Learning to Rank Features to Enhance Graph Neural Networks for Graph Classification
Authors: Fouad Alkhoury
Tamas Horvath
Christian Bauckhage
Stefan Wrobel
Venue: Accepted by TMLR ()

Abstract: A common strategy to enhance the predictive performance of graph neural networks (GNNs) for graph classification is to extend input graphs with node- and graph-level features. However, identifying the optimal feature set for a specific learning task remains a significant challenge, often requiring domain-specific expertise. To address this, we propose a general two-step method that automatically selects a compact, informative subset from a large pool of candidate features to improve classification accuracy. In the first step, a GNN is trained to estimate the importance of each feature for a given graph. In the second step, the model generates feature rankings for the training graphs, which are then aggregated into a global ranking. A top-ranked subset is selected from this global ranking and used to train a downstream graph classification GNN. Experiments on real-world and synthetic datasets show that our method outperforms various baselines, including models using all candidate features, and achieves state-of-the-art results on several benchmarks.

Published in Transactions on Machine Learning Research (12/2025)
Learning to Rank Features to Enhance Graph Neural Net- works for Graph Classification
Fouad Alkhoury
alhhoury@hii..unk wni.iooiiiiiiionnnnnmmm de
University of Bonn
Lamarr Institute for Machine Learning and Artificial Intelligence
Tamás Horváth
horvath@cs.com uni-born..de Morruuth@@cs.umiibbrn...
de
University of Bonn
Prounhofer LAIS
Lamarr Institute for Machine Learning and Artificial Intelligence
Christian Bauckhage
bauckhage@Waii uni-born.n...
University Bonn
Praunhofer IAIS
Lamarr Instiuute for Machine Learning and Artificial Intelligence
Stefan Wrobel
wrobel@css uni-boren, de
Universily of Bonn
Fraumhofer TATS
Lamarr Institute for Machine Learning and Artificial Intelligence
Reviewed on OpenReview: https:// oppnrrveepeereveeeu.u net/ forum? WmZGuWRAWb
Abstract
common strategy to enhance the predictive performance graph neural networks (GNNs) for graph classification is extend input graphs with node- and graph-level features. How- ever, identifying the optimal feature set for a specific learning task remains a significant challenge, often requiring domain-specific expertise. To address this, we propose gen- eral two-step method that automatically selects compact, informative subset from large pool of candidate features to improve classification accuracy. In the first step, GNN is trained to estimate the importance of each feature for a given graph. In the second step, the model generates feature rankings for the training graphs, which are then aggregated into a global ranking. top-ranked subset is selected from this global ranking and used to train downstream graph classification GNN. Experiments on real- cal-world and synthetic datasets show that method outperforms various baselines, including models using all candidate features, and achieves state-of-the-are results several benchmarks.
1 Introduction
Graph neural networks (GNNs) (see, e.g., data, especially in node and graph classification tasks. However, standard GNNs are limited by the expres- sive power of the 1-dimensional Weisteiler-Leaan test (Morris et al. 2019), which restricts their ability to distinguish certain non-isomorphic graphs. This limitation is particularly problematic in practical learning scenarios where structural differences are also task-relevant. A common strategy to address this issue is to enrich GNNs with additional feature information. This espocially crucial for graph classification, the focus of this work, where effective graph representations depend on both node- and graph-level features. Yet, the success of this approach strongly depends the relevance and quality of the features provided.
e.g., Hamilton 2020
widely used for learning from graph-structured

---

Published in Transactions on Machine Learning Research (12/2025)
Merely supplying GNNs with large set of task-independent features does not guarantee improved per- formance. Since GNNs treat all input features as potentially relevant, their implicit feature extraction mechanisms cannot fully eliminate the negative influence of irrelevant or redundant features on generaliza- tion. In particular, such features may dominate and distort message passing, leading to degraded quality of learned representations. This issue becomes especially critical graph classification, where global rep- resentations aggregate information from many nodes, amplifying the negative effect of noisy or irrelevant features. For example, in molecular property prediction, only a subset of atomic descriptors typically influ- ences activity (Ponzoni et al. 2
Existing methods for incorporating additional features typically rely on predefined static feature sets (Barceló et al. 2021 Bouritsas et al.
2023 Cui et al.) 2022; Duong et al. 2019). ; which require substantial domain expertise and often fail to generalize across datasets. More recent work on dynamic feature selection for GNN node classification (Naik et al. 2024) offers more flexibility but focuses on local graph patterns, neglecting global features crucial for graph-level tasks. In a recent work (Alkhoury et al., 2025), we proposed feature- ranking GNN that, learns to select. relevant. features for node classification on unseen graphs, improving accuracy and reducing computational cost. However, it is limited to node classification and cannot be directly extended to graph classification, where global feature selection is essential.
These gaps reveal that while GNNs possess implicit feature extraction capabilities, they remain sensitive to noisy and irrelevant features and lack principled mechanisms for targeted, data-driven feature selection at the graph level. To overcome these limitations, we propose a general framework that automates feature selection through dedicated GNN architecture, jointly identifying informative local and global features during representation learning- Our approach enhances graph classification performance beyond what is possible via implicit feature extraction alone, offering new perspective how explicit feature selection in GNNs can improve predictive accuracy while reducing training and inference time.
Building on the framework we introduced in Alkhoury et al. (2025), we present an automatic and scalable feature selection method for gruph classification. Our method proceeds in two major steps. First, given a set of training graphs, we sample a small, random subset of the data and compute all features from a universal pool for each graph in this subset, resulting in feature vectors of uniform dimensionality. These vectors, along with their corresponding class labels, are then used for feature ranking. To generate these rankings, we considered three different approaches: random forests, support vector machines, and local explanation methods from explainable AI. Among them, random forests consistently delivered the most reliable feature rankings. Following the approach we proposed in Alkhoury et al. (2025), we then train a feature-ranking GNN (FR-GNN) using the original graphs and their feature rankings. This enables the FR-GNN to predict feature importance for all remaining graphs in the training set without the need to compute any features. The local rankings are aggregated into single global ranking, which is then applied to all training graphs in the second step and to unseen graphs later during class prediction.
In the second step, the top K features from the global ranking are selected and computed for all training graphs. A graph classification GNN (GC-GNN) is then trained using these graphs, augmented with only the K selected features. Since both feature selection and ranking rely on a small subset of data and a limited number of features, the overall process remains computationally feasible.
To assess the offectiveness of our approach, we conducted experiments on both real-world and synthetic datasets, utilizing 124 local and global graph features as well as three GNN architectures (GCN (Kipf & Welling 2016), GAT (Velickovic et al. 2018). and GraphSAGE (Hamilton et al. 2017)), and compared our method to three bascline approaches.
On the real-world datasets, using only the top six features selected by our method (K = 6), the trained GC-GNN consistently outperformed the baseline that used no features, demonstrating the importance of incorporating features. Furthermore, our method surpassed the baseline that used all 124 features by an average margin of 7%, suggesting that including irrelevant or redundant features can lead to overfitting and degrade performance. Additionally, it consistently outperformed GC-GNNs trained on six randomly selected features, indicating that the features chosen by method are genuinely informative rather than selected by chance. Notably, for the real-world datasets where ofate-of-the-art (SOTA) algorithm results are
2

---

Published in Transactions on Machine Learning Research (12/2025)
publicly available (together with code), our method either outperforms achieves comparable predictive performance.
To further evaluate robustness, we generated synthetic graphs using various random graph models with increasing classification difficulty. This was achieved by attaching graph motifs (graphlets) and defining target classes through logical formulas of varying complexity, where literals indicate the presence or absence of specific motifs. Our method consistently outperformed the baselines that used no features or random features, even on the most challenging tasks. While the bascline using all features achieved high accuracy (2 95%) on synthetic data, method using just six selected features often performed slightly better. In one particularly complex case involving four classes defined by nested logical conditions, the all-fcature bascline outperformed our approach; however, increasing our selection to the top 20 features (K = 20) narrowed the performance gap. This result confirms that our method remains competitive even as task complexity increases.
The rest of the paper is organized as follows. Section 2 proposed method. The experimental results are reported in Section 4 Finally, in Section 5 we conclude and mention some problems for future work.
overviews the related work. Section 3 describes the
2 Related Work
Research on graph classification spans a wide spectrum of approaches, from substructure-based kernels to deep neural architectures. A central challenge across these methods is the identification of informative features while minimizing redundancy and noise. Since our framework focuses on effective feature ranking and selection, we concentrate on methods most relevant to this aspect of graph classification. We organize related work into five calegories and discuss how our approach differs from each.
Substructure and Graphlet-Based Methods A common approach to graph classification relies graph kernels, such as the grophlet kernel (Shervashidze et al.) 2009), which measures graph similarity by counting small subgraphs (graphlets). While polynomial-time enumeration is feasible for small graphs, it becomes computationally prohibitive for large ones. To address this limitation, efficient subgraph estimation techniques have been proposed, such as graphlet counts approzimation without full enumeration (Rossi et al., 2018). More recently, the Substructure Assembling Network (SAN) (Yang et al., 2022) learns graph representations by hierarchically composing local substructures with a recurrent unit and soft attention mechanism, enabling the construction of discriminative graph-level features. Our method differs from these approaches in two key aspects. First, rather than exhaustively enumerating estimating substructures we rank and select compact subset of candidate features without computing them across the entire training data, substantially reducing overhead. Second, our candidate fcature set extends beyond substructures to include global graph properties and statistical summaries of node features, providing a richer and more versatile feature space for graph classification.
Feature Selection and Noise Reduction Real-world graphs often exhibit noise, sparsity, and redundant connections Dai et al. 2022 making it difficult to extract meaningful patterns. Several approaches have been proposed to to mitigate the effects of noise or irrelevant information. For example, Fu et al. (2020):
Ma et al. (2021) present theoretical frameworks interpreting GNN aggregation as graph signal denoising process, suggesting that GNNs smooth node features to reduce noise. ES-GNN (Guo et al.) 2024) explicitly distinguishes relevant from irrelevant edges to prevent the propagation of uninformative connections. Unlike these works, our method filters and ranks fcatures prior to GNN training, achicving both computational efficiency and improved predictive accuracy. In fact, our experiments show that using the full feature set degrades performance, underscoring that GNNs alone cannot fully suppress the influence of irrelevant redundant features.
Dual-Network Architectures Several works employ dual-network architectures to jointly address feature selection and classification. For example, Akkol et al. (2021) use two GNNs within a variational autoencoder for action recognition and prediction, while Maurya et al. (2023) propose a Dual-Net GNN for node classi- fication, where one network selects node features for the other. Similarly, DualNetGO (Chen Luo (024) alternates between selector and classifier networks for protein function prediction, starting from randomly
3

