efficiency, but I did not find a comparison of efficiency between the proposed method and the existing ones.

**Reply:** Thanks for the comment. As can be seen in Tab. 6 of our original draft, we provide a detailed efficiency comparison between our one-shot-subgraph method (with 10% entities) and two SOTA methods, i.e., NBFNet and RED-GNN (the vanilla implementation with 100% entities). **Tab. 6 below shows that the training time is significantly reduced when learning with our method.** Notably, on the large dataset YAGO3-10, **94.3%** and **94.5%** of training time (for one epoch) can be saved for NBFNet and RED-GNN, respectively. 

| Table 6                          | WN18RR    |          |          |               | YAGO3-10  |          |          |               |
| ----------------------------------------- | --------- | -------- | -------- | ------------- | --------- | -------- | -------- | ------------- |
| Metrics                                   | MRR       | H@1      | H@10     | Training Time | MRR       | H@1      | H@10     | Training Time |
| NBFNet (100% entities)                    | 0.551     | 49.7     | **66.6** | 32.3 min      | 0.550     | 47.9     | 68.3     | 493.8 min     |
| NBFNet + one-shot-subgraph (10% entities) | **0.554** | **50.5** | 66.3     | **2.6 min**   | **0.565** | **49.6** | **69.2** | **28.2 min**  |
| RED-GNN (100% entities)                   | 0.533     | 48.5     | 62.4     | 68.7 min      | 0.559     | 48.3     | 68.9     | 1382.9 min    |
| RED-GNN+ one-shot-subgraph (10% entities) | **0.567** | **51.4** | **66.6** | **4.5 min**   | **0.606** | **54.0** | **72.1** | **76.3 min**  |

Besides, we conduct an efficiency study to investigate the improvement of efficiency brought by the proposed method. The training time and GPU memory of an $8$-layer GNN are summarized in Tab. 7 (see below). As can be seen, a notable advantage of our method is that it has a lower computing cost in terms of running time and memory cost. Particularly on the YAGO3-10 dataset, the existing GNN-based methods will run out of memory (OOM) with a deep architecture. **However, with our one-shot-subgraph sampling of lower ratios of $r^q_{\mathcal{V}}$ and $r^q_{\mathcal{E}}$, the learning and prediction of GNNs become feasible with less memory cost and achieving state-of-the-art performance.**

| Table 7   |                     |                     | WN18RR |        | NELL-995 |        | YAGO3-10 |        |
| --------- | ------------------- | ------------------- | ------ | ------ | -------- | ------ | -------- | ------ |
| phase     | $r^q_{\mathcal{V}}$ | $r^q_{\mathcal{E}}$ | Time   | Memory | Time     | Memory | Time     | Memory |
| Training  | 1.0                 | 1.0                 | OOM    | OOM    | OOM      | OOM    | OOM      | OOM    |
| Training  | 0.5                 | 0.5                 | 26.3m  | 20.3GB | 1.6h     | 20.1GB | OOM      | OOM    |
| Training  | 0.2                 | 1.0                 | 12.8m  | 20.2GB | 1.2h     | 18.5GB | OOM      | OOM    |
| Training  | 0.2                 | 0.2                 | 6.7m   | 6.4GB  | 0.6h     | 8.9GB  | 2.1h     | 23.1GB |
| Training  | 0.1                 | 1.0                 | 7.2m   | 9.8GB  | 0.8h     | 12.1GB | 1.3h     | 13.9GB |
| Training  | 0.1                 | 0.1                 | 6.6m   | 5.1GB  | 0.3h     | 5.3GB  | 0.9h     | 10.2GB |
| Inference | 1.0                 | 1.0                 | 7.3m   | 6.7GB  | 17.5m    | 12.8GB | 1.6h     | 15.0GB |
| Inference | 0.5                 | 0.5                 | 6.0m   | 4.3GB  | 8.3m     | 4.5GB  | 1.1h     | 10.1GB |
| Inference | 0.2                 | 1.0                 | 3.2m   | 5.8GB  | 4.2m     | 12.1GB | 0.7h     | 14.7GB |
| Inference | 0.2                 | 0.2                 | 2.8m   | 1.9GB  | 3.6m     | 2.5GB  | 0.6h     | 3.7GB  |
| Inference | 0.1                 | 1.0                 | 2.7m   | 2.7GB  | 3.1m     | 9.4GB  | 0.4h     | 9.7GB  |
| Inference | 0.1                 | 0.1                 | 2.3m   | 1.7GB  | 2.9m     | 1.9GB  | 0.4h     | 3.1GB  |

