Johannes F. Lutzeyer

Michail Chatzianastasis, Johannes F. Lutzeyer, George Dasoulas et al. · harvard

Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.

Ariel R. Ramos Vela, Johannes F. Lutzeyer, Anastasios Giovanidis et al.

Graph Neural Networks (GNNs) have achieved great successes in many learning tasks performed on graph structures. Nonetheless, to propagate information GNNs rely on a message passing scheme which can become prohibitively expensive when working with industrial-scale graphs. Inspired by the PPRGo model, we propose the CorePPR model, a scalable solution that utilises a learnable convex combination of the approximate personalised PageRank and the CoreRank to diffuse multi-hop neighbourhood information in GNNs. Additionally, we incorporate a dynamic mechanism to select the most influential neighbours for a particular node which reduces training time while preserving the performance of the model. Overall, we demonstrate that CorePPR outperforms PPRGo, particularly on large graphs where selecting the most influential nodes is particularly relevant for scalability. Our code is publicly available at: https://github.com/arielramos97/CorePPR.

Guillaume Salha-Galvan, Johannes F. Lutzeyer, George Dasoulas et al. · harvard

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction (LP). Their performances are less impressive on community detection (CD), where they are often outperformed by simpler alternatives such as the Louvain method. It is still unclear to what extent one can improve CD with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on LP in a multi-task setting. In this workshop paper, summarizing results from our journal publication (Salha-Galvan et al. 2022), we show that jointly addressing these two tasks with high accuracy is possible. For this purpose, we introduce a community-preserving message passing scheme, doping our GAE and VGAE encoders by considering both the initial graph and Louvain-based prior communities when computing embedding spaces. Inspired by modularity-based clustering, we further propose novel training and optimization strategies specifically designed for joint LP and CD. We demonstrate the empirical effectiveness of our approach, referred to as Modularity-Aware GAE and VGAE, on various real-world graphs.

Inès Benito, Johannes F. Lutzeyer, Benjamin Doerr

Baldwinian and Lamarckian evolution have existed for a long time in evolutionary algorithms (EAs) without ever dominating the academic literature or practical applications. In this work, we use modern empirical and theoretical methods to revisit Lamarckian and Baldwinian evolution and rigorously compare them with the generic Darwinian evolution. On the empirical side, we run a comprehensive suite of experiments on graphs from six different datasets from the recent GraphBench benchmark on Maximum Independent Set and Maximum Cut problems. Our results show that Baldwinian and Lamarckian evolution consistently outperform Darwinian evolution, confirming the great potential of local search augmented evolutionary algorithms. Notably, in the great majority of cases, all EAs outperform recent deep learning baselines and approach the performance of highly specialised heuristic and exact solvers. We furthermore report a high-performing set of generalist parameters for all studied evolution types that we hope will be of use to practitioners in future. On the theoretical side, we extend the existing Deceptive Leading Block benchmark to arbitrary block length and use tools from modern theoretical runtime analysis to prove upper and lower bounds on the expected runtime. For block lengths greater than two, Baldwinian evolution is asymptotically faster than Lamarckian which is asymptotically faster than Darwinian evolution. When accounting for the cost of the local search procedure in fitness evaluations, the ordering depends on the implementation with Baldwinian evolution staying fastest from small block lengths onwards, explaining its strong empirical performance.

Ye Zhu, Kaleb S. Newman, Johannes F. Lutzeyer et al.

Despite high semantic alignment, modern text-to-image (T2I) generative models still struggle to synthesize diverse images from a given prompt. This lack of diversity not only restricts user choice, but also risks amplifying societal biases. In this work, we enhance the T2I diversity through a geometric lens. Unlike most existing methods that rely primarily on entropy-based guidance to increase sample dissimilarity, we introduce Geometry-Aware Spherical Sampling (GASS) to enhance diversity by explicitly controlling both prompt-dependent and prompt-independent sources of variation. Specifically, we decompose the diversity measure in CLIP embeddings using two orthogonal directions: the text embedding, which captures semantic variation related to the prompt, and an identified orthogonal direction that captures prompt-independent variation (e.g., backgrounds). Based on this decomposition, GASS increases the geometric projection spread of generated image embeddings along both axes and guides the T2I sampling process via expanded predictions along the generation trajectory. Our experiments on different frozen T2I backbones (U-Net and DiT, diffusion and flow) and benchmarks demonstrate the effectiveness of disentangled diversity enhancement with minimal impact on image fidelity and semantic alignment.

Sofiane Ennadir, Yassine Abbahaddou, Johannes F. Lutzeyer et al.

