ST-GCond: Self-supervised and Transferable Graph Dataset Condensation
Authors: Beining Yang
Qingyun Sun
Cheng Ji
Xingcheng Fu
Jianxin Li
Venue: ICLR 2025 Poster (2025)
Keywords: Graph Neural Network; Graph Dataset Condensation
Primary area: learning on graphs and other geometries & topologies
TL;DR: Current graph dataset condensation only designed for single task&dataset, showing poor performance in transferring scenarios. Hence, we redesign the supervised condensation framework and include self-supervised tasks, enhancing final transferability.

Abstract: The increasing scale of graph datasets significantly enhances deep learning models but also presents substantial training challenges. Graph dataset condensation has emerged to condense large datasets into smaller yet informative ones that maintain similar test performance. However, these methods require downstream usage to match the original dataset and task, which is impractical in real-world scenarios. Our empirical studies show that existing methods fail in "cross-task" and "cross-dataset" scenarios, often performing worse than training from scratch. To address these challenges, we propose a novel method: Self-supervised and Transferable Graph dataset Condensation (ST-GCond). For cross-task transferability, we propose a task-disentangled meta optimization strategy to adaptively update the condensed graph according to the task relevance, encouraging information preservation for various tasks. For cross-dataset transferability, we propose a multi-teacher self-supervised optimization strategy to incorporate auxiliary self-supervised tasks to inject universal knowledge into the condensed graph. Additionally, we incorporate mutual information guided joint condensation mitigating the potential conflicts and ensure the condensing stability. Experiments on both node-level and graph-level datasets show that ST-GCond outperforms existing methods by 2.5% to 18.7% in all cross-task and cross-dataset scenarios, and also achieves state-of-the-art performance on 5 out of 6 datasets in the single dataset and task scenario.

Published as a conference paper at ICLR 2025
ST-GCOND: SELF-SUPERVISED AND TRANSFERABLE GRAPH DATASET CONDENSATION
Beining Yang', Qingyun Sun?; Cheng Ji Xingcheng Fu', Jianxin Li?,
Univerisity of Edinburgh 2 Beihann University Guanggi Normal University Yang- 320 sms. ed. al.acc.u uk, sungy@buaa, edu. on
ABSTRACT
The increasing scale of graph datasets significantly enhances deep learning mod- els but also presents substantial training challenges. Graph dataset condensation has emerged to condense large datasets into smaller yet informative ones that maintain similar test performance. However, these methods strictly require down- stream usage to match the original dataset and task, leading to failures in cross- task and cross-dataset scenarios. To address such cross-task and cross-dataset challenges, we propose a novel Self-supervised and Transferable Graph dataset Condensation method named ST ST-GCond, providing effective and transferable condensed datasets. Specifically, for cross-task challenge, we propose a task- disentangled meta optimization strategy to adaptively update the condensed graph according to the task relevance, encouraging information preservation for various tasks. For cross-dataset challenge, we propose a multi-teacher self- supervisee opti- mization strategy to incorporate auxiliary self-supervised tasks to inject universal knowledge into the condensed graph. Additionally, we incorporate mutual infor- mation guided joint condensation mitigating the potential conflicts and ensure the condensing stability. Experiments on both node-level and graph-level datasets show that ST-SS-T-e GCCon outperforms existing methods by 2.5% ~ 18.7% in all cross-task and cross-dataset scenarios, and also achieves state-of-the-ar performance on 5 out of 6 datasets in the single dataset and task scenario.
INTRODUCTION
Dataset plays an essential role in contemporary machine learning research (Liu et al., 2024; Ghorbani al., 2022). It also widely believed that there is a scaling law between dataset size and the power of deep learning models (Kaplan et al., 2020). Graph datasets, in particular, contain vast amounts of relations and entities that represent complex interactions, such as those found in social networks, molecules, and recommender systems. These datasets serve as the foundation for many powerful models designed support various analytical applications (Schroff al., 2015; Wu et al., 2019; Battaglia et al., 2018; Sun et al., 2022). However, large-scale graph datasets also present significant challenges in terms of storage, processing, and computational resources. On one hand, specific applications like neural architecture search (Zhang et al., 2022: Guan al., 2022) and continual learning (Choi et al., 2024) require repetitive training on datasets, resulting in significant computational costs. On the other hand, for users with limited computational resources, training on large-scale graph datasets can be exceedingly time-consuming or even impractical. Recently, several graph dataset condensation methods (Xu al., 2024; Sun al., 2024) have been proposed to address this and show remarkable success in preserving essential information with extremely small datasets.
However, as shown in Fig. 1a, all existing graph condensation methods designed to condense specific dataset tailored for single dataset and task. This limitation is incompatible with real-world requirements, where users may encounter new or user-defined data and tasks that significantly differ from those condensed graph datasets derived by open-access datasets. Unlike applying applications to few public graph datasets, such scenarios are much more common and challenging. Though there exist other lines of studies (e.g., graph transfer learning (Zhuang et al., 2020), graph meta learning (Mandal et al., 2022), and graph foundation models(Liu et al., 2023a)) that could also address
"Corresponding author.

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Published as a conference paper at ICLR 2025
Performance (AC0%)
Cross-task Performance on Oghn-arxiv
(X.A.Y)
Gs [X X
Ophn- arsir
Nade chavellcationn
Ogbn-aradv
SEDO
clasification
GROM
(Cool
Original
Supervised taok
Condessed Graph
Only use for same &atssct&tnsik
Cmoph
Test Epochs
(a) Condense dataset only for the single dataset&task
(c) "Cross-task" challenge
Croes daraset Performance Comparison
(X.A.Y)
Node [X,, YO. V
Bundem
0.73
1.0
clansficaation
Ogha-arziv
Mehhole
CCood
SC100
0,87
9.91
0.64
0.48
Oghe-
andi
PABRUIS
Node rlaatering
Link predlictios
ST-OCwod
GEOM
SFGC
0.86
0.75
0.33
0.31
9.5
Original
Grahh Supervise tasks
Supervised tackd
Condensed
Gmoph
Use for vanous dasaseess&tukks
1,02
1.05
Taxt Datendt
1.03
0.38
(b) Condense dataset for various datasets&tasks
(d) "Cross-dataset" challenge
Figure We illustrate the pipeline of existing graph condensation methods (Fig. la), which are designed for single dataset and task. We enhance these methods to make the condensed graph transferable to various downstream needs (Fig. lb). We achieve faster and more effective performance in both cross-task (Fig. Ic) and cross-dataset (Fig. Id) scenarios.
this issue, they require fixed model architecture design complex training strategies, and relatively huge computational resources. Therefore, it is natural to ask question: Can the condensed graph dataset be used train models for various tasks and upon various datasets?
To simplify the discussion, we extend the concept of model transferability to data-level transferabil- ity, which evaluates how well the condensed dataset, when used train model, enables the model to transfer effectively to new datasets or new tasks. Ideally, enhanced transferability would allow users to train models more efficiently, achieving faster convergence and better results when applied to their own data or task (Fig. lb). However, we empirically find there are two main challenges for addressing the problem of transferability on the current graph dataset condensation methods.
