GOTHAM: Graph Class Incremental Learning Framework under Weak Supervision
Authors: Aditya Hemant Shahane
Prathosh AP
Sandeep Kumar
Venue: Accepted by TMLR ()

Abstract: Graphs are growing rapidly and so are the number of different categories associated with it.  Applications like e-commerce, healthcare, recommendation systems, and various social media platforms are rapidly moving towards graph representation of data due to their ability to capture both structural and attribute information. One crucial task in graph analysis is node classification, where unlabeled nodes are categorized into predefined classes. In practice, novel classes appear incrementally sometimes with just a few labels (seen classes) or even without any labels (unseen classes), either because they are new or haven't been explored much. Traditional methods assume abundant labeled data for training, which isn't always feasible. We investigate a broader objective: Graph Class Incremental Learning under Weak Supervision (GCL), addressing this challenge by meta-training on base classes with limited labeled instances.  During the incremental streams, novel classes can have few-shot or zero-shot representation. Our proposed framework GOTHAM efficiently accommodates these unlabeled nodes by finding the closest prototype representation, serving as class representatives in the attribute space. For Text-Attributed Graphs (TAGs), our framework additionally incorporates semantic information to enhance the representation. By employing teacher-student knowledge distillation to mitigate forgetting, GOTHAM achieves promising results across various tasks. Experiments on datasets such as Cora-ML, Amazon, and OBGN-Arxiv showcase the effectiveness of our approach in handling evolving graph data under limited supervision.

Published in Transactions on Machine Learning Research (04/2025)
GOTHAM: Graph Class Incremental Learning Framework under Weak Supervision
Aditya Hemant Shahane Deportment of Electrical Engineering Indian Institute of Technology Delhi
ee:2484350ee.itd ittee.iid..oc.
Prathosh A. P.
prathosh Mattsooshhisc.coo Niscc.c..in
Department Electrical Communiiatiinn Engineering Indian Institute of Science Bengaburu
Sandeep Kumar
ksandeep iild in
Department of Electrical Engineering
Yardi School of Artificial Intelligence
Bharti School of Telecommunication Technology and Management
Indian Institute of Technology Delhi
Reviewed on OpenReview: https: // openreview. net/ http://wwwwwhaaoo/////////o/aaaa
Abstract
Graphs are growing rapidly, along with the number of distinct label categories associated with them. Applications like e-commerce, healthcare, recommendation systems, and var- ious social media platforms are rapidly moving towards graph representation of data due to their ability to capture both structural and attribute information. One crucial task in graph analysis is node classification, where unlabeled nodes calegorized into predefined classes. In practice, novel classes appear incrementally sometimes with just few labels (scen classes) or even without any labels (unseen classos), either because they are new or haven't t. been explored much. Traditional methods assume abundant labeled data for train- ing, which isn't it always feasible. We investigate a broader objective: Graph Class Incremen- tal Learning under Weak Supervision (GCL), addressing this challenge by meta-training on base classes with limited labcled instances. During the incremental streams, novel classes have few-shot zero-shot. representation. Our proposed framework GOTHAM effi- ciently accommodates these unlabeled nodes by finding the closest prototype representa- tion, serving as class representatives in the attribute space. For Text-Attributed Graphs (TAGs), our framework additionally incorporates semantic information to enhance the rep- resentation. By employing teacher-student knowledge distillation to mitigate forgetting, GOTHAM achieves promising results across various tasks. Experiments on datasets such as Cora-ML, Amazon, and OBGN- showcase the effectiveness of our approach in han- dling evolving graph data under limited supervision. The code implementation is available here: https::/encr.pu////
1 Introduction
Graph-structured data are ubiquitously used in many real-world applications, such as citation graphs Cum- biomedical graphs
mings Nassar 2020 Tang et al.
2008),
(Subramanian et al. 2005 Zhai et al. 2028
circuit optimization (Shahane et al.
2023
Hakhamaneshi et al. 2023) and social networks (Qi al.
2012
Recently, Graph Neural Networks
(GNss have been proposed [Cao al.
2016
Subramanian et al.
2005
Henaff al. 2015 Xu et. al.] 2019
Kipf
Welling 2017
Veličković et al.
2018
Hamilton al.] 2017 7 to

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model graph-structured data by leveraging the structural and attributed information along the graph. As central task in graph machine learning, node classification (Wang et al. 2020b; Xhonneux et al. 2020: Wang et al. 2021b Zhu et al. 2021) has achieved remarkable progress with the rise of GNNs. While these methods concentrate on static graphs to classify unlabeled nodes into prodetermined classes, real-world graphs are
dynamic. In practice, graphs grow (You et al. 2022 Lu el al. 2022 Tan et al., 2022 rapidly incorporating nodes and edges belonging to novel classes incrementally. For example, (1) think of a biomedical graph. Each node represents a rare disease category, and edges show how these diseases relate to each other. As new disease categories emerge, they are gradually added to this graph. Such methods significantly aid the drug discovery process. (2) For food delivery systems nodes correspond to various zip codes and the edges indicate the spatial distances between them. As the company expands its reach, new zip codes are systematically incorporated into this graph, lacilitating efficient supply chain management. GNNs lypically require a large amount of labeled data to learn effective node representations (Ding et al. 2020b Zhou et al.) 2019b). In practice, catching up with these newly emerging classes is tough, and obtaining extensive labeled data for each class is even harder. The annotation process can be extremely time-consuming and expensive (Ding) et al. 2022 Guo et al.) 2021 Wang et al. 2022c). Naturally, it becomess crucial to empower models to classify the nodes from: limited labeled classes and those unseen classes having no labeled instances, collectively referred to as weakly supervised. In this regard, we investigate the problem of Graph Class Incremental Learning under Weak Supervision (GCL).
Recent studies (Lu et al. 2022: Tan et al. 2022), have delved into a specific aspect of the broader problem, termed graph few-shot class incremental learning (GFSCIL). This approach operates under the assumption that the base classes possess abundant labeled instances, while novel classes introduced during streaming sossions always have representations in the form of k-shots. Additionally, there is separate line of rescarch (Wang et al. 2021b 2023b] Hanouti & Borgne| 2022), focusing on zero-shot node classification. Furthermore, addressing the issue of limited labeled data availability during base training, which impacts the model's generalizability for better node representations during finetuning, is discussed in Wang et al.] Finally, studies like (Wang et al., 2023a] Wang et al.) address few-shot node classification. Graph data, existing in a non-Fuclidean space with constantly changing network structures, poses unique challenges. Unlike the progress made in class incremental learning in computer vision, incremental learning in graphs remains relatively unexplored. Therefore, for developing framework for GCL the key challenges include: (1) Can the model learn good node represenlations wilh just k-shols for base training clusses during fineluming? (2) Is there a universal frumework to address both the GFSCIL problem (classes in novel streams represented by k-shots) and the GCL task (including classes with no truining instances)? and finally, (3) How to prevent forgetting old knowledge while learning new information?