Reviewer comment (Reproducibility):
The hyperparameter searching is not trivial. It would be helpful if the authors could explain more about hyperparameter searching when facing a new knowledge graph and how to select the best configuration.

Author response:
**Q3.** About the hyperparameter searching.

> The hyperparameter searching looks inefficient. The hyperparameter searching is not trivial. It would be helpful if the authors could explain more about hyperparameter searching when facing a new knowledge graph and how to select the best configuration.

**Reply:** Thanks for the valuable feedback. We would like to explain the detailed hyper-parameter searching process from three aspects, i.e., search space, search problem, and search algorithm. For a better understanding, we also add Fig. 2 to illustrate the technical details.

**The search space.** We denote the sampler's hyper-parameters as $\phi_{\text{hyper}}$ and the predictor's hyper-parameters as $\theta_{\text{hyper}}$. Specifically, $\phi_{\text{hyper}}$ contains $(r^q_{\mathcal{V}}, r^q_{\mathcal{E}})$, while $\theta_{\text{hyper}}$ contains several intra-layer or inter-layer designs, as illustrated in Fig. 2(a).

**The search problem**. Next, we propose the bi-level optimization problem to adaptively search for the optimal configuration $(\phi^*_{\text{hyper}}, \theta^*_{\text{hyper}})$ of design choices on a specific KG, namely,
$$
\phi^*_{\text{hyper}} = \arg \max_{ \phi_{\text{hyper}}} \mathcal{M}( f_{(\theta_{\text{hyper}}^*, \theta_{\text{learn}}^*)}, g_{ \phi_{\text{hyper}}}, \mathcal{E}^{\text{val}}), \\  
				 \text{s.t. }
				 \theta_{\text{hyper}}^*  =
				\arg \max_{ \theta_{\text{hyper}}}
				\mathcal{M}(f_{( \theta_{\text{hyper}},  \theta_{\text{learn}}^*)}, g_{\bar{ \phi}_{\text{hyper}}}, \mathcal{E}^{\text{val}}),
$$

where the performance measurement $\mathcal{M}$ can be Mean Reciprocal Ranking (MRR) or Hits@k. Note the non-parametric sampler $g_\phi$ only contains hyper-parameters $\phi_{\text{hyper}}$. As for predictor $f_\theta$, its $\theta   =   (\theta_{\text{hyper}}, \theta_{\text{learn}})$ also includes the learnable parameter $\theta_{\text{learn}}$ that $\theta_\text{learn}^*   =   \arg \min_{\theta_{\text{learn}}} \mathcal{L} (f_{(\theta_\text{hyper}, \theta_\text{learn})}, g_{\bar\phi_{\text{hyper}}}, \mathcal{E}^{\text{train}})$.

**The search algorithm.** Directly searching on both data and model spaces is expensive due to the large space size and data scale. Hence, we split the search into two sub-processes as Fig. 2(b),

- First, we freeze the sampler $g_{\bar\phi}$ (with constant $\phi_{\text{hyper}}$) to search for the optimal predictor $f_{\theta^*}$ with (1) the hyper-parameters optimization for $\theta^*_{\text{hyper}}$ and (2) the stochastic gradient descent for $\theta^*_{\text{learn}}$.