Challenge O: Efficient and Fast Cross-task Adaptation. In this context, a "task" refers to either
changes task types or changes label sets. We provide detailed explanation of these distinctions and present experiments for both scenarios in Sec. 4.2. Here, we focus on example of label set changes, as illustrated in Fig. 1c. Using the Ogbn-arxi dataset, we apply condensation based on only half of the supervised data (i.e., 20 classes). A 2-layer GCN model, trained on this condensed graph, is then tested on the remaining 20 classes by fine-tuning the final linear layer. We show the performance of various methods over fine-tuning epochs (test epochs), with the gray lines representing the results a naive 2-layer GCN model. Existing methods underperform by 4.2% compared to the ground truth averagely, highlighting the difficulty of cross-task transferability.
Challenge @: Cross-dataset Universal Information Preservation. We further investigate cross- dataset scenarios in the Fig. 1d, where 2-layer GCN model trained on condensed Ogbn rxii data is generalized to four different datasets by replacing the final layer with a new linear layer. To illustrate the differences more clearly, we normalize each result the performance of the naive 2- 2-layer GCN model. In this context, Random refers to a model that was not trained on the condensed dataset but instead fine-tunes only the final layer. While current methods outperform the Random baseline, they still fail to surpass the performance of a simple GCN model, remaining below 1.0 ratio.
To address the above challenges, we propose a Self-supervised and Transferable Graph dataset Condensation framework named ST-GCond. Unlike existing methods focused on condensing a specific dataset for a single task, ST-GCond is designed to encourage the condensed graph to preserve the most general and informative patterns, leading to better transferability across tasks and datasets. Specifically, to achieve better cross-task transferability, the ST -Coon utilizes a task-disentangled meta optimization strategy to adaptively update the condensed graph according to the task relevance.
To achieve better cross-dataset transferability, the ST-CCond adopts a multi-teacher self-superviser optimization strategy: pre-train several sule--upe models teachers and adaptively combine them to extract fundamental information from the original dataset. To align above two strategies for joint condensing, we introduce mutual information guided joint condensation strategy, which
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mitigates potential conflicts between supervised and self-supervised tasks. We empirically evaluate our ST-GCond on node-level and 5 graph-level real-world graph datasets. For the cross-datased and cross-task scenario, ST-GCond outperforms the existing graph condensation methods 2.5% to 18.7%. In the traditional single dataset and task scenario, ST-GCond also gets state-of-art performance on 5 out of 6 datasets, demonstrating its versatility. The contributions
follows:
We propose ST-GCond, a self-supervised and transferable graph dataset condensation framework. To the best of our knowledge, ST-GCond is the first graph condensation method that is designed for cross-datase and cross-task scenarios.
ST-GCond incorporates the dikennssntad and self-supervised optimization to inject the universal knowledge into the condensed graph, enhancing both cross-task and cross-dataset transferability.
Extensive experiments on 10 real-world datasets demonstrate that ST-GCend enjoys the state- of-art performance on both single task and cross-datasse/crossstas scenarios.
2
RELATED WORKS
2.1 DATASET DISTILLATION
Dataset distillation (Wang et al., 2018; Bohdal al., 2020; Cui et al., 2022; Wu al., 2024) is proposed to significantly reduce the scale of the dataset but ensuring the test performance of the distilled dataset. It is suitable for various applications like continual learning, neural architecture search, and for users who have limited computational resources. However, there is still much more gap between the condensed dataset and the original one. For example, the dataset provides more intrinsic knowledge beyond the numan-made labels (Kaplan et al., 2020) and can be transferred to benefit the new dataset's 's tasks (Noroozi et al., 2018; Zamir et al., 2018). Although KRR-ST (Lee et al., 2024) is proposed to distill transferable dataset fitting this goal, the cost is that the distilled dataset cannot be effectively leveraged by traditional continual learning and neural architecture search applications. Therefore, there is a need to comprehensively fill the dataset gap.
2.2 GRAPH DATASET CONDENSATION
Graph data have its unique feature that the samples (nodes) are not independent. Therefore, distilling (condensing) graph is more difficult for jointly considering the node and structure. Recently, several graph dataset condensation methods (Xu et al., 2024; Gao et al., 2024) have been proposed to achieve single dataset and tasks. For instance, GCond (Jin et al., 2022c) first introduce
better performance the gradient matching method in condensing graph, SGDD (Yang et al., 2023) and SFGC (Zheng al., 2023) enhance GCond through diffferent ways: further considering the structure and removing the structure. And the most recent GEOM (Zhang et al., 2024) following SF achieves lossless results (even better than solely training a GCN model on the original graph). DosCond (Jin et al., 2022b) and KiDD (Xu et al., 2023) provide way to condense the graph classification datasets, while KiDD propose to use the Kernel ridge regression efficiently reduce the condensing time. However, existing methods are still designed for specific datasets and tasks. How to achieve transferable condensation remains under-explored and requires further research.
SELF-SUPERVISED AND TRANSFERABLE GRAPH DATASET CONDENSATION
3.1 OVERALL FRAMEWORK OF ST-GCOND
In this paper, we aim to propose a transferable graph dataset condensation method for cross-task and cross dataset scenarios. Given graph dataset G = (X, A, Y), where X E N represents the feature matrix, A E N represents the adjacency matrix, N is the number of nodes, and denotes the node feature dimension. Our goal is to generate a smaller synthetic graph dataset
G. = (X,, A., Y with nodes (m << N), aiming make any model trained on G. achieve similar test performance to a model trained on & on the same task (defined by the label Y) without lost the generalization ability when transferring such model to the new datasets tasks. Unlike traditional condensation methods where the condensed graph is restricted to a specific dataset and task, transferable graph dataset condensation aims to expand the usage scope of the condensed graph.
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Iask-disentangled Metn Optimization
Mutual Information Guided Joint Condensing
Hard condensed lahe!
Pele Lote yy (p) 55¹
meta cls
yh
g
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X
A
Multi-teacher Supe-Supe Optimization
MI
As
Pre-tmined lask model
gs
Pre-imised model
Pre-tmined takk model Pre-trained
Lself
10k 10M nodes
- 100 nodes
Weighting
Soft condensed label
Figure 2: Overall framework of ST-GCond. The original large graph dataset G, consisting of X, A, and ,, is condensed using task-disentangled vetta-opimmiztiin to synthetic hard label Y and @ multi-teacher self-supervised optimization generate soft label Y along with their shared X., As.. @ To avoid conflicts in optimization directions, mutual information-gun guided joint condensation is employed to serve as the mutual information regulations loss term.
To this end, we propose the Supe-supe and Transferable Graph dataset Condensation framework, termed ST-GCond. As illustrated in Fig. 2, our goal is to condense the original graph dataset G into a smaller yet informative graph dataset, G. (A., Xs,
s, Yh. 81 Y:). is worth noting that we include a soft label, Y to handle more complex scenarios.
(1) Tast-disent Meta Optimization. (Challenge 1) We first disentangle the given task (i.e., classes) into parts, with each part containing h classes (h > 1) as sub-task {T. In every epoch, the condensed graph Ge will first be fast updated through the guide each sub-task to be the H. then optimize the Ge through the joint evaluation loss on all sub-tasks. The motivation behind this is to let the condensed graph not only be aware of the difference of the tasks but can quickly adapt to the optimal state of each sub-task. Such process is associated with the hard condensed label Y Rmx1
(2) Multi-teacher Self-Supervised Optimization. (Challenge @) We leverage self-supervised tasks extract the universal knowledge of G. Specifically, we load k pre-trained models, each trained on distinct self-supervised task, denoted as {.f (-,, ()), (.), S (-)}. We further propose a synthetic soft label Y E mmd to unify the labels across these tasks. Consequently, the condensed graph guided by multiple self-supervised tasks, enabling acquire more transferable cross-dataset knowledge.