Sometimes, Less is Plenty. By heuristically sampling the neighborhood corresponding to the k-shot rep- resentations, our approach extends the support set for each class. These prototypes serve a crucial role in steering the orientation of both base and novel classes within the graph during streaming sessions. We adopt the popular meta-learning strategy, called episodic learning (Finn et al. 2017,, which has shown great promise in few-shot learning. Wc propose Graph Orientation Through Heuristics And Meta-learning (GOTHAM), an incremental learning framework that elfectively addresses all the aforementioned issues. Finally, the teacher-student knowledge distillation in GOTHAM prevents catastrophic forgetting. The pa- per is structured into seven sections, focusing on class orientation through prototypes, proposed approach, experimental analysis, and concluding remarks.
2 Related Work
Continual Graph Learning:
The Continual Graph Learning Benchmark (CGLB) ZZHAGG et al. 2022
catogorizes tasks in evolving graph structures into Continual Graph Learning (CGL)) Wang et al. 2022a Xu
et al. 2020 Daruna el al.) 2021 Ahrabian et al. 2021 Kou et. al. 2020), Dynamic Graph Learning (DGL)
Galke et al. 2020 Wang et al. 2020al Yu et al. 2018 Han et al. 2020), and Few-Shot Graph Learning
(FSGL) (Zhou et al. 2019a Guo et al. 2021 Yao et al., 22000p. CGL focuses on mitigating catastrophic
forgetting without relying on past data, DGL captures temporal dynamics with access to historical data, and FSGL enables rapid adaptation to new tasks using meta-learning. Our work lies at the intersection of
2

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CGL and FSGL. We review related work on few-shot, zero-shot, and incremental learning for graph- tasks, positioning our contributions within this broader framework.
Few-Shot Node Classification: Despite several advancements in applying GNNs to node classification
tasks (Kipf & Welling, 2017 Veličković et al. 2018: Hamilton et al., 2017 Wang et al. 2022b more recently,
many studies (Ding et al. 2020b] [Wann et al. 2021a Zhou et al.] 2019b Wang et al.p have shown that the
performance of the GNNs severely affected when number of labeled instances are limited. Consequently,
there has been surge in interest in the area of few-shot node classification. These works are broadly
categorized into two main streams: (1) Optimization based approaches [Zhou et al.
2019b Huang & Zitnik, 2023a
2020 Liu et al. 2021 Lan et al. 2020) and (2) Metric based approaches (Wang et al.
Wang et al.) [Snel]
et al. 2017a Yao et al. 2020). These approaches operate under the strong assumption that information for
all classes is available simultaneously, which renders them ineffective for class incremental learning scenarios.
Zero-Shot Classification: As emerging classes continue to grow in dynamic environments, interest in a related field called 'no-data learning' is surging. However, the existing approaches (Wang et al. 2021b 2023b;
Hanouti & Borgne 2022 Lu et al. 2018 Wan et al.) 2019b Song et al., 2018) suffer from two key limitations:
(I) Many of these methods assuine access to unlabeled instances of unseen classes during training, limiting their gencralizability and (2) They typically only classify test instances into the set of unseen classes, which
isn't practical. In computer vision (Verma et al. 2019 Wu et al. 2023): some approaches have addressed these issues and even integrated incremental learning successfully. However, similor advancements in the gruph domain are lacking.
Class Incremental Learning: also known lifelong learning has been extensively studied across various computer-vision tasks (Li & Hoiem 2018 Rebuffi et al. 2016 Hou ct al. 2019). However, these approaches often assuine access to extensive labeled datasets during streaming sessions, which is impractical. Few- shot class incremental learning (FSCIL) has been introduced in the realms of image classification in (Tao ctt al. 2020: Cheraghian et al.) 2021]. Unlike images, graph data exhibits non-i.i.d characteristics, making incremental learning more challengig. Most recent works (Lu et al., 2022: Tan et al. 2022) have addressed the graph few-shot class incremental learning framework. However, a common but naive assumption these approaches is the abundant availability of base classes, which often isn't the case in practice. Our proposed framework aims to bridge the gap by directly addressing the limitations found in various existing works.
3 Methodology
In this section, we begin by presenting the problem and explaining the key terms related to it. Then, we introduce some foundational concepts that will help build our formulation. Finally, we outline several crucial modules and provide detailed explanations for each.
3.1 Problem Statement
We denote an attributed graph as GVVV", E',x', X'), where V = =²= [of, ub, ,.....,,, 15,....,uf,
is the vertex set and E C V² x 4* is the edge set. X 22..,, E Rlv is the node feature matrix where d is the feature dimension. In the base training stage, we have base graph Ghase with [[base] number of classes. Due to weak supervision, the number of labeled samples corresponding to Obuse is extremely limited. In the streaming sessions, evolving graphs are presented {G', G²...., GT) with {C), (C',c?,... "r,,,..,,,0 CT) sets of classes. In the GFSCIL. framework, every streaming session introduces 5Ch new classes, each represented by k-shots. It is essential to note that 50 n 8C 0 and Ct =Chase + + 8C
Problem definition: Graph Class Incremental Learning under weak supervision
In cach strcaming session, G introduces 8C* new classos, which are divided into two categories: 8C and o0 SC classes, termed as seen classes, have few training instances (lypically k-shots), while 8C classes, referred to as unseen classes lack any training instances. During the streaming session, we encounter both 50%J and 8C classes, forming the class set denoted as C C U Ct.U where stands for seen classes and denotes unscen classes at time 't". Specifically, C Chose + Ei 80 and CtU = = 804,, Additional information, in terms of class semanties descriptions (CSDs), is provided for all the classes. The
3

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?
?
?
?
?
?
?
?
Few-shot nodes
Zero-shot nodes
Unlabeled nodes
Semantic Attribute
Novel Classes
?
(A)
Base Graph
(B) Streaming Graph Snapshots
base
Chase
Gttremm [ C? G ++ Citream = C2, C!
Figure 1: Graph Class Incremental Learning under Weak Supervision:(A) In the base graph Glose the base classes Chase have extremely limited labeled instances. (B) In the streaming sessions, graph G* has C number of classes. Depending upon the availability of the training instances, the classes are further classified as C (seen classes) and C (unseen classes). Seen classes are represented with k-shots, along with semantic altributes (CSDs). For unseen classes, only CSD information is available. The goal, classify the unlabeled instances into Of classes encountered so far (Lu et al., 2022 Tan et al. 2022
CSD matrix is denoted as A, = {a=1, a..,..., a.c+) A U 1 with each row containing description of class. Class semantics descriptions (CSDs) have been extensively studied in Wang et al. (2023b); Hanouti & Borgne (2022); Wang et. al. (2021b); ; Ju et al. (2023). Throughout the paper, we interchangeably refer to "class semantics descriptions (CSDs)* and "semantic attributes'. The goal is to classify all the unlabeled nodes (belonging to both seen and unscen classes) into C classes encountered so far.