Graph Neural Networks (GNNs) have emerged as the dominant approach for machine learning on graph-structured data. However, concerns have arisen regarding the vulnerability of GNNs to small adversarial perturbations. Existing defense methods against such perturbations suffer from high time complexity and can negatively impact the model's performance on clean graphs. To address these challenges, this paper introduces NoisyGNNs, a novel defense method that incorporates noise into the underlying model's architecture. We establish a theoretical connection between noise injection and the enhancement of GNN robustness, highlighting the effectiveness of our approach. We further conduct extensive empirical evaluations on the node classification task to validate our theoretical findings, focusing on two popular GNNs: the GCN and GIN. The results demonstrate that NoisyGNN achieves superior or comparable defense performance to existing methods while minimizing added time complexity. The NoisyGNN approach is model-agnostic, allowing it to be integrated with different GNN architectures. Successful combinations of our NoisyGNN approach with existing defense techniques demonstrate even further improved adversarial defense results. Our code is publicly available at: https://github.com/Sennadir/NoisyGNN.

Yassine Abbahaddou, Sofiane Ennadir, Johannes F. Lutzeyer et al.

Graph Neural Networks (GNNs) have demonstrated state-of-the-art performance in various graph representation learning tasks. Recently, studies revealed their vulnerability to adversarial attacks. In this work, we theoretically define the concept of expected robustness in the context of attributed graphs and relate it to the classical definition of adversarial robustness in the graph representation learning literature. Our definition allows us to derive an upper bound of the expected robustness of Graph Convolutional Networks (GCNs) and Graph Isomorphism Networks subject to node feature attacks. Building on these findings, we connect the expected robustness of GNNs to the orthonormality of their weight matrices and consequently propose an attack-independent, more robust variant of the GCN, called the Graph Convolutional Orthonormal Robust Networks (GCORNs). We further introduce a probabilistic method to estimate the expected robustness, which allows us to evaluate the effectiveness of GCORN on several real-world datasets. Experimental experiments showed that GCORN outperforms available defense methods. Our code is publicly available at: \href{https://github.com/Sennadir/GCORN}{https://github.com/Sennadir/GCORN}.

Roman Bresson, Konstantinos Divriotis, Johannes F. Lutzeyer et al.

We introduce GraViti, a transformer-based graph-level variational autoencoder that maps entire graphs to compact latent vectors. This design produces a true graph-level latent space that supports smooth interpolation, property-guided search, and other downstream tasks beyond the constraints of node-level embeddings. On molecular benchmarks, GraViti learns to decode valid samples that follow the chemical constraints present in the training data, showing that the model recovers domain rules directly from graph-level representations. We also show that, in domains where a reliable canonical node ordering exists such as molecules or bayesian networks, enforcing permutation invariance can prove detrimental for consistent reconstruction. GraViti achieves state-of-the-art reconstruction accuracy on large datasets, and provides solid generative performance. Its single-step decoding offers a lightweight alternative to more complex generation pipelines while maintaining practical sample quality.

Benjamin Doerr, Johannes F. Lutzeyer

In recent work, Lissovoi, Oliveto, and Warwicker (Artificial Intelligence (2023)) proved that the Move Acceptance Hyper-Heuristic (MAHH) leaves the local optimum of the multimodal CLIFF benchmark with remarkable efficiency. The $O(n^3)$ runtime of the MAHH, for almost all cliff widths $d\ge 2,$ is significantly better than the $Θ(n^d)$ runtime of simple elitist evolutionary algorithms (EAs) on CLIFF. In this work, we first show that this advantage is specific to the CLIFF problem and does not extend to the JUMP benchmark, the most prominent multi-modal benchmark in the theory of randomized search heuristics. We prove that for any choice of the MAHH selection parameter $p$, the expected runtime of the MAHH on a JUMP function with gap size $m = O(n^{1/2})$ is at least $Ω(n^{2m-1} / (2m-1)!)$. This is significantly slower than the $O(n^m)$ runtime of simple elitist EAs. Encouragingly, we also show that replacing the local one-bit mutation operator in the MAHH with the global bit-wise mutation operator, commonly used in EAs, yields a runtime of $\min\{1, O(\frac{e\ln(n)}{m})^m\} \, O(n^m)$ on JUMP functions. This is at least as good as the runtime of simple elitist EAs. For larger values of $m$, this result proves an asymptotic performance gain over simple EAs. As our proofs reveal, the MAHH profits from its ability to walk through the valley of lower objective values in moderate-size steps, always accepting inferior solutions. This is the first time that such an optimization behavior is proven via mathematical means. Generally, our result shows that combining two ways of coping with local optima, global mutation and accepting inferior solutions, can lead to considerable performance gains.

