Refining High-Quality Labels Using Large Language Models to

Enhance Node Classification in Graph Echo State Network

Ikhlas Bargougui

1,3

, Rebh Soltani

and Hela Ltifi

1,2

Research Groups in Intelligent Machines, University of Sfax,

National Engineering School of Sfax (ENIS), BP 1173, 3038, Sfax, Tunisia

Computer Science and Mathematics Department, Faculty of Science and Technology of Sidi Bouzid,

University of Kairouan, Sidi Bouzid, 9100, Tunisia

Computer Science and Mathematics Department, Faculty of Economics and Management Sciences,

University of Sfax, Sfax, 3018, Tunisia

Keywords: Large Language Models, Graph Echo State Network, Reservoir Computing, Node Classification.

Abstract: Graph learning has attracted significant attention due to its applicability in various real-world scenarios

involving textual data. Recent advancements, such as Graph Echo State Networks (GESN) within the

reservoir computing (RC) paradigm, have shown notable success in node-level classification tasks, especially

for heterophilic graphs. However, graph neural networks (GNNs) suffer from the need for a large number of

high-quality labels to achieve promising performance. Conversely, large language models (LLMs), with their

extensive knowledge bases, have demonstrated impressive zero-shot and few-shot learning abilities,

particularly for node classification tasks. However, LLMs struggle with efficiently processing structural data

and incur high inference costs. In this paper, we introduce a novel pipeline named LLM-GESN, which

involves four flexible components: k-means clustering for active node selection, LLM for difficulty aware

annotation, adaptable post-selection, and GESN model training and prediction. Experimental results

demonstrate the effectiveness of LLM-GESN on text-attributed graphs from the Cora, CiteSeer, Pubmed,

Wikics, and ogbn-arxiv datasets. Our LLM-GESN achieved significant test accuracy of 86.67%, 76.63%,

74.58%, 77.09%, and 58.79%, respectively, compared to state-of-the-art methods.

1 INTRODUCTION

Deep learning (DL) has revolutionized numerous

machine learning tasks, including image

classification (Li S. S., 2019), video processing

(Sharma, 2021), speech recognition (Soltani,

Newman-Watts-Strogatz topology in deep echo state

networks for speech emotion recognition, 2024), and

natural language processing (Otter, 2020). The

majority of DL models involve data in Euclidean

space. However, many applications, such as paper

citations, web page links, social network interactions,

and molecular bonds, involve data from non-

Euclidean domains represented as graphs. The

complexity and richness of graph-structured data,

along with the availability of large datasets, have

driven a surge in developing DL models for adaptive

graph processing. In recent years, GNNs have been

widely employed in various graph analysis tasks,

including node-focused tasks (e.g., node

classification, link prediction) and graph-focused

tasks (e.g., graph similarity detection, graph

classification) (Abadal, 2021).

Node classification is an essential area of research

due to its wide range of applications, one of the best-

known traditional pipelines for this task are: the first

is the GNN-based pipeline that involves a fixed

training set with truth labels and the GNN is trained

on these truth labels from the graph then predicts the

labels of the rest of the unlabeled nodes in the test

phase (Huang, 2020), the second graph active

learning-based pipeline aims to select a group of

nodes from the pool in order to maximize the

performance of the GNN models trained on these

graphs with labels (Chen Z. M., 2023). Both pipelines

neglect the subtleties of the annotation process which

can be both costly and error-prone in practice, even

for simple tasks. Moreover, this can be even more

difficult if active learning of graphs is taken into

account; with improvements in annotation diversity

Bargougui, I., Soltani, R. and Ltiﬁ, H.

Reﬁning High-Quality Labels Using Large Language Models to Enhance Node Classiﬁcation in Graph Echo State Network.

DOI: 10.5220/0013220600003890

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2025) - Volume 2, pages 555-565

ISBN: 978-989-758-737-5; ISSN: 2184-433X

555

inevitably increasing the difficulty of ensuring

annotation quality for these reasons other pipelines

appears. In order to overcome these limitations,

authors of (Chen Z. M., 2023) propose a pipeline

capable of exploiting LLM to automatically generate

high-quality annotations and use them to train a GNN

model with promising performance. LLMs, in

contrast to GNN, excel in zero-shot and few-shot

node classification on TAGs with unlabeled nodes.

