ICLR 2026 Papers

We introduce *TopoFormer*, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences. At the core of our method is *Topo-Scan*, a novel module that decomposes a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations. These sequences capture multi-scale structural patterns, from local motifs to global organization, and are processed by a Transformer to produce expressive graph-level embeddings. Unlike traditional persistent homology pipelines, *Topo-Scan* is parallelizable, avoids costly diagram computations, and integrates seamlessly with standard deep learning architectures. We provide theoretical guarantees on the stability of our topological encodings and demonstrate state-of-the-art performance across graph classification and molecular property prediction benchmarks. Our results show that *TopoFormer* matches or exceeds strong GNN and topology-based baselines while offering predictable and efficient compute. This work opens a new path for parallelizable and unifying approaches to graph representation learning that integrate topological inductive biases into attention frameworks.

Neural Radiance Fields (NeRFs) have emerged as a groundbreaking paradigm for representing 3D objects and scenes by encoding shape and appearance information into the weights of a neural network. Recent studies have demonstrated that these weights can be used as input for frameworks designed to address deep learning tasks; however, such frameworks require NeRFs to adhere to a specific, predefined architecture. In this paper, we introduce the first framework capable of processing NeRFs with diverse architectures and performing inference on architectures unseen at training time. We achieve this by training a Graph Meta-Network within an unsupervised representation learning framework, and show that a contrastive objective is conducive to obtaining an architecture-agnostic latent space. In experiments conducted across 13 NeRF architectures belonging to three families (MLPs, tri-planes, and, for the first time, hash tables), our approach demonstrates robust performance in classification, retrieval, and language tasks involving multiple architectures, even unseen at training time, while also matching or exceeding the results of existing frameworks limited to single architectures. Our code and data are available at [this https URL](https://cvlab-unibo.github.io/gmnerf).

Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as the Dirichlet energy. We argue that these metrics have critical limitations and fail to reliably capture oversmoothing in realistic scenarios. For instance, they provide meaningful insights only for very deep networks, while typical GNNs show a performance drop already with as few as 10 layers. As an alternative, we propose measuring oversmoothing by examining the numerical or effective rank of the feature representations. We provide extensive numerical evaluation across diverse graph architectures and datasets to show that rank-based metrics consistently capture oversmoothing, whereas energy-based metrics often fail. Notably, we reveal that drops in the rank align closely with performance degradation, even in scenarios where energy metrics remain unchanged. Along with the experimental evaluation, we provide theoretical support for this approach, clarifying why Dirichlet-like measures may fail to capture performance drop and proving that the numerical rank of feature representations collapses to one for a broad family of GNN architectures.

Learning on text-attributed graphs has motivated the use of Large Language Models (LLMs) for graph learning. However, most fusion strategies are applied uniformly across all nodes and attain only small overall performance gains. We argue this result stems from aggregate metrics that obscure when LLMs provide benefit, inhibiting actionable signals for new strategies. In this work, we reframe LLM–GNN fusion around nodes where GNNs typically falter. We first show that performance can significantly differ between GNNs and LLMs, with each excelling on distinct structural patterns, such as local homophily. To leverage this finding, we propose **GLANCE** (**G**NN with **L**LM **A**ssistance for **N**eighbor- and **C**ontext-aware **E**mbeddings), a framework that invokes an LLM to refine a GNN's prediction. GLANCE employs a lightweight router that, given inexpensive per-node signals, decides whether to query the LLM. Since the LLM calls are non-differentiable, the router is trained with an advantage-based objective that compares the utility of querying the LLM against relying solely on the GNN. Across multiple benchmarks, GLANCE achieves the best performance balance across node subgroups, achieving significant gains on heterophilous nodes (up to +5.8%) while simultaneously achieving top overall performance (up to +1.1%). Our findings advocate for adaptive, node-aware, GNN-LLM architectures, showing that selectively invoking the LLM where it adds value enables scalable application of LLMs to large graphs.