(3) Mutual Information Guided Joint Condensation. (Resolving the potential conflicts) Through the discussion of previous literature (Jin et al., 2022a; Fan et al., 2024) and our empirical findings in Tab. we observe that directly combining different self-supervised tasks with the supervised task can propose constrain the mutual information I(Y;; Y²)), which adaptively adjusts the weights for each self-supervised task and ensures that the final distribution closely approximates the ideal distribution of Y thereby resolving potential conflicts in the joint condensing process.
lead to unexpected performance drops. Therefore,
3.2 CROSS-TASK TRANSFERABILITY TASK-DISENTANGLED META OPTIMIZATION
Existing methods for graph dataset condensation primarily focus on task performance related the single task and dataset, making the condensed graph only reserve knowledge specific to such single task, which significantly hampers its transferability to other tasks (see Fig. 1c, Table 4, and Table 5).
Since the actual downstream task information is unknown, preparing an optimal condensed graph tailored for a specific task is impossible. Inspired by MAML (Finn et al., 2017; Zhou et al., 2019), modify the optimization strategy to search for "global minimum" across all tasks, enabling the condensed graph to rapidly and effectively adapt to new tasks. Given a distribution over tasks p(Y). randomly sample label sets (w: p(Y) and induce the sub-task graph GT, This process is
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similar class-level sampling in GCond, but our focus the task level makes it more suitable for addressing challenge.
Initialization of the Condensed Graph G.. We initialize (Xa. Y by randomly selecting subset of the original data. Following GCond, we use an MLP 9g as the structure generator, where A, (gal (x.)) - 6), Here, 5 serves the sparsity parameter filter out edges with lower weights. Note that Y is analogous the labels Y NN1 of G, encompassing C' classes.
Fast Adaptation and Meta Optimization Strategy. The key step is simulating the cross-task scenario in the condensing stage with Gs- Following MAML((inn al., 2017), we use the meta optimizing strategy, specifically, given the i-th sub-task G,", we update a copy of G, as follows:
G t g. Vg. fi Gs). The final optimization for Ge is then calculated using the following:
Σ C
claa
The difference is that the meta-loss term is calculated using the fast-adapted condensed graph, simulating the scenario where users update their models on new data and test on the updated versions.
Kernel Ridge Regression-Basse Based Condensing Objective. The term Lets in Eq. (1) serves as the surrogate condensing objective. For instance, gradient matching (Jin et al., 2022c; Yang al., 2023) mimics the real gradients occurring in the original dataset, while trajectory matching (Zheng et al., 2023; Zhang et al., 2024) simulates the learning trajectories. In contrast, we adopt the Kernel Ridge Regression (KRR) method (Xu et al., 2023; Wang et al., 2024) to simplify the condensing process, aligning it with the requirements of task-disentangled meta optimization. Formally, Lets is:
1 9. 2 Koc, (Koee, + +cI) Y 11:
CV
min
where K GXG, xm denotes the kernel function, it a simple algorithm that involving the structure to the kernel calculation. We adopt SNTK (Wang et al., 2024) for calculating the node-level and LigHtGNTK (Xu et al., 2023) for graph-level calculating. Y! denotes the corresponding label sets in the hard condensed labels Yh. Then G. could be adapted to G by Bq. (I), which represents that the condensed graph G. update through task GT., The || indicates the Mean Square Error (MSE) loss function.
3.3 CROSS-DATASE TRANSFERABILITY. MULTTITEACCHER SUPERISUER OPTIMIZATION
Regarding the "cross-datase"" transferability challenge, the natural approach is to extract and distill fundamental knowledge into the condensed graph. Beyond human- made labels (supervised task), we propose leveraging self-supervised tasks to automatically extract latent knowledge. Furthermore, as each task preserves only one aspect of the dataset (Jin et al., 2022a), we propose use multi-teacher self-supervised optimization to better consider the diverse aspects of the dataset.
Unifying Self-Supervised Task Labels. Directly incorporating self-supervised tasks is not trivial, as existing graph condensation methods require explicit labels. For classification tasks with C' classes, synthetic labels Y, E g must be assigned to G., Assigning numerous synthetic labels for multiple self-supervised tasks is impractical. In addition, simultaneously training such tasks from scratch in condensing, in previous graph condensation methods, is complex and time-consuming.
Inspired by the knowledge distillation works (Fan al., 2024), we opt to load the pre- pre-trained models as teachers, and then we can unify all the tasks to the target [E= >ufT (X, Nxd, where ( are the weights of teachers and we discuss it in Sec. 3.4. Thus all the target pseudo labels turn to be same d-dimension tensors. We only need to craft soft condensed label Y E R " in condensing:
min Coets (PT A), Y.).
(3)
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where PT (T(,AA) = (Ei_) (XT(,A)) denotes the adjusted distribution of the pre-trained
teacher models' output. It is also worth noting that loading the pre-trained tasks instead of training model from scratch, as existing methods do, can save considerable optimization time and resource.
Kernel Ridge Regression- -Baedd Optimizing Objective. Here we also use kemnel ridge regression (KRR) (Lee et al., 2024) for optimizing the g. and the soft condensed label Y:. The motivation is that the naive gradient matching and trajectory matching methods are hard to support continuous labels and are heavily coupled with supervised tasks. Formally, the KRR-based self-supervised loss Seel is:
1 |P' (X - Kgs, (Ko.c. + +IY Lisll A min 2
(4)
where K(.) is similar to that in Eq. (1), is the identity matrix improving the robustness, and PJ (X, A) represents the weighted combination of the teacher models' output.
3.4 MUTUAL INFORMATION GUIDED JOINT CONDENSATION
Following the existing KRR-based graph condensation methods (Xu et al., 2023; Wang et al., 2024), the overall condensing objective is the weight sum of Las and Leels as: ming, L = Lave aLself- However, empirically find there may exist potential conflict in calibrating multiple self-supervised and supervised tasks (see Table 6). Such findings drive us to find an optimal guiding solution in adjusting.
As similar issues discussed in the previous knowledge distilling literature (Fan et al., 2024; Wu al., 2022), the key to condensing the beneficial information from teachers is let the probability distribution of teachers approximate the true (Baysian) distribution of the downstream tasks (Menon al., 2021). However, due to the invisibility of downstream labels, we intuitively use the label Y from G to serve as the target ideal distribution. The mutual information to calculate the dependency between the (T((, A) and labels:
())
A));
(5)
where (X, solving Eq. (5) is computationally intensive and may not yield optimal results due to the sampling process involved in Sec. 3.2. address this issue, we propose optimizing the mutual information LMI = L(Y:: Y substitution (Yuan et al., 2024; Fu et al., 2024). We further demonstrate that the mutual information of the condensed graph labels, I(Y;; 5 Y!) is related to the upper bound of I(P" A); Y):
(T(X, A) represents weighted combination of the multi-teacher output. However, directly
Theorem 1. Given that Y and Y are approximations through kernel ridge regression, the mu- tual information of the condensed graph 1(Y;; Yh) is related to the upper bound of the mutual information I [(P (X, A); Y) follows:
I(:: Y!! S IIPPT(IAAAAA (X.A):Y).