Nonetheless, they struggle to capture graph structural

patterns as effectively as GNNs. LLMs are also

limited by input context length, reducing their ability

to utilize extensive labels for fine-tuning.

Consequently, LLMs may underperform compared to

well-trained GNNs and have higher prediction costs,

making them less scalable for large datasets.

However, most GNNs utilize a layered architecture

that performs local aggregation of node features. This

local aggregation progressively smooth node features

in deeper layers, creating difficulties in GNN models

(Xie Y. L., 2020). This bias towards locally

homogeneous graphs is particularly problematic in

node classification tasks involving graphs with a large

number of inter-class edges, or a low degree of

homophily. The GESN was introduced by (Micheli,

2023). In GESN, input data is encoded via a randomly

initialized reservoir, requiring learning only at the

linear readout stage, which enhances efficiency and

mitigates the issues arising from local feature

aggregation.

In this paper, we exploit the strengths of LLM and

GESN in node classification by investigating the

potential of exploiting the zero-shot learning

capabilities of LLM to alleviate the substantial

training data demands of GESN while addressing

their inherent weaknesses. Our LLM-GESN involves

four flexible components: k-means clustering for

active node selection, LLM for difficulty aware

annotation, adaptable post-selection, and GESN

model training and prediction. LLMs are utilized to

annotate a small subset of nodes, which are then used

to train GESNs to predict the remaining nodes. This

approach presents unique challenges: selecting the

most beneficial nodes for LLM annotation to

optimize GESN training, and ensuring that LLM

annotations are of high quality, representativeness,

and diversity to enhance GESN performance.

The remaining of this paper is organized as

follows: Section 1 provides an overview of related

works, focusing on Graph Echo State Networks

(GESN) for graph node classification and the use of

Large Language Models (LLMs) in graph structures.

Section 2 introduces our proposed method in detail.

Section 3 presents the evaluation of our model on

node classification tasks ranging from medium- to

large-scale graphs with different degrees of

heterophily., including experimental settings and a

comprehensive performance. Finally, we conclude

our study and discuss potential future directions in

Section 4.

2 RELATED WORKS

2.1 Graph Echo State Network for

Graph Nodes Classification

Echo State Networks (ESNs) (Soltani, 2023) (Soltani,

2024) (Soltani, 2024)are recurrent randomized neural

networks that feature a large, fixed, recurrent

reservoir. In this framework, there are three layers:

input layer, reservoir layer and the readout layer.

Only the weights of the readout layer are trained.

When applied to graph structures, GESN

computes graph representations, or embedding, as

fixed points of a dynamical system. Initially

introduced as the GESN (Micheli, 2023) (Jellali,

2023), this approach was later extended into deep

architectures (Micheli, 2023). GESN was applied in

the literature, on all types of graph tasks including

graph classification, edge classification and node

classification. Recent research has explored graph

classification to predict graph molecular toxicity

using GESN. Gallicchio et al. (Gallicchio, 2020)

introduced a constructive algorithm for GESN,

applying reservoir computing to graph classification

domains for toxicology tasks.

Moreover, GESN has emerged as an efficient

approach for processing dynamic graphs. The

Dynamic Graph Echo State Network (DynGESN)

model has been proposed for discrete-time dynamic

graphs, offering competitive accuracy and improved

efficiency compared to temporal graph kernels and

convolutional networks (Tortorella, 2021).This

approach provides vector encodings for dynamic

graphs without requiring training, making it suitable

for large-scale data. Building on this concept, the

Grouped Dynamical Graph Echo State Network

(GDGESN) introduces a snapshot merging strategy to

enhance performance in spreading process

classification tasks (Li Z. F., 2023). These reservoir

computing-based models offer a balance between

predictive performance and computational efficiency.

GESN has also shown promise in node

classification tasks on graphs. Traditional approaches

involve fixed connections in the hidden layer and

training only the output weights (Gallicchio, 2020).

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

556

However, recent research suggests that output weight

training can be omitted in favor of supervised

clustering based on principal components of reservoir

states, potentially improving classification accuracy

(Prater, 2016). GESN have demonstrated

effectiveness in addressing heterophily challenges in

node classification, outperforming many fully trained

deep models (Micheli, 2023). GESN computes node

embeddings recursively using an untrained message-

passing function, effectively encoding structural

relationships.