---

Published in Transactions on Machine Learning Research (12/2025)
FC
DFR
Compute Features
G2
G₁
0.9
0.5
RF Ranking
F16
Fst
FR-GNN
Gm
0.7
Gm
F121
F12
D Dtrain
CC
DGC
GC-GNN
Top-K
Fy > Fs ...
Global Ranking:
F24
Gms1
Gm+2
Fio
Fez
F66
Fg
G
Fy
F6z
Figure 1: High-level overview of the FR-GNN training step (top) and the GC-GNN training step (bottom).
combined features. Our approach also adopts two GNNs, but with key differences: (i) it operates at the graph-level rather than for node classification, (ii) the feature ranking and classification stages are explicitly decoupled, simplifying optimization, and (iii) instead of relying random initialization or domain-specific heuristics, it integrates a feature ranking stage to begin with compact and relevant feature set.
Graph Representation Learning and Pooling Other approaches learn graph-level representations without explicit feature selection. Fei & Huan (2008) identify frequent subgraphs based on spatial distribution consistency, whereas we use subgraph counts as explicit features. HGP-SL (Zhang et al., 2019) combines hierarchical graph pooling with structure learning, implicitly refining the graph topology via learned node importance scores. In contrast, graph-level features prior to training using interpretable model, namely random forests. Cui et al.) 2022) investigate the impact of hand-crafted features on GNN performance but without ranking or selecting features, unlike our approach.
method follows feature-driven strategy: rank and select informative
GNN-Based Feature Ranking Learning In our closely related recent work (Alkhoury et al. 2025 we proposed a Iramework to improve predictive performance node classification by identifying important features using a random forest-based selection mechanism. In contrast, our approach focuses on graph classification and explores both node-level and graph-level features, requiring entirely different techniques. In particular, while the fealure-ranking GNN classifier in (Alkhoury et al. 2025) is trained on synthetic datasets designed to exhibit structural diversity, our method operates directly on the training graphs of the target dataset, ensuring that the resulting feature ranking reflects the specific patterns relevant to the classification task at hand. Another key difference lies in the aggregation strategy: whereas their method produces a separate feature ranking for each input graph (as needed for node classification), our approach aggregates feature importance scores across all training graphs, resulting in dataset-level feature ranking suitable for graph classification.
3
The Method
This section presents our method] [ for automatically selecting a compact subset of features from a large pool of candidates, with the goal of improving the predictive performance of GC-GNN using the selected additional features. Our method consists of two steps (see Fig. [ for schematic overview of the process).
(Step 1) Training a Feature Ranking GNN (FR-GNN): Given a set of training graphs Dirains we first select small random set DPR C Drains compute a feature ranking for each graph in DFR using random forests, and train FR-GNN these graphs and their corresponding fcature rankings. This enables the FR-GNN to learn to predict feature importance rankings for unseen graphs.
Codee available at Waltlaaawwrauuuuaaaaeeeaeaaaainn

---

Published in Transactions on Machine Learning Research (12/2025)
Table 1: Overview of the 124 features used in the experiments, grouped into three categories: graphlets, aggregated node features, and global graph properties.
Category
Description
Graphlet Features (62)
31 count features and 31 binary indicator features for all connected, non-isomorphic subgraphs (graphlets) of 2-5 nodes, plus the bexagon Statistics (mean, std, skewness, kurtosis) for degree, centrality measures (eigenvector, closeness, harmonic, and betweenness), largest first coloring, number edges within egonet, node clique number, number of cliques, clustering coefficient, square clustering coefficient, pagerank, hubs, core number number nodes, number of edges, diameter, avg. and std. of path length, random feature
Aggregated Node Features (56)
Global Graph Properties (6)
(Step 2) Training a Graph Classification GNN (GC-GNN): We then take the remaining training data DGc = Dirain \ Drn, use the trained FR-GNN to predict a feature ranking for each graph in Doc; and aggregate these individual rankings into a global ranking. The top features from this global ranking are then selected, computed for all graphs Dec, and used to augment them with corresponding feature vectors of length K. A GC-GNN is subsequently trained on these augmented graphs to classify unseen graphs using only the most informative features.
We discuss these two steps in detail in Sections 3.2
3.3 below. Before that, in Section 3.1 we first discuss
the types of candidate graph-level features used in our experimental evaluation.
3.1 Candidate Features
The success of our approach depends, among other factors, on the appropriate selection a universal pool of candidate fcatures. This pool not tailored to specific task. Instead, should capture a broad range of global graph statistics and struetural properties, which can either be intrinsic the graph derived by aggregating node-level features. Capturing such structural properties is crucial for the quality of the trained model, especially when graphs from the same target class are expected to share common patterns that distinguish them from graphs of other classes. Aggregating node-level features into graph-level representations allows us to embed graphs into a common feature space, thereby facilitating effective graph classification.
Graphlet Features These features are computed directly over the entire graph and are used in both binary and counting forms. They encode the presence (binary form) or frequency (counting form) small subgraphs, known as graphlets, such as, for example, triangles or 4-cliques. The counts of these graphlets capture how often characteristic structural patterns appear as subgraphs, providing highly indicative information about the graph's properties and potentially capturing structural differences between graphs from different classes.
Aggregated Node Features In contrast to graphlets, aggregated node features (e.g., node degree, be- tweenness centrality) are computed at the node level before being summarized to form graph-level features. To derive graph-level features from a particular node feature for graph G, we compute statistical summaries characterizing the feature's distribution across all nodes of G. Specifically, we use the following four descriptive statistics for aggregation: (1) mean, (2) standard deviation, (3) skewness, defined by [2-1)(n22) E (E==)) measuring the asymmetry of the distribution, and (4) kurtosis, defined as 1 Ei ( 3,, quantifying the peakedness or flatness of the distribution
n
relative the normal distribution. Here, n denotes the number of nodes in G, x; the node feature value for node i, the mean of the node feature values, and their standard deviation.
5

---

Published in Transactions on Machine Learning Research (12/2025)
Algorithm Learning Feature Ranking GNN
Input: set DER of labeled graphs, candidate feature set Output: FR-GNN model 4FR
1: for all G E Drn do
2: compule the feature vector Te defined by C for G
3: D 0
4: for all G DFR do
5:
: G" E DrR and CLASS(G") # CLASS(()) Gc =
6:
for i- :i.......4 do
7:
select number & uniformly at random from {3,4,5} select random subset G' of Ga with 9 = k train random forest F; for the training set {(Eo, +) ((Er,)) eg'
compute ranking Ta, of C from their "importance" in F; 11: compute an aggregated ranking To of C from (TG.)...,,.G. Jo.)
10:
12: add (G, mG) to D
13:
PFR f learn a feature ranking GNN model from D
14:
return 4FR
Global Graph Properties These graph-level features provide high-level summaries of a graph's connec- tivity and topology. Examples of such global properties include the number of nodes and the average shortest path length.
Altogether, these three feature types yield 124 candidate features (see Table 1 Given the diversity of graph datasets, the importance of these features can vary significantly across graphs. The key challenge is to automatically identify a small subset for the task at hand that most informative for the majority of training graphs.
3.2 Step 1: Training the FR-GNN Model
The first step of our method (see Algorithm and the top part of Fig. 1 begins by selecting a random subset DER S Dusin. In the experiments reported in Section we consistently used 10% of the graphs in Dusin.
For cach graph in DrR, the mothod computes all features from the pool C of candidate features. Node-level Teatures are then aggregated into graph-level representations, as described in Section 3.1. In this way, each graph is mapped to a feature vector of dimension |C| (see the top-left matrix in Fig. and lines 2 of Alg.
To compute fcature ranking specific to cach graph in DFR, adopt binary classification strategy based random forests (see the top-right feature ranking matrix in Fig. I and lines 5 of Algorithm 1 More precisely, for all G' E Drn. we sample set of graphs from DrR that have different target label than G. In our experiments, the number of these graphs randomly varies between 3 and 5. This sampling strategy ensures that the random forest learns to distinguish between graphs with different target labels, facilitating the identification of discriminative features. The training data for the random forest classifier consists of the graph-level fcature vectors extracted from the sampled graphs, where the fcature vector of G is assigned the label '+', and those of the other graphs are assigned the label i A random forest classifier with T trees (T 128 in the experiments) is then trained on this data, using / candidate features each split. Feature importance scores are computed using the Gini gain, which measures the total reduction in node impurity due to splits on that feature, normalized over all trees in the forest.
To ensure robustness, this procedure is repeated times (t = 10 in the experiments). each time with a newly obtained by aggregating the importance sampled set of graphs from DFR The final ranking के for graph scores across the independent runs, resulting in a feature ranking for G (see the top-right matrix in Fig. which contains the individual rankings for each graph).