Labeled training instances called 'support sets' (8), while unlabeled testing instances termed 'query sets" (Q). Unseen classes, which lack training instances, have their unlabeled instances presented only during inference.
3.2 Preliminaries: Label smoothness and Poisson Learning (Random walk perspective)
To enhance classification accuracy in scenarios with extremely low labeled data, leveraging additional samples is crucial. Semi-supervised learning, which combines labeled and unlabeled data, has shown significant improvements by utilizing the topological structure of the data (Zhu et al. 2003 Zhou & Schölkopf 2004 Zhou et al.) 2003). Methods such as Poisson learning (Calder et al. 2020) have further extended the concept by incorporating structure-based information on graphs through random walks. The underlying assumption that samples that are close each other can potentially share similar classes. Previous rescarch (Solomon et al. 2014 Belkin al. 2006 Kalofolias] 20166), has emphasized the importance of the smoothness assumption for label propagation in scenarios with extremely low label rates. These findings form the basis of our proposed approach, which extends support sets through random walks without requiring extensive labeled nodes. This extended support set enhances the representation of prototypes for each class, leading to improved classification performance.
3.3 Prototype representation
Definition: The prototype a class corresponds to a representative embedding vector which captures the overall characteristies of a class in the attribute space. Prototype representation has boen extensively studied
across various works (Snell al. 2017b Rebuffi al. 2017 Lu al.) 2022 Tan al. 2022) in the domain
of few-shot representation learning.

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The foundational works, (Snell et al. 2017b Rebuffi al. 2017) suggested using the mean of the support
samples for prototype representation. Building upon this foundation, subsequent studies (Tu et al. 2022 Tan
et al. 2022) introduced attention-basee
prototype generation techniques. These approaches were designed to address challenges such as class imbalance and mitigate biases arising from noisy support sets. Recent studies (Wang al. 2023a) highlighted the importance neighborhood sampling techniques, such as Poisson learning and personalized page rank (PPR), obtain a more informed support set.
MLP
P C
MLP 8
GNN,
P c
Pes
P u
P seen Prototype representation
(1) Prototype representation ( Pe s) w/o semantics ($een classes)
(ii) Prototype representation (X P. s) with semantics (Seen classes)
(iii)
P c, P c, U with semantics (Seen Unseen classes)
Figure 2: Prototype representation: For the GFSCIL task, we propose representing prototypes (Pe,s) using the averaged extended support set, illustrated in (i). As demonstrated in (ii), integrate semantic attributes (CSDs) to enhance the prototypes (Pe.s) in TAGs. For GCL tasks with classes having training instances, the semantic attributes (CSDs) are encoded as prototypes (Pe.)).
However, these approaches (Snell et al. 2017b Rebufii et al. 2017 Lu et al. 2022 Tan al. 2022 Wang
et al. 2023a suffer due to the weak supervision setting. Hence, we additionally leverage the label smoot hness principle to gather the local neighborhood of the support nodes. The extended support set contains the labeled support nodes and the unlabeled neighbors gathered through random walks. The final node set for a class can be represented as S2,c = Se VV, where Sc, corresponds to nodes with labels and Vo is the sampled unlabeled node set for class C belonging the seen classes. The prototype thus obtained will be the average of the embeddings of all the nodes within the extended support S2,0 represented as:
1S..cl
Pc,s = SS Σ
1
GNN, (v:)
(1)
where, GNN, (e:) corresponds to embeddings of the node 04, which are generated by aggregating information from its neighbors. Refer to Figure 2(i) for further details. In Text Attributed Graphs (TAGs), refer to Figure 2(i),, we enhance the protolype representation by incorporating semantic attributes associated with each class. The semantic loss, which will be elaborated upon later, facilitates the integration of attribute and semantic space. The encoded semantic attributes MLP (a.c), for the same seen class C' are merged with the original prototype to obtain the new prototype representation: Pc.s Pe.stMLPP.... For the GFSCIL framework, the prototype will consist of Ps (Pc,s, Po.s). depending on the type of graph used as input. For a class Č, with no training examples (where Ć E C*UU), we rely on additional information in the form semantic attributes. Refer to Figure (iii) for further insights into this representation. The prototype representation for such unseen classes is: Pe. GNNN (a.c), where GNNg (a.c), represents the vector representation of the semantic attributes, where each attribute connects only to itself (self-loop) in its adjacency. In the GCL scenario, the prototype representation set denoted as P {Po,s, Pc
3.4 Transferable Metric Space Learning
Graphs constantly change, posing a challenge in how different node classes are positioned in metric space. As information for all classes isn't available once, it crucial to establish criteria to prevent overlap
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between old and novel classes. Additionally, distinguishing novel classes as seen unseen adds another layer of complexity, especially when some classes have very few samples while others appear only during inference. To address these challenges, the model is trained using the following loss functions:
Intra-class clustering loss: The goal here to group instances that belong to the same class together.
Several data augmentation strategies have been suggested previously (Li al. 2018 Verma et al. 2020 Ding ett al., 2018 Qiu et al., 2020), which generate consistent samples without affecting the semantic label. How- ever, in few-shot scenarios, these methods can introduce bias by generating samples that do not fully capture the true distribution of the class. To avoid this, we take simpler approach: sampling the neighborhood of the original node to obtain a correlated view. In our case, the original nodes correspond to the labeled k-shot representative nodes for each seen class. Neighbor nodes are sampled with the approach discussed in section: 3.2. The class prototype responsible for grouping these nodes, employing the clustering loss defined as:
max m (u,) Pj,s|1173 iEn, keny max GNN, (vk) - 1..11-7:0)
Lets,5 == |C
Σ JEC
(2)
Here, Ct. refers to the set seen classes encountered up to the current streaming session at a time "t" The number of samples for each class from the extended support set is represented by "ny". The parameter 'n' defines the boundary from the prototype. Samples for a certain class are encouraged stay within this boundary. The max(.) function ensures that only samples outside the boundary contribute to the loss.
Inter-class segregation loss: Unlike existing augmentation strategies [Li et al. 2018 Verma et al. 2020;
Ding et al.) 2018 Qiu et al. 2020), which generate correlated pairs within a class, we do not rely on explicitly sampling negative pairs. Instead, we promote class separability by loveraging representative embedding vectors, known as class prototypes. These prototypes enhance dissimilarity between samples from different classes, preventing class overlap among all classes (C*) encountered up to the current streaming session time 't", The segregation loss is defined follows:
Lseg == 104
Σ
log||P, -pll
(3)
JEC PEC
Here, C = (Ct. U CLU) is the set of all classes, including both seen and unseen classes. Similarly, the prototypes belong to the prototype representation set P (Po.s. This loss function applies to both seen and unseen classes.
