MAGIC: Deep Geometric Evolution with Structural Consensus for Temporal Knowledge Graph Reasoning

Multi-curvature progressive fusion for knowledge graph completion

Knowledge graphs have become a fundamental representation for structured knowledge, yet their incompleteness remains a major obstacle to reliable reasoning. Missing links may interrupt relational paths and limit the evidence available for downstream inference. Knowledge graph completion addresses this problem by predicting missing facts from observed relational patterns. Existing methods have made notable progress, but many of them rely on a single geometric space or fuse multiple geometric representations in a static manner. This limits their ability to capture heterogeneous graph structures, especially when hierarchical dependencies, local relational patterns, and cyclic motifs coexist in the same knowledge graph. In this paper, we propose multi-curvature progressive fusion (MCPF), a geometry-aware graph neural reasoning framework for knowledge graph completion. MCPF learns relation-aware representations in Euclidean, hyperbolic, and hyperspherical spaces, which provide complementary inductive biases for conventional relational interactions, hierarchical organization, and cyclic structures. Instead of directly aggregating these representations, MCPF progressively refines them through cross-space interactions and uses a query-conditioned gating mechanism to determine their relative contributions. This design enables the model to emphasize reliable geometric signals while suppressing less informative ones for each query. The fused representation is then used within a graph neural reasoning architecture for message passing and link prediction. Experiments on four benchmark datasets demonstrate that MCPF achieves competitive results against representative baselines and consistently outperforms its ablated variants.

SynAlign: cross-curvature synergistic Euclidean–hyperbolic entity alignment for knowledge graphs

Entity alignment is a fundamental step for knowledge graph (KG) integration, yet the complex and heterogeneous structures of real-world KGs make accurate alignment particularly challenging. KG entity alignment faces two main challenges. First, representations learned in a single Euclidean or hyperbolic space struggle to simultaneously capture local structure, global centrality, and hierarchical semantics. Second, most existing pipelines employ sophisticated encoders but rely on simple, weakly optimized decoders. To address these issues, we propose SynAlign, a cross-curvature Euclidean–hyperbolic framework for KG entity alignment. SynAlign adopts a decoupled multi-view, multi-geometry encoder: Euclidean embeddings model local structure and graph centrality, while hyperbolic embeddings emphasize hierarchical and containment relations, providing complementary multi-scale structural signals. On top of these embeddings, a hybrid collaborative supervision scheme jointly optimizes representation learning and matching. A margin-based feature loss encourages separability between aligned and non-aligned entities, whereas a collaborative alignment decoder combines soft matching scores with structural consistency constraints via Sinkhorn-based optimal transport to produce globally consistent soft alignments. Experiments on multiple benchmark datasets show that SynAlign consistently outperforms strong baselines in terms of Hits@1 and maintains robust performance under sparse supervision and structurally complex graphs.

AdaGeM: Adaptive Geometric Learning on Manifolds for Hyper-Relational Knowledge Graphs

FlowPath: From Discrete Paths to Continuous Semantic Flows for Knowledge Graph Completion

Knowledge graph completion (KGC) aims to infer missing facts based on existing triplets. Traditional path-based methods formulate reasoning as a discrete multi-hop traversal, which suffers from exponential search space and error accumulation.In this paper, we propose FlowPath, which rethinks the reasoning process by transforming discrete symbolic paths into a continuous semantic flow in the latent space. Specifically, we formalize the inference from a head entity to the target tail entity as an Ordinary Differential Equation (ODE) governed by a relation-conditioned neural velocity field, which learns to steer a smooth and expressive semantic transformation along the reasoning trajectory. To prevent the continuous flow from drifting into invalid semantic regions, we further introduce a structure-anchored guidance mechanism that leverages factual multi-hop paths from the knowledge graph as topological constraints, grounding the learned flow in the discrete relational structure. Moreover, a uncertainty weighting strategy is employed to adaptively balance the joint optimization of link prediction, flow generation, and structural guidance. By bridging discrete symbolic paths and continuous neural dynamics, FlowPath inherits the interpretability of path-based reasoning while possessing the flexibility and expressiveness of generative modeling. Extensive experiments on benchmark datasets demonstrate that FlowPath achieves competitive performance, and additional analysis confirms the effectiveness of modeling the reasoning paths of KGC as a continuous semantic flow.

Beyond Euclidean Tokens: Hyperbolic Structure-Aware Mapping for Dual-Task Scene Parsing With Only Minimal Trainable Parameters.

Achieving unified scene parsing that simultaneously outputs cross-domain semantic segmentation and depth estimation without scene-specific retraining is crucial for robust perception in complex real-world environments, yet remains a challenging goal. While recent monocular depth estimation models such as DepthAnything V2 exhibit strong domain generalization, semantic segmentation still suffers from severe structural degradation under domain and viewpoint shifts. We observed a persistent hierarchical calibration gap, where Euclidean representations exhibit larger calibration gaps between child and parent categories under domain shifts, suggesting limitations of existing Euclidean-based methods in preserving semantic hierarchies. To address this issue, we propose HyperMapper, a hyperbolic structure-aware mapping framework that bridges semantic understanding and geometric priors through hyperbolic token-to-feature interactions. By exploiting the negative curvature of hyperbolic space, HyperMapper helps capture hierarchical relationships and maintains geometric consistency across domains. Furthermore, by combining the expressive priors of vision foundation models (VFMs) with parameter-efficient fine-tuning (PEFT), HyperMapper achieves cross-domain adaptation with minimal trainable parameters in backbone while retaining the strong depth estimation capability of DepthAnythingV2 without retraining. Extensive experiments on multiple cross-domain and cross-viewpoint benchmarks demonstrate that HyperMapper achieves a higher mIoU for both parent and child categories while consistently improving segmentation accuracy over strong baselines. Our approach establishes a promising direction for task-preserving dual-task adaptation, bridging semantic and geometric learning and paving the way toward unified, cross-domain scene parsing.

Topology-Aware Neural Collapse for Generalized Category Discovery on Graphs

Learning a stable yet highly discriminative representation space that can simultaneously recognize known categories and discover novel ones from limited labeled data is fundamental to Generalized Category Discovery (GCD) on graphs. Recently, Neural Collapse (NC) theory has emerged as a powerful geometric principle for GCD, yielding maximally separated and well-structured class representations by encouraging feature embeddings to converge toward Simplex Equiangular Tight Frame (Simplex ETF) prototypes. However, when extending this paradigm to graph-structured data, a critical challenge arises. Graph representations are inherently shaped by topological dependencies, where neighborhood-based message passing enforces local smoothness among connected nodes. This topology-induced smoothing conflicts with the strict geometric convergence required by Simplex ETF, making neural collapse difficult to realize on graphs. To address this issue, we propose TopoNC, a topology-aware neural collapse framework for Graph GCD. Specifically, it fixes Simplex ETF prototypes as global geometric targets and introduces a Dual-Stream Encoder that decouples topology smoothing from feature-discriminative learning, adaptively balancing the two streams via a gating mechanism. In addition, we further design a Topology-Conditioned Pseudo-Labeling strategy that integrates Sinkhorn-based global balancing, Old-Class Top-K Admission Masking, and Neighborhood-Consensus Screening, to reliably guide feature collapse. Extensive experiments on several benchmark datasets have demonstrated that TopoNC consistently outperforms existing methods, highlighting the importance of topology-aware neural collapse for Graph GCD.