(6)
The detailed proof is provided in Appendix C. In our experiments, implement the neural estimation method (Belghazi et al., 2018) for the gradient backward pass. The final objective function is expressed as: ming, L = Lmmta +aLset + BL The overall algorithm is presented in Appendix F.1.
EXPERIMENT
4.1 EXPERIMENTAL SETUPS
Datasets. We evaluate our method on 6 node-level datasets (Cora (Kipf & Welling, 2017). Citeseer (Kipf& & Welling, 2017), Ogbn-arxiv arxiv (Hu et al., 2020a), Reddit (Hamilton et al., 2017) and Flickr (Zeng et al., 2020)) and 5 graph-level datasets (GEOM (Axelrod & Gomez- Bombarelli, 2020), BACE (Wu et al., 2018), ClinTox (Gayvert et al., 2016), and SIDER (Kuhn et al., 2016)). For the supervised node classification task, we follow the settings from GCond (Jin et al., 2022c). For the other types of task, we follow the public split of the dataset. We report the details of the datasets in Appendix A.

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Baselines. We compare ST-GCond with 10 baselines: (1) graph coreset methods (Random, Herding (Welling, 2009), and K-Center (Wolf, 2011)), (2) node-level graph condensation methods (GCond (Jin et al., 2022c), SGDD (Yang et al., 2023), SFGC (Zheng et al., 2023), and GEOM (Zhang et al., 2024)), (3) graph-level graph condensation methods (DosCond (Jin et al., 2022b), ki DD (Xu et al., 2023)), and (4) one self-supervised condensation method, KRR-ST (Lee et al., 2024). For the Random method, we randomly select nodes from the original graph to induce a subgraph. We implement Herding to filter nodes that are close to the centroids and K Center to select nodes that play critical role in minimizing the distance between samples and their nearest centers following (Jin al., 2022c).
Implementation Details. In the condensing stage, for the supervised task, we randomly split the classes of the task into 3 parts, with each part containing h classes (h > 1) as a sub-task. For the auxiliary self-supervised tasks, we select 5 classic tasks for node-level condensation (DGI (Velickovic al., 2019), CLU (You et al., 2020b), PAR (You et al., 2020b), PAIRSIM (Jin et al., 2020), and PAIRDIS (Peng et al., 2020)) and 7 tasks for graph-level condensation ( AttrMask (Hu et al., 2020b), ContextPred (Hu et al., 2020b), EdgePred (Hamilton et al., 2017). GPT-GNN (Hu et al., 2020c), GraphLoG (Xu et al., 2021), GraphCL (You et al., 2020a), and InfoGraph(Sun et al., 2019)). We briefly introduce them in Appendix B. For each dataset, the condensation ratio r is defined by the number of nodes in the condensed graph r m where 0 < < 1. For each dataset, condense graphs with different random seeds and report average performance. We provide our
In the testing stage, we choose the appropriate testing paradigm according the specific scenario. (1) Single dataset and task scenario. When the downstream dataset and task match the condensing one, similar to the previous graph dataset condensation methods, we use (Xs: As, Y Y or {X,, A. Yb to train a model and test it on the original graph dataset G. (2) cross-dataser and task scenario. When the downstream dataset and task differ, we use Ag. Y to train a model and then use the downstream data to train a linear classifier. For other graph condensation methods, we replace the last layer of the trained model with linear classifier in a similar manner. Our code is available at https: // // thub. com hamm/inng RRnggDStackk/ /ST-GCond.
4.2 EXPERIMENTAL RESULTS
To evaluate the performance of ST-GCond, we conduct experiments on three scenarios: single task and dataset scenario; (2) cross-dataset scenario; (3) cross-task scenario.
(1) Performance comparison on single dataset and task. In this scenario, ST-GCond utilizes Y to train a GNN feature extractor and further uses Y! to train a linear classifier. We also report a variant ST-GCond- Y of ST-GCond, which exclusively uses Y!h during the training stage. As shown in Table 1, GCoond achieves state-of-the-art results in 14 out of 15 ratios across datasets, particularly excelling at the lowest ratio. The maximum improvement is 2.71% %. Furthermore, ST-GCond outperforms ST-GCond- Y variant by an average margin of 0.5% to 1.9%.
From the experiment, observe that while our method is specifically designed for cross- coss-dataset and cross-task scenarios, it also demonstrates non-trin trivial improvements in single-dataset and single-task settings. Notably, in three out of five datasets, the results are even lossless compared to whole dataset accuracy according to the definition from GEOM (Zhang et al., 2024). We attribute this improvement to the integration of both supervised and self-supervised information. This approach effectively mimics the property in the original dataset, as highlighted in various studies (Wang et al., 2019; Hou et al., 2022: Liu al., 2023b), which emphasize the importance of self-supervised learning in enhancing performance. Furthermore, the ST-GCond- Y also achieves the comparable performance comparing to the baselines, demonstrating the versatility of using the hard labels Y;, independently with the condensed graph.
(2) Performance comparison on cross-dataset scenario. We compare ST-GCond with baselines under cross-dataset transfer learning settings. For node-level datasets, we use Ogbn-arxi v as the source dataset and test the condensed graph on four other target datasets. For graph-level datasets, we use GECM as the source dataset and test the condensed graph on four other target datasets. We compare ST-GCond with GCond, SGDD, SFGC, and GEOM for node-level condensation, and with DosCond and KiDD for graph-level condensation. MLP (w/o pre) shows the naive results that solely use the linear model in the target datasets, a common strategy for low cow-resource computation. The results are shown in Table 2 and Table 3.
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Table 1: Node classification performance (Accuracy%* std) comparison under the single task and dataset scenario. Best results are in bold and the runner-up is underlined. We use red text to indicate the lossless results (better than solely using GCN on the original graph).
Datasets Ratlo(r)
Random (A....YY)
Herding (A,X., Ya)
K-Center (A. X.)
GCond (A.)..
SGDD (A. Y.)
SEGC (X.
GBOM (X..Y))
37-0Cond-y4 (A.X.5))
SI-GUend (A. (A..Y22.
Whole Datasel
0.905
54,4244
57.1 667211
S24
70.51a
69.5 5a0
70420.
69.8 69.8
71,5
715
Citescer
1.908
64,2-17
64.321
706600
70 202
70.1.0a
80.8
608811
71.6
71.7
3,00%
69.1,6a
62.0.1
00.1
69.8
714...
70.3
09.6100
63.6..7
6..
64.0ga
79.8
107
80.1...
62.5ga.
81.8a0
_3.4gos
Cora
2.00%
72.8-11
7344g1
23
80 Lane
806
81,7
83.622
81.4210
83.3-0
81 81.2
5.20%
76.8
768
76
79.3.0s
50441
8146
K2. K2.8
81 81.8
83.6 K3.6
0.05%
47.
52.4,18
472
59.2211
65.5
65.5 05.5
66. 15.1
66.8
Ogbn-arxiv
0.25%
57,3_11
58.6.1.
63.2,na
65.811
66.1
65.6.33
65.6
66.8
714g01
0.50%
60.0g0s
60/4gu
60.3
64.0gn4
66.
66.8
67.6ea
2u
28.1
41.8-2.