- Then, we freeze the predictor $f_{\theta^*}$ and search for the optimal sampler $g_{\phi^*}$, simplifying to pure hyper-parameters optimization for $\phi^*_{\text{hyper}}$ in a zero-gradient manner with low computation complexity.

Specifically, we follow the sequential model-based Bayesian Optimization (BO) to obtain $\phi^*_{\text{hyper}}$ and $\theta^*_{\text{hyper}}$. Random forest (RF) is chosen as the surrogate model because it has a stronger power for approximating the complex and discrete curvature compared with other common surrogates, e.g., Gaussian Process (GP) or Multi-layer Perceptron (MLP).

Besides, we also devise a data split trick that balances observations and predictions. It saves time as the training does not necessarily traverse all the training facts. Specifically, partial training facts are sampled as training queries while the others are treated as observations, i.e., we randomly separate the training facts into two parts as $\mathcal{E}^{\text{train}}   =   \mathcal{E}^{\text{obs}} \cup \mathcal{E}^{\text{query}}$, where the overall prediction system $f_\theta \circ g_\phi$ takes $\mathcal{E}^{\text{obs}}$ as input and then predicts $\mathcal{E}^{\text{query}}$ (see Fig. 2(c)). Here, the split ratio $r^{\text{split}}$ is to balance the sizes of these two parts as $r^{\text{split}}   =   \frac{|\mathcal{E}^{\text{obs}}|}{|\mathcal{E}^{\text{query}}|}$. Thus, the training becomes $\theta^*   =  \arg\min_\theta \Sigma_{(u, q, v) \in \mathcal{E}^{\text{query}}} \mathcal{L} \big( f_\theta(G_s), v \big)$  with the split query edges $\mathcal{E}^{\text{query}}$, where $G_s = g_\phi (\mathcal{E}^{\text{obs}} , u, q)$ with the split observation edges $\mathcal{E}^{\text{obs}}$.

The above contents have been added to Sec 4.2 of our latest draft and highlighted in blue.

Reviewer comment (Writing):
The paper appears to use terms and phrases that make it sound quite bombastic and somewhat unscientific (see below).

Author response:
**Reply:** Thanks for your kind suggestions. **We have made several modifications to our draft. Please refer to our latest draft, where the modified contents are highlighted in blue.** Specifically,

- **Word use.** We update the words used in our draft, e.g., "paradigm" -> "manner", "KG reasoning" -> "link prediction", and "reasoning" -> "prediction". The keyword of our method is fine-tuned to "one-shot subgraph link prediction" and formally defined in Def. 1. We delete those repeated claims, e.g., the two-step prediction pipeline with sampling and predicting.
- **Technical details.** We move some technical details from the appendix to the main contents. Please refer to Sec. 4.2, where the implementation details of search space, search problem, and search algorithm are elaborated. Besides, for a better understanding, we also add Fig. 2 to illustrate the technical details.
- **Experimental intuitions.** The intuitions of the experiments are further explained and highlighted in Sec. 5. For example, in Fig. 5, the below distributions of degree and distance show the statistical properties of each subgraph. More importantly, the visualization of Fig.5 shows that the local structure of query entity $u$ is well preserved, while the true answers $v$ are also covered in the subgraphs, which contributes to the model's performance. 
- **Mathematical symbols and equations.** We add more description to the used variables in Sec. 4.3 and leave the detailed proof in Appendix A.3. We also label the formulas in Secs. 4.2 and 4.3 with numbers.

We thoroughly consider the questions the reviewer mentioned and try our best to address the concerns. Please tell us if some content needs to be further modified, and we will do it as soon as possible.

Reviewer comment (Writing):
Algorithm 1 is not clearly defined (see below).

Author response:
**Reply:** Thanks for the feedback. We provide a detailed explanation as follows, along with the corresponding modifications in the revised submission.

