Title: Geometric Logit Decoupling for Energy-Based Graph Out-of-distribution Detection
Venue: NeurIPS 2025
Accepted: yes
Keywords: out-of-distribution detection; confidence calibration
Abstract: GNNs have achieved remarkable performance across a range of tasks, but their reliability under distribution shifts remains a significant challenge. In particular, energy-based OOD detection methods—which compute energy scores from GNN logits—suffer from unstable performance due to a fundamental coupling between the norm and direction of node embeddings. Our analysis reveals that this coupling leads to systematic misclassification of high-norm OOD samples and hinders reliable ID–OOD separation. Interestingly, GNNs also exhibit a desirable inductive bias known as angular clustering, where embeddings of the same class align in direction. Motivated by these observations, we propose GeoEnergy (Geometric Logit Decoupling for Energy-Based OOD Detection), a plug-and-play framework that enforces hyperspherical logit geometry by normalizing class weights while preserving embedding norms. This decoupling yields more structured energy distributions, sharper intra-class alignment, and improved calibration. GeoEnergy can be integrated into existing energy-based GNNs without retraining or architectural modification. Extensive experiments demonstrate that GeoEnergy consistently improves OOD detection performance and confidence reliability across various benchmarks and distribution shifts.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes GeoEnergy, a geometric logit decoupling strategy designed to enhance energy-based out-of-distribution OOD detection in GNNs. By normalizing class weight vectors while preserving node embedding norms, the approach explicitly disentangles direction and magnitude, leveraging the natural angular clustering observed in GNNs. Without requiring retraining or architectural changes, GeoEnergy can be seamlessly integrated into existing energy-based frameworks. Extensive experiments across multiple benchmarks demonstrate improvements in OOD detection performance, calibration, and self-training.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n1. Presents a clear geometric motivation supported by empirical analysis, identifying the coupling between embedding norm and direction as a root cause of misclassification.\n2. The method is simple, generalizable, and compatible, can be added to existing energy-based OOD frameworks without modifying the backbone network or retraining.\n3. Demonstrates consistent and substantial improvements across a range of datasets and OOD scenarios.\n4. Additionally improves confidence calibration and pseudo-label quality in self-training, extending the impact beyond OOD detection.\n\nWeaknesses\n1. The theoretical contribution is largely heuristic, lacks rigorous analysis of generalization guarantees or robustness under distribution shifts.\n2. Experiments focus primarily on small to medium-scale homogeneous graphs; scalability and effectiveness on large-scale heterogeneous graphs are not addressed.\n3. The current selection of the scaling factor s mainly relies on empirical tuning or validation set search. However, the optimal value of s can vary significantly across different datasets, graph structures, and numbers of classes. The paper lacks theoretical justification or analytical discussion for this variation.\n\nQUESTIONS:\n1. How resilient is GeoEnergy to perturbations or noise that specifically target the embedding norm?\n2. The method relies on empirical tuning of the scaling factor s. Have the authors considered developing a data-dependent or theoretically grounded approach to automatically adapt s to varying graph structures and distribution shifts?\n\nLIMITATIONS:\n1. The paper lacks formal theoretical analysis, relying primarily on empirical evidence and geometric intuition.\n2. In real-world scenarios, such as cold start settings, the lack of a validation set, or the presence of distributional shifts, validation data may become unavailable or unreliable. This limitation poses a significant challenge to adapting or tuning the scaling factor s dynamically during deployment.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes GeoEnergy, a geometric logit decoupling framework designed to enhance energy-based out-of-distribution (OOD) detection in graph neural networks (GNNs). The authors identify that the coupling between the norm and direction of node embeddings in GNNs undermines the reliability of conventional energy-based OOD detection. GeoEnergy addresses this issue by normalizing class weights while preserving embedding norms, thereby decoupling the influence of magnitude and direction in logits. This geometrically principled approach improves intra-class alignment, enlarges inter-class angular margins, and stabilizes energy scores, leading to more reliable OOD detection. The framework is plug-and-play, compatible with existing energy-based GNNs, and demonstrates consistent improvements in OOD detection performance and confidence reliability across diverse benchmarks and distribution shifts.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n1. This geometrically principled approach improves the reliability of energy-based out-of-distribution (OOD) detection.\n2. GeoEnergy is a plug-and-play framework that can be seamlessly integrated into existing energy-based GNNs without requiring retraining or architectural modifications.  \n3. This paper conducts extensive experiments across multiple benchmark datasets (e.g., Cora, Citeseer, Pubmed) and diverse OOD scenarios (e.g., structure manipulation, feature interpolation, label leave-out). \n4. This work is well-written and easy to follow. \n\nWeakness:\n1. The paper assumes that graph data exhibits homophily (i.e., connected nodes tend to belong to the same class), which may limit the performance of GeoEnergy in heterophilic graphs where connected nodes often belong to different classes.  \n2.  The main experimental results lack diversity, which might not fully eveluate the generlizability of the proposed methods. \n3. The efficiency of the proposed method should be analyzed.\n\nQUESTIONS:\n2.  The main experimental results lack diversity, which might not fully eveluate the generlizability of the proposed methods. \n3. The efficiency of the proposed method should be analyzed.\n\nLIMITATIONS:\nThe paper assumes that graph data exhibits homophily (i.e., connected nodes tend to belong to the same class), which may limit the performance of GeoEnergy in heterophilic graphs where connected nodes often belong to different classes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes GeoEnergy, a simple plug-and-play framework to improve energy-based OOD detection for Graph Neural Networks by decoupling class weight magnitudes from logits and preserving embedding norms as confidence signals. The authors claim that conventional energy-based methods suffer from unstable energy scores due to coupling between logit norm and direction. By normalizing class weights and leveraging angular clustering in GNN embeddings, GeoEnergy aims to stabilize energy scores and improve OOD detection. Multiple experiments on graph benchmarks demonstrate consistent gains over baselines.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper addresses a relevant and under-explored issue in graph OOD detection: the instability of energy scores due to logit coupling.\n2. The proposed solution is simple, intuitive, and easy to integrate into existing GNN models without retraining.\n3. The idea of leveraging angular clustering properties in GNNs for OOD detection is interesting and has practical potential.\n\nWeaknesses:\n1. The method keeps embedding norms as part of the energy score, but embedding norms in GNNs often correlate with node degree, which can introduce noise and harm energy stability in heterophily or imbalanced graphs.\n2. The assumption of angular clustering only holds on small, homophilous graphs like Cora and Pubmed, but may not generalize to heterophilous or large real-world graphs.\n3. Proposition 1 and Proposition 2 are trivial and formalize obvious properties without offering deeper theoretical justification for improved OOD separation.\n4. The decoupling only applies to class weight magnitudes, while embedding norm-induced variance remains and can still destabilize the energy scores. A fully norm-independent scoring function might be cleaner.\n5. Most experiments are on small homophily graphs. The method’s scalability and effectiveness on large-scale or heterophily graphs remain untested.\n\nQUESTIONS:\nThe experiment lacks comparisons with recent state-of-the-art methods, such as [1],[2],[3].\n\n[1] Revisiting Score Propagation in Graph Out-of-Distribution Detection. NeurIPS'24\n\n[2] GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation. ICLR'25\n\n[3] Spreading Out-of-Distribution Detection on Graphs. ICLR'25\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}