Existing rule-based explanations for Graph Neural Networks (GNNs) provide global interpretability but often optimize and assess fidelity in an intermediate, uninterpretable concept space, overlooking the grounding quality of the final subgraph explanations for end users. This gap yields explanations that may appear faithful yet be unreliable in practice. To this end, we propose LogicXGNN, a post hoc framework that constructs logical rules over reliable predicates explicitly designed to capture the GNN's message-passing structure, thereby ensuring effective grounding. We further introduce data-grounded fidelity ($Fid_D$), a realistic metric that evaluates explanations in their final-graph form, along with complementary utility metrics such as coverage and validity. Across extensive experiments, LogicXGNN improves $Fid_D$ by over 20% on average relative to state-of-the-art methods while being 10-100 times faster. With strong scalability and utility performance, LogicXGNN produces explanations that are faithful to the model's logic and reliably grounded in observable data.

Large Language Models (LLMs) have shown strong performance on text-attributed graphs (TAGs) due to their superior semantic understanding ability on textual node features. However, their effectiveness as predictors in the few-shot semi-supervised setting, where labeled nodes are rather limited, remains constrained since fine-tuning LLMs usually requires sufficient labeled data, especially when the TAG shows complex structural patterns. In essence, this paper targets two key challenges: (i) the difficulty of generating and selecting reliable pseudo labels on TAGs for LLMs, and (ii) the need to mitigate potential label noise when fine-tuning LLMs with pseudo labels. To counter the challenges, we propose a new framework, GNN-as-Judge, which can unleash the power of LLMs for few-shot semi-supervised learning on TAGs by incorporating the structural inductive bias of Graph Neural Networks (GNNs). Specifically, GNN-as-Judge introduces a collaborative pseudo-labeling strategy that first identifies the most influenced unlabeled nodes from labeled nodes, then exploits both the agreement and disagreement patterns between LLMs and GNNs to generate reliable labels. Furthermore, we develop a weakly-supervised LLM fine-tuning algorithm that can distill the knowledge from informative pseudo labels while mitigating the potential label noise. Experiments on different TAG datasets demonstrate that GNN-as-Judge significantly outperforms existing methods, especially under low-resource regimes.

The inclusion of symmetries as an inductive bias, known as *equivariance*, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for symmetries chosen *a priori*, and not applicable to datasets with other symmetries. This precludes the development of flexible, multi-modal foundation models capable of processing diverse data equivariantly. In this work, we build a single model --- the Any-Subgroup Equivariant Network (ASEN) --- that can be simultaneously equivariant to several groups, simply by modulating a certain auxiliary input feature. In particular, we start with a fully permutation-equivariant base model, and then obtain subgroup equivariance by using a symmetry-breaking input whose automorphism group is that subgroup. However, finding an input with the desired automorphism group is computationally hard. We overcome this by relaxing from exact to approximate symmetry breaking, leveraging the notion of 2-closure to derive fast algorithms. Theoretically, we show that our subgroup-equivariant networks can simulate equivariant MLPs, and their universality can be guaranteed if the base model is universal. Empirically, we validate our method on symmetry selection for graph and image tasks, as well as multitask and transfer learning for sequence tasks, showing that a single network equivariant to multiple permutation subgroups outperforms both separate equivariant models and a single non-equivariant model.

Model-level explanations for Graph Neural Networks (GNNs) aim to identify class-discriminative motifs that capture how a classifier recognizes a target class. Because the true motifs relied on by the classifier are unobservable, most approaches evaluate explanations by their target class score. However, class score alone is not sufficient as high-scoring explanations may be pathological or may fail to reflect the full range of motifs recognized by the classifier. To bridge this gap, this work introduces sufficiency risk as a formal criterion for whether explanations adequately represent the classifier’s reasoning, and derives distribution-free certificates that upper-bound this risk. Building on this foundation, three metrics are introduced: Coverage, Greedy Gain Area (GGA), and Overlap which operationalize the certificates to assess sufficiency, efficiency, and redundancy in explanations. To ensure practical utility, finite-sample concentration bounds are developed for these metrics, providing confidence intervals that enable statistically reliable comparison between explainers. Experiments on synthetic data and with three state-of-the-art explainers on four real-world datasets demonstrate that these metrics reveal differences in explanation quality hidden by class scores alone. Designed to complement class score, they constitute the first theoretically certified framework for evaluating model-level explanations of GNNs.