Semantic manipulation loss: Each modality offers a unique perspective on class representation, con- tributing to a more comprehensive view of prototypes. While extensively explored in the image domain (Zhang al. 2023 Xing et al.] 22019; Xu & Le 2022 Guan et al. (201)), graphs provide an additional advantage by incorporating structural information (orientation) associated with each class within the graph. Class-somantic descriptors (CSDs)
semantic attributes, derived from class names and descriptions, are encoded and represented as MLP & (a.c) for C' E C*.S The objective is to align the encoded semantics with the prototypes of the seen classes. The corresponding loss function is expressed as follows:
Tisem.S
Σ JECUS
||MLP (A.j) - -P.s
(4)
This loss function is responsible for integrating the attribute and semantic space. The newly learned semantic embeddings are later merged to obtain new prototype representation (discussed previously). This loss function is specifically applied only to seen classes.
Knowledge refinement through experience: As the graph evolves incrementally, the learner model may tend to forget previously learned information when exposed to new knowledge, leading to catastrophic forgetting. To address this, it's crucial to preserve the previously acquired knowlodge while integrating new information. This process is known as knowledge distillation. Among various techniques (Zhang et al., 2020: Rezayi et al.] 2021 Feng et al. 2022), we opt for the teacher-student approach. The teacher model distills

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both attribute and semantic information using the following loss function:
L
1
Σ
GNN
(vs) - GNNatudent (wi)
(5)
0
1C(
VERg(t
MLPleacher pteacher (azz)
MMLPsuuden (aaj)
1
(6)
10(--1),9
MMPP preckeer (aas)
MLPssadent (azs)
jEC(t-12,8
The total loss is: LKDSS A1 Lemb,s + X2 Latign, For the GFSCIL problem, where text attributes are not available, knowledge distillation is solely performed across the node-embeddingg (attribute information). This loss function applies only to seen classes.
4 Understanding Prototype Distortion in Evolving Graphs
Although we introduce various components maintain model performance in continual learning setup with class increments, the key question remains: Can protolype represenlations truly be preserved across evolving data streams? The answer depends on how well GNNs express and adapt these prototypes as the graph evolves. In this subsection, we evaluate the stability of prototype representations within an evolving graph.
GNNs suffer from representation distortion over time Liang et al. [2018) Wu et al. 2022 ; Lu et al. (0223)
leading to gradual performance degradation. This shift can result from the continuous addition of nodes and edges, structural changes, new feature introductions, or the emergence of new classes. Additionally, the lack of labeled data further increases the challenge. As shown in Figure 5 our experimental evaluations confirm this trend model performance steadily declines as novel classes are introduced over incremental stages. To better understand this degradation, we build on insights from Lu et al. (2024), and extend the concept of representation ion distortion to prototype distortion in our case. Before presenting the results, we first outline the following assumptions:
Assumptions: We consider an initial graph Glase (Vo, E X with nodes. (1) The feature matrix X follows continuous probability distribution over nxd (2) At each time step t, new nodes belonging classes indexed 8C* added, connecting to existing nodes with positive probability while preserving existing edges. In citation networks, for instance, the new papers cite existing ones, maintaining stable relationships. Over time, emerging research fields introduce papers from previously unseen domains. (3) The feature matrix X has zero mean conditioned on prior graph states, i.c., "[x"0"|G" (Go..., G*-1] Oa. 14 2 This follows common assumption in deep learning models.
We specifically examine the prototypes corresponding to the classes in AC = C' n C++1, representing the shared classes between consocutive time steps obtained through the GNN parameterized by 8. We define the expected distortion for protolype P: at time as the expected difference between its representation at time and t + 1, given by: A(P,, öt) (t+++t++) (t) where A(P,, öt) denotes the expected distortion of prototype P; over the time interval öt.
Theorem:
f represents the veclorized parameter set {ag Wybb)))f where each coordinate 0g is drawn from the uniform distribution U(,, centered at 0 (optimal parameters), the expected deviation A(P., 5t) due to the perturbed GNN model at time 2 O for prototype P., where i E AC, is lower bounded by:
[(nite)) d,(P))
1 )²
A(P,, 5t) 2t) 2E
Σ
||
KEN((P)
where the set Ny(P.); denotes the neighborhood comprising the extended support set of the prototype P. and (P)),), (P.) refers to degree information respective time steps. The proof of the theorem can be found in the Appendia.

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Under the ever-growing assumption, distortion is unavoidable, and Theorem confirms that the expected distortion of the model output increases strictly over time. This effect is particularly pronounced for larth models, emphasizing the inherent trade-off in continuously evolving systems.
Remark:
5 Proposed Algorithm
In this section, we present our proposed framework: Graph Orientation Through Heuristics And Meta-learning (GOTHAM). At any given time t, we have graph G as input, where the total classes C = C encompass both the seen (few shots) and the unseen (zero shots) class representation. The choice of framework type depends on the input, as illustrated in Figure 3. Based on the input, the following procedure is used lo perform the node classification:
(1) Episodic Learning: Based on the choice of framework, tasks (7) are sampled for the corresponding graph G Each task T p(T), drawn from the task distribution, consists of an extended support set (8%) and query set (Qt) required for episodic learning. Episodic learning, which has demonstrated great promise in the area of few-shot learning (Rebuffi et al.) [017]] TTn et al. 2022 Huang & Zitnii 2020 Vinyals et al. 2016 Zhou et al. 2019b), involves sampling tasks and learning from them, rather than directly training and then fine-tuning over batches of data. (2) Prototype representation: For each support set (S),, prototypes are generated for all the classes. If the class set. C contains samples only from the seen classes (i.e. Ct =C*S), the prototype set will be Ps and the problem becomes a GFSCIL input, which offer additional semantic attribute information,
setting. Furthermore, if TAGs given it results in new prototype representation. For the GCL setting where C C U CA. the prototype representation set is denoted as P = prototypes, meta-training is performed using a combination of loss functions. In the GFSCIL scenario without TAGs, the model is trained using clustering loss and separability loss. With TAGs in both GFSCIL and GCL scttings, semantic loss also incorporated. The corresponding meta-training loss defined as: Ltrain = Q1 Lela.s + a2 Leeg a3 Leem,S. Meta-learning performed on the base graph. Once the model trained the support set (S)), its performance is validated the corresponding query set (Q)). The model is then frozen and used for meta-finet meta-finetuning. During meta-fnnttuing, the loss is defined as: finetune := 01 Lets.S + Q2 Leeg + a3 Lsem.s s + 04 LKD.S. (4) Knowledge distillation: During finetuning, knowledge distillation preserves previously learned class representations. The corresponding loss is defined as: LKD.S == A Lemb.s + X2 Sa (5) Node classification: For any graph G as input at time L, the model ultimately performs C'-way node classification.
(3) Mcta-learning and Finctuning: After obtaining
Algorithm GOTHAM III.o
Input: G Ar,
Output: Label prediction query nodes in Q' T
3: # Initialise 8, o; Sample T T' p(T)
Base Training (L= 0, Chhae)
5: for T'= (8% UQ) Chione
Prototype (P (Posase,s) using eq:1 Compute Lerain on St Obtain node labels for Q' Update 0, using gradient descent.
