DREAM: Dual Structured Exploration with Mixup for Open-set Graph Domain Adaption
Authors: Nan Yin
Mengzhu Wang
Zhenghan Chen
Li Shen
Huan Xiong
Bin Gu
Xiao Luo
Venue: ICLR 2024 poster (2024)
Keywords: Open-set Recognization
Graph Classification
Domain Adaptation
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Recently, numerous graph neural network methods have been developed to tackle domain shifts in graph data. However, these methods presuppose that unlabeled target graphs belong to categories previously seen in the source domain. This assumption could not hold true for in-the-wild target graphs. In this paper, we delve deeper to explore a more realistic problem open-set graph domain adaptation. Our objective is to not only identify target graphs from new categories but also accurately classify remaining target graphs into their respective categories under domain shift and label scarcity. To solve this challenging problem, we introduce a new method named Dual Structured Exploration with Mixup (DREAM). DREAM incorporates a graph-level representation learning branch as well as a subgraph-enhanced branch, which jointly explores graph topological structures from both global and local viewpoints. To maximize the use of unlabeled target graphs, we train these two branches simultaneously using posterior regularization to enhance their inter-module consistency. To accommodate the open-set setting, we amalgamate dissimilar samples to generate virtual unknown samples belonging to novel classes. Moreover, to alleviate domain shift, we establish a k nearest neighbor-based graph-of-graphs and blend multiple neighbors of each sample to produce cross-domain virtual samples for inter-domain consistency learning. Extensive experiments validate the effectiveness of the proposed DREAM in comparison to various state-of-the-art approaches in different settings.

Published as a conference paper at ICLR 2024
DREAM: DUAL STRUCTURED EXPLORATION WITH MIXUP FOR OPEN-SET GRAPH DOMAIN ADAPTION
Nan Yin', Mengzhu Wang2; Li Shen', Zhenghan Chen', Huan Xiong', Bin Gu', Xiao Luo I Mohamed bin Zayed University of Artificial Intelligence Hebei University of Technology
3 JD Explore Academy 4 Peking University $ University of California, Los Angeles Syinnan8911 dreamk mathshenli pandaarych (emaycchhh@mmmm11m @gmail com {huan. xiong, bin. gu @mbzuai ac. ae, xiaoluoêcs ucl volla... edu
ABSTRACT
Recently, numerous graph neural network methods have been developed to tackle domain shifts in graph data. However, these methods presuppose that unlabeled target graphs belong to categories previously seen in the source domain. This as- sumption could not hold true for in-the- wild target graphs. In this paper, we delve deeper to explore a more realistic problem open-set graph domain adaptation. Our objective is to not only identify target graphs from new categories but also accurately classify remaining target graphs into their respective categories under domain shift and label scarcity. To solve this challenging problem, we introduce a new method named Dual Structured Exploration with Mixup (DREAM), DREAM incorporates a graph-level representation learning branch as well as a subgraph- enhanced branch, which jointly explores graph topological structures from both global and local viewpoints. To maximize the use of unlabeled target graphs, we train these two branches simultaneously using posterior regularization enhance their inter-module consistency. To accommodate the open-set setting, we amalga- mate dissimilar samples to generate virtual unknown samples belonging novel classes. Moreover, to alleviate domain shift, we establish a k nearest neighbor- based graph-of-graphs and blend multiple neighbors of each sample to produce cross-domain virtual samples for inter-domain consistency learning. Extensive experiments validate the effectiveness of the proposed DREAM in comparison various state-of-ther approaches in different settings.
INTRODUCTION
The ubiquity of graph-structured data on the Internet has captivated the interest of the graph machine learning community (Yoo et al., 2022; Yang et al., 2022; Zhang et al., 2021: Feng et al., 2022a). Cutting-edge graph neural network (GNN) approaches (Cui et al., 2022: Liu et al., 2022: Feng et 2022b) have recently demonstrated exceptional capabilities in graph representation learning. Typically, these methods employ the message- pasauigggp mechanism to generate effective node-level representations. Then, range of graph pooling procedures (Yin et al., 2023b; Ying et al., 2018; Lee et al., 2019; Bianchi et al., 2020; Wang et al., 2020) has been devised, offering graph-level rep- resentations embedded with topological semantics for numerous downstream tasks including graph property prediction (Lu et al., 2019; Wieder et al., 2020; Chen et al., 2021; Li et al., 2022b).
Despite their promising performance, the majority of these approaches rely on supervised learning. requiring a substantial volume of labeled data. To mitigate the burden of data annotation, a variety of graph domain adaptation approaches have been devised (Yin et al., 2022; Ychudai et al., 2021). These methods enhance the model by integrating labeled graphs from a distinct yet related source domain. However, these methods presuppose that source and target graphs share the same label space, which often does not hold true in practical scenarios (Scheirer et al., 2012: 2014; Rizve et al., 2022). Consequently, trustworthy GNN systems should be endowed with the ability to infer what they have never encountered before. In academic literature, dittr--ddstribution (OOD) detection
"Equal contribution.
1 "oorrsponniig author.

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has been extensively studied in various safety-critical applications (Amodei et al., 2016) including medical diagnosis (Kukar, 2003), autonomous driving (Dai & Van Gool, 2018), and among others. Although several intriguing strategies have been proposed for OOD detection in visual and text do- mains (Bitterwolf et al., 2022; Panareda Busto & Gall, 2017; Tan et al., 2019), this problem remains underexplored in graph-structured data. Towards this end, this paper investigates the problem of open-set graph domain adaptation, which involves identifying OOD target graphs from unknown classes and classifying the remaining graphs into their corresponding classes.
In fact, the problem is quite different owing to the reasons as follows: (1) Semantic Drift. Traditional graph domain adaptation techniques (Yin et al., 2022: Yehudai al., 2021; Wu et al., 2020a) often utilize pseudo-labeling to extract knowledge from unlabeled target graphs. However, substantial domain shift and label shift can generate biased pseudo-labels for target graphs, leading to an aceu- mulation of errors during subsequent optimization. (2) Inadequate Supervision. Extensively labeled in-distributions (ID) samples are accessible in the majority of out-of-detection methods (Hein al., problem could encounter both data scarcity and label scarcity on the target domain as graph data is more difficult to acquire, which would increase the difficulty of identifying target samples from novel classes. As consequence, powerful frame- work that can extract sufficient topological information from unlabeled graph samples to provide additional high-quality supervision is highly desired.
2019; Hendrycks et al., 2018). However,
In this paper, we propose a novel framework named Dual Structured Exploration with Mixup (DREAM) for open-set graph domain adaption. The key idea of our DREAM is to intensively mine graph topological structures using complementary branches (i.e., the graph-level representation rtnentttinn branch and subgraph-enhance branch), which are then incorporated into a trustworthy and domain- invariant framework. On the one hand, our graph-level representation branch employs a message- passing mechanism to encode topological knowledge into node representations, subsequently em- ploying an attention mechanism for their aggregation from diverse perspectives. On the other hand, our subgraph-enhanced branch composites each graph into several subgraphs using graph cluster- ing. Then, hierarchical GNNs are utilized to extract localized functional components and their corresponding interactions. We amalgamate the strengths of both branches by employing posterior regularization, which enhances the coherence between the predictions from the two branches and thus mitigates biased and overconfident pseudo-labels. Furthermore, to accommodate the open-set scenario, we blend dissimilar source samples in the latent space, generating virtual OOD samples for additional supervision. To further mitigate domain shift, we construct a k-nearest neighbor- based graph-of-graph, where nodes represent graph samples. Multiple neighbors of each graph sample are then combined to generate a cross-domain virtual sample. We strongly encourage inter-domain consistency in the predictions between each sample and its corresponding cross-domain counterpart. Our proposed DREAM has demonstrated remarkable effectiveness when compared to state-of art approaches in various challenging scenarios. Moreover, we conduct extensive ablation studies and visualization to validate the superiority of our DREAM.