Graph Neural Networks (\textsc{Gnn}s) are increasingly being deployed in sensitive, user-centric applications where regulations such as the GDPR mandate the ability to remove data upon request. This has spurred interest in graph unlearning, the task of removing the influence of specific training data from a trained \textsc{Gnn} without retraining from scratch. While several unlearning techniques have recently emerged, the field lacks a principled benchmark to assess whether these methods truly provide a practical alternative to retraining and, if so, how to choose among them for different workloads. In this work, we present the first systematic benchmark for \textsc{Gnn} unlearning, structured around three core desiderata: \emph{efficiency} (is unlearning faster than retraining?), \emph{utility} (does the unlearned model preserve predictive performance and align with the retrained gold standard?), and \emph{forgetting} (does the model genuinely eliminate the influence of removed data?). Through extensive experiments across diverse datasets and deletion scenarios, we deliver a unified assessment of existing approaches, surfacing their trade-offs and limitations. Crucially, our findings show that most unlearning techniques are not yet practical for large-scale graphs. At the same time, our benchmarking yields actionable guidelines on when unlearning can be a viable alternative to retraining and how to select among methods for different workloads, thereby charting a path for future research toward more practical, scalable, and trustworthy graph unlearning.

Peer effect refers to the difference in counterfactual outcomes for a unit resulting from different levels of peer exposure, the extent to which the unit is exposed to the treatments, actions, or behaviors of its peers. In practice, peer exposure is typically captured through an explicitly defined exposure mapping function that aggregates peer treatments and outputs peer exposure. Exposure mapping functions range from simple functions like the number or fraction of treated friends to more sophisticated functions that allow for different peers to exert different degrees of influence. However, the true function is rarely known in practice and when the function is misspecified, this leads to biased causal effect estimation. To address this problem, the focus of our work is to move away from the need to explicitly define an exposure mapping function and instead introduce a framework that allows learning this function automatically. We develop EGONETGNN, a graph neural network (GNN), for heterogeneous peer effect estimation that automatically learns the appropriate exposure mapping function and allows for complex peer exposure mechanisms that involve not only peer treatments but also attributes of the local neighborhood, including node, edge, and structural attributes. We theoretically and empirically show that GNN models that use peer exposure based on the number or fraction of treated peers or learn peer exposure naively face difficulty accounting for such influence mechanisms. Our evaluation on synthetic and semi-synthetic network data shows that our method is more robust to different unknown underlying influence mechanisms when compared to state-of-the-art baselines.

Full-graph and mini-batch Graph Neural Network (GNN) training approaches have distinct system design demands, making it crucial to choose the appropriate approach to develop. A core challenge in comparing these two GNN training approaches lies in characterizing their model performance (i.e., convergence and generalization) and computational efficiency. While a batch size has been an effective lens in analyzing such behaviors in deep neural networks (DNNs), GNNs extends this lens by introducing a fan-out size, as full-graph training can be viewed as mini-batch training with the largest possible batch size and fan-out size. However, the impact of the batch and fan-out size for GNNs remains insufficiently explored. To this end, this paper systematically compares full-graph vs. mini-batch training of GNNs through empirical and theoretical analyses from the view of the batch size and fan-out size. Our key contributions include: 1) We provide a novel generalization analysis using the Wasserstein distance to study the impact of the graph structure, especially the fan-out size. 2) We uncover the non-isotropic effects of the batch size and the fan-out size in GNN convergence and generalization, providing practical guidance for tuning these hyperparameters under resource constraints. Finally, full-graph training does not always yield better model performance or computational efficiency than well-tuned smaller mini-batch settings. The implementation can be found in the anonymous link: https://anonymous.4open.science/r/GNN_fullgraph_minibatch_training-8040/README.md.