10:
end
11: # Freeze the trained model
12: Finetuning (t > 0, Cd Cdose Eim SC")
13: # Load pre-trained model; Perform knowledge distillation
14: for T (St U Q') C*:
15:
Prototype (Pot) using eq:1 Compute Lfinetune on S
16:
17:
Obtain node labels for Q'
18:
Update 8, using gradient descent
19:
end

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2
3
5
Few Semantis Zero
Type
Episodic Learning
Prototype representation
Knowledge
X
COTHAM
Clustering loss
Distillation
MLP
x
GOTHAM
GOTHAM
-
O
P
P
Semantic Alignment
5 U O'
MLP
GNN. h
Node Alignment
Node Classification
Semantic 50g
GNN
+
P..
+
Peu
5o0s Congpppnno 1
GNN
S.T
OT
(Protolypes are genercted for wapport wel of wach Leak))
Gt
Graph Orientation Through Heuristics And Meta-learning (GOTHAM I11.0)
Figure 3: GOTHAM III.o: At any time f, the framework uses the graph G as input. The total classes are C === C CLU The steps are: (1) Create tasks (T') with support sets (S) and query sets (Q) for episodic learning. (2) Obtain prototype representations for each support set (S)) (3) Apply loss functions. (4) Use
knowledge distillation to transfer knowledge from the teacher model to the student model. (5) Perform node classification.
6 Experiments
Dalasets: We assess the performance of our proposed framework, GOTHAM, on three real-world datasets- Cora-ML, Amazon, and OBGN-Arxiv. We summarize the statistics of the datasets in Table ! For more details about the dataset refer to the Appendie.
Table 1: Statistics of datascts used in the experiments
Dataset
Nodes
Features
Classes
Class Labels
Tasks GFSCIL, GCL
Cora-ML
2,708
1,433
7
Neural Network, Rule Learning, Reinforcement Learning, Probabilistic
Methods, Theory, Genetic Algorithms, Case-based
Amazon 13,752
767
10
Label names Unavailable
GFSCIL GESCIL, GCL
OBGN-Arxiv
169,343
128
40
Arxiv as na, Arxiv cs mm, Arxiv cs lo, Arxiv es cy, Arxiv cr, Arxiv de, Arxiv es he, Arxiv es cv, Arxiv cs ai,
Experiment settings: We partition the dataset into base stage and multiple streaming sessions respectively. We assess our framework across two main problem settings: (1) Graph Few-shot Class Incremental Learning
(GFSCIL) and (2) Graph Few-shot Class Incremental Learning under Weak Supervision (GCL). Cora-MI. and OBGN-Arxiv are Text-Attributed Graphs (TAGs), enriched with semantic attributes. We generate semantic attributes/ Class Semantics Descriptors (CSDs) using 'word2vec' (Mikolov et al. 2013 which transform textual descriptors into word embeddings. To simplify computation, we utilize Label- CSDs Waan ct al. 2021b). Initially, we evaluate all datascts under the GFSCIL setting. For the Cora-ML and Amazon dataset, we choose five classes as the novel classes and keep the rest as base classes, and adopt 1-way, 5-shol setting, which means we have 6 sessions (1 base sessions + 5 novel sessions). For the OBGN-Arxi dataset, we keep ten classes base classes and the rest as novel, employing a 3-way, 10-shot setting (totaling sessions). Our framework seamlessly integrates semantic attribute information Cora-ML and OBGN-Arxiv. Finally, our framework under the GCL setting, focusing on Cora-MI. and OBGN-Ars to demonstrate its

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Published in Transactions on Machine Learning Research (04/2025)
During each streaming session, one class is designated zero-shot, lacking training instances. Unlabeled instances for these classes are only available during inference. All the experiments are performed five times to ensure reproducibility. The top results are highlighted in bold, while the second best ones are underlined.
effectiveness.
Baseline methods: In the GFSCIT, setting, we benchmark our results against several state-of-the-art frame- works for few-shot class incremental learning and few-shot node classification, including: Meta-GNN (Zhou et al. 2019b), GPN (Ding et al., 2020a), iCaRL (Rebuffi et al., 2017]. HAG-Meta (Tan et al. 2022). Ge- ometer [Lu et al, 2022) and CPCA (Ren et al. 2023). Unlike previous methods, during base training, we provide only a limited number (5- shots for Cora-ML and Amazon and 10-shots for OBGN-Arriu) of labeled instances for each class. In streaming sessions, novel classes receive k-shot represent itons.. In the GCL setting, where novel classes have both few-shot and zero-shot representations, we compare against zero-shot learning frameworks with inductive learning as baselines. These approaches include DCDFL, (741 2024). GraphCEN (Ju al., 2023), (CDVSe, BMVSc, WDVSc) (Wan et al., 2019a) and Random guess, introducod naive baseline. Unlike the traditional approach, the seen classes have only limited labeled instances (5- shots for Cora-ML and 10-shots for OBGN-Arzie) available for training, and unseen classes have semantic attributes only. Under the GCL setting, the unlabeled instances will be classified into C" classes encountered, resembling a generalized zero-shot with inductive learning framework. A detailed summary of the baseline methods and hyper-parameters employed is available in the Appendia.
Graph Few-shot Class Incremental Learning (GFSCIL): We conducted experiments on the Amazon dataset, focusing on the GFSCIL problem as previously described. The results, detailed in Table 2 show average improvement of around 6% across various streams. Visualizing the class prototypes generated by the GOTHAM framework reveals distinct separations among classes across streams, ensuring consistent performance.
Table 2: GFSCIL setting: (Left) Model performance (%) on the Amazon dataset under GFSCIL setting, (Right) Visualization of class prototypes for the Amazon datasct across different streaming sessions.
Amazzn (L-way 6-2bot CFSCIL setting)
Stream
Base
31
344
Meta-GNN
99.60
82 63:13
17.75 77.75
70.52
67
GPN
74
T3.40
65.11
63.36
:Caft.
66.20
47.33
39
35.
29.53
29
HAG-Meta
95.43
88.76
76.67
09:58
67:21
01.86
GEOMETER
95.45 -4
90.05
77 36
74.27
73.08
74.36
CPCA
95.37
87 96
83.57
77. 1.3
76.37
08 32
COTHAM L.
20.01
00.01
88.80
84.35
78.52
73.81
Vagain
05.74
00.00
Clas: Prototyper Arnzon Dotoset
We extend our experiments to the Cora-ML and OBGN-Arxiv datasets, both Text-Attributer Graphs (TAGs) enriched with semantic attributes. Following the previously outlined experimental conditions, GOTHAM achieved an average improvement ranging from 6.4% to 13.5% over the baseline methods. We explored two variants of the framework: GOTHAM Lo, which solely relies on feature-based information, and GOTHAM IL., which integrates semantic attributes. Table 3 demonstrates that incorporating semantic attributes in GOTHAM IL. notably enhances performance for both datasets.