---

Published in Transactions on Machine Learning Research (12/2025)
This process is repeated for all graphs in DER, producing dataset, denoted D in the algorithm, that consists of training examples of the form (G,mg) for all G' E DFR, where aG is the feature ranking computed for G' as described above. The algorithm then trains an FR-GNN on D and returns the resulting model 2FR (see lines
13 14 of Algorithm | and the top-right box in Fig. D
Remark During preliminary experiments, we observed that the feature importance vectors produced by random forests often contain many values close to zero. These low scores can introduce unnecessary com- plexity into the PFR model. To address this, we introduce dynamic thresholding strategy that adaptively identifies and removes low-importance features, retaining only those that make clear contribution to the classification task. Specifically, for cach graph, the feature importance values are first sorted in asconding order. We then compute the differences between consecutive values, defined as A; = fi+1 ---- fi. If A; exceeds the importance value f; itself, we set f, and all smaller values to zero. This adaptive mechanism effectively filters out features whose contribution is negligible, climinating the need for a manually defined threshold. The remaining non-zero values correspond to features that exhibit sufficiently sharp increase in importance relative to the preceding values, signaling their discriminative potential. These final rankings are then used as input to the FRR model.
3.3 Step 2:
Training the GC-GNN Model
Given the feature learning model PFR obtained in the previous step, we apply it to each graph G in the subset DGc Dirain \ DFR to obtain a predicted feature ranking for G. These individual rankings are then aggregated to derive global ranking of the candidate features. From this aggregated ranking, the top- K features are selected and subsequently computed for the graphs in Dac- We again stress that this is the step where the benefits of our method become apparent: it computes only the top- features from the pool C for each training graph in Dec, rather than calculating all features in C. Using the training set formed by the labeled graphs in Dac, augmented with these top-K features, the method trains a GC-GNN model to classify unseen graphs (see the bottom pipeline in Fig. D.. If the training graphs in Dtrain are originally associated with node-level features, these features are used throughout the process and aggregated in the same way as the node-level features in C' (see Section 3.1
4 Experimental Evaluation
In this section, we experimentally evaluate the performance the proposed method using worldw bench- mark and synthetic datasets. The experiments are designed address the following research questions:
(Q1) To what extent do features improve the predictive performance of GNNs for graph classification? If they do, how much improvement can be expected?
(Q2) How does the predictive performance of GC-GNN using the feature set selected by our method compare to using all features in the pool? How robust is this performance as the classification task becomes increasingly difficult?
(Q3) Are the K features selected by our method genuinely relevant to the learning task, or does a randomly selected subset of K features perform similarly?
4.1 Datasets
To address the above questions, conducted experiments on diverse collection of real-wowr real-world and synthetic datasets. This section provides detailed description of the datasots used.
World Dalasels To evaluate our method, we selected a diverse set of thirteen real-world graph classifi- cation benchmarks spanning the domains of molecular chemistry, bioinformatics, and computer vision. For molecular datasots, we considered MUTAG (Debnath et al. 1991 Kriege & Mutzel 2012), BZR, DHFR, and
COX2 (Sutherland et al. 2003), NCI1 and NCI-H23H (Wale al. 2008 Kim et al., 2025 Shervashidze al., 2011), PTCMM and PTCFR (Helma et al. 2001
Kriege & Mutzel 2012). These datasets consist. of graphs
7

---

Published in Transactions on Machine Learning Research (12/2025)
where nodes represent atoms and edges denote chemical bonds, with target labels indicating biological ac- tivity. Specifically, MUTAG, BZR, DHFR, and COX2 focus classifying molecules based on mutagenicity, activity against the benzodiazepine receptor, enzyme inhibition, and cyclooxygenase 2 activity, respectively. NCI1 targets activity against human non-small cell lung cancer, while PTCMM and PTCER prodict rodent carcinogenicity in male mice and female rats, respectively. The PROTEINS dataset (Borgwardt et al. 2005;
Dobson & Doig, 2003) from bioinformatics consists of protein structures, where nodes represent sccondary structure elements and edges denote spatial proximity between them. The classification task in PROTEINS is to distinguish enzymes from non-enzymes. Finally, the MSRC9 dataset (Neumann et al. 2016 from com- puter vision, derived from image segmentation, represents segmented images as graphs, with nodes and edges corresponding to superpixel relationships, and labels indicating object classes. We additionally evaluated our method on three social network datasels: Reddit-Binary, Reddit-Multi-5K, and Redddi--Multi-12K (Ya- nardag & Vishwanathan 2015). In these datasets, nodes represent users, and an edge is created between two nodes if one responded to the other's comment. The task in Roddit-Binary is to classify each discussion graph as either a question peeestion/answer-ee /answer-based community or discussion-basel community. In Reddit-Multi-5K and Reldit-Multi- Multi-12K, the goal is to predict the subreddit category to which each discussion graph belongs. The three Reddit datasets, together with NCI-H23H, will also be used to investigate the scalability of our algorithm. Dataset statistics are summarized in Table 2 in Appendix B
Synthetic Datasets To evaluate our method's ability to detect structural features defining target classes, we conducted experiments on synthetic graph datasets with known ground truth. For each learning problem defined below, we generated four datasets, each with 600 connected base graphs from one of four standard random graph models: Barabási-Albert (BA) (Barabási & Albert 1999), Firöös-Rény (ER) (Erdös & Rényi 1959), Watts-Strogatz (WS) (Watts & Strogatz, 1998), and Power- Law (PL) cluster (Holme & Kim 2002
We defined the target classes using four distinct graphlet motifs: the 4-clique (Gs), the path - - U/ U4- Ub on five vertices with chords f1 and U2 (G20), the house graph (G21), and the hexagon (Gxo) ) (see Fig. g in Appendix [A). They are pairwise topologically incomparable (i.c., none is subgraph isomorphic to any another), and the base graphs to which they are subsequently allached were generated to exclude all of them. Furthermore, the graphlets were attached in such way that each graph satisfies exactly one class condition.
This design ensures that the presence of the graphlets acts as a discriminative signal rather than a background artifact. The four motifs are explicitly included in the candidate feature set, and the logical formulas defining each target class depend exclusively on the presence and interaction or absence of these motifs. This setup enables us to construct a hierarchy of graph classes through logical formulas of increasing structural complexity, all grounded in these four motifs. Importantly, provides a controlled testbed for systematically evaluating the sensitivity and expressiveness of our feature selection mechanism. Specifically, if our method fails to distinguish classes that differ only in the combination of these known motifs, its limitations are revealed in precise and interpretable manner.

---

Published in Transactions on Machine Learning Research (12/2025)
For each base graph type, considered five learning tasks, with target classes defined by the following logical formulas (G; below denotes the absence of motif G.):
: (CLASS c Gg Go A G21) A
(CLASS = 02 - Gg A G20 A G21) A
(CLASS = C3 +
Gg A G20 A G21) A
(CLASS C4 F
Gg A 22 A G21)
(1)
22 (CLASS = C1 F
Gg A 2o A G21) A
(CLASS 02 + Gg A G20 G21) A
(CLASS = C3 -
Gg A G2 A G21)
(2)
4 (CLASS < Gs A G2n A G21) A
(CLASS - G8 G2n G21)
(3)
44 (CLASS Co Gg A G2 A G21 A
(CLASS = C - (G&A G20 A Gn) V (G& A G20 A G2) VG G2 Gz1) A
(CLASS = C - (Gg A G20 A G21) V (Gg A G20 A G21) V (Gg A G20 A G21) A
(CLASS = C3 + Gg A G20 A G21)
(4)
4 (CLASS = C F
(G& V G2o) A G21 A G30) A
(CLASS C2
(Gg G20 V G21) A G30)
(CLASS = C3
G21 A G30)
(CLASS = CA +
Go A 2 A ((G21 A Gso) V (G2z A Go))
(5)
In 11, the four classes are pairwise disjoint and determined by the presence of exactly one motif or none, corresponding to a one-hot encoding over the three motifs. D2 defines three classes, each by the presence of exactly two motifs, making the problem more challenging due to feature overlaps. 43 is a concept learning task where the target class requires the presence of all three motifs, highlighting the difficulty for random forests with the Gini index, which evaluates features individually and is therefore less sensitive to feature interactions. In 4,, four classes are defined by the presence of exactly motifs (i 2,). 45 introduces fourth motif and higher logical formula depth, testing robustness class definitions become more complex.
4.2 Experimental Setting
For the experiments, use three widely adopted GNN architectures: Graph Convolution Networks
(GCN) (Kipf & Welling 2016 Graph Attention Networks (GAT) (Velickovic et al. 2018). and Graph-
SAGE (Hmmllon et al., 2017). The dataset is split such that 10% of the graphs are used to train the FR-GNN, while the remaining 90% are further divided 70/30 for training and testing the GC-GNN. We re- port the average accuracy over independent runs. For feature ranking, for each graph G DFR E (8,4,5) graphs with different labels are sampled. Feature importance is computed via random forest with 128 trees and / C features per split.
All GNN models optimized using Adam, with hyperparameters selected via grid search (learning rate of 0.005, dropout rate of 0.5). Experiments are run on an AMD Ryzen 9 5950X 16-core CPU @ 3.40GHz with 125 GB of memory. The Pyroo Geometric library (Fey & Lenssen 2019 is used for data handling.
For all experiments, except those involving synthetic data with target classes defined by Eq. (5), we consis- tently used K 6, i.c., selected the top six features. (We discuss the rationale for this choice in Sect. 4.3.1] To address questions Q1-Q3, we compare the proposed method, denoted T-6 (short for "top 6*), against three baselines: F-O: using features (Q1), F-C: using all features (Q2), and R-6: using six features selected
9

---

Published in Transactions on Machine Learning Research (12/2025)
GCN
100
Accuracy (%6
60
20
GAT
100
Accuracy (%)
60
GraphSAGE
Accuracy (%6
60
40
20
ER
PL
WS
PL
WS
WS
0
0g
04
F-O F-C
R-6
T-6
Figure 2: Grouped bar charts summarizing model performance the synthetic datasets for the four clas- sification tasks @ 44- The top, middle, and bottom panels correspond to GCN, GAT, and GraphSAGI respectively. Within each panel, datasets are grouped by task, and for each dataset, four color-coded bars represent the variants F-O, F-C, R-6, and T-6.
at random from C (Q3). We refer to these the "no-feature", "all-feature", and "random-featuree baselines, respectively.
4.3 Experimental Results
The results presented grouped bar charts in Figs. 2 and and in Fig. 9 in Appendix A for the synthetic and real-world datasels, across all three GNN architectures.
Answer to Q1: The results the synthetic data provide a clear answer to this question (see Fig, 2 and
Tables 4 and 0 in Appendix B): baselines that utilize all features (F-C), or even just six randomly selected features (R-6), significantly outperform the baseline that uses no features (F-0). Across the synthetic experiments, we observe improvements of up to 80% for F-C and up to 70% for R-6 relative to F-0.
The results for real-world datasets are more mixed (see Fig, 3 and Table in Appendix B For all three GNN architectures, F-O is outperformed by both F-C and R-6 on some datasets (e.g., MUTAG), while on others (e.g. DHFR), it actually outperforms the other two baselines. These results suggest that using either too many features small number of randomly selected features can, in some cases, diminish predictive performance.
Furthermore, our method T-6 consistently outperforms F-O across all real-world and synthetic datascts and all three GNN architecturos, with average improvements of about at least 50% on the synthelic and about 14.2% for GCN, 15.8% for GAT, and 14.5% for GraphSAGE on the real- world datasets. On DHFR, where all three GNNs using no features perform better than when using either all or six random features, T-6 achieves a 6% improvement over F-O with GCN. The improvement is even more dramatic on MUTAG, where T-6 outperforms F-0 by around 23% with GAT.
10