Sofiane Ennadir, Oleg Smirnov, Yassine Abbahaddou et al.

Graph Neural Networks (GNNs) have achieved strong performance across a range of graph representation learning tasks, yet their adversarial robustness in graph classification remains underexplored compared to node classification. While most existing defenses focus on the message-passing component, this work investigates the overlooked role of pooling operations in shaping robustness. We present a theoretical analysis of standard flat pooling methods (sum, average and max), deriving upper bounds on their adversarial risk and identifying their vulnerabilities under different attack scenarios and graph structures. Motivated by these insights, we propose \textit{Robust Singular Pooling (RS-Pool)}, a novel pooling strategy that leverages the dominant singular vector of the node embedding matrix to construct a robust graph-level representation. We theoretically investigate the robustness of RS-Pool and interpret the resulting bound leading to improved understanding of our proposed pooling operator. While our analysis centers on Graph Convolutional Networks (GCNs), RS-Pool is model-agnostic and can be implemented efficiently via power iteration. Empirical results on real-world benchmarks show that RS-Pool provides better robustness than the considered pooling methods when subject to state-of-the-art adversarial attacks while maintaining competitive clean accuracy. Our code is publicly available at:\href{https://github.com/king/rs-pool}{https://github.com/king/rs-pool}.

Niklas Kormann, Masoud Ramuz, Zeeshan Nisar et al.

Graph Neural Networks (GNNs) have recently been found to excel in histopathology. However, an important histopathological task, where GNNs have not been extensively explored, is the classification of glomeruli health as an important indicator in nephropathology. This task presents unique difficulties, particularly for the graph construction, i.e., the identification of nodes, edges, and informative features. In this work, we propose a pipeline composed of different traditional and machine learning-based computer vision techniques to identify nodes, edges, and their corresponding features to form a heterogeneous graph. We then proceed to propose a novel heterogeneous GNN architecture for glomeruli classification, called HIEGNet, that integrates both glomeruli and their surrounding immune cells. Hence, HIEGNet is able to consider the immune environment of each glomerulus in its classification. Our HIEGNet was trained and tested on a dataset of Whole Slide Images from kidney transplant patients. Experimental results demonstrate that HIEGNet outperforms several baseline models and generalises best between patients among all baseline models. Our implementation is publicly available at https://github.com/nklsKrmnn/HIEGNet.git.

Mohamed El Amine Seddik, Changmin Wu, Johannes F. Lutzeyer et al.

The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.

Johannes F. Lutzeyer, Changmin Wu, Michalis Vazirgiannis

Message-Passing Neural Networks (MPNNs), the most prominent Graph Neural Network (GNN) framework, celebrate much success in the analysis of graph-structured data. Concurrently, the sparsification of Neural Network models attracts a great amount of academic and industrial interest. In this paper we conduct a structured, empirical study of the effect of sparsification on the trainable part of MPNNs known as the Update step. To this end, we design a series of models to successively sparsify the linear transform in the Update step. Specifically, we propose the ExpanderGNN model with a tuneable sparsification rate and the Activation-Only GNN, which has no linear transform in the Update step. In agreement with a growing trend in the literature the sparsification paradigm is changed by initialising sparse neural network architectures rather than expensively sparsifying already trained architectures. Our novel benchmark models enable a better understanding of the influence of the Update step on model performance and outperform existing simplified benchmark models such as the Simple Graph Convolution. The ExpanderGNNs, and in some cases the Activation-Only models, achieve performance on par with their vanilla counterparts on several downstream tasks, while containing significantly fewer trainable parameters. Our code is publicly available at: https://github.com/ChangminWu/ExpanderGNN.

Niklas Kormann, Benjamin Doerr, Johannes F. Lutzeyer

Over-smoothing and over-squashing have been extensively studied in the literature on Graph Neural Networks (GNNs) over the past years. We challenge this prevailing focus in GNN research, arguing that these phenomena are less critical for practical applications than assumed. We suggest that performance decreases often stem from uninformative receptive fields rather than over-smoothing. We support this position with extensive experiments on several standard benchmark datasets, demonstrating that accuracy and over-smoothing are mostly uncorrelated and that optimal model depths remain small even with mitigation techniques, thus highlighting the negligible role of over-smoothing. Similarly, we challenge that over-squashing is always detrimental in practical applications. Instead, we posit that the distribution of relevant information over the graph frequently factorises and is often localised within a small k-hop neighbourhood, questioning the necessity of jointly observing entire receptive fields or engaging in an extensive search for long-range interactions. The results of our experiments show that architectural interventions designed to mitigate over-squashing fail to yield significant performance gains. This position paper advocates for a paradigm shift in theoretical research, urging a diligent analysis of learning tasks and datasets using statistics that measure the underlying distribution of label-relevant information to better understand their localisation and factorisation.