In summary, our paper makes the following contributions: (1) Problem Formulation: We introduce novel problem of open-set graph domain adaptation, which accommodates unlabeled in-the-wild target graphs from unseen classes. (2) Methodology: We introduce an approach called DREAM that employs two branches to investigate structural semantics and integrates them into trustworthy and framework. (3) Experiments. Comprehensive experiments verify the effectiveness of our proposed DREAM by comparing sfate-of-the-art approaches.
2 RELATED WORK
Graph Neural Networks (GNNs). GNNs (Kipf & Welling, 2017; Bodnar et al., 2021; Qu et al., 2019; He al., 2022; Baek et al., 2021) have proven to be remarkably effective in handling graph- based machine learning tasks including node classification (Cui et al., 2022; Liu et al., 2022; Feng et al., 2022b), link prediction (Nguyen et al., 2022: Zhao et al., 2022; Zhang et al., 2019), and graph classification (Fan et al., 2019; Song et al., 2016; Liao et al., 2021: Wu et al., 2020c). Recently, graph neural networks have also been studied in different OOD settings. Semi-superrised open- world graph classification involves partial unlabeled graphs belonging to unknown classes (Luo et al., 2023). Graph OOD detection aims to detect OOD graph samples without using ground-truth labels (Liu al., 2023). Node-level open-world graph learning aims find OOD nodes on single
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Input Graphs
Interaction Between Branches
Esstep
Graph-level Representation
Subgraph-view
Lx
Leamingg Pe
Representation Learning
M-step
Souree Graphs
Virtual Samples Generation
Source Embedding
A A JAADA
A AAAAA A
Source Embedding
DA
Netrest Neighhours
Nearest Neighhours
Target Embedding
O O
Target Emmiedding
Ls
Target Craphs
Multi-sample Mixup for Domain Alignment
Figure 1: An overview of the proposed DREAM. We feed both source and target graphs into both the graph-level representation branch and subgraph-view representation learning branch. We utilize unified EM-based framework for interaction between two branches. Dissimilar source samples are mixed simulate samples from novel classes. Moreover, we utilize multi-sample mixup to generate cross-domain virtual samples for domain alignment.
graph (Wu et al., 2020b; Hoffmann al., 2023). Compared with these problem settings, our problem is more challenging, which not only detects OOD graph samples, but also overcomes distribution shifts (Ju et al., 2024; Gui et al., 2022; Buffelli al., 2022) across source and target domains.
Graph Domain Adaption. Domain adaptation is a vital problem in the field of machine learn- ing (Huang et al., 2022b; Zhao al., 2021: Pang et al., 2023), which strives transfer knowledge from label-rich source domain to a target domain suffering from label scarcity. This problem has also been explored in graph domains, and various graph transfer learning approaches are developed that incorporate adversarial learning (Dai et al., 2022; Wu et al., 2020a) and pseudo-labels (Yin et al., 2022: Yehudai et al., 2021) into GNNs. However, these approaches are under the assumption that the label spaces of the source graph and target graphs are identical, which often does not hold true in practical scenarios (Panareda Busto & Gall, 2017; Chen et al., 2022). To address this, our study introduces under-explored problem of open-set graph domain adaptation and formulates novel approach DREAM to tackle this problem.
Open-set Recognition. The objective of open-set recognition is to exclude instances that belong to novel classes absent the training data (Geng et al., 2020). Current efforts can be categorized into generative and discriminative approaches. Generative methods use conditional auto-encoders (Oza & Patel, 2019) and data augmentation (Ditria et al., 2020) to simulate the distribution of novel classes, while discriminative models (Scheirer al., 2012: 2014; Rizve al., 2022) build dis- tinct classifiers to detect outliers. Open-set recognition can also be combined domain adaptation settings (You et al., 2019; Chen et al., 2022). Notwithstanding its significance, this problem has primarily been studied in the context of Euclidean data, and remains unexplored in graph-struct struttst data. To the best of our knowledge, we are the first to study open-set graph domain adaptation.
3 THE PROPOSED DREAM
Problem Setup. graph is depicted as G (V,E) with the node set V and the edge set The node attribute matrix is represented by X E g We are given n, labeled graphs from source domain D {G of )e and n, unlabeled graphs Dc [ -- The source and target label spaces are ) and yr, respectively. We assume ) C yt instead of y y in classic domain adaptation settings. Our aim to not only classify known target graphs into their corresponding classes, but also identify target graphs from novel classes y" ///""
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3.1 FRAMEWORK OVERVIEW
This work proposes a new method named DREAM for open-set graph domain adaption. Recog- nizing that subgraphs can provide additional topological information for graph classification under domain shift (Alsentzer et al., 2020), our DREAM introduces two complementary branches, i.e., graph representation learning branch and a subgraph-enhancee branch to learn graph representa- tions. We then integrate these two branches into a unified EM-based framework, which enhances their inter-branch consisteney on target graphs to reduce biased and overconfident pseudo-labels. Additionally, we blend dissimilar source graphs in the latent space to simulate samples from novel classes, thereby enhancing the capacity to identify OOD samples. To further alleviate the impact of domain shift, we construct a k nearest neighbor-based graph-of-graph and employ multi-sample mixup to transform graphs into virtual cross-domain samples for inter-domain consistency learning. A detailed illustration of the proposed DREAM can be found in Figure 1.
3.2 GRAPH-LEVEL REPRESENTATION LEARNING FOR OPEN-SET CLASSIFICATION
The preliminary point of graph classification is to map each graph sample into a compact embed- ding. Previous methods usually utilize GNNs and graph pooling operators (Kipf & Welling, 2017; Veličković et al., 2018; Xu et al., 2019; Back et al., 2021; Lee et al., 2019) for graph classifica- tion. To involve more multi-view semantics, after generating node representations using GNNs, we employ the attention mechanism (Veličković et al., 2018), which summarizes them into super-node representations from different perspectives, ultimately producing a graph-level representation. Sub- sequently, to detect OOD samples (Chen et al., 2022: Saito et al., 2020; Li et al., 2023) in the graph domain, we introduce an open-set classifier for identifying novel classes in our problem and then generate virtual samples using manifold mixup techniques ( (Verma et al., 2019) for extra supervision.
denotes the representation of node E V at layer I. We first introduce a GNN V (:--) update node representations:
In particular, given a graph sample = (V, h
n (1) AGGREGATEE" (fng-":: :)-)))))(()))) 20 = COMBINE (n.-") n (1)
(1)
where (11) denotes the neighbours of i. AGGREGATE!") (.) and COMBINE (.) denote aggre- gation and combination operators at layer 1, respectively. After stacking L layers, we can generate final node representation matrix H Φb (G,
[hf.-. ... Mfvll- Instead of directly summa- rizing these node representations, we adopt the attention mechanism to generate super-nodes that reflect different aspects of graphs. Here, we introduce query matrix @ E Txxd and then introduce a different GNN (-.-)) to generate T views of graphs. In formulation,
(2.K*) Vd H, K = $' X),
softmax
"' Yr] E Txd collects T super-node representations of G. Finally, we con- catenate all these representations into matrix E Rddd, and then utilize an MLP to summarize the information in A E Td into graph-level representation h = FG)) (G) where F9 denotes the whole graph-level representation learning branch.
where r
Open-set Classifier. To connect graphs into their corresponding classes, we introduce a classi- fier (-). which maps graph representations into label distributions, i.e., (y]G)) = 4:8 (h²) gbo (F)) with parameters #. Further, we extend the closed- world classifier by introducing an extra dimension, which outputs the probability of graphs belonging to novel classes Since we do not get access to labeled from the unseen classes, we turn to manifold mixup techniques (Verma et al., 2019). Here, we choose two graph samples from different classes and then leverage linear interpolation to generate virtual samples in the hidden space. Given of # vブ, we have:
h (G)) + (1 F) (G:).