---

Published in Transactions on Machine Learning Research (12/2025)
GCN
100
Accuracy (%)
80
60
40
GAT
100
Accuracy (%)
80
60
GraphSAGE
100
Accuracy (%6
80
60
MUTAG
MSRC9
PTCMM
PTCFR
82R
COX2
Proteins
NC11
F-O
F-C
R-6
SOTA
Figure 3: Grouped bar charts summarizing the results from Table in Appendix across three GNN architectures (top: GCN, middle: GAT, bottom: GraphSAGE) Each panel presents the accuracies across five variants - F-O, F-C, R-6,T-6, and the reproduced SOTA results, shown as color-coded bars
B for the real-world datasets
In summary, answer to question Q1 is conditionally affirmative: features substantially enhance predictive performance, as long as they are not overly numerous randomly selected.
A Answer to Q2: The accuracy results Fig. (see also Table in Appendix B clearly show that T-6 consistently outperforms F-C on real-world datasets across all three GNN architectures. Specifically, method achieves average accuracies of 74.8% (GCN), 73.9% (GAT), and 75.1% (GraphSAGE) across 13 real-world benchmarks, compared to F-C's accuracies of 67.6% (GCN), 66.4% (GAT), and 69.0% (GraphSAGE). This corresponds to average improvements of 7.2%, 7.4%, and 6.2%, respectively. The most significant improvement, around 20% across all GNN architectures, was obscrved on the Protoins datasct. These rosults support our conjecture that too many features can lead to overfilling
In contrast, on synthetic datasets (see Fig. 2 and Tables and in Appendix B F-C achieves at least 90% accuracy on all five problems (Φ) 25), across all four types of random graphs. Remarkably, for - the six features selected by our method perform at least as well as F-C, which attains nearly 96% accuracy, and sometimes even improve upon these results by up to 2%.
However, &6 (see Fig. and Table 5 in the Appendix), which involves four classes and more complex logical formulas, our method with six features achieves lower predictive performance than F-C. Nevertheless, the number of selected features increases, the performance difference becomes negligible (see the comparison between F-C and T-20).
In summary, GC-GNNs using the six features selected by our method consistently outperform those using all features on real-world datasets, demonstrating improved accuracy and reduced overfitting, On synthetic datasets, our method matches or exceeds the performance of using all features for simpler tasks and remains robust, with only negligible performance gap as task complexity and the number of selected features increase.
11

---

Published in Transactions on Machine Learning Research (12/2025)
Answer to Q3: Regarding the question of whether the six features selected by method (T-6) are genuinely relevant to the learning task, we compared the accuracy results obtained by T-6 with those obtained using six features selected uniformly at random from the candidate pool. A closer look at Figs. 2 and 3 (sce, also, Tables 3 reveals that T-6 consistently outperforms R-6 across all datasets and all three GNNs, In particular, on the real-world datasets, T-6 perffrrmss R-6 on average by 10.2% (GCN), 12.2% (GAT), and 12.3% (GraphSAGE). In some cases, the difference is dramatic (e.g., R-6 achieves 52.5% (GCN) on Proteins, while T-6 achieves 80%).
In summary, based on these results, we can provide a clear affirmative answer to Q3: The feature set returned by our method is genuinely relevant to the learning task and not selected by chance.
4.3.1 Further Results on the Real-World Data
We now present and discuss additional results obtained on the real-world benchmark datasets.
Comparison to SOTA Results To contextualize the predictive performance of our approach, we compared it against existing SOTA results on the same real-world datasets. Specifically, we included only results that were published in peer-reviewed conference or journal papers, with publicly available code that could be executed on the corresponding datasets. Of the 13 benchmark datascts, eight met these criteria. For each of these eight datasets, we ran the respective algorithm and reported both the accuracy published in the literature and the accuracy achieved upon re-exccution of the authors' code. In total, three recent algorithms (Akyol et al. 2021: Vincent-Cuaz et al. 2022; Wen et al. 2024 allained SOTA performance on at least one of these eight datasets.
On three of the eight datascts, our approach either outperforms or matches the accuracy reported in the literalure within 2% (see the upper table in Table g in Appendix B.. However, when comparing against results reproduced using the authors' publicly available code our approach outperforms or closely matches the reproduced results (within 2%) on all eight datasets (including MUTAG, Proteins, NC11 (Vincent-Cual et al. 2022). MSRC9 (Akyol et al. 2021). and PTCMM, PTCFR, BZR, and COX2 (Wen et al. 20244).
Statistical Sigmificance We evaluated the statistical significance of the observed differences in predictive performance between T-6 and the three baselines (F-0, F-C, and R-6) on the real-world datasets. For this purpose, we first applied the Kruskal- Wallis test. The null hypothesis (i.e., no performance differences) was rejected at a = 0.01 (99% confidence level) with p = 0.0016, indicating strong evidence of performance variation across the methods. Given this result, we proceeded with Dunn's 's post-hoc test {Dunn 1961) with Holm adjustment to identify pairwise differences. We found that T-6 significantly outperforms R-6 at the 99% confidence level, and achieves statistically significant improvements over both F-O and F-C at the 95% confidence level. Thus, the improvements by T-6 are not only consistent but also statistically significant.
Choice of K All experimental results presented in this paper, except. those for the problems defined by $5. were obtained using K = 6. This value was selected by computing the average accuracy for all values of == 1, 10 and choosing the value (i.c., 6) that yielded the highest average porformance. In Fig. (left), we present not only the overall average accuracies but also the accuracy results for different K values on the MUTAG and PTCMM datasets. While the optimal value of K is 6 for MUTAG, it is 5 for PTCMM. We note that K can alternatively be selected automatically for each dataset individually, by using small validation subset of the training data and choosing the smallest value of K that yields the highest predictive performance on this subset. Notice that, regardless of the technique used to select the optimal value of K (c.g., via a validation set using Bayesian optimization), the following steps need to be performed only once: computing all features in C for the graphs in DFR, training the random forest and the FR-GNN model, and predicting the feature ranking for the graphs in Dec. Moreover, each feature considered for any value of K must only be computed once for the graphs in DGc. In contrast, the GC-GNN model must be retrained from scratch for every value of K considered by the algorithm.
Feature Analysis To further validate our feature selection approach, we conducted a qualitative analysis of several top-ranked features identified by our method for the real-world datasets. Specifically, we examined
for Akkyl al. 2021
githabb.om//eddeevveennneerr/eee TFGW for (Vincent-Cupe et al. 2024)
2022 and gilhub.comm/TaaWao000///// for (Wen
12

---

Published in Transactions on Machine Learning Research (12/2025)
100
0.025
Accuracy (%)
Density
80
0.015
70
0.010
60
0.005
50
3
6
9
10
0.000
K
Triangles Count Values
Figure 4: Left: Model accuracy of the top K features selected by our method for different values of K on two datasets: MUTAG (blue) and PTCMM (green), along with the average accuracy across all datasets using GCN (red). Right: Kernel density estimation (KDE) plots of the top-ranked feature for MUTAG (triangle count), showing the distribution of feature values across the two graph classes.
All-Feature
Top-K Features
log
10
20*
Total Runtime
10a
10
PTCMM
PTCPR
MUTAG
BZR
COK2
MSRCY
DNFR
NC1
PROTEING
NGHH23H
Redsit Binany
Reddlt Multii-Multt-Kk 5K
Redsft Multi
Figure 5: Total wall-clock runtime for each of the 13 benchmark datasets on both variants: the all-feature baseline and the proposed top-K method. Datasets sorted in ascending size, defined as (number of graphs) X (average number of edges). The three large Reddit datasets, containing much larger graphs are shown separately on the right and sorted by number of graphs to demonstrate scalability. Note the logarithmic scale on the y-axis.
the distributions of these features across graph classes using kernel density estimation (KDE), which allowed us to assess their discriminative power: The selected features exhibit meaningful and clas-ddseriminativo palterns. As an illustrative example, top-ranked features (see Fig. 4 right). The KDE plot shows that class graphs consistently exhibit higher triangle counts, suggesting that the triangle graphlet structure is strong indicator of mutagenic activity and is effectively captured by our selection method.
the MUTAG datasel, the triangle count emerged as one of the
Empirical Runtime and Accuracy Figure 5 presents the total runtime per dataset for both the all-feature bascline and our top-K feature selection mothod (note the logarithmic scale on the y-axis). The datasets are sorted in ascending order according to the product the number graphs and the average number of odges.
While the runtime improvement is mixed across the first nine datascts, a clear advantage emerges for NCI- H23H (which contains many small graphs) and for the three Reddit datasets (which comprise increasing mumbers large graphs). For these four datasets, where the runtime of the all-feature baseline becomes particularly critical, our approach demonstrates a pronounced benefit. Specifically, it achieves up to a 90% reduction in total wall-clock time while simultancously improving classification accuracy. The improvement is most pronounced for Reddit-Multi-12,, where the all-feature baseline required more than 557 hours.
13

---

Published in Transactions on Machine Learning Research (12/2025)
Accuracy vs. Runtime
100
4
Datasets
All-Feature Top-K Features
PTCHw
90
PTcra
MUTAG
Accuracy (%)
B2R
COM2
70-
NSRCO
60
50-
Binary
Redatt Multi-x
Reactt Mults
30
10a
10e
Runtime (seconds. log scale)
Figure 6: Accuracy-runtime comparison across 13 benchmark datasets. Each datasct is represented by a unique color, with circles denoting the all-feature baseline and triangles the proposed Top-K method. Dashed lines connect paired results for the same dataset. The x-axis shows total wall-clock runtime in seconds (log scale) and the y-axis shows classification accuracy.
whereas our approach completed the task in approximately 57 hours.
Importantly, this considerable reduction in computational time does not come at the expense of predictive performance; our method maintains, and in several cases improves, the classification accuracy compared to the all-feature baseline. The relationship between accuracy and total runtime is illustrated in Fig. 6 Our method achieves significantly lower runtimes on large-scale datasets while preserving or enhancing predictive performance. On smaller benchmarks, the feature ranking phase introduces a minor computational overhcad; however, this cost is negligible compared to the consistent improvements in classification accuracy achieved by our method.
Runtime Analysis We now analyze the runtime required by our approach. Spocifically, we compare the total time of the all-feature baseline (Tc) to that of our method (Tx), and then proceed to compare the inference times of the two approaches.
Recall that the training data, Derain, is partitioned into two subsets: DFR and Dec, where DFR (respectively, Dec) is used to train the FR-GNN (respectively, GC-GNN). Let Fx demote the set of K features selected by our method. The total training time for each approach can be expressed by
Tc TGC-GNN Praain (Drrain C)
Tk TFR-GNN (DFR. C) + TGC-GNN (Doc, Fk)
Here, TGC-GNN (Dirain C) denotes the time required to compute all features in C for all graphs in Dtrain (T(a1)), plus the time to train a GC-GNN using Dirain with the resulting feature vectors (T(a2)). The term TFR-GNN (DyR, C) in Tk consists of the runtime of the following steps: Computing all features in for all graphs in DpR (T(3)), training random forest on the computed feature vectors and calculating feature ranking for all graphs in DFR (T(32)), and training the FR-GNN Drr with the associated feature rankings (T(3s)). Finally, Tec-oxN(DGc. Fx) in Tr includes the time to predict feature ranking for each graph in DGC using the FR-GNN model (T(1)), the time to determine the top K features from these predicted rankings (T(72)), the time required to compute the K features in Fx for all graphs in Dec (T(7))), and the time to train a GC-GNN using the resulting feature vectors (T(7)).
It follows that our approach achieves superior runtime performance compared the all all-feature baseline whenever Te Tk, that is, if
T(a)) + T(az) >
+ + (()))))((((()))++))+)))))))++))+ T(m) + T(7)) + T(7s) ) + T(1))
(6)
Using T(a2) R T(3)) + T(74) (follows from Blakely et al. (2021 and the notation
T=T(3) + T(x) + T(22)
14