42.5
42.0
465.ps
469aux
466
Leac
46
47.2
Plickr
0.50%
44.0
43.9g0n
43.2zm1
47.1
47.
47.0go.1
21.0g9
47.0
47,5 47.5
47.2
1.00%
44.6_64
44.4.0
44.1
47.1
47.1go
47.1go.1
47.3
47.1
47.5.g..4
0.05%
46.1244
$3.a25
46.622
88.0a18
90.521
89 89.7.a.
91.1
91. 91.4
91.8
Roddit
0.10%
58.0-112
62.721
$3.
91 8119
900
9144
91.5202
91.7-002
93.0
0.20%
66.3
71.0g14
58.5211
20.1
91.6g18
89.9
91.3ga4
91.9204
92.4g00
Table 2: Node classification performance (Accuracy% + std) comparison under the cross-dataset scenario. Best results are in bold and the runner-up is underlined. We use the red text to indicate the lossless results (better than solely using GCN on the target datasets).
Node-level: Dgbbn -ariiarxivvvv- Target datasets
Methods
Cora
Ciseseer
Flickr
Reddit
0.05%
0,25%
0.50%
0.05%
0.25%
0.50%
0.05%
0.25%
0.50%
0.05%
0.25%
0.50%
MLP (wlo poe)
54.8.6s
60.1
28.75
68.5
Random
42.9ans
41.9_1.
43.721a
5805ss
19.1
58.121
26,022
27.3g84
28.1
68.2491
68.3
69.2gs
Herding
48.721a
47.3-1a
50.2250
62.2s5
64.1
66.8.1.
28.0g2.
29.1=25
29.7+25
73.8222
74.742.
75.3220
GCond
65.3414
63.7=2a
69.7=2
67.3-18
61.8a1a
64.6-.4
33.2+1..
29.9-1
29.7
86.2+1
84.9
82.8a21
SGDD
65.
63.6-1.
67.022
701=20
6644na
67.
35.241.3
33.5=27
32.4-2.
85.8
85.241.2
84.1218
SFGC
65.0+2a
63.5-o.
64.3424
62.9-21
60,9
61.0-..
37.340.
37.2an4
35,2+14
85.4299
85.5e0.5
85/4224
GEOM
61,5203
66.0_.1
65.9.21
64.0g26
68.9204
67.7.1.4
36.2,0.s
34.2.17
34.7
84.5
87.1
87.5gn
ST-GCoad
74.
81.5 3.1
8188
69.8.17
71.4.0.7
72.8 6.6
43.610.
47.2gn1
47.8.04
88.7
90.8,0.3
92.1.na
We observe that ST-GCond exceeds all rumner-up methods by an average of 2.5% to 15.5% on node- level classification and 4.1% % to 18.79% on graph classification. These improvements demonstrate the effectiveness of incorporating self-supervised tasks to extract "universal knowledge," enabling the condensed graph to benefit various downstream datasets. While corset methods perform similarly to MLP results, existing graph condensation methods show improvements over MLP, indicating the versatility of the condensed graph. Additionally, ST-GCond achieves better results target datasets than using the GCN model alone. Thus, downstream users can achieve similar test performance to expensive GCN models with significantly lower computational costs by training models on the condensed graph and using a simple linear classifier.
(3) Performance comparison on cross-task scenario. In the cross-task scenario, our definition of "task" encompasses two distinct meanings. First, it refers to different task types, such as node classification, node clustering, and link prediction, which we term the "lype-changing cross-task setting." Second, it refers to the variation in class labels within the same type of supervised task, which we define as the "label-set set changing cross-task setting." Such two settings are widely We conduct experiments in both of these settings to validate our approach.
In the task type changing cross-task setting, we use node classification for condensation and link prediction or node clustering as downstream tasks. The results are shown in Table 4 and Table 5. We use VGAE (Kipf & Welling, 2016) and ARGA (Pan et al., 2018) as baselines. As shown in Table 4, while existing methods produce comparable results, they are sub-optimal compared to the baselines. In contrast, ST GT-GCond achieves better AUC and AP metrics on Cora, and the AP metric on Citeseer, indicating that our condensed graph retains beneficial knowledge for cross task scenarios. Table shows more pronounced improvements among existing methods, which can be attributed to the inherent relationship between clustering and labels (Jin et al., 2020).
In the label-set changing cross-tast task setting, the dataset's label set is divided into two parts: one for condensation and the other for downstream tasks. Figure shows the performance over test.
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Published as a conference paper at ICLR 2025
Table Graph classification performance (ROC-AUC(%)) + std) comparison under the cross-dataset scenario. Best results are in bold and the runner-up is underlined. We use the red text to indicate the lossless results (better than solely using GCN on the original graph)
Graph-level: GEOM
Target
BACE
BBBP
ClinTox
SIDER
0.001%
0.005%
0.01%
0.001
0.005%6
0.01%
0.001%
0.005%
0.013
0.0018
0.005%
0.01%
MLP pre)
48.7.6.
49.3
43.7gna
47.1
43.6
45.8_oo
46.2.07
38.5
33.1
...
42.8
43.5
45.8
43.7
48.5
44.2
Herding
47.0
49.0-6.7
50.0204
40.0g04
38.0
29.
45.0go.
46.5g0s
47.0a0.5
46.0210
47.5g1.5
48.0g13
DooCCond
54.610.
55.7_6.1
51.7203
47.0.0
48.510s
49.0.68
50.510.9
$1.0.10
52.010.7
50.5g1
52.0,155
530.11
KIDD
53.8
53.5
54.417
52.8.09
$4.0.0
$5.0go.s
$6.0.a
52.0a0a
51.5408
51.1210
51.0gv
ST-GCoad
68.621
714
73.6
S8.
61.400
62.8
64.129.7
64.820
71.3204
55.6203
56.8.o.
55.7
Table 4: Link prediction results under the cross-task scenarios, where each graph condensation method observes only the classification task information.
Table 5: Node clustering results under the cross-task scenarios. We use the bold denotes the best results, the underline indicates the runner-ups. 'V. indicate the increase/decrease compared baseline VGAE/ARGA.
Cora
Citeseer
Citeseer
Method
AUC(%)
AP(%)
AUC(%)
AP(%)
Method
NMI(%)
F1(5)
ARI(%)
NMI(%)
FI(8)
ARI(%)
VGAF
91.4
92.6
90.8
92.0
VGAF
51.4
57.5
38.7
34.8
55.6
28.5
ARGA
92.4
93.2
91.9
92.1
ARGA
50.8
65.6
34.7
40.0
54.6
GCond
81.6]
83.7
73.51
74.8)
GCond
48.61
54.41
36.8.
31.61
52.8
27.41
SGDD
85.4]
88.3
74.3]
76.91
SGDD
$1.87
69.41
38.7
35.11
58.8
26.5
SFGC
83.31
85.11
73.61
73.91
SEGC
50.7]
68.21
36.9
34.81
58.11
25.61
GEOM
84.7.
85.0)
73.2
74.81
GEOM
48.2.
55.7]
32.9.
33.1
49.3.
21.31
ST-GCond
93.31
94.87
90.61
92.31
ST-GCond
53.8
71.4
40.7
40.8
62.71
41.71
epochs. Since the model trained on the condensed graph cannot be directly applied to the downstream task, the final layer is replaced with linear layer and fine-tuned with the target training data. Our task-disentangled meta-optimization strategy allows the condensed graph to acquire cross- task knowledge, evidenced by ST-GCond achieving faster and superior results compared other methods, particularly the naive GCN (gray line), demonstrating the versatility of our approach.