Table 3: GFSCIL with semantics: Node classification accuracy (%) in the GFSCIL setting- leveraging se- mantic attributes for enhanced class representation on Cora-MI, and OBGN-Arxiv datasets with GOTHAM.
Core-Mi
CFSCIL
OBGN Arxiv 10-shot GFSCIL
Rg
25
3g
2gg
Mcin-GNN
51
Mein-GNN
20.17
20.53
30.12
HAG--Mtt
MAG-Matta
GEOMETER
98.46
$4.50
62.76
CEOMETER
80.08
22.22
CPCA
07.67
20.50
30.96
OPCA
60.71
80
GOTHAN
COTHAM
72.40
GOTHAM
Kggsin
%gaain
Graph Class Incremental Learning under Weak Supervision (GCL): In a broader problem setting where novel classes have both few-shot and zero-shot representation, conducted extensive experiments
10

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Published in Transactions on Machine Learning Research (04/2025)
the Cora-ML and OBGN-Arxiv datasets. The results in Table indicate average improvement of 7% to 54% across various streams over the baselines, showcasing the ellectiveness of our framework.
Table GCL setting: Node classification accuracy (%) on the OBGN-Arxiv dataset under the GCL
setting. In each streaming session, one class is designated zero-shot, lacking any training examples.
AIsiN-Ardiv (2-way 10-shnt, Doshat (GCIL. entting)
Stream
51
5g
S-
5g
18.10
12.50
03:44
05.00
CDVSe
85
50
0/
37.
25
11.48
BMV3c
68.35
51.54
44. 25
38.
35. 33
27.22
21.95
20.
19.78
10.58
WDVSc
67.22
50.98
45. 02
36. 78
29. 54
20.77
21.87
18.34
16.88
11.50
07.58
GrapECEN
27.13
02.37
51.76
33.42
28: 92
18.50
15.38
10.
08.92
08.50
06.53
DCDFL
64.66
53.42
46.06
32.76
30.42 48
30.07
28.44
20.89
24.15
22.00 23.00
10:62
COTHAM IIL.o
82.91
68.11
$9.90
47.08
43.057
435.31
38.76
35.44
$4.00
322.53
300.28
76gain
07.49
15.78
43.27
41.07
43.20
47.05
64.333
We conducted detailed analysis our framework across three different aspects: (A) Contribution of different loss functions: Various loss functions contribute differently to optimal model performance. For this analysis, we selected the Cora-ML dataset, and the corresponding plot is available Figure (A). (B) Support set sampling: We categorized the dataset into small, moderate, and large-sized graphs. To ensure generalizability across other datascts, performed support set sampling using k-hop random walks, with the ideal hop length observed between 2-4 hops from the labeled nodes. Refer to Figure 4 (B) for more details. (C) GNN backbones: We examined the role of different GNN architectures within the GOTHAM framework for the Cora-ML and Amazon datasets, Interestingly, performance remained consistent across different architectures, indicating model-agnostic behavior. Refer to Figure (C) for more details.
Ablation Study:
100
100
100
95
90
90
90
85
Car--ML
GAT
80
70
Clustering
75
Cova-MLL
Amrzon
60
Custering + Segragationn
Clustering Segragation
70
Amazon
OBGN- AINN
60
IKN
Clustering Segregation
Base
s1
52
53
54
Base
Figure 4: (A) Contribution of different loss functions on the Cora-ML dataset. (B) Support set sampling: determining ideal randon-walk length. (C) Different GNN backbones on Cora-ML and Amazon datasets. (A) and (C) displays performance streaming sessions, while (B) shows performance random-wald length.
Figure (5) presents a detailed analysis of the Graph Class Incremental Learning under Weak Supervision (GCL) setting, showcasing the performance of our model across different variants of GOTHAM for various tasks on the Cora-MI. and OBGN-Arxiv datasets. The plots offer an overview of GOTHAM's performance across different representations encountered during few-shot and zero-shot learning scenarios. Notably, the model maintains consistent performance even when faced with heavy influence of unseen classes during streaming sessions. To simplify understanding: the experimental setup for base training remains consistent throughout. During streaming sessions, where adopt n-way, k-shot strategy, experiment with different values of while setting & to zero.
7 Conclusion
this study, we introduced GOTHAM, a class incremental learning framework designed for weakly super- vised settings. We initially addressed the GFSCIL problem setting, where access to labeled data during base training limited. Our experiments highlighted the advantages of incorporating semantic attributes for Text-Attributdd Graphs (TAGs). We then expanded scope to broader objective, Graph Class
11

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Published in Transactions on Machine Learning Research (04/2025)
OBGN- Arxiv
GFSCIL
100
Cora-ML
GFSCIL
80
GFSCIL + semantics
GFSCIL semantics
GCL (1-way, 0-shot)
90
GCL (1-way, 0-shot)
70
GCL (2-way, 0-shot)
80
60
(3-wy, 0-shot)
70
50
60
40
50
30
40
20
Base 51
52
53
54
55
56
57
S8
59
510
Base
51
52
$3
54
$5
Performance analysis of GOTHAM framework on OBGN-Arxiv and Cora-MI. datasets. (Left)): GCL with a 3-way k-shot setting shows consistent performance, even in zero-shot learning cases. (Right)): GCL with the 1-way k-shot setting on Cora-ML.
Figure 5:
Incremental Learning under Weak Supervision (GCL), where novel classes have both a few-shot and zero- shot representation. Through extensive experiments, we conclusively established the generalizability and effectiveness of our framework across diverse tasks.
8 Acknowledgment
We sincerely thank the reviewers for their valuable feedback and insightful suggestions, which have greatly improved the quality of this paper. We also appreciate the support and engaging discussions from the MISN lab, led by Dr. Sandeep Kumar, and Dr. Prathosh A.P. from IISc Bangalore. This rescarch supported by the DST Inspire Faculty Grant (MI02322G), and Dr. Prathosh A.P. is additionally supported by the Infosys Foundation Young Investigator Award.
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9 Appendix
9.1 Datasets
We assess the performance of our proposed framework, GOTHAM, on three real-world datasets- Cora-ML, Amazon, and OBGN-Aráv, The detailed description is in Table
Table 5: Statistics of datasets used in the experiments
Dataset Cora-ML
Nodes
Features
Classes
Class Labels
Tasks GISCIL, GCL
2,708
1,433
7
Neural Network, Rule Learning, Reinforcement Learning, Probabilistic
Methods, Theory, Genetic Algorithms,
Case-based
Amazon
13,752 169,343
767
10
Label names Unavailable
GFSCIL CISCIL, GCL
OBGN-Arxiv
128
40
Arxiv na, Arxiv Arxiv os ey, Arxiv cs cr, Arxiv de, Arxiv es he, Arxiv ev, Arxiv cs ai,
Arxiv cs lo,
Cora-ML (Bojchevski & Günnemann 2017): This is an academic network of machine learning papers. The dataset contains 7 classes, with each node representing a paper and each edge representing citation between
papers.