(3)
where À is sampled from (0. 1). After generating set of virtual samples D' with their labels C++1, we will train the whole neural network by minimizing the following objective:
Ls -B(G, [lo()((y]G)] B(ih))DD [log (g)(CC 1]
(4)
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3.3 SUBGRAPH- VIEW REPRESENTATION LEARNING FOR SEMANTIC ENHANCEMENT
Due to potential domain shift and label scarcity on the target domain, our graph-level representa- tions could be biased for target data. Note that subgraph and patching strategies have been popular in graph representation learning (Han et al., 2022; He et al., 2022; Luo et al., 2022), which are underex- plored in graph domain adaptation. Towards this end. we introduce a subgraph-level representation learning branch to provide a complementary view, which can focus on key local functional parts in graphs and generate graph representation using hierarchical GNN architecture.
In detail, we leverage the graph clustering algorithm (i.e., Metis (Karypis & Kumar, 1998)) to gen- erate R subgraphs as follows:
(5) where each F" is comprised of edges between nodes in Vr. Then, we adopt GNN (-) to gener- all the subgraph representations using h, SUM( xx)) where SUM(-) summarizes updated node representations. Then, we calculate new adjacency matrix to model the interaction between subgraphs. In particular, we have:
"G',..,, "",...,,''']] [[V',
{V E
Anrr Σ
Σ Aij:
where AG is the weight between and j in the original graph. Given these graphs with the stacked subgraph representation matrix H R we adopt a GNN कh to model the in- teraction between subgraphs and summarize them into a graph-level representation, i.e., h SUM( (G, H)). Similarly, we can utilize different classifier (-) to generate (o(G)) = (h*) = 1 (F+(G) where J summarizes the subgraph-enhanced branch with parameters é.
3.4 INTERACTION BETWEEN TWO BRANCHES
We have built graph-level representation learning branch and subgraph-ennaaced branch. In this part, we combine the advantages of these two branches by posterior regularization (Ganchev et al., 2010: Qu al., 2019; Lin et al., 2019) to enhance the consistency between the predictions from the two branches.
In detail, propose maximize the log-likelihood of graph representation learning, i.e., EGED [log PG))). Then, we have the following lemma with the posterior distribution (o) Lemma 3.1. EceD [log (G))
[log
pa po(G.w where the equality holds when ?s[v[G].
Go(y = Gv)
The proof is given in Appendix A. Therefore, we minimize the KI. divergence between the predic- tion from two branches on the target domain:
EGED' L(gs (g (y))))
To minimize the inconsistency, adopt an EM-style optimization manner. In particular, we first up- date the graph-level representation learning branch, and then update the subgraph-enhanced branch.
E-step. We first fix 0 and update the posterior distribution, i.e., the subgraph-enhanced branch. Here, we adopt the reserved KL divergence to simplify the calculation, i.c., min K (Le (pp(p) (v)))) Note that EGED (olgo(()))) (G) [0 log go (x) = O, we have:
(8) From Eqn. we generate the pseudo-labels target graphs based on the prediction from both two branches, which can reduce the overconfident pseudo-labels through their collaboration.
DEGEDI K (pe (y/ (') qs (yl G)) 0e = dE -r-(pp((l G)) [- log qo (y G)] /06.
M-step. Then, we update the graph representation learning branch with & fixed. Similarly, we have:
DEGGER-y--o (p-(p tuc(l))))))))) log (elgge(yy))) /00. (9) In summary, generate confident pseudo-labels for target graphs using both two branches, which takes the intersection of confident pseudo-labels from two branches Then, they are utilized to opti- mize our two branches in an alternative manner with:
DEGED K LLgs (y/ (glG))
Lt EGED (o-(pattl())oooollc)) [- log Po G) log (x))))
(10)
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3.5 MULTI-SAMPLE MIXUP FOR DOMAIN ALIGNMENT
However, the challenge of serious domain shift in our problem still exists, which could potentially in- troduce biased pseudo-labels. To tackle this issue, propose multi-sample mixup strategy (Zhang et al., 2022; Verma et al., 2019), which combines multiple cross-domain neighboring samples for virtual samples. With the assumption of similar semantics for close graph representations (Long et al., 2018; Luo et al., 2021; 2023; Zhao et al., 2021), we aim to maximize the consistency of predictions between original and virtual samples for domain alignment.
In detail, we first identify cross-domain neighbors in the whole dataset. Here we take the first branch as an example and omit the superscript of graph representations. Since there would be target graphs from novel classes, we utilize a k mutual nearest neighbor graph-of-graph G where each node represents a graph sample in the dataset. To save the computational cost, we introduce a memory bank M with size [M], which is updated in
fashion. The adjacency matrix A is:
{
1
G E (A() CMVG E (x(G;) CM otherwise,
Aij =
(11)
where (-)+) collecting k- neneess neighbours the hidden space. Then, for each source graph sample G we take the combination of all neighbours in G:
Σ Xyhl.
(12)
where X; = C, s(G;, GG)) and s(;;, GJ) denotes the cosine similarity between two graphs in the hidden space. Similarly, we can generate cross-domain virtual features for each target graph. Then, we maximize the consistency between the original graphs and their corresponding cross-domain virtual ones. In particular, we have:
LD B(G.))D-UD! KT(p(vlG)
(13)
where z denotes the cross-domain features generated by G.
Framework Summarization. Finally, the overall training objective can be summarised as:
L= Ls + aLr + SLDA:
(14)
where and 3 are dyper-parameee We utilize mini-batch stochastic gradient descent (SGD) to update the whole DREAM. The detailed algorithm shown in Algorithm C.
4 EXPERIMENT
4.1 EXPERIMENTAL SETTINGS
Evaluation Datasets. To validate the effectiveness of DREAM, we perform extensive experiments on six widely used graph classification datasets from TUDataset and BatthmarkDattaset, includ- ing MSRC_21 (Neumann et al., 2016), Letter-high (Riesen et al., 2008), COIL-DEL (Nene et al., 1996: Riesen al.. 2008), COIL-RAG (Riesen al., 2008; Nene et al., 1996). MNIST (Dwivedi et al., 2020), and CIFARIO (Dwivedi et al., 2020). The specific statistics and details introduction of experimental datasets are presented in Appendix D.
Evaluation Protocols. Under the open-set domain adaptation settings, we first divide the classes into known and unknown classes which are shown Appendix D, and then we divide datasets into different domains (i.e., source and target domains) by the density of graphs (i.e., the ratio between graph nodes and edges) indicated by P1 and P2 (Li et al., 2022a) and the target domain also consists of unknown graphs. Specifically, in the open-set setting, class, and when the prediction of samples belonging to known classes with the correct labels or novel classes with the unified class, we declare they are correct.
treat all the unknown classes a unified
Compared Methods. We compare our proposed DREAM with a wide range of state-of-the-an approaches, including seven graph classification methods (i.e., GMT (Back et al., 2021). Graph- Mix (He et al., 2022), GCN (Kipf & Welling. 2017), GraphSage (Hamilton et al., 2017), GIN (Xu al., 2019), SAG Pooling (Lee al., 2019) and GraphCI. (You et al., 2020)), well as three of

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Published as a conference paper at ICLR 2024
Table I: Classification accuracy comparisons four benchmark graph classification datasets (I).
The best results are in boldface. P1 and P2 denote different domains in the datasets.
2SRC
Letter-high
COIL-DEL
COIL-RAG
Methods
P1
P1
P1-+2
P2-P1
P1 P1-P2
P2-+P1
P1-P2
P2- P1
GMT
63.34:3.7
1.5
45.84288
10.7+:144
34.6.3.11
17.9
57.41:11
60.6+1.3
GraphMix
64.5++2..8
65.74:2.4
46.0+2.3
45.6+:111
36.6+266
35.8
49.5
50.6422.1
GCN
63.5+:3.4
63.64:2.8
40.24:4.1
38.6
20.6+3.7
20.3+2222
$8.3+177
56.8
GruphSage
60.54:2.3
54.14:3.3
50.043.6
45.9:22.0
24844411
14.422
58.422.2
54,7114
GIN
66.3:43.2
63.3422.7
47.3422.2
46.2+:100
30.6+2.3
13,9
58.0+0.77
52.9-0.7
SAG Pooling
61.7::4.4
$6.94-4.2
44.943.11
40.4:0077
24.1
114-1.
58,542,3
14
GraphC1.