Joshua Southern, Francesco Di Giovanni, Michael Bronstein et al.

While message passing neural networks (MPNNs) have convincing success in a range of applications, they exhibit limitations such as the oversquashing problem and their inability to capture long-range interactions. Augmenting MPNNs with a virtual node (VN) removes the locality constraint of the layer aggregation and has been found to improve performance on a range of benchmarks. We provide a comprehensive theoretical analysis of the role of VNs and benefits thereof, through the lenses of oversquashing and sensitivity analysis. First, we characterize, precisely, how the improvement afforded by VNs on the mixing abilities of the network and hence in mitigating oversquashing, depends on the underlying topology. We then highlight that, unlike Graph-Transformers (GTs), classical instantiations of the VN are often constrained to assign uniform importance to different nodes. Consequently, we propose a variant of VN with the same computational complexity, which can have different sensitivity to nodes based on the graph structure. We show that this is an extremely effective and computationally efficient baseline for graph-level tasks.

Sofiane Ennadir, Johannes F. Lutzeyer, Michalis Vazirgiannis et al.

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a spectrum of graph-related tasks, however concerns persist regarding their vulnerability to adversarial perturbations. While prevailing defense strategies focus primarily on pre-processing techniques and adaptive message-passing schemes, this study delves into an under-explored dimension: the impact of weight initialization and associated hyper-parameters, such as training epochs, on a model's robustness. We introduce a theoretical framework bridging the connection between initialization strategies and a network's resilience to adversarial perturbations. Our analysis reveals a direct relationship between initial weights, number of training epochs and the model's vulnerability, offering new insights into adversarial robustness beyond conventional defense mechanisms. While our primary focus is on GNNs, we extend our theoretical framework, providing a general upper-bound applicable to Deep Neural Networks. Extensive experiments, spanning diverse models and real-world datasets subjected to various adversarial attacks, validate our findings. We illustrate that selecting appropriate initialization not only ensures performance on clean datasets but also enhances model robustness against adversarial perturbations, with observed gaps of up to 50\% compared to alternative initialization approaches.

Yassine Abbahaddou, Johannes F. Lutzeyer, Michalis Vazirgiannis

In light of the recent success of Graph Neural Networks (GNNs) and their ability to perform inference on complex data structures, many studies apply GNNs to the task of text classification. In most previous methods, a heterogeneous graph, containing both word and document nodes, is constructed using the entire corpus and a GNN is used to classify document nodes. In this work, we explore a new Discriminative Graph of Words Graph Neural Network (DGoW-GNN) approach encapsulating both a novel discriminative graph construction and model to classify text. In our graph construction, containing only word nodes and no document nodes, we split the training corpus into disconnected subgraphs according to their labels and weight edges by the pointwise mutual information of the represented words. Our graph construction, for which we provide theoretical motivation, allows us to reformulate the task of text classification as the task of walk classification. We also propose a new model for the graph-based classification of text, which combines a GNN and a sequence model. We evaluate our approach on seven benchmark datasets and find that it is outperformed by several state-of-the-art baseline models. We analyse reasons for this performance difference and hypothesise under which conditions it is likely to change.

Yassine Abbahaddou, Fragkiskos D. Malliaros, Johannes F. Lutzeyer et al.

Graph Neural Networks (GNNs) have proven to be highly effective in various graph learning tasks. A key characteristic of GNNs is their use of a fixed number of message-passing steps for all nodes in the graph, regardless of each node's diverse computational needs and characteristics. Through empirical real-world data analysis, we demonstrate that the optimal number of message-passing layers varies for nodes with different characteristics. This finding is further supported by experiments conducted on synthetic datasets. To address this, we propose Adaptive Depth Message Passing GNN (ADMP-GNN), a novel framework that dynamically adjusts the number of message passing layers for each node, resulting in improved performance. This approach applies to any model that follows the message passing scheme. We evaluate ADMP-GNN on the node classification task and observe performance improvements over baseline GNN models.

Abderrahim Bendahi, Benjamin Doerr, Adrien Fradin et al.