2.2 Large Language Models for

Graphs

LLMs are employed as Enhancers in graph learning

by initially processing graph data enriched with

textual information, thereby enhancing node

embedding or labels to augment GNN training. This

approach addresses issues with diverse initial node

embedding, which may lack clarity and diversity,

potentially leading to suboptimal GNN performance.

Recent advancements leverage LLMs' language

modelling capabilities to generate more meaningful

and effective embedding for improved GNN training

output. Several methods use this approach. For

instance, G-Prompt added a GNN layer to pre-trained

LLMs for task-specific node embedding using

prompt tuning (Fang, 2024). SimTeG fine-tunes text

embedding obtained from LLMs for node

classification tasks using GNNs (Duan, 2023).

GALM utilizes BERT for text embedding and

employs unsupervised learning tasks to optimize

model parameters for various applications (Xie H. Z.,

2023). LLMRec enhances user-item interaction data

using GPT-3.5 to enrich node embedding with rich

textual profiles, thereby improving the performance

of recommender systems (Wei, 2024).

LLMs also serve as Labelers in graph learning,

where labels generated by LLMs are used to

supervise GNN training. This method extends beyond

simple categorical labels to include embedding and

other forms of information. Leveraging LLMs in this

manner provides supervision signals that aid in

optimizing GNN performance across various graph-

related tasks. Examples of this approach include

OpenGraph, which uses LLMs to generate nodes and

edges, addressing sparse data issues through sampling

and refinement strategies (Xia, 2024). LLM-GNN

employs LLMs to annotate nodes with confidence-

scored category predictions, enhancing GNN training

with diverse labels (Micheli, 2023). GraphEdit

utilizes LLMs to predict and refine candidate edges in

comparison to original graph edges, improving edge

prediction accuracy (Guo, 2024).

Figure 1: Our proposed pipeline method LLM-GESN.

Reﬁning High-Quality Labels Using Large Language Models to Enhance Node Classiﬁcation in Graph Echo State Network

557

Despite the advancements made by these methods

in enhancing graph learning performance, a notable

limitation remains: the decoupling of LLMs from

GNNs necessitates a two-stage learning process. This

separation is often due to resource constraints posed

by large graphs or complex LLM parameters, which

strongly influences GNN performance reliant on pre-

generated LLM embedding and task-specific

prompts.

3 PROPOSED METHOD

Figure1 provides a detailed explanation of our

proposed pipeline method. This pipeline consists of

four main steps: data preprocessing, LLM

confidence-aware annotation, post-selection, and

GESN training.

3.1 Data Preprocessing

GESNs need numerous high-quality labels for

optimal node classification performance. The main

challenge is actively selecting nodes for annotation by

LLMs to enhance GESN training. Leveraging LLMs

for high-quality, representative, and diverse

annotations can significantly improve GESN

performance.

The active node selection process identifies a

small set of candidate nodes for LLM annotation,

maintaining a manageable budget and considering

diversity and representativeness as the original

baseline. It is also important to consider label quality,

as LLMs can produce noisy labels with significant

variance across different node groups. Therefore,

establishing heuristics that link to the annotation

difficulty of various nodes is crucial. A preliminary

analysis of LLM annotations provides insights into

how to infer annotation difficulty based on node

features showing that the accuracy of annotations

generated by LLMs is closely related to the clustering

density of the nodes.

To demonstrate this correlation, k-means

clustering, as shown in Figure 2, is applied to the

original feature space, setting the number of clusters

to match the distinct class count. We sample 1000

nodes from the entire dataset and annotate those using

LLMs. These nodes are then sorted and divided into

ten equal-sized groups based on their distance to the

nearest cluster center. This distance serves as a

heuristic to estimate annotation reliability.Given that

the number of clusters matches the number of distinct

classes, we refer to this heuristic as 𝜙



(𝑉



calculated as:

𝜙

𝑑𝑒𝑛𝑠𝑖𝑡𝑦

(𝑉

𝑖

1+𝐸𝐷(𝐸𝑀

𝑉

𝑖

,𝐶𝐶

𝑉

𝑖

)

(1)

Where ED is the Euclidean distance metric, 𝐸𝑀





is the embedding of node v

and 𝐶𝐶





is the center of

the cluster that 𝑉



belongs to. A higher value of

𝜙



(𝑉



) indicates that 𝑉



more representative

within the embedding space.

We then integrate this annotation difficulty

heuristic into the active selection process, B Nodes in

the unlabeled pool are chosen based on their highest

scores. To enhance model performance, the selected

nodes should balance annotation difficulty with

traditional active selection criteria, such as

representativeness and diversity (Zhang, 2021).