67.2:1333
67.0:33.1
47.3:12.4
46.2::0088
30.6:2..1
23.9
58.6:11.8
56,222.3
CSSR
73.8:13.3
75.8:1277
49.8133.3
42.51222
37.0:1.,4
36.21188
54.9:2.11
58.0112.6
DIAS
70.4::2.9
68.8:42.1
52.4:422
$2.61:133
30.8:13.3
2122
$1.3424
$5.7
OSR
58.14:4.1
61.5::344
48.1
42.7::144
33.24:2.0
36.42099
54.7::4.2
51,1-122
DREAM
74.3+t5.4
75.24:3.7
58.7:+3..5
53,3--0.88
44.0:12..6
40.2::0.55
65.4
62.5+1199
Improvement
12.0%
1.3%
18.9%
10.4%
11.6%
3.1%
the most advanced open-set recognition methods (i.e., CSSR (Huang et al., 2022a), DIAS (Moon al., 2022) and OSR (Vaze al.. 2022)). More details about the compared baselines can be found Appendix E.1. We also compare our proposed DREAM with RIGNN (Luo et al., 2023), OpenWGL. (Wu al., 2020b), OpenWRF (Hoffmann al., 2023), DEAL (Yin et al., 2022) and CoCo (Yin et al., 2023a) in Appendix F.2.
Implementation Details. As for the network architecture, we first pre-train the dual branches (i.e., graph-level and subgraph-enhancee branches) on the labeled domain, followed by training the net- work using our proposed framework. To avoid memory overflow, we utilize the memory bank mechanism to store the previous embeddings and employ it to train DREAM on these dataset. For the three open-set recognition methods, we use the GIN model as the backbone encoder to obtain the graph-level features. The dropout ratio is set to 0.5. During training, the hidden dimension of all the methods is set to 128, and we use the Adam (Kingma Ba, 2014) optimizer and set the batch size 64 default. The total number of training epochs is 200, and the learning rate is set 0.001. The hyper-parameters and B are set to 1.0, 1.0, respecitvely.
4.2 EMPIRICAL PERFORMANCE
Overall Comparison. The open-set domain adaptation accuracy on dif- ferent datasets compared with base- lines presented in Table and Ta- ble 2. From the results, we ob- serve that the proposed DREAM achieves better performance in both P1 + P2 and P2 + P1 scenarios in most cases, which demonstrates the superiority of DREAM. We at- tribute the reason to two aspects: the enhancement of interaction between two branches and the Mixup strate- gies that help align different domains. On the one hand, the interaction be- tween two branches helps the model learn a consistent representation, which fits the framework of EM al- gorithm (Moon, 1996). On the other hand, the multi-sample mixup mod- ule generates cross-domain counterparts by linearly combining multiple samples, further reducing domain discrepancy. Moreover, with the enhancement brought by combining dissimilar source sam- ples, DREAM can better classify graph samples in unknown classes. The existing graph classifica- tion methods perform worse than DREAM in the open-set task. This is because these methods
Table 2: Classification accuracy comparisons on two graph classification datasets (II). The best results are in boldface. P1 and P2 denote different domains in the datasets.
MNIST
CIFARIO
Methods
P1-P2
P2-P1
P1-P2
P2-PP1
GMT
64.243.4
63.5+2.3
37.7+28
37.2+1.3
GraphMix GCN
65.5+4..1
65.74.1.9
42.++3.1
43.2+1.4
63.4+22.5
62.242.7
26.3+2.1
2..8+1.7
GraphSage
57.0+33.7
63.6433.0
27.9+2.7
29.4+1.5
GIN
63.54:2.7
62.94224
21.743.4
27.8-008
SAG Pooling
64.24:3.1
63.6:t1.9
28.744.1
34.0-10.8
GraphCL.
62.8++2.3
62.9-11.4
27.8+2288
30.9+1077
CSSR DIAS
70.8+3.0
68.2+2.2
45.3+2.1
44.7+1.1
72.6+22.7
70.8++2.7
46.3+t1.9
45.5+
OSR
74.7:1:.2
70.2:13.1
36.8+12.7
1..4+:16
DREAM
84.1+-2.8
81.8+-1.5
48.3++2.3
47.0++0.4
Improvement
12.6%
15.5%
4.3%
3.3%

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(a) GMT
(b) CSSR
(c) DREAM
Figure 2: The T-SNE visualization of latent representation with GMT, CSSR, and DREAM MNIST dataset. Each point represents a unit's latent representation, and the colors indicate the corresponding labels.
designed for closed-set tasks without the consideration of unknown classes and neglect the seman- tic shift. Additionally, the results of DREAM outperform the aforementioned open-set recognition methods in most cases. The potential reason is that traditional open-set recognition methods usually use prototype learning to separate the unknown class from all seen classes, which would suffer from the semantic shift and label scarcity in our scenarios.
Visualization. For the purpose of achieving an intuitive effect, we demonstrate the visualization of the graph representations for different methods in Figure 2. We visualize the MNIST dataset and compare with two models (GMT and CSSR). From the results, we can find that the visualiza- tion results of the closed-set graph model cannot have an evident conclusion since a wide range of similar graphs are not clustered with huge overlap of points from different classes. This because the det model cannot effectively separate the unknown samples from the known samples. Compared with GMT, CSSR demonstrates a more structured visualization where we can tell the re- lationship across different classes. Nevertheless, the boundaries of different classes still blurry, indicating that although open-set recognition methods can effectively recognize unknown classes, they cannot tackle domain shift and label scarcity in graph data effectively. From the visualization of our proposed DREAM, the graph representations from the same classes are close in comparison these baselines. In addition, can observe that the boundaries of different classes produced by our DREAM are quite clear, demonstrating that our proposed DREAM is capable of producing high-quality and discriminative graph representations.
Ablation Study. We perform abla- tion studies investigate the contri- butions of different components with six variants. particular, we intro- duce six model variants: 1) DREAM w/o it replaces the attention mech- anism with the global pooling. 2) DREAM w/o MM: it is trained with- the multi-sample mixup frame- work. 3) DREAM w/o IB: it removes the interaction between two branches. 4) DREAM w/o OC: it ignores the open-set classifier during training. 5) DREAM w EG: it ensembles two graph-level representation branches with different parameters. 6) DREAM w ES: it ensembles two eengrapp-enhanneee branches with different parameters.
Table 3: Ablation study of different components DREAM. P1 and P2 denote different domains in the datasets.
Ligh
COIL-DEL
Methods
P1 >P2
P2 xP1
>P2
P2 >P1
DREAM w/o
55.4
51.0
40.3
38.7
DREAM w/o MM DREAM DREAM w/o
56.1
51.3
41.0
39.1
52.1
43.7
38.3
55.3
51.0
41.7
37.4
DREAM BG
57.4
52.4
42.8
39.5
DREAM ES
58.1
52.7
43.5
40.0
DREAM
58.7
53.3
44.0
40.2
Table 3 shows the results of different variants and we can have the following observations. Firstly, DREAM w/o A achieves worse performance than DREAM, validating the effectiveness of the tention mechanism for super-nodes. Secondly, DREAM w/o MM performs worse than our full model. This can attributed to the fact that the malti-sample mixup framework maps each instance to cross-domain samples, which effectively aligns the domain features and leads to better perfor- mance. Thirdly, by ignoring the interaction between branches, the performance of DREAM w/o IB decreases compared with DREAM Letter-high and COIL-DEL datasets. The potential reason that with the mutual supervision between different branches. DREAM tends to learn consistent results for classification, thus increasing the reliability of the results. Fourthly, DREAM w/o OC
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2.00
0.5
0145
Acsuncy
2.30
2.56
Accumit
2.0
0.4
Accumic
030
24
240
20
[MC]
[X]]
[M]
(a) Letter-high P1 - P2
(b) Letter-highh P2 - P1
COIL-DEL P1 P2
(d) COIL-DEL P1 P2
Figure 3: Hyperparameter sensitivity analysis of the memory bank capability [M] on Letter-high and COIL-DEL datasets. [M] is the memory capability and ranges from to 1024. The solid line corresponds to the mean results and the shaded area represents the standard deviation.