---

Published in Transactions on Machine Learning Research (12/2025)
6
implies
T(a1) > + + T(hs).
(7)
Consider the case that
T T(3)) T(1s)
(8)
holds if Then 7
T(m) ((T(3)) + T(s)))
(9)
Assuming that the average runtime to compute a feature from C for graph in Duran equals that for features from FK in Dec and for features from C in DFR. (9 can be expressed by
CC [Periial Tr 2 (IC) [Der] Tr K |Decl TT)
which, in turn, holds whenever
|Deel Deraii
|C| 2([C] - K)
(10)
because Dirain is the disjoint union of DFR and DeC.
In summary, under the above assumption, our approach achieves better runtime than the all-feature baseline whenever both inequalities and (10) hold. Specifically, ( requires that the total time to (i) train the random forest, (ii) compute feature ranking for each graph in DER, (iif) predict feature rankings for all graphs in Dec using the FR-GNN model, and (iv) select the top K features from these predicted rankings is no greater than the time needed to compute all features for all graphs in DFR plus the time to compute the K features in Fx for all graphs in DGc-
In Fig. al): we present the three runtime terms from ( for each real-world benchmark datasot analyzed our experiments. Of the datasets considered, (8) is satisfied by five: MSRC9, NCI-H23H, Reddit-Binan Reddit-Multi-5K, and Reddit-Multi-122 bascline (sce Fig. 5 in accordance with (9). given that [Dacl [Puaial 0.86 and |ci- 1.05 in all experiments. Notably, the four computationally expensive datasets (i.e., those requiring at least 1,000 seconds) are among this group, and the speed-up for the three Roddit datascts is at least one order of magnitude (note the log-scale on the y-axis).
For these datasets, our approach is faster than the all-feature
|C|
We finish our runtime analysis by noting that our approach consistently offers an advantage in terms of inference time. Specifically, for each graph to be classified, it requires computing only K features from the full candidate set C. This is particularly important for applications in which the GC-GNN model must be applied to (potentially very) large number of graphs.
Scalability To assess scalability, we extended our experimental evaluation to include four larger benchmarks: Reddit-Binary, Reddit-Multi-Ske Reddit-MMulti-122 and NCI-H23H, with dataset statistics summarized in Table 2 Appendix B The three Reddit datasets each comprise graphs of similar size, whereas the average graph size in NCI-H23H is approximately one order of magnitude smaller.
We first. investigate how our approach scales with increasing average graph size. For the Reddit datasets, which all contain large graphs, the per-graph runtime of the all-feature baseline ranges from 168 to 208 seconds, while our method achieves 17 to 21 seconds per graph-an magentuf-manituude reduction. On the large NCI-H23H dataset, containing many small graphs, both methods yield very low per-graph runtimes (0.07 seconds for the baseline 0.04 seconds for our method), but method remains more efficient.
15

---

Published in Transactions on Machine Learning Research (12/2025)
Puntime Composition (%)
Runtime Compositon
60
40-
40-
20-
20
Gloppe
Best
Rodd Hosil
Andell Roary
FR-GNN Feature Computation (1f:)
Festure Computation X&))
Top Features Computing Riys
Top K Festures Computing ilm)
T- (62) Ky) + flys)
M--MNN Training
Rf Training X80
Training
(a) Inequality Terms Runtime Breakdown
(b) Full Runtime Breakdown
Figure 7: Normalized percentage breakdown of running time per dataset. The stacked bars show the relative contribution of different computational components. (a) Breakdown corresponding to the terms defined in incquality 8 (b) Full docomposition of the end-to-end pipcline, including all components.
Thus, for our method, increasing the average graph size by one order of magnitude results in a roughly of--orddr-o--maanitudd increase per-graph runtime.
This behavior is expected, since the candidate feature set includes computationally expensive operations (e.g., graphlet counts). A closer examination of Fig. 7 confirms that, for the three Reddit datasets, the time required to compute the full feature set for the graphs in DER dominates the total runtime.
When considering only the three Reddit datasets, which contain graphs of similar size, the per-dataset computational time scales linearly with the number of graphs. Indeed, the per-graph computational time is nearly equal for these datasets (Reddit-Binary: 19.40 sec, Reddit-Multi-B 21.31 sec, 17.22 sec). This indicates that increasing database cardinality alone does not significantly affect the per- graph computational elfort.
In summary, the primary determinant of per-graph runtime is the average graph size. This implics that for (very) large graphs, the time complerity of computing a condidate feature should be quasilinear in the namber of verlices.
4.3.2 Further Results on the Synthetic Data
Other Feature Ranking Ayproaches We evaluated the performance three methods: random forests (RF), support vector machines (SVM) (Cortes & Vapnik 1995), and neural networks coupled with the LIME, local explainer (Ribeiro et al.] 2016) LNN+LIME), in identifying key graphlet features across the five learning problems Φ1-0, defined in Section 4.1 RF consistently identified the three key graphlets (Gs, G20, and G21) among the top-ranked features for the problems defined by - Notably, other features, such the total number of cliques and the node clique number, were also frequently selected as important. Upon investigation, we found these features to be semantically aligned with the identified graphlets, particularly since Gg corresponds to a 4-clique. SVM exhibited similar, though slightly less consistent, behavior, with the key graphlets appearing lower the ranking compared RF. contrast, NLIL could not consistently identify the relevant graphlets. For problem 4G, all three methods struggled to consistently rank the four relevant graphlets among the top features. However, RF demonstrated comparatively stronger performance, as the four features associated with 4g were ranked higher than by SVM and NN+LIME.
We also compared the runtime of these three algorithms. NN+LIME required the longest training time, followed by RF, while SVM was the fastest but less accurate in identifying the most. informative features. Since accuracy was our primary concern, we chose RF for all subsequent experiments.
The Count-Based Problem We also explored a learning problem (denoted 46) where the class label was determined by the number of graphlets from Gg, G2n, and G21 present in the graph. Specifically, graphs
16

---

Published in Transactions on Machine Learning Research (12/2025)
containing at most motif from this set were assigned to class 0, those containing two to four motifs to class 1, and graphs with five or more motifs to class 2. The results exhibited behavior similar to that observed in learning problems d 24 (see Fig. 9 and Table 6 in the Appendix).
5 Concluding Remarks
We have proposed method that automatically selects small subset of relevant features from a large pool of candidate features to improve the predictive performance of GNNs for graph classification. Our experimental results on thirteen nine benchmark datasets and three GNN architectures clearly demonstrate that: (1) incorporating node features can significantly enhance predictive performance compared to vanilla GNNs, (2) to prevent overfitting, it crucial to select a small, informative subsct of features from a large candidate pool rather than using all available features, and (3) the features selected by our method are genuinely relevant to the learning task, rather than being chosen by chance.
We also evaluated the relevance of the selected features in a more controlled and precise setting. Specifically, generated synthetic base graphs and defined target classes using logical formulas of increasing complexity, based on the presence or absence of a small set of motifs. Our results show that the approach can accurately identify relevant features and successfully learn these classification tasks. However, as the complexity of the formulas increases, more features must be selected to maintain high accuracy.
While our method demonstrates effective feature selection for improving GNN-basod graph classification, several promising avenues remain for future exploration. First, scaling the approach to handle very large graphs is a natural next step. In experiments, the FR-GNN trained separately for each dataset. We also explored training single, global FR-GNN across all datasets. Although this global model led to GC- GNNs with higher average accuracy than the three baselines, its performance gains were less pronounced than those achieved by individually trained FR-GNNs (see Table 7 in the Appendix). Thus, another question is how to adapt and extend our approach to train a global FR-GNN that can produce task-specific GC- GNNs with predictive performance at least comparable to those reported here. Additionally, investigating the robustness of our method to noisy or adversarial features, developing theoretical guarantees for feature subset optimality, and establishing bounds generalization error or subset optimality would further deepen the understanding and reliability of our approach. Finally, it would be useful to modify the method to account for feature compulation time, selecting the most informative features with the smallest cumulative runtime.
Broader Impact Statement
Our framework automates feature subset selection for graph classification by choosing small, task-specific subset from user-defined universe of candidate features. This improves predictive performance and reduces feature computation time. However, the method docs not scale well to very large graphs, limiting applicability in such settings. The key ethical consideration is in defining the universal candidate feature set, which requires careful design by domain experts to avoid bias and ensure relevance. Transparent reporting and validation are necessary, especially for sensitive or high-stakes applications. By balancing expert knowledge, automation, and efficiency, our approach supports responsible and interpretable AI for graph-structured data.
References
Gamze Akyol, Sanem Sariel, and Eren Erdal Aksoy. A variational graph autoencoder for manipulation action recognition and prediction. In 2021 20th International Conference on Advanced Robotics (ICAR), pp. 968 973. IEEE, 2021.
Fouad Alkhoury, Tamás Horváth, Christian Bauckhage, and Stefan Wrobel. Improving graph neural networks through feature importance learning. Machine Learning, 114(8):178, 2025. ISSN 1573-0565 doi: 10.1007/ 5109944-025-6615--0 URL http://pss///aaoooo////..//////0
17