These criteria can be expressed as a score function.

An effective method for integrating the difficulty

heuristic into this learning process is ranking

aggregation. This method is more robust to

differences in scale because it only considers the

relative order of the elements. We incorporate the

difficulty heuristic by first converting 𝜙



(𝑉



)

into a rank 𝑟





(𝑉



) . Then, we combine these

two rankings to obtain:

𝑓



(

𝑉



)

=𝛼



×𝑟





(

𝑉



)

+𝛼



×𝑟





(

𝑣



)

(2)

Where 𝑓



(𝑣



) is the initial score function for

active graph learning, 𝑟





(𝑣



) is its ranking by

decreasing percentage and “DA” means difficulty

aware. The hyperprameters α0 and α1 allow us to

balance sannotation difficulty with traditional criteria

for active graph learning, such as representativeness

and diversity. Nodes vi with higher 𝑓



(𝑉



)

scores are then selected for annotation by the LLMs,

forming the 𝑉



set.

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

558

Figure 2: K-means clustering for active node selection.

3.2 LLM Confidence Aware Annotation

After selecting nodes (candidate set 𝑉



) easily to

annotate with difficulty-aware active node selection,

we then utilize the strong zero-shot ability of LLMs

to annotate those nodes with confidence-aware

prompts. But LLM annotations, akin to human

annotations, can exhibit a certain degree of label

noise. That’s means we are not aware of how the

LLM responds to the nodes at that stage. It leads to

the potential of remaining low-quality nodes. To

figure out the high-quality annotations, we need some

guidance on their reliability, such as the confidence

scores that can help to identify the annotation quality

and help us filter high-quality labels from noisy ones.

Inspired by recent literature on generating

calibrated confidence from LLMs, we aim to identify

the most effective prompts in terms of accuracy,

confidence calibration, and cost-efficiency.

We observe that LLMs exhibit promising zero-

shot prediction performance across all datasets. Zero-

shot annotation is a technique where a model is used

to annotate data without having seen examples of the

specific annotation task during its training. The

consistency strategy involves ensuring that the

annotations are consistent across similar instances in

the dataset. In Table 1 a comprehensive prompt

example for zero-shot annotation with a consistency

strategy.

Table 1: Complete prompt for zero-shot annotation with

consistency strategy used across all datasets.

nput: Question: (Contents) Paper:

Title: #the title of the suggested paper#

bstrac

: #the abstract of the suggested paper#

Tas

: There are following categories:

[category

, category

, …., category]

hat’s the cate

of this paper?

rovide your 3 best guesses and a confidence numbe

hat each is correct (0 to 100) for the followin

question from most probable to least. The sum of al

confidence should be 100.

or example, [ {” answer”: <your first answer>,

”

confidence”: <confidence for first answer>}, ...]

Output:

3.3 Post-Selection

The post-selection step aims to eliminate low-quality

annotations by using confidence scores generated by

the LLMs. By leveraging these scores, we refine the

set of annotated nodes by removing those with lower

confidence, ensuring the labels remain high-quality.

However, directly filtering out low-confidence nodes

can result in a shift in label distribution and reduce the

diversity of the selected nodes, which may degrade

the performance of the trained models.

During the post-selection stage, label distribution

is readily available, allowing us to directly consider

the label diversity of the selected nodes. To measure

the change in diversity, a simple score function called

Change of Entropy (COE) is proposed. This function

measures the entropy change of labels when

removing a node from the selected set and can be

computed as follows:

𝐶𝑂E(𝑣

𝑖

)=𝚮(Α

𝑉𝑠𝑒𝑡

−{𝑣

𝑖

})−𝚮(Α

𝑉𝑠𝑒𝑡

)

(3)

Where 𝑉

𝑠𝑒𝑡

is the current selected set of nodes, Α

present the annotation generated by LLMs and H () is

the Shannon entropy function (Shannon, 1948).