A geometric graph associated with a set of points $P= \{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$ and a fixed kernel function $\mathsf{K}:\mathbb{R}^d\times \mathbb{R}^d\to\mathbb{R}_{\geq 0}$ is a complete graph on $P$ such that the weight of edge $(x_i, x_j)$ is $\mathsf{K}(x_i, x_j)$. We present a fully-dynamic data structure that maintains a spectral sparsifier of a geometric graph under updates that change the locations of points in $P$ one at a time. The update time of our data structure is $n^{o(1)}$ with high probability, and the initialization time is $n^{1+o(1)}$. Under certain assumption, our data structure can be made robust against adaptive adversaries, which makes our sparsifier applicable in iterative optimization algorithms. We further show that the Laplacian matrices corresponding to geometric graphs admit a randomized sketch for maintaining matrix-vector multiplication and projection in $n^{o(1)}$ time, under sparse updates to the query vectors, or under modification of points in $P$.

Post-hoc instance-level graph neural network (GNN) explainers are developed to identify a compact subgraph (i.e., explanation) that encompasses the most influential components for each input graph. A fundamental limitation of existing methods lies in the insufficient utilization of structural information during GNN explainer optimization. They typically optimize the explainer by aligning the GNN predictions of input graph and its explanation in the graph label space which inherently lacks expressiveness to describe various graph structures. Motivated by the powerful structural expression ability of vectorized graph representations, we for the first time propose to shift the GNN explainer optimization from the graph label space to the graph representation space. However, the paradigm shift is challenging due to both the entanglement between the explanatory and non-explanatory substructures, and the distributional discrepancy between the input graph and the explanation subgraph. To this end, we meticulously design IDEA, a universal dual-stage optimization framework grounded in a prototypical graph representation space, which can generalize across diverse existing GNN explainer architectures. Specifically, in the Structural Information Disentanglement stage, a graph tokenizer equipped with a structure-aware disentanglement objective is designed to disentangle the explanatory substructures and encapsulate them into explanatory prototypes. In the Explanatory Prototype Alignment stage, IDEA aligns the representational distributions of the input graph and its explanation unified in the prototypical representation space, to optimize the GNN explainer. Comprehensive experiments on real-world and synthetic datasets demonstrate the effectiveness of IDEA, with the average improvements of ROC-AUC by 4.45% and precision by 48.71%. We further integrate IDEA with diverse explainer architectures and achieve an improvement by up to 10.70%, which verifies its generalizability.

Graph Neural Networks (GNNs) have achieved state-of-the-art results in many relevant tasks where decisions might disproportionately impact specific communities. However, existing work on fair GNNs often assumes that either sensitive attributes are fully observed or they are missing completely at random. We show that an adversarial missingness process can inadvertently disguise a fair model through the imputation, leading the model to overestimate the fairness of its predictions. We address this challenge by proposing Better Fair than Sorry (BFtS), a fair missing data imputation model for sensitive attributes. The key principle behind BFtS is that imputations should approximate the worst-case scenario for fairness---i.e. when optimizing fairness is the hardest. We implement this idea using a 3-player adversarial scheme where two adversaries collaborate against a GNN classifier, and the classifier minimizes the maximum bias. Experiments using synthetic and real datasets show that BFtS often achieves a better fairness x accuracy trade-off than existing alternatives under an adversarial missingness process.

Despite significant advances in Graph Neural Networks (GNNs), their limited expressivity remains a fundamental challenge. Research on GNN expressivity has produced many expressive architectures, leading to architecture hierarchies with models of increasing expressive power. Separately, derivatives of GNNs with respect to node features have been widely studied in the context of the oversquashing and over-smoothing phenomena, GNN explainability, and more. To date, these derivatives remain unexplored as a means to enhance GNN expressivity. In this paper, we show that these derivatives provide a natural way to enhance the expressivity of GNNs. We introduce High-Order Derivative GNN (HOD-GNN), a novel method that enhances the expressivity of Message Passing Neural Networks (MPNNs) by leveraging high-order node derivatives of the base model. These derivatives generate expressive structure-aware node embeddings processed by a second GNN in an end-to-end trainable architecture. Theoretically, we show that the resulting architecture family's expressive power aligns with the WL hierarchy. We also draw deep connections between HOD-GNN, Subgraph GNNs, and popular structural encoding schemes. For computational efficiency, we develop a message-passing algorithm for computing high-order derivatives of MPNNs that exploits graph sparsity and parallelism. Evaluations on popular graph learning benchmarks demonstrate HOD-GNN’s strong performance on popular graph learning tasks.