4.3 ABLATION STUDY AND SENSITIVITY ANALYSIS
Ablation study. To investigate the impact of task-disentangled meta optimization, multi-teacher self-supervised optimization, and MI- MI-guided joint condensation, we duct an ablation study presented in Ta- ble 6. We select cross-dataset experiments to evaluate the transferability of these com- ponents. We take Ogbn-arxin arxiv as the source dataset and evaluate on Cora and Reddit. The ablations include: w/o self (excluding self-supervised tasks), w/o meta (excluding task disentanglementt, and w/o MI (excluding mutual information con- straints). denotes the condensation ratio for Oognn-rxiiii
Table 6: Mean accuracy(%) and standard deviation of node classification.
Ogbn-arxiv + Cora
Ogbn-arxiv + Roddit (Ratio r)
Methods
(Ratio r)
0.25%
0.50%
0.25%
0.50%
Random
58.1 19.1
68.3
69.0.n.
Herding
47.3
50.243.
74.7424
75.3
SGDD
63.6120
67.0
85.2
84.1
GEOM
66.0
65.9
87.1
87.5
ST-GCond w/o self
78.4
77.4
88.6go
89.0
ST-GCond w/o meta
76. 76.4
73.4
88,9+0.s
89.7+0.1
ST-GCond w/o MI
68.5
74.4
87.4
87.4
ST-GCond
81.5+11
81.8+1.
90.8
92.1
As observed, ST-GCond w/o self and ST-GCond w/o meta demonstrate strong performance relative to the baselines, likely due the shortcomings of naive methods, which tend overemphasize task-specific information. However, both variants still fall short when compared to the results obtained using the full dataset (e.g., accuracies of 81.2% Cora and 93.9% Reddit), emphasizing the necessity of combining these components for optimal performance. Nevertheless, the naive combination of such parts (ST-GCond w/o M/) underperforms both individual variants. Sim-

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Published as a conference paper at ICLR 2025
Cross-task Performance on Reddit
Cross-task Performance Flickr
Performance (ACC/%)
100
Perfoormance (ACC%)
-00
80-
70
OCN
5000
30
GCN
SGEO
CEOM
OKlvad 5T-0Coed
GROM
CCual
SeGe
60
Test Epochs
Test Epochs
Figure 3: Displaying performance v.s. test epochs under the cross-task scenarios. Except for the GCN curve (the gray line), all other methods only observe the other half of the supervised information.
0.40
0:41
N6689900 Value
0.35
90
0.25
M5
R5
0.15
0.20
15
0.20
Accuracy
Accuracy
80
au05
0.10
0.10
0.05
15
75
3.00
25 50 75
100 125 150 Epochs
0.00
6
23 50 15
100 Epochs
125
130
0.1
0.3
0.5
0.7
0.9
0.0
PORDSS
PUTDOS
Oea
Chutor
Rodi
Cau
Choss
3658
(a) Cora Weights
(b) Citeseer Weights
(c) Sensitivity of k
(d) Sensitivity of a
Figure 4: Ablation Study and Sensitivity Analysis. Fig. (a) and Fig. (b) illustrate the convergence of adaptive task weights by the end of training, Fig. (c) shows an increasing performance trend with respect to the number of teachers (k), while Fig. (d) does not show a significant trend.
ilar observations have been discussed in prior works Jin et al. (2022a); Fan al. (2024), further highlighting the critical role of LMS in resolving such conflicts and improving overall functionality.
Evolution process of teachers' weights ( As discussed in Sec. 3.4, the combination of the teachers' outputs should approximate the true (Bayesian) distribution of the downstream tasks. the downstream tasks, we use Y as a surrogate target. Fig. 4a and 4b illustrate the evolution of weight values during the condensing process. It is observed that the same method may have different weights across various datasets, and the weights of the five tasks eventually stabilize and converge steady values. According Table incorporating the weights of self-supervised tasks results in improvements ranging from 3.4% to 13%, highlighting the necessity of addressing conflicts among tasks.
However, since we cannot access the true distribution
Sensitivity analysis of hyperparameters k, a, and 3. We present a sensitivity analysis for two hyperparameters: the number of self-supervised tasks (k) and the loss weight (a. 8). Fig. 4c and 4d show that a larger k generally results in better performance, indicating the effectiveness of the mutual information constraint strategy. For the hyperparameter a and (Appendix. G.1), the performance varies with different a and 39 values, suggesting that they should be selected through grid search.
CONCLUSION
We propose ST-GCond, a novel framework for self-supervised and transferable graph dataset condensation. Unlike existing works focus on condensation for a single task and dataset, our approach creates condensed dataset with higher data-level transferability, enhancing downstream models ability when it applied to various new datasets and tasks. We introduce aask-disettnngled meta-updating for cross-task knowledge preservation and incorporate multiple supervised tasks to extract "universal knowledge". Finally, to avoid the potential conflict of jointly using self-supervieed and supervised information as the optimization directions, we leverage the mutual information loss term to guide the condensation process. Experiments demonstrate ST-CCona' 's effectiveness in both single-task/snnge maskk/siglledatase and cross- tassssttss//rosssdeae While the condense ratio is adjustable. dynamic user demands require re-condensation each time, bringing potential computation costs.
scenarios. Limitations and Future Work:
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Published as a conference paper at ICLR 2025
ACKNOWLEDGMENT
The corresponding author is Qingyun Sun. The authors of this paper are supported by the National Natural Science Foundation of China through grants No.62225202 and No.62302023, and the Fundamental Research Funds for the Central Universities.
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Fan Zhou, Chengtai Cao, Kumpeng Zhang, Goce Trajcevski, Ting Zhong, and Ji Geng. Meta-GNNG On few-shot node classification in graph meta-learning. CIKM 2019, pp. 2357-2360. ACM, 2019. doi: 10. T..11433357788.333555 106.
Jiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann, Leman Akoglu, and Danai Koutra. Beyond homophily in graph neural networks: Current limitations and effective designs. In NeurlPS, 2020.
Fuzhen Zhuang, Zhiyuan Qi, Keyu Duan, Dongbo Xi, Yongchun Zhu, Hengshu Zhu, Hui Xiong, and Qing He. A comprehensive survey on transfer learning. Proceedings of the IEEE, 109(1):43-76 2020.
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Appendix
A DATASET DETAILS
We use 5 node-level graph datasets (Cora, Citeseer (Kipf & Welling, 2017), Ogbn-arixy (Hu et al., 2020a), F Flia ckr (Zeng et al., 2020), and Reddit (Hamilton et al., 2017)) and 5 graph-level graph datasets (GEOM (Axelrod & Gomez-Bombarde et al., 2012), ClinTox (Gayvert et al., 2016), and SIDER (Kuhn et al., 2016)). We further provide the statics datasets in Table Al.
2020), BACE (Wu et al., 2018), BBEP (Martins
Table A1: Statistics of datasets.