---

Published in Transactions on Machine Learning Research (12/2025)
Alsert-László Barabási and Réka Albert. Emergence of scaling in random networks. Science, 286(5439): 509-512, 1999.
Pablo Barceló, Floris Geerts, Juan L. Reutter, and Maksimilian Ryschkov. Graph neural networks with local graph parameters. In 35th Annual Conference Neural Information Processing Systems (NeurIPS), pp. 25280-25293, 2021.
Derrick Blakely, Jack Lanchantin, and Yanjun Qi. Time and space complexity of graph convolutional networks. Accessed on: Dec, 31:2021, 2021.
Karsten M Borgwardt, Cheng Soon Ong, Stefan Schönauer, SVN Vishwanathan, Alex J Smola, and Hans- Peter Kriegel. Protein function prediction via graph kernels. Bioinformatics, 21(suppl 1):147 156, 2005.
Giorgos Bouritsas, Fabrizio Frasca, Stefanos Zafeiriou, and Michael M. Bronstein. Improving graph neural network expressivity via subgraph isomorphism counting. IEEE Trans. Paltern Anal. Mach. Intell., 45 (1):637-668, 668, 2023.
Zhuoyang Chen and Qiong Luo. Dualnetgo: a dual network model for protein function prediction via effective feature selection. Bioinformatics, 40(7):btae4337, 2024.
Corinna Cortes and Vladimir Vapnik. Support-vector networks. Mach. Learn., 20(3):273 297, 1995. doi: 10. 10000//000094008.. URL htttss:/doo http://d...0rr//10...00/////////
Hejie Cui, Zijie Lu, Pan Li, and Carl Yang. On positional and struct ural node features for graph neural net- works on non-attributed graphs. In Proceedings of the 31st ACM International Conference on Information & Knowledge Monagement, pp. 3898-3902, 2022.
Enyan Dai, Wei Jin, Hui Liu, and Suhang Wang. Towards robust graph neural networks for noisy graphs with sparse labels. In Proceedings of the fifteenth ACM international conference on web search and data mining, pp. 181- 191, 2022.
Asim Kumar Debnath, Rosa L Lopez de Compadre, Gargi Debnath, Alan J Shusterman, and Corwin Hansch. Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds, correlation with molecular orbital energies and hydrophobicity. Journal of medicinal chemistry, 34(2):786-799) 1991.
Paul D Dobson and Andrew J Doig. Distinguishing enzyme structures from non-enzymes without alignments. Journal of molecular biology, 330(4):771-783, 2003.
Olive Jean Dunn. Multiple comparisons among means. Journal of the American statistical association, 56 (293):52 64, 1961.
Chi Thang Duong, Thanh Dat Hoang, Ha The Hien Dang, Quoc Viet Hung Nguyen, and Karl Aberer. On node features for graph neural networks. arXiv preprint arXim:1911.08799 2019.
P. Erdós and A. Rényi. On random graphs Publicationes Mathematicae Debrecen, 6:290 297, 1959.
Hongliang Fei and Jun Huan. Structure feature selection for graph classification. In Proceedings of the 1 17th ACM conference on Information and knowledge management, pp. 991-1000, 2008
Matthias Fey and Jan Eric Lenssen. Fast graph representation learning with pytorch geometric. CoRR, 0bs//193..0248,, 2019.
Guoji Fu, Yifan Hou, Jian Zhang, Kaili Ma, Barakeel Fanseu Kamhoua, and James Cheng. Understanding graph neural networks from graph signal denoising perspectives. arXio preprint arXiv:2066.04, 04386, 2020.
Jingwei Guo, Kaizhu Huang, Rui Zhang, and Xinping Yi. Es-gnn: Generalizing graph neural networks beyond homophily with edge splitting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024.
William L. Hamilton. Graph Representation Learning. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers, San Rafael, 2020.
18

---

Published in Transactions on Machine Learning Research (12/2025)
William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In
Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett (eds.), Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, pp. 1024-1034, 2017.
Christoph Helma, Ross D. King, Stefan Kramer, and Ashwin Srinivasan. The predictive toxicology challenge 2000-2001. Bioinformatics, 17(1)1107-108, 2001.
Petter Holme and Beom Jun Kim. Growing scale-free networks with tunable clustering. Physical review 65(2):026107, 2002.
S. Kim, J. Chen, T. Cheng, A. Gindulyte, J. He, S. He, Q. Li, B. A. Shoemaker, P. A. Thiessen, B. Yu,
L. Zaslavsky, Zhang, and E. E. Bolton. Pubchem 2025 update. nucleic acids res., 2025. PubChem
Thomas N. Kipl and Max Welling, Semi-supervised classification with graph convolutional networks. CoRR, abs/1609.02907,, 2016.
Nils Kriege and Petra Mutzel. Subgraph matching kernels for attributed graphs. ar preprinl arXiv:1206. 6483, 2012.
Yao Ma, Xiaorui Liu, Tong Zhao, Yozen Liu, Jiliang Tang, and Neil Shah. A unified view graph neural net- works graph signal denoising. In Proceedings of the 30th ACM international conference on information & knowledge management, pp. 1202-1211, 2021.
Sunil Kumar Maurya, Xin Liu, and Tsuyoshi Murata. Feature selection: Key to enhance node classification with graph neural networks. CAAI Transactions Intelligence Technology, 8(1):14-28, 2023.
C. Morris, M. Ritzert, M. Fey, W. L. Hamilton, J. E. Lenssen, G. Rattan, and M. Grohe. Weisfeiler and Leman go neural: Higher-order graph neural networks. In The 33rd AAAI Conference on Artificial Intelligence, pp. 4602-4609, 2019.
Harish Naik, Jan Polster, Raj Shekhar, Tamás Horváth, and György Turán. Iterative graph neural network enhancement frequent subgraph mining explanations. CoRR, abs/2403.07883 07844, 2024.
Marion Neumann, Roman Garnett, Christian Bauckhage, and Kristian Kersting. Propagation kernels: effi- cient graph kernels from propagated information. Machine learning, (02:209-245, 2016.
Ignacio Ponzoni, Victor Sebastián-Pérer María J Martínez, Carlos Roca, Carlos De la Cruz Pérez, Fiorella Cravero, Gustavo E Vazquez, Juan A Pácz, Mónica F Díaz, and Nuria E Campillo. Qsar classification models for predicting the activity of inhibitors of beta-secretase (bacel) associated with alzheimer's disease. Scientific Reports, 911:9100, 2019. doi: 10.1038 10.1038/s41159 /0/////11199-------1 019-4552-3,, URL https: //www nature. com/ arriciles//11199--994445222
Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. Why should i trust you? explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135-1144 ACM, 2016.
Ryan A Rossi, Rong Zhou, and Nesreen K Ahmed. Estimation of graphlet counts in massive networks. IEEE transactions on neural networks and learning systems, 30(1):44-57, 2018.
Nino Shervashidze, SVN Vishwanathan, Thomas Petri, Kurt Mehlhorn, and Karsten M Borgwardt. Efficient graphlet kernels for large graph comparison. In Artificial intelligence and statistics, pp. 2009.
PMLR,
Nino Shervashidze, Pascal Schweitzer, Erik Jan Van Leeuwen, Kurt Mehlhorn, and Karsten M Borgwardt. Weisfeiler-Ichman graph kernels. Journal of Machine Learning Research, 12(9), 2011.
Jeffrey Sutherland, Loe A O'brien, and Donald F Wcaver. Splino-fitting with genetic algorithm: A method for developing classification structure- activity relationships. Journal of chemical information and computer sciences, 43(::11906 19911 2003.
19

---

Published in Transactions on Machine Learning Research (12/2025)
Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. In 6th International Conference Learning Regresentations, TCLR 2018. OpenReview.net, 2018. URL Sttpss///opnnrerreee.ee////////
Cédric Vincent- Rémi Flamary, Marco Corneli, Titouan Vayer, and Nicolas Courty. Template based graph neural network with optimal transport distances. Advances in Neura Information Processing Sys- lems, 35:11801 1800-11814, 2022.
Nikil Wale, Ian A Watson, and George Karypis. Comparison of descriptor spaces for chemical compound retrieval and classification. Knowledge and Information Systems, 14:347-377 335, 2008.
Duncan J Watts and Steven Strogatz. Collective dynamics of Sonall-wordd'netwweee works.. nature, 393(6684): 440 442, 1998.
Tao Wen, Elynn Chen, and Yuzhou Chen. Tensor-view topological graph neural network. In International Conference on Artificial Intelligence and Statistics, pp.
PMLR, 2024.
Pinar Yanardag and SVN Vishwanathan. Deep graph kernels. In Proceedings of the 21th ACM SIGKDD international conference knowledge discovery and data mining, pp. 1365-1374, 2015.
Yaming Yang, Ziyu Guan, Wei Zhao, Weigang Lu, and Bo Zong. Graph substructure assembling network with soft sequence and context attention. IEEE Transactions on Knowledge and Data Engineering, 35(5): 4894-4907, 2022.
Zhen Zhang, Jiajun Bu, Martin Ester, Jianfeng Zhang, Chengwei Yao, Zhi Yu, and Can Wang. Hierarchical graph pooling with structure learning. arXiv preprint 05954, 2019.
20

---

Published in Transactions on Machine Learning Research (12/2025)
A
Appendix: Figures
Gs
200
G21
G
Figure 8: The four graphlets used our experiments. isomorphic another).
They are pairwise incomparable (i.e., none is subgraph
GCN
100
(%)
60
40
GAT
60
GraphSAGE
Accuracy
60
20
BA
ER
WS
PL
BA
ER
W5
PL
Og
F-O
F-C
R-6
T-6
T-10
T-20
Figure 9: Grouped bar charts summarizing the results from Table and Table in Appendix classification tasks 2s (left) and the count-based learning problem 4 across three GNN architectures (top: GCN, middle: GAT, bottom: GraphSAGE).
B for the
21

