Transductive Generalization via Optimal Transport and Its Application to Graph Node Classification

In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation. In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels. These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available. Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes. We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpening/tunedGNN.

Graph Neural Networks (GNNs) deliver strong performance on graph tasks, but their accuracy drops significantly under out-of-distribution (OOD) scenarios. Under distribution shifts, GNNs often fit environmental noise and spurious correlations instead of stable causal mechanisms, leading to weak OOD robustness and unstable predictive representations. Existing solutions based on environment invariance or causal reasoning are insufficient for node classification, as they do not explicitly model the fine-grained latent geometry required by the task. We further observe a training instability named Info-Jitter, where the mutual information between predictive representations and ground-truth labels fluctuates throughout training. To address these issues, we construct a node-classification-specific causal graph derived from the task's geometric objective. Using do-calculus to block non-causal paths caused by environmental noise, we derive a deconfounded interventional objective and a variational lower bound to disentangle representations into intra-class and inter-class components. We then propose Causal-Guided Representation Learning (CGRL), a framework with two core modules. First, a multi-branch re-weighted representation learning (RRL) module learns a causal modulation matrix to amplify causal signals and suppress environmental noise during message passing. Second, an optimization strategy combining intra-class aggregation, inter-class separation, energy-based reconstruction and supervised prediction regularizes the latent space for robust node-level generalization. Experiments on multiple benchmark datasets show that CGRL outperforms strong baselines across various distribution shifts and effectively mitigates the Info-Jitter phenomenon.

Node representation learning has advanced rapidly, yet most existing methods rely on per-dataset training and hyperparameter tuning. This dataset-specific optimization comes from the difficulty of designing reusable graph models that generalize across diverse graph datasets. In this work, we introduce Node4All, a node representation learner applicable to arbitrary graph datasets without any dataset-specific optimization. Node4All is built on two complementary ideas. At the architectural level, we introduce the Channel Graph Transformer (CGT), which enables a single fixed parameterization to process arbitrary graph datasets. At the learning level, we propose a self-supervised learning based on a series of synthetic graphs. Together, these components enable generalization beyond individual datasets, which is infeasible with existing architectures and learning frameworks. We extensively evaluate Node4All on node classification across 25 benchmarks against 21 baselines, covering both supervised and self-supervised methods. Despite all baselines being trained and optimized for each dataset, a single Node4All, applied uniformly across the datasets, achieves a competitive ranking of 5th among 21 baselines. Moreover, Node4All supports one-shot and in-context learning with an appropriate predictor and outperforms recent graph foundation models (GFMs) in these settings. These results demonstrate that Node4All not only achieves reusability across arbitrary graph datasets, but also remains an effective solution in practice. Code and model checkpoints are available in https://github.com/dooho00/node4all.