8.50
3.46
0.425
8.575
0:575
Asquracy
0.400
26330
8339
26524
3.38
8475
336
0.75
(a) Letter-high P1 - P2
(b) Letter-high P2 P1
(c) COLL--DEL P1 P2
(d) CELL-DEL P1 P2
Figure 4: Hyperparameter sensitivity analysis of the similar samples on Letter-high and COIL- DEL datasets. i denotes the number of similar samples sampled from the other domain. The solid line corresponds to the mean results and the shaded area represents the standard deviation.
removes the open-set classifier, which achieves the worst results mostly. The potential reason is that the open-set classifier introduces the unseen classes with Mixup into the closed-set set settings, making the model more generalized to the unseen classes in the other domain. Fifthly, DREAM w EG and DREAM w ES perform worse than the full model, indicating the importance of interaction between two different branches from two complementary views.
Sensitivity Analysis. In this part, we investigate how the hyperparameters influence the performance of DREAM. In our implementation, |M| controls the number of historical features of the memory bank, and controls the number similar samples in another domain corresponding to each sample. We set [M] and & in (64, 128, 256, 512, 1024) and {10, 20, 30, 40, 50) with other parameters fixed, and the results are presented Figure and Figure 4. From the results, we can find that when the value of IM rises, the performance tends to improve gradually. The potential reason is that with the increase of memory capability, DREAM will remember more historical features for domain large |M] will lead memory overflow. Therefore, the default value of JM] is set to 1024 for these datasets. Moreover, the accuracy of DREAM tends increase first and decrease gradually when & rises. This is because fewer ls cannot provide sufficient information for the domain alignment. When with larger k, one sample would collect much more samples from the other domain, which may introduce more noisy instances, leading the worse performance. Therefore, we set the k to 20 as the default.
alignment. However, with the limitation of GPU memories,
CONCLUSION
This work addresses the challenging problem of open-set graph domain adaptation and presents novel method named DREAM. Our DREAM incorporates two branches, a graph-level representa- tion learning branch and subgraph-enhanced branch, which are trained jointly to explore graph topological structures from different perspectives and ensure inter-module consistency. To handle open-set scenarios, we generate virtual unknown samples belonging to novel classes for additional supervision the open-set scenarios. To further mitigate domain shift, we construct nearest neighbor-based graph-of-graph to generate cross-domain counterparts using multi-sample mixup, which helps to improve cross-domain consistency. Extensive experiments on six datasets validate the superiority of our proposed DREAM over existing sfate-of-the-ar approaches. In our future work, we would extend our DREAM to more realistic problems such as universal graph domain adaptation and test-time graph domain adaptation.

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Published as a conference paper at ICLR 2024
ACKNOWLEDGEMENT
This work is supported by STI 2030 2030-Major Projects (No. 20212D0201105).
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A PROOF OF LEMMA 3.1
Lemma 3.1. EGED: [log pe()) 2 EGED (-
Pe(G.y) where the equality holds when as (x]
pe(u|G) Us ())
Proof. We have:
EGED: [logpo((]) po() EGED: (log Σ Po
Po Po y)
EGED [log Σ
90 (v)
(o(y)))
y
(15)
Σ G)) log (G,
RGEDI (log]
(o(y)G)
(ulc Llog Po (G,
Lo G)
The inequality comes from the Jensen's inequality and the equality holds when G)) (1 y) is a constant. Since pa (G.v) y) = (yy))) G), we have go (o (v( is constant. Therefore, the equality holds when ( ()
B COMPLEXITY ANALYSIS
Here, analyze the computational complexity of the proposed DREAM. The computational com- plexity primarily relies on two different branches for graph representations, Given a graph G, ||A||o the number of nonzeros in A, d denotes the feature dimension, L denotes the number of layers, T' denotes the number of views, R. denotes the number of clusters. The graph-level representation learning branch takes |[L||A| d L d2 Td + Tdd). The subgraph-view representation learning branch takes O V dl R d). In our case, R < ||Allo, T < d and T < [V]. Therefore, the complexity of the proposed DREAM and GraphCL are both OLL]|A|lod L (d') for each graph sample, which is linearly related to ||Allo and VV. We would further explore the complexity of our method in more complicated scenarios in our future works.
C ALGORITHM
Algorithm Learning Algorithm of DREAM
Input: Source data D*; Target data D
Output: Parameters 0 and & for two branches.
1: Warm up to initialize 0 and d.
2: while not convergence
3: Update the memory bank M;
4: Annotate target graph samples using Po(y(G) and go(u)G);
5: I/ E-step
6:
Optimize model parameters é with fixed 0:
7: I/ M-step
8: Optimize model parameters with fixed d.
9: end while
D DATASETS
D. DATASET DESCRIPTION
We conduct extensive experiments on six public benchmark graph datasets. Four them, i.c., MSRC 21, Letter-high, COIL-DEL, COIL-RAG are from TUDataset. The rest released by
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Table 4: Statistics of the experimental datasets.
Dataset
#Graph
#Classes
#Avg. Nodes
#Avg. Edges
#Known
#Unknown
MSRC.21
563
20
77.52
198.32
16
4
Letter-high
2,250
15
4.67
4.50
12
3
COIL-DEL
3,900
100
21.54
54.24
80
20
COIL-RAG
3,900
100
3.01
3.02
80
20
MNIST
70,000
10
70.57
564.53
2
CIFARIO
60,000
10
117.63
941.07
8
2
Benchmark Dataset, i.e. MNIST and CIFARIO. The dataset statistics can be found Table 4, and their details are shown follows:
MSRC.21. The images in MSRC_21 (Neumann al., 2016) represented by the conditional Markov random field graph, with nodes representing each image's 's superpixels and edges as the connection if the superpixels are adjacent.
Letter-high. Letter-high (Riesen al., 2008) consists of capital letters with straight lines (i.e., A, E, F, H, I, K, I,, M, N. T, V. W, X, Y, 2). A prototype line drawing is built for each class, and then converted into graphs with edges denoting lines and nodes denoting ending points.
COIL-DEL. COIL-DEL (Riesen et al., 2008) applies the Harris corner detection and Delaunay Triangulation to extract corner features from images. The graph is described with lines by edges and their ending points by nodes. Each node has a 2D attribute and edges are unlabeled.
COIL-RAG. COIL-RAG (Riesen et al., 2008) begins with segmenting each picture into regions of homogeneous color, and then transforms into graphs with nodes representing regions and edges representing the adjacency of regions. Each node is labeled with attributes specifying the color histogram and each edge is associated with the length of the common border of their corresponding adjacent regions.
MNIST, MNIST (Dwivedi et al., 2020) is converted from the original MNIST dataset by using super-pixels as nodes and utilizing kNN to characterize the relationships between super-pixels.
CIFAR10. CIFARIO (Dwivedi al., 2020) constructed similarly the MNIST dataset, which is more challenging since the large graphs with detailed semantic information.
D.2 DATA PROCESSING
In our implementation, we process the datasets with different methods in corresponding models. For both branches, we process the four TUDataset by adding the self-loop connection of each node, and we use the one-hot embeddings for node attributes if the node features are not available. As for the Benchmark Datasets, add the position information into the node features.
E IMPLEMENTATION DETAILS
E. BASELINES
In this part, we introduce the details of the compared baselines as follows:
Graph Classification Methods. We compare DREAM with seven popular graph classification approaches, i.e., GMT (Baek al., 2021). GraphMix (He al., 2022). GCN (Kipf & Welling, 2017), GraphSage (Hamilton al., 2017), GIN (Xu et al., 2019), SAG Pooling (Lee et al., 2019) and GraphCL (You et al., 2020). For GCN and GIN, we use the Open Graph Benchmark' implement the model. For GMT, GraphMix. GraphSage, SAG Pooling and GraphCL, provided by the corresponding paper. As for these baseline methods, we vary the dropout rate the range of 10.1.0.3.0.5.007 and then choose the best one. The hidden dimension in these methods is set to 256 for a fair comparison.
the source codes
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GMT. GMT (Back et al., 2021) incorporates multi-head attention into the graph pooling layer, which enables the model to effectively consider the structural dependencies in the graph.