- The two-dimensional degree matrix is denoted as $D  \in  \mathbb{R}^{|\mathcal{V}| \times |\mathcal{V}|}$ , and adjacency matrix is $A  \in  \{0,1\}^{|\mathcal{V}| \times |\mathcal{V}|}$. These two matrixes together work as the transition matrix in PPR, wherein $A_{ij}  =  1$ means an edge $(i, r, j)  \in  \mathcal{E}$ and $D_{ij}  =  \text{degree}(v_i)$ if $i  =  j$ else $D_{ij}  =  0$. Besides, $K$ is the maximal PPR iterations, and the damping coefficient $\alpha$ ($=0.85$ by default) controls the differentiation degree.
- The definitions of Alpha, K, A, and D in Algorithm 1 are consistent with Eqn. 3 in Step-1 of Sec. 4.1. We have revised their descriptions in Sec. 4.1 to be clearer and updated the "Require part" of Algorithm 1, including the definitions of all these variables. In addition, Algorithm 1 is moved to the end of introducing three steps. We think the logical flow can be more smooth, and this algorithm provides an overview of the link prediction system.

Reviewer comment (Writing):
To the above point, regarding language usage, specific issues include: using the term "KG Reasoning" while in fact solving the link prediction task (a term used only once in the whole paper); repeated use of the word "paradigm" even though there isn't anything fundamentally new in theory in their proposal/approach; the use of the word "blazes" on p.1.

Author response:
**Reply:** Thanks for your kind suggestions. **We have made several modifications to our draft. Please refer to our latest draft, where the modified contents are highlighted in blue.** Specifically,

- **Word use.** We update the words used in our draft, e.g., "paradigm" -> "manner", "KG reasoning" -> "link prediction", and "reasoning" -> "prediction". The keyword of our method is fine-tuned to "one-shot subgraph link prediction" and formally defined in Def. 1. We delete those repeated claims, e.g., the two-step prediction pipeline with sampling and predicting.
- **Technical details.** We move some technical details from the appendix to the main contents. Please refer to Sec. 4.2, where the implementation details of search space, search problem, and search algorithm are elaborated. Besides, for a better understanding, we also add Fig. 2 to illustrate the technical details.
- **Experimental intuitions.** The intuitions of the experiments are further explained and highlighted in Sec. 5. For example, in Fig. 5, the below distributions of degree and distance show the statistical properties of each subgraph. More importantly, the visualization of Fig.5 shows that the local structure of query entity $u$ is well preserved, while the true answers $v$ are also covered in the subgraphs, which contributes to the model's performance. 
- **Mathematical symbols and equations.** We add more description to the used variables in Sec. 4.3 and leave the detailed proof in Appendix A.3. We also label the formulas in Secs. 4.2 and 4.3 with numbers.

We thoroughly consider the questions the reviewer mentioned and try our best to address the concerns. Please tell us if some content needs to be further modified, and we will do it as soon as possible.

Reviewer comment (Theory):
On p. 3, Advantage 2. Why is the exploration/exploitation relevant for the proposed algorithms? While there is some intuition behind the analogy with exploration/exploitation, the algorithm doesn't really formulate the problem using this analogy. For example, there is no way to trade/balance the two. So this comparison relies on broad intuition, hence this advantage is a weak one at best.

Author response:
**Reply:** Thanks for the insightful feedback. Conceptually, in our case, exploration indicates the range of message propagation w.r.t. the query entity $u$, while exploitation indicates the depth. Structural methods that adopt the massage passing with a BFS manner can only explore and exploit the full L-hop neighbors of u, whose range and depth are exactly the same. By contrast, our paradigm is more flexible in scopes that are not restricted to L-hop, and the range and depth can be different, which is a clear advantage over the common structural models without sampling.

We have simplified and clarified this part to avoid misunderstanding, and the updated Advantage 2 is

> **Advantage 2** (Flexible propagation scope). The scope here refers to the range of message propagation starting from the query entity $u$. Normally, an $L$-layer structural method will propagate to the full $L$-hop neighbors of $u$. By contrast, our one-shot sampling enables the bound of propagation scope within the extracted subgraph, where the scope is decoupled from the model's depth $L$.