---

Published in Transactions on Machine Learning Research (12/2025)
B
Appendix: Tables
Table 2: Summary of datasets used our experiments. For each datasct, we provide the number of graphs, average nodes and edges per graph, number of node attributes, and number of graph classes.
dataset
#graphs avg. #nodes
avg. #edges
#attributes
#classes
MUTAG
188
17.90
39.60
7
BZR
405
35.75
38.36
53
DHER
756
42.43
44.54
53
COX2
467
41.22
43.45
35
NCT1
4110
29.87
32.30
PTCMM
336
13.97
14.32
20
PTCFR
351
14.56
15.00
19
Proteins
1113
39.10
145.60
3
2
MSRC9
221
40.58
97.94
10
8
NCI-H23H
353
46.67
48.69
0
2
Reddit-Binary
2000
429.63
497.75
0
Reddit-Multi-5K
4999
508.52
594.87
Roddit-Multi-12K
11 929
391.41
456.89
11
22

---

Published in Transactions on Machine Learning Research (12/2025)
Table 3: Classification accuracy (%) on real-world datasets using GCN, GAT, and GraphSAGF architectures. Results are shown for our method (T-6) and the baselines (F-0, F-C, and R-6). The best result per dataset within each GNN architecture is indicated by v (GCN), t (GAT), and $ (GraphSAGE); the overall best result per dataset across all three architectures is highlighted by a box. SOTA results from the literature are provided for each dataset (second-to-las row of the upper table). Specifically, MUTAG, Proteins and NCI1 results from /Vincent-Cuaz et al. 2022), .SRC99 from (Akyol et al. 2021), PTCMM, PTCFR, BZR, and COX2 from (Wen et al.) 2024). Only peer-reviewed conference and journal publications have been considered. Where possible, reproduced results using the authors' code (last row of the upper table). The bottom table reports results for datasots where reproducing the SOTA results was not possible.
MUTAG
MSRC9
PТCMM
PTCER
BZR
COX2
Proteins
NCI1
GCN
F-0
77.0+-.11
88.745.3
50.0+4.77
66.743.7
80.7+1111
77.742.2
65.5+4.99
60:2-0.6
F-C
82.5+22.2
92.5+335
60.1+:4.7
60.0+3.
81.9=0.9
81.1+1.5
59.5+9.3
62.3=1.1
R.6
77.64+1.3
89.2:14.6
60.8:15.9
52.5:13.2
79.4:10.9
7..
52.5:18.8
59.4:0.33
T-6
90.5+1.11
96.3+11.8 Y
65.0: 1
67 07.5=2.6*
86,9:20.99
82,243.2
80.0:25.7
08.0=1.1*
GAT
F-0
65.94-5.6
87.5+3.5
61.7422.3
62.5+22.4
79.4+22.7
76.6+1.8
67.5+4.99
56.9=1.9
F.C
81.11336
90.04:..1
60.0:19.4
55.0:17.6
83.1:14.4
81.113.3
65.7.19.9
59.1=117
R-6
7..7+113
85.0+0.2
63.14003
57.5++3.3
82.5++2.44
73.3422.5
53.74998
54.9-5.8
T-6
88.91118
96.2455.
67.6133.5
70.0:33.2
89.4:10.9
84.3::2
74.522.11
61.2=3.11
GraphSAGE
F-0
78.5:13.3
91.21:17
60.3:1:.1
52.5:14.5
81.9:16.2
80.11:4.4
62.110011
64.2-111
F.C
87.2110.7
91.7:11..
61.6:12288
57.5:1
89.3:14.4
82,2:2.22
54.7499.
0.40=0.4
R-6
79.71:1.6
88.745.3
56.62008
60.0:1.9
86.2:1177
76.6414
48.5:6.3
63.0=0.7
1-6
90.4+-1.4
95.0+H1.1
64.14+1.2
65.0+114
95.0++1.22
85.5+-2.47
74.0+-2.8
75. 75.15
SOTA
reported (paper) results reproduced (our run) results
96.4433.3
95.4
74.1+4.66
73.2433.9
87.4:12666
86.7433.4
82.9+2.77
88.1=2.5
88.2:11.5
90.91334
69.1::2.11
65.3:12.0
84.1:11777
80.8:11.3
73.8:14.7
75.2=0.8
DHFR
NCI H23H
Reddit Binary
Reddit-Multi- 12K
GCN
F-0 79.5.10.3
50.9 +: 1.3
49.8 +: 244
19.1 +: 14
21.8 + 2.1
F-C
66.9+2.6
98.5 0.8
66.9 + 1.9
36.4 = 2.5
30.1 = 1.4
R-6
76.9+0099
91.8 2.6
61.7 + 4.5
40.8 + 3.7
22.0 + 3.3
T-6
85.9110.5
99.2 0.7
73.3 2.0
48.7 2.1
31.2 2.2 V
GAT
F-0 70.9+9.11
51.1 + 2.1
46.2 + 1.4
19.3 + 1.1
20.5 1.8
F-C
61.64 61.627.5
98.6 = 1.0
72.5 + 244
37.4 + 2.6
28.4 + 1.6
R-6
60.3+:10
68.2 = 466
67.7 + 3.7
37.2 # 3.0
23.5 - 2.7
T-6
76.3+1.31
99.1 0.91
73.3 + 2.8
46.9 # 2.1
30.5 = 1.4'
GraphSAGE
F-0 77.145.0
50.8 1.6
49.5 2.9
19.7 1.5
20.7 1.9
F-C 66.2455.3
98.6 1.2
73.2 + 2.0
35.8 2.7
29.5 2.0
R-6
74.3++0.8
64.3 3.8
66.4 + 3.5
29.2 4.5
23.4 244
T-6
79.6:16.6
99.1 0.8
80.5 1 2.7
42.6 1 1.6
31.0 + 1.5
23

---

Published in Transactions on Machine Learning Research (12/2025)
Table 4: Classification accuracy (%) of the four classification tasks defined by Eq. 1 4 on synthetic datasets generated using four graph models: Barabási-Albert (BA), Erdös- Rényi (ER), Watts-Strogatz (WS), and the Power-Law (PL) Cluster. Bold indicates the best result per graph model within each GNN architecture, while underlining highlights the overall best performance for each task.
GCN
GAT
GraphSAGE
F-0
F-C
R-6
T-6
F-C
R-6
T-6
F-O
F-C
R-6
T-6
41 defined by Eq.
BA
18.247.1
10040.0
86.111.2
10040.0
19.916.4
10010.0 80.3.II11
100+0.0
22.415.3
100-0.0
70.612.1
100:10.0
ER
24.3+2.4
100+0.0
88.5+288
100+0.0
24.3+3.2
98.9+0.3
82.1+-2.
100+0.0
24.1+1.6
100-0.0 0.0 87.0+2.55
100+00
WS
27.6+7.8
100+0.0
82.2+6.4
100+0.00
25.4+6.9
100+0.0 96.2+1.1
100+0.0
26.3+4.55
100-0.0 84.1+4.1
100+0.00
24.3+3.5
96.2+008
42.149.9
9..
17.3+2.3
98.2+1.0 69.8+5.6
98.1+0.33
21.8+3.2
95.9+0.9
55.3+3.2
97.3-14
4 defined by Eq. 2
29.1+2.1
100+0.0
69.0+7.7
100+00.0
27.8+3.6
100+0.0 40.1=IT8
100+0.00
29.1+2.4
100-0.0
73.6+3.3
100+00.0
ER
20.8+11.3
100+0.0
61.8+3.6
100+0.00
33.3+7.44
100+0.00
82.3+2.7
100+0.0
32.8+5.6
100-0.0
90.5+3.9
100=0000
WS 28.9+44.
100+0.0
87,4+188
100+0.0
29.742.1
100+0.0
72.2+2.3
100=0.0
34.243.9
100-0.0
76.3+3.2
100+0.0
PL
31.7+1177
100+0.0
88.1+1.3
100+0.0
27.3+1.8
100+0.0
73.6+1.3
100+0.0
17.3+2.1
100-0.0
84.2+1.7
100+0.0
43 defined by Eq. 3
46.242.1
98.2-0.6
80.145.7
10010.0
45.9+1.8
10040.0 89.4-I.5
100+0.0
46.342.7
99.040.1
77.0=2.5
100=0.00
ER 48.343.5
100+0.0
7320.7
100+0.00
42.2#3.2
99.1#0.2
86.163.6
100+0.0
51.5422
100-0.0
72.822.9 100:10.0
WS
46.7+:1.7
98.3=0.7
79.1
100=0.0
48.242.2
99.0#0.2 71.9#3.2
100=0.0
48.643.9
100-0.0
71.9#3.0
100=0.0
PL
10.9+1.9
99.1=0.2
66.241.6
100+0.0
47.8+3.7
100 82.8+2.8
100+0.0
16.411.6
100-0.0
77.8#2.4
100=0.0
4 defined by Eq. 4
17.8414
94.8111
62.813.6
10010.0
22.011.3
97.410.2 52.7-2.9
100+0.0
23.34:3.
95.040.8 58.726.3
100
ER 18.848.4
97.7-0.4
66.623.5
100
22.811.5 08.010.1 65.013.1 100+0.0
25.242.0
97.1 72.91411
100-10.0
WS
22.945.3
07.120.6
63.912.7
100
24.912.1
96.610.3 71.322.6 100+0.0
26.812.1
97.210.5
67.312.9
100+0.0
PL
30.942.1
96.2=13 72.1119
100+0.0
29.412.3
98.210.2
73.1#2.1 99.110.2
29.143.1
98.240.2
73.242.3
100
24