GraphMix. GraphMix (He et al., 2022) is the abbreviation of Graph MLP-Mixer, which capa- ble of establishing long-range connections within graphs. It first divides each graph into range of subgraphs with overlap and then leverages the self-attention mechanism to generate graph rep- resentations with node and patch position embeddings.
GCN, GCN (Kipf& & Welling, 2017) is the most popular approach to encoding the graph struc- ture. It aggregates the neighborhood information update the node representations in iterative manner.
GraphSage. GraphSage (Hamilton et al., 2017) aims to tend the transductive node classification to the inductive setting. It samples nodes from the neighborhood for each node instead of using all neighborhood nodes to increase computational efficiency. Through this, it can capture both the topological structure and the distribution of neighboring node features.
GIN. GIN (Xu et al.. 2019) is powerful graph neural network which follows the message passing mechanism. It simply modifies the network architecture, which enhances its expressive capabil- ity in exploring diverse graph structures. It has been proven that the architecture has the same expressivity as the Weisfeiler-Lchman graph isomorphism test.
SAG Pooling. SAG Pooling (Lee al., 2019) first adopts the self-attention mechanism to learn the semantics of both node features and graph topology, and then masks unimportant nodes to reduce the number of nodes in each graph sample. The graph pooling layer is combined with the convolution layer and readout layer in the whole backbone.
GraphCL. GraphCL (You et al., 2020) GraphCL a popular framework for learning effective graph representations in supervsd manner. It adopts four augmentation strategies including node dropping, edge dropping, attribute masking and subgraph to generate different views of graph samples and then maximizes the mutual information between different views of the same graph.
Graph Domain Adaptation Methods. We compare DREAM with two state-of-the-art graph do- main adaptation methods, i.., DEAL (Yin et al., 2022) and CoCo (Yin et al., 2023a).
DEAL. DEAL (Yin al., 2022) is domain adaptation method for graph classification, which contains an adversarial perturbation module and a pseudo-label distilling module. It adopts adver- sarial learning transfer semanties from the source domain the target domain.
CoCo. CoCo (Yin et al., 2023a) consists of a graph convolutional network branch as well as hierarchical graph kernel branch to explore topological information. To address the gap between the source and the target domain, it utilizes a cross-domain contrastive learning objective, which follows the EM algorithm.
Open-world Graph Learning Methods. We compare DREAM with three open-world graph learning methods, i.e., RIGNN (Luo et al., 2023), OpenWGL (Wu et al., 2020b) and Open- WRF (Hoffmann al., 2023).
RIGNN. RIGNN (Luo et al., 2023) takes rationale view to detect components containing the most information related to the label space and classify unlabeled graphs into known class or an unseen class.
WGLn OpenWGL (Wu et al., 2020b) a framework that utilizes the variational framework to learn effective node representations in open-won worldworld settings. We adapt the framework to graph-level framework.
Open WRE OpenWRF (Hoffmann al., 2023) introduces framework which decreases the sen- sitivity to thresholds in OOD detection.
Open-set Recognition Methods. We also compare our DREAM with three state-of-the-art meth- ods, i.e., CSSR (Huang et al., 2022a), DIAS (Moon et al., 2022) and OSR (Vaze et al., 2022).
CSSR. CSSR (Huang et al., 2022a) leverages an autoencoder-based architecture to measure whether instances belong known classes or not while preserving high classification accuracy on known classes. It learns a specific autoencoder for each known category, which can produce individual manifold well.
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0.86
0.82
Accuracy
0.84
Accuracy
0.80
0.76
0.80
0.74
0.78
0.72
2
2
2
n
2
2
2
2*
2
JM
J.
(a) MNIST P1 - P2
(b) MNIST P2 P1
0.68
0.65
0.66
Accuracy
0.64
Accuracy
0.60
0.62
0.55
0.60
0.50
0.58
26
27
230
27
28
[M]]
J.V]
COIL-RAG P2
COIL-RAG P1
Figure 5: Hyperparameter sensitivity analysis of the memory bank capability |M on MNIST and COIL-RAG datasets. |M| the memory capability and ranges from 1024. The solid line corresponds to the mean results and the shaded area represents the standard deviation.
DIAS. DIAS (Moon et al., 2022) aims to improve the capability of detecting unknown samples by introducing a difficulty-awe aware instance augmentation strategy. In particular, improves the training procedure by generating both hard-difficulyy and easy-difficuly examples to enhance the model's ability handle unknown samples.
OSR. OSR (Vaze et al., 2022) demonstrates that the performance of open-set recognition is highly related close-set results. Then, it improves the baseline approaches using the maximum logit score to detect open-set samples, which can achieve state-of-the-art performance with limited modification.
E.2 OUR IMPLEMENTATION
We implement our proposed DREAM with PyTorch (Paszke al., 2017) and PyTorch Geometric library (Fey & Lenssen, 2019) on TUDataset and Benchmark dataset², We first pre-train the dual branches (i.e., graph-level and angraph--nhannee branches) on the labeled domain, followed by the open-set classifier to train the network. Then, we start from the pre-trained model to implement the interaction between two branches and multi-sample mixup for domain alignment. Furthermore, to avoid memory overflow, we utilize the memory bank mechanism to store the previous embeddings and employ it train DREAM on the unlabeled open-set dataset. Additionally, we search the number of sample neighbors from { (10, 20, 30, 40, 50), and the size of the memory bank from {64, 128, 256, 512, 1024). During training, the hidden dimension of all the methods is set to 128, and the Adam (Kingma& & Ba, 2014) optimizer and set the default batch size to 1024. The total number training epochs is 200.
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0.87
0.83
0.86
Accuracy
0.85
Accuracy
0.82
0.84
0.81
0.83
0.80
0.82
0.81
0.79
10
20
30
40
50
10
20
30
40
50
k
k
(a) MNIST P1 P2
(b) MNIST P2 P1
0.64
0.67
0.63
0.66
Accuracy
Accuracy
0.65
0.64
0.61
0.63
0.60
0.62
0.59
10
20
30
40
50
10
20
30
40
50
k
k
(c) COIL-RAG P1 P2
(d) COIL-RAG P1
Figure 6: Hyperparameter sensitivity analysis of the similar samples & on MNIST and COIL-RAG datasets. the number similar samples sampled from the other domain. The solid line corre- sponds to the mean results and the shaded area represents the standard deviation.
Table 5: Classification accuracy comparisons four benchmark graph classification datasets (I).
The best results are in boldface. Pl and P2 denote different domains in the datasets.
MSRC
Lettr-high
COIL-DEL DEL
COIL-RAG
Methods
P1-P2
P2-P1
P1-P22
P2-P1
P1+P22
P2-P1
P1-P2
P2-P1
RIGNN
72.6=4.33
73.8++2.4
51.1+3.2
43.8+2.1
34.2+2.9
33.5+:3.3
57.642..1
57.2+3.1
OpenWGI.
70.7+44.2
69.5+3.3
48.2+2.8
40.9+2.3
36.4+2.1
33.8+119
56.3+3.3
54.8+2.3
OpenWRF
73.0=3.7
70.442.5
42.642.6
40.4
31.511.8
30.2128
55.3122
$4.8+2.4
DEAL
68.3=3.8
67.943.2
50.7+2.9
47.3-2.3
31.41:4.3
27.712.4
58.142.3
$4.242.7
CoCo
69.8=4.7
68.342.11
50.343.4
49.8-1.4
33.743.11
19.811.7
61.31114
55.7+1.6
DREAM
74.3=5.4
75.2+33.7
58.7++3.5
53.3--088
44.0++2.6
40.2:10.5
65.4+11.7
62.5+1199
F MORE EXPERIMENTAL RESULTS
F.1 MORE SENSITIVITY ANALYSIS
As introduced Section 4.2, we set [M] and & in (64, 128, 256, 512, 1024] and {10, 20, 30, 40, 50} with other parameters fixed, and conduct the experiments MNIST and COIL-RAG. The results are presented in Figure 5 and Figure We can have similar observations as in Letter-high and COIL-DEL in Section 4.2.