Level
Dataset
# Classes Tasks
#Nodes / # Graphs
# Edges
# Features
Cora
7
2,708
5,429
1,433
Citeseer
3,327
4,732
3,703
Node-level
Ogbn-Arxiv
40
169,343
1,166.243
Flickr
89,250
899,756
Reddit
210
232,965
57,307,946
602
BACE
1,513
BBBP
2,039
Graph-level
ClinTox
1,478
Sider
27
1,427
B SELF-SUPERVISED TEACHER TASKS
In the paper, utilize different self-supervised task guided models as the way extract the "universal knowledge" from the original dataset G. Here, we present each model we used.
For node-level classification tasks, follow AutoSSL (Jin al., 2022a) and adopt five classic tasks:
DGI (Velickovic et al., 2019): Maximizes the different views' representations (graph v.s. nodes).
CLU (You et al., 2020b): Predicts pseudo-labels from K-means clustering on node features.
PAR (You al., 2020b): Predicts pseudo-labels from Metis graph partition (Karypis & Kumar,
1998).
PATRSIM (Jin al., 2020): Predicts pairwise feature similarity between nodes.
PAIRDIS (Peng al., 2020): Predicts the shortest path length between nodes.
In the graph-level classification tasks, follow WAS (Fan al., 2024) to adopt 7 classic tasks:
AttrMask (Hu et al., 2020b): Learns the regularities of node/edge attributes.
ContextPred (Hu et al., 2020b): Explores graph structures by predicting contexts.
EdgePred (Hamilton al., 2017): Predicts the connectivity of node pairs.
GPT-GNN (Hu et al., 2020c): Introduces an attributed graph generation task to pre-train GNNs.
GraphLoG (Xu et al., 2021): Introduces a hierarchical prototype to capture the global semantic clusters.
GraphCL (You et al., 2020a): Constructs specific contrastive views of graph data.
InfoGraph (Sun et al., 2019): Maximizes the mutual information between the representations of the graph and substructures.
C PROOF OF THBOREM 1
Proof. We aim to prove that:
T(Y:: Y!) & T(PT (X, A): Y).
(A.1)
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Since Y; and Y are obtained from Pd (X, A) and Y through kernel ridge regression- which is deterministic mapping, they can be expressed as:
Y: = (PT (X, Y -(Y),
(A.2)
(A.3)
where / and ! are the regression functions.
According to the data processing inequality (Beaudry & Renner, 2012), applying deterministic functions random variables does not increase mutual information. Therefore, have:
(Y::: Y!) (PT ().
(A.4)
D TIME COMPLEXITY ANALYSIS
ST-GCond primarily consists two parts: sampling sub-tasks for meta updating and involving self-supervised tasks to guide condensing. For the former, bi-level optimization. Following GCond (Jin et al., 2022c), we start with an L-layer GCN, where the large-scale graph has N nodes, the small yet informative condensed graph has nodes, and the hidden dimension is d. The computation cost for single task involves a forward pass through the GNN, which is O(Lm²d + Lmd), and through Jo, which is dmm² The inner optimization of kernel ridge regression
treat them composition of
be expressed O(Nmr² + Nm) (Wang al., 2024). Therefore, the single task complexity is O(Lm²d + Lmd + m²d + Nmr? - Nm). Denoting the split tasks as the complexity for the former part can be shown (O + Lmnd + 22 Nmy + Nm).
For the latter, the calculation process is similar to the former, although we introduce multiple self- supervised models during the condensing stage. Thanks the benefits of the offline strategy, only need the extra computation complexity of kO(LEd + LNdd), where k denotes the number of self-supervised tasks. Therefore, the overall complexity can be expressed (t + 1)0 (Lm²d Lmd + md + Nmr + Nm) + kO(LEd + LNd Note that and & are not set to be too large.
To intuitively demonstrate the efficiency comparison, we present the running time (in seconds) the proposed ST-GCond and GCond over 50 epochs on single A100 GPU. Thanks to the efficiency of kernel ridge regression, we avoid the time-consuming triple-level optimization. As result, our method is empirically 1.14 to 2.17 times faster than the previous GCond method.
Table A2: Comparison of running time of GCond and ST ST-GCond(in seconds).
Ogbn-arxiv
r=0.55
r=0.25 %
r=0.5 %
GCond (Jin et al., 2022c)
217.18 178.27
386.71 278.44
765.12 12
ST-GCond
399.15
E COMPUTATION RESOURCE
We conduct all experiments with:
Operating System: Ubuntu 20.04 LTS.
CPU: Intel(R) Xeon(R) Platinum 8358 CPU@2.60GHA with 1TB DDR4 of Memory.
GPU: NVIDIA Tesla 100 SMX4 with 80GB of Memory.
Software: CUDA 10.1, Python 3.8.12 PyTorch (Paszke et al., 2019) 1.7.0.
F ALGORITHMS
F.I ALGORITHM I
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Table A3: Fixed key parameters.
Parameters
Value
Table A4: Search space of the key parameters.
GNN backbone
GCN, GIN
Number of layers
2
Parameters
Search Space
Hidden Units
256
Ir
0.1, 0.01, 0.001 (0.0, 1.0) (0.0, 1.0)
Activation
LeakyReLU
Dropout Rate
0.5
a
g
&
5
Split meta tasks 6
0.5
Algorithm 1 ST-GCond: Self-supervised and Transferable Graph Dataset Condensation
Graph dataset G (X, A, Y). pre- pre-trained teachers {ST .o)....,(((())) steps T, condensation ratio r, and graph sparsity parameter
Input:
2: Output: Condensed graph dataset G. = (X,, A., Y Y:).
3: Initialize weights {A, k-m. X, by selecting r% features/class, Y with labels.
4: Initialize A, go (X.). Y: Φ A.fT (X., A.).
for 0.......
6: Initialize ~ Pg.
7: while not converge do
8: D' =.
Sample tasks T. p(Tr). for Ti do
10:
11:
Sample G ~ G, 95 ~ Gs.
12:
// Meta--raininn
13:
Adapt parameters with Ciels on G.:: 6, + X (GNN I/ Meta--ppatie
14:
15:
Combine representation: Y ΣK A
Compute Leta, Leets, and Les on Ti:
D'+DD D' + Vor C Cii (GNN gJ a CT (Y + +v (V: Y.).
17:
end for
18:
Update { A X., YA, p. and 6.
19:
end while
20:
end for
21: Generate the condensed graph: A. ReLU(g((X.) -). G. (X.,A,, Y.,
G MORE EXPERIMENTS
G.1 PARAMETER SENSITIVITY
We further investigate the sensitivity of the weight of LMI, which controls the influence of the mutual information loss. From Figure A1, we observe that as 3 increases, the accuracy of each dataset initially rises, then fluctuates. We perform a grid search to identify the optimal setting for B. Empirically, we select 0.5, O.6, 0.7 based on the specific dataset.
G.2 VISUALIZATION OF CONDENSED GRAPH
We visualize the condensed graph in the Figure A2 and report statistics in the TableA5. From the figure, we see that the learned graph is denser compared to the original, likely due to information concentration. If the condensed graph maintained the same sparsity, it might lack sufficient edges to enable effective message passing. Additionally, for the Citeseer and Cora datasets, homophily reduced compared to the original graphs, with nodes within each class less tightly clustered. We believe it pose more challenge to learned graph neural networks, which may have better generalization ability.
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90
Accuracy (%)
80
75
0.1
0.3
0.5
0.7
0.9
Figure Al: Sensitive of 3.