The value of COE can be either positive or

negative, with a small COE (𝑣

𝑖

) value indicating that

removing the node could negatively impact the

diversity of the selected set, potentially affecting the

performance of the trained models. When a node is

removed, the entropy adjusts, requiring a re-

computation of COE. This re-computation is

computationally efficient since the size of the selected

set 𝑉

𝑎𝑛

is much smaller than the entire dataset. COE

can be combined with the confidence score 𝑓

𝑐𝑜𝑛𝑓

(𝑣

𝑖

)

to balance diversity and annotation quality through

ranking aggregation, also 𝑟

𝜙

𝑑𝑒𝑛𝑠𝑖𝑡𝑦

(𝑣

𝑖

) is available in

Reﬁning High-Quality Labels Using Large Language Models to Enhance Node Classiﬁcation in Graph Echo State Network

559

the post-selection phase. The final selection score

function can be calculated as

𝑓

𝑠𝑒𝑙𝑒𝑐𝑡

(𝑣

𝑖

)=𝛿

× 𝑟

𝑓

𝑐𝑜𝑛𝑓

(𝑣

𝑖

)

+𝛿

×𝑟

𝐶𝑂𝐸(𝑣

𝑖

)

+𝛿

×𝑟

𝜙

𝑑𝑒𝑛𝑠𝑖𝑡𝑦

(𝑣

𝑖

)

(4)

Where 𝑟

𝑓

𝑐𝑜𝑛𝑓

is the high-to-low ranking percentage of

the confidence score 𝑓

𝑐𝑜𝑛𝑓

. To conduct post-

selection, each time we remove the node with the

smallest 𝑓

𝑠𝑒𝑙𝑒𝑐𝑡

value

until a specified maximum

number is attained

, δ

,δ

are hyper-parameters

introduced to balance label diversity and annotation

quality.

3.4 GESN Training

GESN operates within the RC framework, where

input data is processed by a randomly initialized

reservoir, and only the linear readout layer requires

training. This approach benefits from the dynamic

properties of reservoirs, making it suitable for

handling diverse graph structures.

Another crucial aspect of the training process is

the choice of the loss function. While GNNs usually

utilize cross-entropy loss, the presence of noisy labels

from the LLMs makes a weighted cross-entropy loss

more appropriate. By using the confidence scores

from the previous section as weights, we can enhance

the model's robustness and improve the overall

quality of the annotations.

GESNs create whole graph embedding from node

embedding using simple pooling functions like sum

or mean. These node embedding are generated by

updating a non-linear dynamical system iteratively,

similar to GNN models.

According to Figure 3, Node embedding is

recursively computed by the non-linear dynamical

system:

𝒉



(



)

=𝑡𝑎𝑛ℎ𝑾



𝒙



+ 𝑾



∈



()

𝒉



(



)

,

𝒉



(



)

=𝟎

(5)

Where W

∈ ℝ

H×X

and W



∈ ℝ

×

are,

respectively, the input-to-reservoir and the recurrent

weights, for a reservoir with H units (input bias is

omitted). Reservoir weights are initially randomized

using a uniform distribution within the range [−1,1].

They are then rescaled to achieve the desired input

scaling and reservoir spectral radius, all without the

need for any training. Equation (1) is iterated over k

up to K times, after which the final state 𝑋

(

)

is used

as the node embedding.

For node classification tasks, a linear readout is

applied to node embeddings:

𝐲



=𝐖



𝐡



()

+ 𝐛



(6)

Where the weights w



∈ℝ

×

,𝐛



∈ℝ



are

trained by ridge regression on one-hot encodings of

target classesy



The dynamical system (1) has been designed to be

asymptotically stable, which means that it converges

to a fixed point h

(∞)

as K → ∞. This convergence is

ensured by the graph embedding stability (GES)

property (Gallicchio, 2020), which also guarantees

that the system is independent of its initial state 𝒉

𝑣

(0)

A sufficient condition for the GES property is to

ensure that the transition function defined in (1) is

contractive, i.e. has a Lipschitz constant such that

||𝐖



|| ||𝐀|| 𝟏.

In standard reservoir computing, recurrent

weights are initialized based on a necessary condition

for the Generalized Echo State (GES) property, which

is 𝜌(𝑤)

𝛼



, where ρ (-) denotes the spectral

radius of a matrix, and 𝛼=𝜌(𝐴) is the spectral

radius of the graph.

Figure 3: GESN general design.

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

560

Table 2: Dataset Characteristics and Metadata.