F.2 MORE PERFORMANCE COMPARISON
In this part, include five more additional baselines, i.e., RIGNN (Luo al., 2023), Open- WGL (Wu et al., 2020b), OpenWRE (Hoffmann et al., 2023), DEAL (Yin et al., 2022) and CoCo (Yin al., 2023a). From the results in Table 5, find that proposed DREAM
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Table 6: Ablation study of different components in DREAM. P1 and P2 denote different domains in the datasets. DREAM w/o MM removes the multi-sample mixup framework; DREAM w/o IB removes the interaction between two branches; DREAM w/o OC ignores the open-set classifier during training: DREAM w EG ensembles two graph-level representation branches with different parameters; DREAM w ES ensembles two subgraph-enhancee branches with different parameters.
MSRC 21
COIL-RAG
MNIST
CIFARIO
Methods
Pl
P2 +P1
P1-+12
P2-P1
P1-+P2
P2-P1
Pl
P1-P2
P2
PI
DREAM w/o MM
72.4
72.8
62.2
60.3
82.4
79.6
45.6
DREAM w/o IB
73.2
74.1
64.7
61.1
82.3
80.4
47.1
45.3
DREAM w/o OC
70.3
70.7
61.3
59.1
80.8
77.4
44.2
42.3
DREAM EG
73.1
73.7
64.4
61.5
82.7
80.4
47.0
45.4
DREAM ES
73.8
74.4
64.7
61.3
82.4
80.7
DREAM
74.3
75.2
65.4
62.5
84.1
81.8
48.3
47.0
0.80
0.60
0.55
0.75
Accuracy
MSHL
OOIL-AG P3- CAI P2
Accuracy
0.50
Letier F1 F1
COO DEL P1-22
0.70
MSRC
22-P1
Loter F2--P F2-PL
COn DEL P2
0.45
0.40
0.60
0.35
0.6
0.8
1.0
1.2
1.4
0.6
0.8
1.2
1.4
α
α
0.80
0.60
0.55
0.75
Accuracy
Accuracy
0.50
Latier- ligh P1-422
COILDEL PL-12
0.70
MSRC
OOIL P2-PP
Latier digh P2
COILDEL P2-05
0.45
0.65
0.40
0.60
0.35
0.8
1.0
1.2
0.6
0.8
1.2
1.4
ß
β
Figure 7: Hyperparameters analysis of and 8 on MSRC_21, COIL-RAG, Letter-high and COIL- DEL.
can achieve better performance in comparison to these baselines, which can validate the superiority of the proposed DREAM again.
F.3 MORE ABLATION STUDIES
To validate the effectiveness of the different components, conduct more experiments with five variants on different datasets, i.e., DREAM w/o MM, DREAM w/o IB, DREAM w/o OC, DREAM EG and DREAM w. The results shown in Table 6. From the results, have similar observa- tions as summarized in Section 4.2.
F.4 HYPERPARAMETERS ANALYSIS
In this part, we provide additional parameter analysis for loss combination. Here, we add the weights by modifying the overall loss to I. L.g aTer 3LD. A. To determine the hyper-parameters of
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Table 7: The compared performance of RIGNN and DREAM more complicated scenarios with diverse environments.
MSRC 21
Letter-high
Methods
P1-12
P1-+33
PI-+P4
PL-+P5
P1-+22
P1-+3
PI-+P4
P1-+P5
RIGNN
60.8
61.4
60.3
59.7
45.1
44.5
43.9
42.6
DREAM
63.2
63.8
61.1
62.1
47.3
45.9
46.8
44.6
Ground Truth: 0 (Known Class) Our Prediction: 0 (Correct)
Ground Truth: 6 (Known Class) Our Prediction: (Comect) Baseline Prodiction: (Incorrect)
Ground Truth: (Unknown Class)
Our Prediction: OOD (Correct) Baseline Prediction: (Incorrect)
Bascline Prediction: 0 (Correct)
(a)
(b)
(c)
Ground Truth: (Unknown Class)
Ground Truth: 5 (Known Class) Our Prediction: (Corret)
Ground Truth: (Unknown Class)
Our Prediction: OOD (Correct)
Our Prediction: (Incorrect) Baseline Prediction: (Incorrect)
Baseline Prodiction: (Incorrect)
Baseline Prediction: (Incomecc)
(d)
(c)
Figure 8: Visualization of graphs on the CIFAR10 dataset. We can observe that our model has the potential to detect unknown samples, which the baseline model cannot identify.
and B, we study the sensitivity analysis with and 8 in the range of (0.6, 0.8, 1.0, 1.2, 1.4), which shown in the Fig. 7. We can find that our performance robust to both and Therefore, we directly set the default parameter to 1.0.
F.5 COMPLICATED SCENARIO WITH DIVERSE EN ENVIROMENTS
To apply the proposed DREAM to more complicated scenarios, we separate the dataset into five parts, including four different target domains and one source domain for each dataset. The perfor- mance comparison of different methods is shown in Table 7. From the results, can conclude that our DREAM achieves better generalization capacity comparison with the baseline.
F.6 VISUALIZATION OF GRAPH STRUCTURES
We provide visualization of the graph structures in Figure to further illustrate their complex- ity. We also provide the prediction results of our proposed DREAM and the baseline model GIN. can be observed that the graphs possess intricate structures. It becomes apparent that employ- ing only branch, either the graph-level view or the subgraph view, is insufficient for effective representation learning. This observation supports the importance and necessity utilizing both branches concurrently, which enhance the quality of the learned representations. By leveraging
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the complementary information from both views, we capture comprehensive understand- ing of the underlying graph structures and improve the overall performance to detect samples from unknown classes. However, when graph structures are too complex (see Figure 8 (f)), both our pro- posed DREAM and the baseline would fail. Therefore, we will further improve our model to face more complicated scenarios.