Cora, r 2.5%
(b) Citeseer, 1.8%
(c) Ogbn-arxiv, r = 0.05%
(d) Flickk. 0.1%
(c) Reddit, r 0.1%
Figure A2: Visualizations of the condensed graph by ST- GCond. The edge weights are represented by varying line thickness, and node classes are denoted by different colors.
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Table A5: Statistics of the condensed graph, compared with the whole graph to highlight the differences. Note that homophily is calculated using the algorithm introduced by (Zhu al., 2020).
Citeseer,
Coza,
Ogbn-EExwiv, r=0.25%
Whole
3T-GCond
Whole
ST-GCond
Whole
ST-GCond
Whole
37-GCord
Whole
3T-GCond
Accuracy
70.7
71.5
81.5
83.4
71.4
66.8
14..1
47.5
93.9
91.7
#Nodes
169,343
44,625
153
#Edges
4,732
1.434
5,429
2,131
1,166.243
8.681
218.140
331
10,753,238
3427
Sparsity
0.09%
77.3%
0.15%
84.10%
0.01%
8.42%
0.02%
34,20%
0.09%
29.18%
Homophily
Storage
47.1MB
L.MB
14.9MB
0.8MB
100.AMB
1.3MB
86.5MB
0.3MB
43B
0.7MB
19


Reviews:
[{"review_id": "cGEhhECMY8", "reviewer": "Reviewer_AjtW", "summary": "This manuscript studies graph dataset condensation from a different perspective. It proposes a method for condensing the graph dataset in a cross-dataset and cross-task manner. The proposed ST-GCond condenses the dataset while preserving the most universal/general information, which is task-agnostic.  Specifically, there are two components of the method. The first is task-disentangled meta optimization which makes the condensed dataset aware of the task difference. The second is multi-teacher self-supervised optimization which makes the dataset hold some uniserval information. Experiments and ablation studies are well-done with nontrivial performance gain.", "questions": "Please refer to the weaknesses part.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- It is great to see that the proposed method improves under the setup even in the single dataset and task. The performance gain under the setup of cross-dataset and cross-task is indeed nontrival. \n\n- The proposed method is applicable for both node-level and graph-level tasks, making it more general. \n\n- The proposed method makes it work with the combination of multi-task learning and self-supervised learning on the dataset condensation, which might inspire more researchers on this research topic.", "weaknesses": "- For the \"Mutual Information Guided Joint Condensation\", it is unclear why the performance is dropped when we use both the hard label from the supervised condensation and the soft label from the self-supervised condensation. The author argues that this is due to the conflict \n\n- The cross-task and cross-dataset dataset condensation settings are indeed interesting and are more applicable in real scenarios. However, such settings are a little bit overlap with that of the graph model pertaining. The pertaining of the model can also achieve faster adaption to the new task or dataset. Can the authors provide a more detailed discussion of the differences? \n\n- From the ablation studies, it is shown that the proposed method can even achieve the best performance with either only the \"self\" part or the \"meta\" part. Why do the authors say that \"ST-GCond w/o self and ST-GCond w/o meta perform poorly on both datasets\"?\n\n- It is a little bit unfair for the comparison as the proposed method utilizes much more information during the dataset condensation. For example the multi-label information (for the meta-training part) and self-supervised models (for the self-training part). \n\n- What if we do not have the multi-task information for the dataset we would like to condense?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sTJ1Q63QQf", "reviewer": "Reviewer_8R18", "summary": "This paper presents a novel graph dataset condensation method termed ST-GCond that enhances transferability across tasks and datasets using a multi-teacher self-supervised optimization strategy. ST-GCond effectively condenses large graph datasets, which can maintain high performance in varied applications by leveraging multiple pre-trained models and self-supervised learning. Experiments demonstrate ST-GCond's effectiveness in both single-task/single-dataset and cross-task/cross-dataset scenarios.", "questions": "Can you provide a detailed analysis of the computational costs and compare them with conventional methods?\n\nWhat strategies are used for tuning hyperparameters like the number of sub-tasks and learning rates? Could you include guidelines for hyperparameter selection?\n\nHow does the quality of pre-trained models affect the performance of ST-GCond?\n\nCan you explain how the weights assigned to each teacher model's output are optimized during training?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "ST-GCond performs well across different tasks and datasets and overcomes the limitations in traditional graph condensation methods.\n\nBy using multiple pre-trained models as teachers, the proposed method captures a wide range of features and knowledge, and thereby improving its ability to generalize.", "weaknesses": "The proposed ST-GCond method introduces substantial computational overhead due to task-disentangled meta optimization and multi-teacher self-supervised optimization. Given the iterative updates for each sub-task and multiple self-supervised models, the overall training time could be significantly increased. It would be beneficial if the authors could provide detailed analysis of computational cost .\n\nThe proposed method would benefit from a thorough exploration of hyperparameter tuning, such as the number of sub-tasks and learning rates.  Including a sensitivity analysis or providing guidelines on hyperparameter selection based on different types of graph datasets could be beneficial.\n\nSignificant disparities between tasks may limit the condensed graph's ability to capture all relevant information, and thereby reducing the effectiveness.\n\nThe power of the multi-teacher strategy relies on the quality of pre-trained models. Will low-quality or irrelevant models impair the performance?\n\nThe effectiveness of the multi-teacher self-supervised optimization strongly hinges on the optimal configuration of the weights  assigned to each teacher model's output. However, this paper does not provide a clear illustration for how these weights are optimized during the training process.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4rhgURbmMp", "reviewer": "Reviewer_z8vT", "summary": "This work addresses the challenge of the transferability of condensing graph datasets in graph condensation, which is an important topic. The authors propose ST-GCond, a self-supervised and transferable graph dataset condensation method with a carefully designed loss function.", "questions": "1. I suggest the authors to provide some visualization of condensed graphs, together with some discussion on some statistical characteristics of them to make the results more credible.  \n2. In the Appendix D, the authors only provide and compare the running time of the proposed method together with one baseline method. Since this is an efficiency-oriented field, more comparison is needed. For example, the VRAM (GPU memory usage) during training. The proposed method introduced too many models (e.g., multiple teacher models), I'm wondering whether this will make the GPU memory usage of the proposed method even higher.\n3. In cross-dataset and cross-task scenario, a finetune step on the original downstream data is needed, what if we do not undergo this step? It's weird to use the actual training data plus the condensed data to train, which leads to a downgrade of the contribution to the work .\n4. What is the actual value of \\alpha and \\beta and other hyperparameters in the final loss function/in the main result tables? I notice the authors provide the search space of them, but did not provide the actual value / their changing trajectory during training.\n5. The authors provide an ablation study on each loss terms. What's the reason for causing such results?\n6. In Line 222, the author claim that \"The most important step is to utilize fast adaptation in Gs.\" What makes it the most important step?\n7. In the Appendix G.1, Line 799, the final matrix is minus by a \\delta term, which comes out of no where. The authors give no explanations.\n\nSome typos:\n1. Line 396: A dot is missed at the end of the caption.\n2. Line 214:  ”global minimum”  ->  \"global minimum\"", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The transferability of condensed graphs is an important topic. The authors make the first effort to deal with it.\n2. Some results are promising.\n3. The motivation is clear and the writing in the introduction is good.", "weaknesses": "Please see the Questions below. \n\nI'm willing to increase my rating as long as the authors can adequately address my concerns.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)