---

Published in Transactions on Machine Learning Research (12/2025)
Table 5: Classification accuracy (%) of the classification task defined by Eq. 15 on synthetic datasets generated using four graph models: Barabási-Albert (BA), Erdós-Rényí (ER), Pratts-Strogatz (WS), and Power-Law (PL) Cluster. Bold indicates the best result per graph model within each GNN architecture, while underlining highlights the overall best performance.
4 defined by Eq. (5) WS
BA
ER
PL
GCN
F-0
20.243.4
21.1#4.1
19.8+2.7
20.
F-C
99.2+0.1
98.3+0.2
100+0.00
89.9+0.2
R-6
73.414.7
86.942.9
70.1
55.3+2.4
T-6
86.2422.3
82.8433.4
85.3+:2.1
90.2+111
T-10
91.9+1.1
90.7+1..3
91.3+1.4
99.210.3
T-20
98.1=0.2
96.4+0.7
100+0000
100 =0.0
GAT
F-0 23.1+3.2
29.243.1
27.411.6
17.7#1.9
F-C
89.9
96.5+0.2
100
96.6.10.4
R-6
48.8=3.1
77.8+1.4
72.2+1.6
64.3
T-6
84.9+2.6
85.2+1.8
88.3+2200
90.1+1.7
T-10
94.1+115
92.8+1..3
88.911.6
97.8+10.3
T-20
99.2#0.2
96.710.2
100+0000
100+0.0
GraphSAGE
F-O
20.7+2.0
18.3+2.6
27.2
23.1
F-C
100+0.0
97.2+0.6
100+0000
100+0.0
R-6
50.842.6
84.642.9
73.8+3.11
68.8+2.0
T-6
90.4+2.5
91.143.1
90.3+2.8
90.0#1.1
T-10
93.0+1.2
92.842.7
94.940.77
89.710.2
T-20
99.2+0.2
93.4+1.44
100+00.0
100+0.0
Table 6: Classification accuracy (%) of the count-based lcarning problem on synthetic datasets generated
using four graph models: Barabási Albert (BA), Erdös Rényi (ER), Watts Strogatz (WS), and Power- Law (PL) Cluster. Bold indicates the best result per graph model within each GNN architecture, while underlining highlights the overall best performance.
$ (the count-based problem)
BA
ER
WS
PL
GCN
F-0 45.3+1.7
50.1+3.33
44.7+:1.9
78.3++3.5
F-C
100+0.0
100+:0.0
100
100+00.0
R-6
78.3+2.9
7..8+1.8
61.7+2.00
93.3+2.1
T-6
96.7+1.1
100+0.0
100+00.0
100+0000
GAT
F-0 44.7++2.6
50.3+1.4
43.3+-1.9
48.3++1.5
F-C
100+0.0
100+:0.0
98.310.5
98.3:10.4
R-6
67.5+4.4
82.5+2.1
78.3+0.9
86.7+1.5
T-6
96.7+11.2
100+0.0
100++0.0
100
GraphSAGE
F-0 43.3+11.7
45.0+1.3
44.8++1.4
43.3422.8
F-C
98.3+0..3
100+00.0
100+0.0
98.3+00.2
R-6
81.743.5
77.5+1.7
95-112
93.3+1..5
T-6
98.4+1.3
100
100-00.0
100
25

---

Published in Transactions on Machine Learning Research (12/2025)
Table Classification accuracy (%) on real-world datasets using GCN, GAT, and GraphSAGE architectures. Results are reported for our target-aware feature ranking method (T-6) and its universal variant (U) which is jointly trained on graphs from multiple domains. Values marked with v indicate the highest accuracy for each dataset and architecture.
MUTAG
MSRC9
PTCMM
PTCFR
BZR
COX2
DHFR
Proteins
NCI1
GCN
TA
90.5
96.3*
65.0
67.5
86.9
82.2*
85.9 76.2
80.0
68.0
U
85.7
89.7
73.3
70.0
92.5*
80.0
65.0
63.1
GAT
TA
88.9
96.2*
67.6*
70.0
89.4
84.5
75.3
74.5%
64.2*
U
71.4
88.5
61.7
55.0
75.0
72.2
60.0
65.2
59.7
GraphSAGH
TA
90.4
95.0%
64.1*
65.0
95.0
85.5
79.6
74.0
75.1
U
83.3
89.7
57.7
62.5
82.5
78.7
83.7V
67.0
68.2
26


Reviews:
[{"review_id": "lIO2VWTD1U", "reviewer": "Reviewer_a3BA", "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": "", "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 goal of this paper is to improve graph classification performance in GNNs by automatically learning and selecting a small, informative subset of node- and graph-level features from a large candidate pool. The paper introduces a two-step method that enhances graph classification by ranking and selecting features to augment GNN inputs. In Step 1, a small subset of training graphs is sampled, and all 124 candidate features—spanning graphlets, aggregated node statistics, and global graph properties—are computed. A random forest classifier is trained per graph using comparisons with other graphs of different labels to produce feature importance rankings. These local rankings are aggregated and used to train a Feature-Ranking GNN (FR-GNN), which generalizes feature ranking predictions to unseen graphs. In Step 2, the FR-GNN is applied to the remaining training graphs to produce a global feature ranking. The top K features from this ranking are then computed and used to augment the training data for a Graph Classification GNN (GC-GNN). This GNN is trained using the compact feature set. The method is benchmarked against baselines that use no features, all features, or randomly selected features, across real-world and synthetic datasets using three GNN architectures (GCN, GAT, GraphSAGE). Evaluation also includes runtime comparisons and tests of statistical significance. Across nine real-world and multiple synthetic datasets, the proposed method consistently outperforms baselines, achieving up to 10% higher accuracy than using all features and showing statistical significance. Even with only six selected features, it matches or exceeds state-of-the-art performance, while reducing overfitting and computation time on large graphs.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The paper presents an effective feature reduction method that selects highly informative features to improve classification while reducing overfitting and runtime. Its main strength is empirical, as it provides extensive evaluations of the proposed ideas, which are tested across diverse domains (e.g., chemistry, bioinformatics, computer vision) and synthetic settings with known ground truths. The performance improvements are validated using the Kruskal-Wallis test and Dunn’s post-hoc test, confirming significance over the baselines.\nHowever, the paper also has room for improvement. First, there is no formal proof of optimality for the selected feature subsets or convergence guarantees for the method. Second, the FR-GNN is trained separately for each dataset. Thus, attempts to build a global FR-GNN yield lower performance gains. Finally, the selection of the number of top features (e.g., K=6) is empirically driven; no adaptive mechanism for optimal K per dataset is proposed.", "audience_yn": "Yes", "audience_explanation": "Although learning to rank is a mature area of research, there is still room for improvement of current techniques. Its combined application on graph neural networks for graph classification will be of interest to most researchers and readers in the TMLR audience.", "requested_changes": "Some elements of the paper can be further clarified. For instance, what conditions must be met for the feature selection to guarantee near-optimal classification performance? Can bounds on generalization error or subset optimality be derived?\nFurthermore, can we design a data-driven strategy to dynamically choose the number of top features K, possibly via validation accuracy curves or information-theoretic criteria? For instance, why not apply a Bayesian optimization over K yield better generalization?\nUltimately, some clarity about the applicability would be beneficial. How can the FR-GNN be adapted or fine-tuned to generalize feature rankings across diverse datasets while preserving task-specific accuracy? Would meta-learning or transfer learning approaches help train a universal FR-GNN?", "broader_impact_concerns": "This is a methods paper for ranking. So a discussion on what implications the technique may have on datasets of associated to human subjects could be important to at least discuss.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "bxU3ZqZo6o", "reviewer": "Reviewer_Mk5k", "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": "", "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 idea put forth in this paper is learning to rank features that are useful for graph classification when the latter is accomplished via graph neural networks. To achieve this, the authors propose a two-step method that automatically selects a subset of features from a pool of candidate features to improve classification accuracy. In the first step, the importance of each feature for a given graph in a reduced training set is estimated via graph neural networks. In the second step, the suggested algorithm generates feature rankings for the training graphs, and said feature rankings are then aggregated into a global ranking. A top-K subset is selected from this global ranking and used to train a downstream graph classification graph neural network of choice. Experiments on real-world and synthetic datasets show that the proposed algorithm outperforms some baselines tested by the authors, including models using all candidate features.", "claims_and_evidence_yn": "Yes", "claims_explanation": "While the authors substantiate their main claims with regard to the baselines, the results are mixed and they acknowledge that.", "audience_yn": "Yes", "audience_explanation": "The topic is relevant to the community following TMLR.", "requested_changes": "-) Release source code.\n-) List wall-clock times for the entire model — how much overhead the first phase adds overall? Just higher accuracy is not enough if your model is much slower to train.\n-) The discussion and justification around the graphlet motifs and their choice/importance is neither well-motivated nor clear.\n-) Circular heatmap diagrams are hard to comprehend. Please switch to a different modality of visualization.", "broader_impact_concerns": "The topic considered is highly important.", "additional_comments": "-) The paper by Alkhoury et al. reduces the overall novelty.\n-) This really is an experiments-oriented paper as the overall algorithm is a marginal extension of current literature.", "extra_scores": {}, "extra_text": {}}, {"review_id": "tGHSQVId8Q", "reviewer": "Reviewer_CQbo", "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": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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 introduces a novel two-step framework for graph classification that learns to rank and select a compact subset of informative features from a large candidate pool. By integrating feature ranking with GNN training, the method improves accuracy, reduces overfitting, and achieves state-of-the-art results on multiple benchmarks.", "claims_and_evidence_yn": "No", "claims_explanation": "The baseline is too few and outdated", "audience_yn": "Yes", "audience_explanation": "The research topic of graph neural networks for graph classification is very relevant to the interests of TMLR's audience.", "requested_changes": "- My major concern is the lack of a clearly articulated research motivation. It remains unclear what precise role feature selection plays in graph classification and why it is particularly meaningful. The authors do not convincingly differentiate their notion of feature selection from the implicit feature extraction already performed by GNNs, nor do they explain why existing approaches are fundamentally insufficient. These issues require deeper theoretical justification and concrete real-world examples to demonstrate the practical necessity and novelty of the proposed framework.\n\n- It is not evident whether the proposed two-step framework can be easily extended to very large graphs, since the feature ranking step may become computationally demanding. The paper lacks a formal theoretical analysis of time complexity and provides only limited runtime comparisons. Moreover, no systematic scalability experiments are presented to demonstrate how the method performs as graph size or dataset scale increases.\n\n- The experimental evaluation is limited by the choice of baselines, which are relatively few and somewhat outdated. The three main comparison methods were published in 2019, 2021, and 2022, meaning all are at least three years old. To strengthen the credibility of the results, the paper should incorporate more recent baselines from 2024 and 2025, ensuring a fairer and more convincing assessment of the proposed method’s advantages.\n\n\n- The discussion of related work is not sufficiently clear or comprehensive. In particular, important directions such as graph classification methods based on substructure assembly are missing [1]. The related work section would benefit from a more systematic organization by categories of approaches, followed by a clearer comparison highlighting how the proposed method differs from and improves upon these alternatives.\n\nRefs:\n\n[1] Graph substructure assembling network with soft sequence and context attention[J]. IEEE Transactions on Knowledge and Data Engineering, 2022, 35(5): 4894-4907.", "broader_impact_concerns": "Since the proposed framework focuses on automated feature selection for graph classification, potential ethical implications include misuse in sensitive domains such as biomedical research, social networks, or financial systems, where biased or misleading feature rankings could amplify existing inequities. A more thorough Broader Impact Statement should discuss these risks, outline safeguards, and clarify the societal contexts in which the method is appropriate or potentially harmful.", "additional_comments": "None", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)