Amazon (Hou al., 2020 This dataset represents segments of the Amazon co-purchase e-commerce network. Each node is an item, and each edge denotes co-purchase relationship by common user. Node features are bag-of- words encoded product reviews, and class labels correspond to product categories.
OBGN-Arxiv Subramaniia et al. 2005): This dataset is a directed graph representing the citation network of Computer Science arXiv papers indexed by MAG. Each node is an arXiv paper, and each directed edge indicates a citation from one paper to another. Each paper has a 128 18--dimensionl feature vector, created by averaging the embeddings of words title and abstract.
9.2 Baseline methods
In the GFSCIL setting, we beuchmark our results against several stale-of-the-arl frameworks for few-shot class incremental learning and few-shot node classification, including:
9.2.1 Few-shot node classification
Meta-GNN (Zhou et al. 2019b): Meta-GNN addresses few-shot node classification graph meta-learning, It learns from numerous similar tasks to classify nodes from new classes with few labeled samples. Meta-GNN is versatile and can be easily integrated into any state-of state-of-the-art GNN.
Graph Prototypical Network (GPN) (Ding al. 2020a): GPN is advanced method for few-shot node classification. It uses graph neural networks and meta-learning on attributed networks for metric-based few-shot learning.
9.2.2 Class incremental learning
Incremental classifier and representation learning (iCaRL) (Rebuffi al. 2017): iCaRL is class- incremental method for image classification. We enhance it by replacing the feature extractor with two-layer GAT network.
Graph Meta-learning (HAG-Meta) (Tan et al. 2022 : HAG-Meta fol-
lows the graph pscudo-increment learning approach, allowing the model to learn new classes incrementally by cyclically adopting them from base classes. It also tackles class imbalance using hierarchical attention modules.
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2023;: CPCA is method Published in Transactions on Machine Learning Research (04/2025)
Graph Few-Shot Class-Incrementes Learning via Prototype Representation (Geometer) (Lu et al. 2022): Geometer predicts a node's label by finding the nearest class prototype in the metric space and adjusting the prototypes based on geometric proximity, uniformity, and separability of novel classes. To address catastrophic forgetting and unbalanced labeling, it uses teacher-student knowledge distillation and biased sampling.
Class Prototype Construction and Augmentation (CPCA) (Ren
that constructs class prototypes in the embedding space to capture rich topological information of nodes graphs, representing past data for future learning. To enhance the model's adaptability to new classes, CPCA uses class prototype augmentation (PA) to create virtual classes by combining current prototypes.
In the GCL setting, where novel classes have both few-shot and zero-shol representations, we compare against zero-shot learning frameworks with inductive learning as baselines. These approaches include:
9.2.3 Zero-shot learning
DCDFL 741 2024]: In DCDFL, a model for zero-shot node classification captures dependencies and learns discriminative leatures. It uses relation-aware network to leverage long-range dependencies ween nodes and employs domain-invariant adversarial loss to reduce domain bias and promote feature representations. Additionally, it enhances the representation by utilizing inter-class separability within the metric space.
GraphCEN (Ju et al. 2023 GraphCEN constructs an affinity graph to model class relations and uses node- and class-level contrastive learning (CL) to jointly learn node embeddings and class assignments. The two levels of CL are optimized to enhance each other.
(CDVSc, BMVSc, WDVSc) (Wan et al. 2019a): Based the observation that visual features of test instances form distinct clusters, a new visual structure constraint class centers for transductive ZSL is proposed to improve the generality of the projection function and alleviate domain shift issues. Three strategios-syyane
Chamfer distance, bipartite matching distance, and Wasserstein distance- are used to align the projected unseen semantic centers with the visual cluster centers of test instances.
Random guess: Randomly guessing an unseen label, introduced as naive baseline.
9.3 Parameter settings
In our proposed framework, various sets of hyper-parameters are involved. These are summarized in Table 0 below. The code implementation is available here: https://encr: http::://encc..///Y00e pw/uY0e2
Table 6: Parameter settings
Parameter
Value
Parameter
Value
word2vec
512 {le le 15 (2,
[01,02,03) 03)
(1,0.25, 1}
meta Ir Random walk fr_rr Boundary (7) weight decay
Hidden layer (MLP)
512
Hidden channels (GNNs)
512
(le le "}
Out channels (MLP)
512
0.01
Out channels (GNNs)
512
5e
{Xr, A2}
{1,1}
9.4 Proof of Prototype Distortion in Evolving Graphs
Proof. The protolype P: for a given class at any time & is defined by Equation (1) in the manuseript. It represents an aggregation of embeddings from all nodes in its extended neighborhood. For simplicity, we refer the prototype P; as the super-node i, and its corresponding extended support set as its neighborhood (i) time t. The embeddings are obtained the output of the GNN model. Equivalently, the super-node be expressed f((;;)) 0), which represents its embedding vector at any time & 0.