Empirically, we found that 

- involving the whole entities degenerates the prediction as too many irrelevant entities are covered (see Tab.4)
- a deeper predictor with a larger $L$ consistently brings better results. 

These observations enlighten us to learn a deeper predictor with small subgraphs.

Reviewer comment (Writing):
Algorithm 1 — define Alpha, K, and define the shape of A and D.

Author response:
**Reply:** Thanks for the feedback. We provide a detailed explanation as follows, along with the corresponding modifications in the revised submission.

- The two-dimensional degree matrix is denoted as $D  \in  \mathbb{R}^{|\mathcal{V}| \times |\mathcal{V}|}$ , and adjacency matrix is $A  \in  \{0,1\}^{|\mathcal{V}| \times |\mathcal{V}|}$. These two matrixes together work as the transition matrix in PPR, wherein $A_{ij}  =  1$ means an edge $(i, r, j)  \in  \mathcal{E}$ and $D_{ij}  =  \text{degree}(v_i)$ if $i  =  j$ else $D_{ij}  =  0$. Besides, $K$ is the maximal PPR iterations, and the damping coefficient $\alpha$ ($=0.85$ by default) controls the differentiation degree.
- The definitions of Alpha, K, A, and D in Algorithm 1 are consistent with Eqn. 3 in Step-1 of Sec. 4.1. We have revised their descriptions in Sec. 4.1 to be clearer and updated the "Require part" of Algorithm 1, including the definitions of all these variables. In addition, Algorithm 1 is moved to the end of introducing three steps. We think the logical flow can be more smooth, and this algorithm provides an overview of the link prediction system.

Reviewer comment (Reproducibility):
How is the adjacency matrix A computed in the subgraph extraction part? Since this is a KG, not a homogeneous graph, there are several adjacency matrices (one for each relation). Are these combined somehow?

Author response:
**Reply:** Thanks for the feedback. Yes, it is exactly your understanding that the adjacencies of different relations are combined. As we introduced in Section 4.1, $A_{ij}  =  1$ means an edge $(i, r, j)  \in  \mathcal{E}$, we combine all the facts of different relations to this two-dimensional adjacent matrix. We have revised this description to be clearer.

Reviewer comment (Presentation):
I think the paper would benefit from pulling some of the technical details from the supplement to the main paper, in favor of reducing some of the verbiage in the main paper. Please consider this modification.

Author response:
**Reply:** Thanks for your kind suggestions. **We have made several modifications to our draft. Please refer to our latest draft, where the modified contents are highlighted in blue.** Specifically,

- **Word use.** We update the words used in our draft, e.g., "paradigm" -> "manner", "KG reasoning" -> "link prediction", and "reasoning" -> "prediction". The keyword of our method is fine-tuned to "one-shot subgraph link prediction" and formally defined in Def. 1. We delete those repeated claims, e.g., the two-step prediction pipeline with sampling and predicting.
- **Technical details.** We move some technical details from the appendix to the main contents. Please refer to Sec. 4.2, where the implementation details of search space, search problem, and search algorithm are elaborated. Besides, for a better understanding, we also add Fig. 2 to illustrate the technical details.
- **Experimental intuitions.** The intuitions of the experiments are further explained and highlighted in Sec. 5. For example, in Fig. 5, the below distributions of degree and distance show the statistical properties of each subgraph. More importantly, the visualization of Fig.5 shows that the local structure of query entity $u$ is well preserved, while the true answers $v$ are also covered in the subgraphs, which contributes to the model's performance. 
- **Mathematical symbols and equations.** We add more description to the used variables in Sec. 4.3 and leave the detailed proof in Appendix A.3. We also label the formulas in Secs. 4.2 and 4.3 with numbers.

We thoroughly consider the questions the reviewer mentioned and try our best to address the concerns. Please tell us if some content needs to be further modified, and we will do it as soon as possible.