The move-acceptance hyper-heuristic was recently shown to be able to leave local optima with astonishing efficiency (Lissovoi et al., Artificial Intelligence (2023)). In this work, we propose two modifications to this algorithm that demonstrate impressive performances on a large class of benchmarks including the classic Cliff$_d$ and Jump$_m$ function classes. (i) Instead of randomly choosing between the only-improving and any-move acceptance operator, we take this choice via a simple two-state Markov chain. This modification alone reduces the runtime on Jump$_m$ functions with gap parameter $m$ from $Ω(n^{2m-1})$ to $O(n^{m+1})$. (ii) We then replace the all-moves acceptance operator with the operator that only accepts worsenings. Such a, counter-intuitive, operator has not been used before in the literature. However, our proofs show that our only-worsening operator can greatly help in leaving local optima, reducing, e.g., the runtime on Jump functions to $O(n^3 \log n)$ independent of the gap size. In general, we prove a remarkably good runtime of $O(n^{k+1} \log n)$ for our Markov move-acceptance hyper-heuristic on all members of a new benchmark class SEQOPT$_k$, which contains a large number of functions having $k$ successive local optima, and which contains the commonly studied Jump$_m$ and Cliff$_d$ functions for $k=2$.

George Panagopoulos, Johannes F. Lutzeyer, Sofiane Ennadir et al.

Genomic studies face a vast hypothesis space, while interventions such as gene perturbations remain costly and time-consuming. To accelerate such experiments, gene perturbation models predict the transcriptional outcome of interventions. Since constructing the training set is challenging, active learning is often employed in a "lab-in-the-loop" process. While this strategy makes training more targeted, it is substantially slower, as it fails to exploit the inherent parallelizability of Perturb-seq experiments. Here, we focus on graph neural network-based gene perturbation models and propose a subset selection method that, unlike active learning, selects the training perturbations in one shot. Our method chooses the interventions that maximize the propagation of the supervision signal to the model. The selection criterion is defined over the input knowledge graph and is optimized with submodular maximization, ensuring a near-optimal guarantee. Experimental results across multiple datasets show that, in addition to providing months of acceleration compared to active learning, the method improves the stability of perturbation choices while maintaining competitive predictive accuracy.

Yassine Abbahaddou, Fragkiskos D. Malliaros, Johannes F. Lutzeyer et al.

Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GRATIN, an efficient graph data augmentation algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications.

Yassine Abbahaddou, Sofiane Ennadir, Johannes F. Lutzeyer et al.

Graph Neural Networks (GNNs), which are nowadays the benchmark approach in graph representation learning, have been shown to be vulnerable to adversarial attacks, raising concerns about their real-world applicability. While existing defense techniques primarily concentrate on the training phase of GNNs, involving adjustments to message passing architectures or pre-processing methods, there is a noticeable gap in methods focusing on increasing robustness during inference. In this context, this study introduces RobustCRF, a post-hoc approach aiming to enhance the robustness of GNNs at the inference stage. Our proposed method, founded on statistical relational learning using a Conditional Random Field, is model-agnostic and does not require prior knowledge about the underlying model architecture. We validate the efficacy of this approach across various models, leveraging benchmark node classification datasets.

Yassine Abbahaddou, Fragkiskos D. Malliaros, Johannes F. Lutzeyer et al.

Graph Shift Operators (GSOs), such as the adjacency and graph Laplacian matrices, play a fundamental role in graph theory and graph representation learning. Traditional GSOs are typically constructed by normalizing the adjacency matrix by the degree matrix, a local centrality metric. In this work, we instead propose and study Centrality GSOs (CGSOs), which normalize adjacency matrices by global centrality metrics such as the PageRank, $k$-core or count of fixed length walks. We study spectral properties of the CGSOs, allowing us to get an understanding of their action on graph signals. We confirm this understanding by defining and running the spectral clustering algorithm based on different CGSOs on several synthetic and real-world datasets. We furthermore outline how our CGSO can act as the message passing operator in any Graph Neural Network and in particular demonstrate strong performance of a variant of the Graph Convolutional Network and Graph Attention Network using our CGSOs on several real-world benchmark datasets.

Guillaume Salha-Galvan, Johannes F. Lutzeyer, George Dasoulas et al.

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction. Their performances are less impressive on community detection problems where, according to recent and concurring experimental evaluations, they are often outperformed by simpler alternatives such as the Louvain method. It is currently still unclear to which extent one can improve community detection with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on link prediction. In this paper, we show that jointly addressing these two tasks with high accuracy is possible. For this purpose, we introduce and theoretically study a community-preserving message passing scheme, doping our GAE and VGAE encoders by considering both the initial graph structure and modularity-based prior communities when computing embedding spaces. We also propose novel training and optimization strategies, including the introduction of a modularity-inspired regularizer complementing the existing reconstruction losses for joint link prediction and community detection. We demonstrate the empirical effectiveness of our approach, referred to as Modularity-Aware GAE and VGAE, through in-depth experimental validation on various real-world graphs.