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To maintain consistent notation throughout the manuscript, reframe the previously defined GNN embeddings for node v4 denoted as GNNo(w:), as (e(;;)) when referring to the embedding of the super- node i. Therefore we have,
N
fe 0) = Σ ajo
Σ
Ty W + by
(8)
de(i)
1=1
REN(()
Thus, the expected loss of the parameter 0* the node i at time is
APP, öt) E (f++1 fc(;;0))²
(9)
1 1e kEN++1(1)
1 de(i)
E Σ aj a
xx W, +
zg W + bj
(10)
kEM)()
Furthermore, recall that each parameter 0g ~ 5) and each element Wa in the weight vector Wj also satisfics W ~ U(W E). Therefore, the differences aj 1y-a az and W,, W j,s are all i.i.d. random variables drawn from distribution E), Therefore, we have
27
N Σ
A(Pr, =E
új
0
de+1(1)
Σ
2x W +b -
de(()
Σ
(11)
i=1
(1)
kENi(i)
ox W +b ))
E
Σ aj
a²)
Σ
26 W, + +b,
Σ
(12)
de+1(()
de(i)
kENe+1
kENi(1)
27
+
Σ
aj 0
Σ
Ix W + -
Σ kEN(()
Ty W, + bi
(13)
deti(i)
de(
==1
kEN++1(1
N
a9) (a
E
Σ (aj
o detallt) k0
Σ
I& W, tb2
Σ
2 N + bj
(14)
de(1)
kENe(1)
+E
Σ j=1
a
Σ
2 W +bb
I W + bb
(15)
1i
de(i)
kEN(41(0)
REN((0)
The third equality holds by the fact. that the differences (az ag)'s are all iid. random variables drawn from the uniform distribution E). Therefore, we have
aj) (o (((a Σ
)) (16)
N
A(P,, 8t) 2 E
Σ ag
(112()) (1)
2 W, + bj
de(())
x WW, + bb Σ
kENi()
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Published in Transactions on Machine Learning Research (04/2025)
Furthermore, since the differences (a, az) are ii.d. random variables drawn from the distribution U(0, E) we must further have
) (17)
A(), 2 E
Σ aj - az) 0
(1i1100) (1+11()) kENo
Σ
2 W + bj
Σ
N +
di(1)
kEN(()
N
(aII10) Σ
17
(a, - -a3)) (
Xo4al
2 + bb -0 de(1)
Σ
Iy W + by
(et1(0))
(EN
kENi(()
(18)
E
tx W + bb
1
Σ
I& W +
(19)
(1)1(1)
de(i)
kENe+I(9)
kEN
Furthermore, the leaky ReLU satisfies that lo(u) a(u)22 B/u v/. The above incquality further implics
In W +bg -a ( Σ
))
N
A(P, 5t) 2
3
E
d
detz(())
Σ
do(1)
x W +bb
(20)
kEN441(1)
kENr(1)
Ig W - bj )
27
5
Σ
Σ
2 W + bj di
Σ
(21)
3
ds+1(1) (1N
j=1
kEN:(()
g2g2
E
Σ
Σ REN(11()WW))))
x TW; + deti(i)
Σ
x W
(22)
de+1(1)
d,(i)
kENi(H)
2
27
8252
N Σ
Σ
x W
+ ddtt
1
Σ
x IWW,
(23)
(i)
de(i)
==1
kENi(1
2
82g2
E
Σ
N
1
1 1)
Σ
It W
IT,,,
(24)
3
de+1(1)
de(t)
kEN(()
Therefore, we have
27
82L2 E
A(P, 2
Σ IIW, kEAi())
(25)
de+1(i)
de(i))
82g2
( 1
E
(1tz2()) de(i) -
Σ
I (W, W3 + +W7)
(26)
3
5=1
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Published in Transactions on Machine Learning Research (04/2025)
825
N
E
Σ
Σ kEN(()
t T - W3)
(27)
3
(i)
di(i)
j=l
+
5
EF
Σ
N
1 de(t)
Σ REN(()
Th W2
(28)
3
di)1(1)
j=1
where the last equality comes from the fact that random vectors (W; - W are i.i.d. random variables drawn from the uniform distribution (0, and are also independent of the graph evolution process. Therefore, we have
A(P,, 8t) 2
Ng262
E
1
Σ kENA(()
2 (W, Wj)
(29)
de())
1
E
I 12
(30)
9
de+1(1)
di(i)
kEN(
Neglecting the specific activation functions and model details, we can summarize our result as:
A(P, 0t) 2 E
Σ
1
de
kEA
This establishes the desired bound and completes our proof.
24


Reviews:
[{"review_id": "X7u7vqaZMv", "reviewer": "Reviewer_VPVs", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. The investigated label-scarce scenario is practically important, because in practice the new incoming classes may emerge with only a few examples.\n\n2. The proposed method can very well handle this scenario and obtains good performance.\n\nWeakness\n\n1. It seems that the literature review is not thorough enough. In my understanding, the class-incremental learning is also a kind of lifelong graph learning or graph continual learning. I would recommend the authors to discuss the setting of tis work with exiting graph continual learning settings, e.g. the ones in 'Cglb: Benchmark tasks for continual graph learning'. Second, the evolving nature of the graph studied in this work is also related to works like 'Temporal Generalization Estimation in Evolving Graphs'. Besides, the prototype based model also looks relevant to some other works, e.g. 'Hierarchical prototype networks for continual graph representation learning','Geometer: Graph Few-Shot Class-Incremental Learning via Prototype Representation', etc.\n\n2. It is mentioned in the abstract that the proposed method also considers the text rich graph. Do the adopted datasets cover this scenario?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies the problem of graph class incremental learning under the weakly supervision setting. Specifically, the new incoming data could have few or no labels. The proposed method adopts a prototype based method, so that the data are classified by being matched to the closest prototypes, which represent the corresponding classes. In this way, whether the labels of new data is abundant does not matter.\n\nThe proposed method obtains better performance than the baselines across three different datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please refer to the weakness above.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "xGd5dilbRm", "reviewer": "Reviewer_9zXd", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n1. The manuscript is easy to read and understand. \n2. The algorithm looks easy to implement.\n\nWeaknesses\n1. The novelty of the proposed method seems limited. The proposed method seems to be a combination of established tools for the node classification task. The manuscript does not propose new computational approaches, improve existing methods, or provide new interpretations of existing methods.\n2. The presentation could be improved. For example, the figures seem to need annotations. Figure 1: What are the definitions of the node colors (purple and green) and what are the question marks? Figure 2: it looks better if the definitions of the shapes (e.g. stars) are given. In Table 2, the plot on the right is not mentioned in the table caption.\n3. Some points are not explicitly explained in the main text. For example, the implementation of classification using protypes is not included in the text. Classification loss is also not mentioned in the algorithm section. It is not clear how the semantic attributes are calculated for the data sets in the experimental results section. I think it is unfair if this semantic information is only available for the proposed method and not for the baselines. \n4. Related to point 3 above, it is not explicitly explained which aspects of the proposed method can lead to the superior performance compared to the baselines reported in the experimental results section.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The manuscript proposes a node classification method in the setting of class incremental learning with a more  realistic assumption on class labels, where new classes are introduced with a few labels or no (zero) labels. The proposed method is implemented using prototype learning based on both attribute and semantic information in the framework of meta-learning.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please revise figures and tables. \nPlease respond to my comments in the above section (strengths and weaknesses).", "broader_impact_concerns": "No concerns on the ethical implication of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ceCmAil1hG", "reviewer": "Reviewer_dzy5", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. This paper provided a good review of related works.\n1. Section 3.1 formulated the problem properly.\n\n\nWeaknesses:\n1. May the author(s) emphasize the key difference between the proposed algorithms and existing algorithms?\n1. What is the possible reason that the GOTHAM algorithm outperforms the exisiting algorithms?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper focused on the node classification problem under weak supervision and aimed to classify nodes with limited labeled instances. It proposed the GOTHAM framework to do so compared the proposed algorithm with baseline algorithms numerically.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I'd appreciate the author(s) to clarify the questions listed in the *Strengths And Weaknesses* section.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The recommendation is to accept the paper subject to minor revisions.  The theoretical analysis in Section 7 should not appear after the conclusion.  It should appear between Sections 4 and 5.  The proof of the lower bound in Equation 8 is missing.  Please add the proof in the appendix.  Finally, a discussion of the implication of this lower bound is needed.  The manuscript acknowledges that the degree of inaccuracy of prototype estimation will increase over time, preventing the approach to generalize properly.   Is there any future work that could be recommended to address this limitation or is this a fundamental limitation that would apply to any approach?
Decision: Accept (poster)