22


Reviews:
[{"review_id": "OYnzYuH1IL", "reviewer": "Reviewer_SVBJ", "summary": "The paper proposes DREAM for open-set graph domain adaptation, which incorporates a graph-level representation learning branch as well as a subgraph-enhanced branch to jointly explores graph topological structures from both global and local viewpoints.", "questions": "See weaknesses", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThe problem of open-set graph domain adaptation is novel.\n2.\tThe paper is well organized and clearly written.\n3.\tThe proposed method is clever and interesting.", "weaknesses": "1.\tThe format of references is not uniform, such as [4] and [5].\n2.\tWhat’s the difference between the open-set graph domain adaptation and universal domain adaptation? Can the proposed model be extended to UDA?", "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": "FIv8Kn93Ec", "reviewer": "Reviewer_9UFe", "summary": "The paper proposes a novel method called DREAM for open-set graph domain adaptation, which aims to accurately classify target graphs into their respective categories under domain shift and label scarcity. DREAM incorporates a graph-level representation learning branch as well as a subgraph-enhanced branch, which jointly explores graph topological structures from both global and local viewpoints. The method also amalgamates dissimilar samples to generate virtual unknown samples belonging to novel classes and establishes a k nearest neighbor-based graph-of-graphs to alleviate domain shift. Extensive experiments demonstrate the superiority of DREAM over state-of-the-art methods.", "questions": "See weaknesses", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Novelty: The paper introduces a new problem of open-set graph domain adaptation, which accommodates unlabeled in-the-wild target graphs from unseen classes. The proposed method, DREAM, is a novel approach that employs two branches to investigate structural semantics and integrates them into a trustworthy and domain-invariant framework. \n2. Effectiveness: The paper demonstrates the remarkable effectiveness of DREAM when compared to state-of-the-art methods in various challenging scenarios. In particular, the performance gain of DREAM over the best existing method is up to an impressive 15.5%. \n3. Flexibility: DREAM is a flexible method that can handle open-set scenarios and mitigate domain shift. It generates virtual unknown samples belonging to novel classes for additional supervision in the open-set scenarios and constructs a k nearest neighbor-based graph-of-graph to generate cross-domain counterparts using multi-sample mixup, which helps to improve cross-domain consistency. \n4. Clarity: The paper is well-written and easy to understand. The authors provide clear explanations of the problem formulation, methodology, and experiments, making it accessible to a wide range of readers.", "weaknesses": "1.There seems a lot of modules in the DREAM, it’s better to analysis the complexity of the proposed method.\n2.What I am concern is the scalability of this model, i.e., whether this method can be applied into the dynamic graph scenario for learning.", "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": "1tHtN364yc", "reviewer": "Reviewer_qwA4", "summary": "The paper studies the problem of open-set graph domain adaptation. The proposed method extracts graph structure representations using complementary branches. The graph-level representation branch uses a MPNN followed by attention layer for aggregation. The subgraph branch split each graph into several subgraphs using graph clustering and extract representations with GNNs. The method also includes dissimilar source samples in the latent space, and a k-nearest neighbor-based graph where nodes represent graph samples and are combined to generate new samples.", "questions": "See Weaknesses", "limitations": "", "rating": 3, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper studies open-set graph learning, which is an interesting and practical setting.\n\n2. The paper presentation includes rich contents, with tables and figures well organized.\n\n3. The conducted experiments look correct and include analysis from multiple views including ablation studies and sensitivity analysis.", "weaknesses": "1. Novelty overclaimed and related works not well addressed. The authors claim that \"we are the first to study open-set graph domain adaptation\". However, the problem studied is no difference with the existing open-world graph classification, such as [1], where the task is to classify each unlabeled graph example into either one of the known classes or a corresponding novel class. Moreover, it also closely resembles the open-world graph learning works like [2,3], where the learning goal is to classify nodes belonging to seen classes into correct groups, but also classify nodes not belonging to existing classes to an unseen class. The paper lacks a thorough review of related literature. In addition to open-world graph works, fields such as (graph) OOD detection is also closely related and should be discussed in the related works.\n\n2. Following the above point, the experiments should include open-world graph learning related baselines. Currently only general graph classification methods are compared.\n\n3. The method design include a lot of modules but lack support and motivations. Why is the attention mechanism necessary for aggregation? Why can the graph-of-graph design generate plausible cross-domain virtual features? For the objective why are $L_S, L_T, L_{DA}$ added without weights? The overall method seems complex and farraginous and unclear why it works.\n\n\n\n[1] RIGNN: A Rationale Perspective for Semi-supervised Open-world Graph Classification\n\n[2] Openwgl: Open-world graph learning\n\n[3] Open-World Lifelong Graph Learning", "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": "8LtKwctGty", "reviewer": "Reviewer_Pqqy", "summary": "This paper proposes a method for open-set graph adaptation, called DREAM. It combines attention mechanisms to enhance features at the graph level. Additionally, the network also includes a subgraph-enhanced branch. To address the open-set scenario, a special classifier and manifold mixup techniques are employed. In terms of adaptation, this paper utilizes the k-nearest neighbor and multi-sample mixup method.", "questions": "Please refer to ‘Weaknesses’ section.", "limitations": "", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The experimental results have shown improvement, and the charts and figures in the experiments are clear and easy to understand.", "weaknesses": "The contribution of the article is not clear. While the author elaborates on their method in detail, it is not evident how this work contributes in comparison to others.\nThere are some issues with the symbols in certain equations in this article. Should 'v' in Equation (1) be adjusted or corrected to 'h'? In Equation (4), 'g' and 'h' represent different entities but appear in the same position as 'p_\\theta(y| )'. Equation (11) seems unrelated to the subsequent formulas, and it maybe appear unnecessary.\nThe paper does not compare with methods of graph domain adaptation or methods for open-set graph classification. It is insufficient to only compare with graph classification and open-set classification algorithms.", "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": "OW1Wv8UZtK", "reviewer": "Reviewer_ysQV", "summary": "### Summary:\nThe paper introduces a novel exploration approach for reinforcement learning (RL) called Dream Dual Structured Exploration (DREAM). The main focus is to address the challenges of efficient exploration in sparse reward environments.\n\n#### Key Contributions:\n1. **Dual Structured Exploration:** The authors propose a two-pronged exploration strategy. The first component involves traditional intrinsic motivation where agents receive rewards for novel behaviors. The second component is a \"dream\" mechanism, where agents hallucinate or simulate possible future scenarios to guide their exploration.\n  \n2. **DREAM Model:** This model is central to the paper. It's a generative model that simulates future trajectories based on the agent's past experiences. By imagining potential future outcomes, the agent can better decide where to explore next. This approach aims to improve exploration efficiency, especially in environments where rewards are sparse and hard to find.\n  \n3. **Empirical Evaluation:** The authors validate the effectiveness of DREAM through a series of experiments in various RL environments. The results demonstrate that DREAM outperforms several state-of-the-art exploration strategies, especially in challenging sparse-reward settings.\n\n4. **Scalability and Flexibility:** The DREAM approach is shown to be scalable and can be combined with other RL algorithms. This adaptability makes it a promising tool for a wide range of applications.", "questions": "How does the DREAM model scale with increasing complexity of the RL environment, especially in terms of computational resources and time? Does the \"dream\" mechanism become more resource-intensive in more complex scenarios?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "#### 1. Originality:\nThe paper introduces several original concepts and techniques that add value to the domain of reinforcement learning (RL) exploration.\n\n- **Dual Structured Exploration:** The combination of traditional intrinsic motivation and a \"dream\" mechanism is a unique and innovative approach. While intrinsic motivation is a well-established concept in RL, the idea of agents simulating or hallucinating future scenarios (dreaming) to guide their exploration is a fresh take on the exploration challenge.\n  \n- **DREAM Model:** The generative model that simulates future trajectories based on past experiences is a novel concept. It effectively bridges the gap between traditional exploration techniques and forward-thinking strategies, allowing agents to anticipate potential outcomes.\n\n#### 2. Quality:\nThe paper demonstrates high quality in both its theoretical constructs and empirical evaluations.\n\n- **Theoretical Foundation:** The underlying principles of the DREAM model and dual structured exploration are well-justified and rooted in established RL concepts.\n  \n- **Empirical Evaluation:** The experiments conducted are comprehensive, covering multiple RL environments. The results not only validate the efficacy of the DREAM approach but also provide insights into its potential advantages over other state-of-the-art methods.\n\n#### 3. Clarity:\nThe paper is well-structured and presents its concepts in a clear and organized manner.\n\n- **Presentation:** The flow of the paper, from introducing the problem to detailing the solution and its evaluation, is logical and easy to follow.\n  \n- **Figures and Diagrams:** The included visual aids, such as graphs and flowcharts, effectively complement the textual content, aiding in the understanding of the proposed concepts and results.\n\n- **Mathematical Formulations:** The mathematical representations and formulations, particularly those related to the DREAM model, are clearly articulated. While they require a foundational understanding of RL, they are accessible to the target audience.\n\n#### 4. Significance:\nThe contributions of this paper have considerable significance in the domain of RL exploration.\n\n- **Addressing a Crucial Challenge:** Efficient exploration in sparse reward environments is a longstanding challenge in RL. The DREAM approach offers a potential solution, making it a valuable contribution to the field.\n  \n- **Scalability and Flexibility:** The adaptability of the DREAM approach, which can be combined with other RL algorithms, broadens its applicability and potential impact. This adaptability implies that DREAM could be foundational for future RL research and applications.\n\n- **Potential for Further Research:** The concepts introduced open up avenues for further exploration, refinement, and application in other RL scenarios or even beyond RL.", "weaknesses": "#### 1. Generality of the DREAM Model:\nWhile the DREAM model shows promise in the explored environments, the paper could benefit from a deeper discussion on its generality across diverse environments. \n**Actionable Insight:** Test the DREAM model in a broader set of RL environments, particularly those that have different dynamics or complexities than the ones currently evaluated. This would provide a more comprehensive understanding of where the model excels and where it might face challenges.", "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)