Weight-space models learn directly from the parameters of neural networks, enabling tasks such as predicting their accuracy on new datasets. Naive methods -- like applying MLPs to flattened parameters -- perform poorly, making the design of better weight-space architectures a central challenge. While prior work leveraged permutation symmetries in standard networks to guide such designs, no analogous analysis or tailored architecture yet exists for Kolmogorov–Arnold Networks (KANs). In this work, we show that KANs share the same permutation symmetries as MLPs, and propose the KAN-graph, a graph representation of their computation. Building on this, we develop WS-KAN, the first weight-space architecture that learns on KANs, which naturally accounts for their symmetry. We analyze WS-KAN’s expressive power, showing it can replicate an input KAN’s forward pass - a standard approach for assessing expressiveness in weight-space architectures. We construct a comprehensive ``zoo'' of trained KANs spanning diverse tasks, which we use as benchmarks to empirically evaluate WS-KAN. Across all tasks, WS-KAN consistently outperforms structure-agnostic baselines, often by a substantial margin.

Graph Neural Networks (GNNs) have advanced graph classification, yet they remain vulnerable to graph-level imbalance, encompassing class imbalance and topological imbalance. To address both types of imbalance in a unified manner, we propose UniImb, a Unified framework for Imbalanced graph classification. Specifically, UniImb first captures multi-scale topological features and enhances data diversity via learnable personalized graph perturbations. It then employs a dynamic balanced prototype module to learn representative prototypes from graph instances, improving the quality of graph representations. Concurrently, a prototype load-balancing optimization term mitigates dominance by majority samples to equalize sample influence during training. We justify these design choices theoretically using the Information Bottleneck principle. Extensive experiments on 19 datasets-including a large-scale imbalanced air pollution graph dataset AirGraph released by us and 23 baselines demonstrate that UniImb has achieved dominant performance across various imbalanced scenarios. Our code is available at GitHub.

Explanations provided by Self-explainable Graph Neural Networks (SE-GNNs) are fundamental for understanding the model's inner workings and for identifying potential misuse of sensitive attributes. Although recent works have highlighted that these explanations can be suboptimal and potentially misleading, a characterization of their failure cases is unavailable. In this work, we identify a critical failure of SE-GNN explanations: *explanations can be unambiguously unrelated to how the SE-GNNs infer labels.* We show that, on the one hand, many SE-GNNs can achieve optimal true risk while producing these degenerate explanations, and on the other, most faithfulness metrics can fail to identify these failure modes. Our empirical analysis reveals that degenerate explanations can be maliciously planted (allowing an attacker to hide the use of sensitive attributes) and can also emerge naturally, highlighting the need for reliable auditing. To address this, we introduce a novel faithfulness metric that reliably marks degenerate explanations as unfaithful, in both malicious and natural settings. Our code is available in the supplemental.

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications, yet classical solvers are computationally costly on large or irregular domains. Neural PDE solvers have emerged as an efficient alternative, but they struggle to generalize to unseen source terms, which represent external forcing such as heat generation, body forces, or reaction rates. Since existing models typically mix the source with the system state, they lack a principled mechanism to capture source responses. We propose DGNet, a discrete Green network that explicitly decouples system evolution from source response. The key idea is to transform the classical Green’s function---a cornerstone of PDE theory---into a graph-based discrete formulation, preserving the superposition principle in a computable update rule. To ensure fidelity on irregular meshes, we construct a hybrid operator by combining physics-based discretizations with GNN-based corrections, while a lightweight residual GNN captures dynamics beyond the operator. Across three categories of spatiotemporal PDE scenarios, DGNet consistently achieves state-of-the-art accuracy. In particular, on the most challenging setting with entirely novel source terms, DGNet maintains stable performance while existing approaches collapse.