Datasets

Nodes

Edges

Tasks

Categories

Homophily

References

CORA

2,708

5,429

Categorize papers by title and abstract

0.81

(Chen Z. M., 2024)

CITESEER

3,186

4,277

Categorize papers by title and abstract

0.74

(Chen Z. M., 2024)

PUBMED

19,717

44,335

Categorize papers by title and abstract

0.80

(Chen Z. M., 2024)

WIKICS

11,701

215,863

Categorize articles by Wikipedia content

(Chen Z. M., 2024)

OGBN-ARXIV

169,343

1,166,243

Categorize papers by title and abstract

0.22

(Chen Z. M., 2024)

Figure 4: Clustered t-SNE Visualization: Grouping of Data Points Around Cluster Centers.

This condition provides the best estimate of the

system's tipping point, beyond which equation (2)

becomes asymptotically unstable.

4 EVALUATION

4.1 Experimental Settings

The experiment begins with an LLM-based

annotation process for preprocessed graph nodes.

This process involves formulating queries based on

node features and local graph structure, which are

then input to the LLM (gpt 3.5 turbo) to produce high

quality labels. Following this, the GESN is employed

for node classification. The GESN consists of a 2-

layer with 256 hidden features. It utilizes sbert

embedding as input and is initialized using carefully

scaled uniform distributions. Our model incorporates

a PageRank-based active learning strategy with

varying budget constraints and employs both

consistency-based and confidence-entropy filtering

mechanisms.

4.2 Datasets

To assess the effectiveness of our model, we use five

benchmark datasets: Cora, Citeseer, PubMed,

WikiCS, and OGBN-Arxiv. All datasets are within

the same domain of node classification. Table 2

details the main characteristics of these datasets.

4.3 Performance Analysis

4.3.1 Performance on Node Clustering

The t-SNE visualization with cluster centers,

presented in Figure 4 shows how data points are

grouped into clusters.

Reﬁning High-Quality Labels Using Large Language Models to Enhance Node Classiﬁcation in Graph Echo State Network

561

Figure 5: Relationship between LLM Annotation Accuracy and Node Distance from Cluster Center.

Figure 6: Correlation between Label Entropy and Average Label Accuracy across Datasets.

Each point is color-coded according to its

assigned cluster (0 to # of classes - 1). The black

crosses represent the center of these clusters.

By analyzing the distribution of points around

each center, we can understand the cohesion and

distinctiveness of the clusters. Here, the resulting

figure for K-means clustering on the Arxiv dataset is

omitted from our manuscript due to the complexity of

visualizing 40 clusters, which would not provide clear

interpretation.

4.3.2 Performance on Node Annotation

Based on Figure 5, in our proposed method, the

accuracy of LLM annotation depends on the distance

of nodes from the cluster center. When nodes are

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

562

close to the center (lower region index), LLM

annotation tends to be more accurate.

These central nodes likely share common features

and context, making them easier for LLMs to annotate

effectively. Conversely, distant nodes (higher region

index) exhibit lower accuracy in LLM annotation.

To optimize LLM annotation quality, prioritizing

nodes near the centroid becomes crucial. By doing so,

we enhance the chances of accurate labeling.

In Figure 6, we explore the relationship between

label entropy and average label accuracy across

various datasets. The x-axis represents the entropy of

labels within different datasets, quantifying the

uncertainty or disorder in a set of labels, with higher

entropy values indicating more diverse or ambiguous

labels.

The y-axis represents the average label accuracy

(in percentage) for each dataset, reflecting how

accurately labels can be applied to data points

Observations from the plot reveal that as the entropy

of labels increases (moving right along the x-axis);

average label accuracy tends to decrease. Datasets

with lower entropy (more certain labels) exhibit

higher accuracy, while those with higher entropy

(more uncertain or diverse labels) experience lower

accuracy.

Figure 7: test accuracies for five different datasets across

three models LLM-GCN, LLM-MLP and LLM-GESN.

4.3.3 Performance on Node Classification

The test accuracy in Figure 7 compares the

performance of three models—LLM-GCN, LLM-

MLP, and LLM-GESN—across five datasets: Cora,

Citeseer, Pubmed, Wikics, and Arxiv. LLM-GESN

Table 3: Comparative Analysis: Our Model Versus State-of-the-Art Test Accuracies Across Datasets.

Reference Model Test accuracy

Cora

(Hou, 2022) Self-supervised GraphMAE 84.2±0.4

(Micheli, 2023) GESN 86.04±1.01

LLM-GESN 86.67 ± 0.00

Citeseer

(Hou, 2022) Self-supervised GraphMAE 73.4±0.4

(Micheli, 2023) GESN 74.51±2.14

LLM-GESN 76.63 ± 0.00

PubMed

(Hou, 2022) GAE 72.1±0.5

(Arnaiz-Rodríguez,

2022

)

GCN 68.19±0.7

LLM-GESN 74.58 ± 0.00

Wikics

(Hoang, 2023) GIN 76.53±0.82

LLM-GESN 77.09 ± 0.00

OBGN-Arxiv

(Sharma, 2021) GESN 48.80±0.22

LLM-GESN 58.79 ± 0.00

Reﬁning High-Quality Labels Using Large Language Models to Enhance Node Classiﬁcation in Graph Echo State Network

563

competes well on Cora and Pubmed, but shows

weaker results on Citeseer and Arxiv. These findings

underscore the efficiency of LLM-GESN on all

datasets.

As displayed in table 3, our proposed pipeline,

LLM-GESN, is evaluated against state-of-the-art

methods across all datasets (Cora, Citeseer, PubMed,

WikiCS, and OBGN-Arxiv).

The results show that the LLM-GESN model

outperforms other models in terms of test accuracy.

For the Cora dataset, LLM-GESN achieved the

highest accuracy of 86.67 ± 0.00, surpassing both

Self-supervised GraphMAE and GESN. In the

Citeseer dataset, LLM-GESN reached an accuracy of

76.63 ± 0.00, again outperforming Self-supervised

GraphMAE and GESN. For the PubMed dataset,

LLM-GESN recorded 74.58 ± 0.00, higher than both

GAE and GCN. On the WikiCS dataset, LLM-GESN

achieved 77.09 ± 0.00, slightly better than GIN. The

most significant improvement was seen in the

OBGN-Arxiv dataset, where LLM-GESN achieved

58.79 ± 0.00, far surpassing GESN. Overall, the

LLM-GESN model demonstrates superior

performance and robustness across all datasets,

highlighting its effectiveness in enhancing test

accuracies compared to state-of-the-art models. We

note that the impact of LLM annotation to enhance

the performance of GESN node classification on

small to large-scale dataset as Cora, Citeseer and

OBGN-Arxiv. Moreover, our model achieves

respectable performance even comparing with other

models like GraphMAE, GAE, GCN, GIN.

However, this model still lacks hyperparameter

optimization for the GESN, which could further

enhance these results. Tuning hyperparameters such

as learning rates, regularization strengths, and

network architectures could potentially improve the

model's performance across different datasets.

Additionally, in terms of real-world applications,

deploying LLM-GESN could be transformative. For

example, in social network analysis, LLM-GESN

could accurately classify nodes based on their

attributes, such as predicting user preferences or

behaviors. This capability could aid in personalized

recommendation systems or targeted marketing

strategies, where understanding and predicting

individual user characteristics are crucial for

enhancing user engagement and satisfaction.

5 CONCLUSION

In this paper, we address two significant challenges in

node classification for graph data as a prominent topic

in data science: the issue of heterophilic graphs and

the requirement of high-quality annotations. We

propose a new model LLM-GESN that investigates

the potential of harnessing the zero-shot learning

capabilities of LLMs to alleviate the substantial

training data demands of GESNs. Comprehensive

experiments on graphs of various scales validate the

effectiveness of our pipeline. Demonstrating that our

model achieves accuracy comparable to or better than

the GESN model and other GNN models that utilize

LLMs for annotation. In future work, we plan to

validate our model in real-world applications,

recognizing the importance of hyperparameters

optimization for GESN.

REFERENCES

Abadal, S. J.-A. (2021). Computing graph neural networks:

A survey from algorithms to accelerators. ACM

Computing Surveys (CSUR), 54(9), 1-38.

Arnaiz-Rodríguez, A. B. (2022). Diffwire: Inductive graph

rewiring via the lov\'asz bound. arXiv preprint

arXiv:2206.07369.

Chen, Z. M. (2023). Label-free node classification on

graphs with large language models (llms). arXiv

preprint arXiv:2310.04668.

Chen, Z. M. (2024). Exploring the potential of large

language models (llms) in learning on graphs. ACM

SIGKDD Explorations Newsletter, 25(2), 42-61.

Chen, Z. M. (2024). Exploring the potential of large

language models (llms) in learning on graphs. ACM

SIGKDD Explorations Newsletter, 25(2), 42-61.

Duan, K. L. (2023). Simteg: A frustratingly simple

approach improves textual graph learning. arXiv

preprint arXiv:2308.02565.

Fang, T. Z. (2024). Universal prompt tuning for graph

neural networks. Advances in Neural Information

Processing Systems, 36.

Gallicchio, C. &. (2020). Fast and deep graph neural

networks. In Proceedings of the AAAI conference on

artificial intelligence (Vol. 34, No. 04, pp. 3898-3905).

Guo, Z. X. (2024). Graphedit: Large language models for

graph structure learning. arXiv preprint

arXiv:2402.15183.

Hoang, V. T. (2023). Mitigating Degree Biases in Message

Passing Mechanism by Utilizing Community

Structures. arXiv preprint arXiv:2312.16788.

Hou, Z. L. (2022). Graphmae: Self-supervised masked

graph autoencoders. In Proceedings of the 28th ACM

SIGKDD Conference on Knowledge Discovery and

Data Mining, (pp. 594-604).

Huang, Q. H. (2020). Combining label propagation and

simple models out-performs graph neural networks.

arXiv preprint arXiv:2010.13993.

Jellali, N. S. (2023). An Improved Eulerian Echo State

Network for Static Temporal Graphs. In International

Conference on Intelligent Systems Design and

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

564

Applications. Cham: Springer Nature Switzerland,

307-318.

Li, S. S. (2019). An overview: Deep learning for

hyperspectral image classification. IEEE Transactions

on Geoscience and Remote Sensing, 57(9), 6690-6709.

(2019).

Li, Z. F. (2023). Dynamical Graph Echo State Networks

with Snapshot Merging for Spreading Process

Classification. In International Conference on Neural

Information Processing (pp. 523-534). Singapore:

Springer Nature Sin.

Li, Z. F.-5. (n.d.).

Micheli, A. &. (2023). Addressing heterophily in node

classification with graph echo state networks.

Neurocomputing, 550, 126506.

Otter, D. W. (2020). A survey of the usages of deep learning

for natural language processing. IEEE transactions on

neural networks and learning systems, 32(2),, 604-624.

Prater, A. (2016). Reservoir computing for spatiotemporal

signal classification without trained output weights.

arXiv preprint arXiv:1604.03073.

Shannon, C. E. (1948). A mathematical theory of

communication. The Bell system technical journal,

27(3), 379-423.

Sharma, V. G. (2021). Video processing using deep

learning techniques: A systematic literature review.

IEEE Access, 9, 139489-139507.

Soltani, R. B. (2023). Echo state network optimization: A

systematic literature review. Neural Processing Letters,

55(8), 10251-10285.

Soltani, R. B. (2024). Hybrid Quanvolutional Echo State

Network for Time Series Prediction. In ICAART (2),

(pp. 40-46).

Soltani, R. B. (2024). Newman-Watts-Strogatz topology in

deep echo state networks for speech emotion

recognition. Engineering Applications of Artificial

Intelligence, 133, 108293.

Soltani, R. B. (2024). Topology-adaptive Bayesian

optimization for deep ring echo state networks in

speech emotion recognition. Neural Computing and

Applications, 1-18.

Tortorella, D. &. (2021). Dynamic graph echo state

networks. arXiv preprint arXiv:2110.08565.

Wei, W. R. (2024). Llmrec: Large language models with

graph augmentation for recommendation. In

Proceedings of the 17th ACM International Conference

on Web Search and Data Mining, (pp. 806-815).

Xia, L. K. (2024). Opengraph: Towards open graph

foundation models. arXiv preprint arXiv:2403.01121.

Xie, H. Z. (2023). Graph-aware language model pre-

training on a large graph corpus can help multiple graph

applications. In Proceedings of the 29th ACM SIGKDD

Conference on Knowledge Discovery and Data Mining

, (pp. 5270-5281).

Xie, Y. L. (2020). When do gnns work: Understanding and

improving neighborhood aggregation. In IJCAI'20:

Proceedings of the Twenty-Ninth International Joint

Conference on Artificial Intelligence,{IJCAI}.

Zhang, W. Y. (2021). Grain: Improving data efficiency of

graph neural networks via diversified influence

maximization. arXiv preprint arXiv:2108.00219.

Reﬁning High-Quality Labels Using Large Language Models to Enhance Node Classiﬁcation in Graph Echo State Network

565