Concorde is an energy‑based framework for link prediction that tackles sparse graphs by decomposing link likelihood into three decoupled branches: a parameter‑free spectral anchor for topological stability, a mixed‑curvature residual on a learnable hyperbolic‑spherical product manifold regularized by a curvature proxy, and a continuous vector field on the hyperbolic tangent bundle for non‑local alignment. These branches are fused via learned gating and trained with an N‑pair ranking loss. On five diverse benchmarks, Concorde achieves state‑of‑the‑art early retrieval precision, nearly doubling P@10% over leading baselines in sparse settings.
arXiv:2608. 06031v1 Announce Type: new Abstract: Dynamic graph prompting freezes a pre-trained temporal backbone and adapts it to label-scarce downstream tasks using lightweight prompts.
arXiv:2608. 07029v1 Announce Type: new Abstract: Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare.
arXiv:2606. 10071v1 Announce Type: cross Abstract: We introduce Temporal Sheaf Neural Networks (TSNN), a temporal link prediction framework that equips each node with a time-varying orthogonal frame and compares node states only after explicit transport between local coordinate systems.
arXiv:2607. 06497v1 Announce Type: new Abstract: We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths.
The paper introduces G^2MLP, a graph‑free MLP trained via distillation from a GNN teacher while preserving the teacher’s graph‑induced geometry. It identifies two spectral failure modes—underfit on sparse graphs and overfit on dense graphs—caused by neglecting geometry during distillation. By using Ollivier‑Ricci curvature to guide supervision between prediction‑level and representation‑level alignment, G^2MLP improves node‑classification performance and reduces the teacher‑student rank gap across benchmarks.
arXiv:2606. 25347v1 Announce Type: new Abstract: Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space.
arXiv:2610. 20684v1 Announce Type: new Abstract: Learning informative representations of mechanical Triply Periodic Minimal Surface (TPMS) metamaterials is important for mechanics analysis and structural design, yet existing methods have rarely explicitly supervised learned representations with information about global structural connectivity that is relevant to mechanical response.
The paper introduces Constant‑Curvature Sliced Gromov‑Wasserstein (CCSGW), a new divergence for aligning probability distributions on heterogeneous constant‑curvature spaces such as hyperbolic and spherical manifolds. It extends sliced Gromov‑Wasserstein by adding geodesic‑based one‑dimensional projections for spherical spaces, enabling efficient and principled comparison across manifolds with different curvatures while preserving intrinsic geometric relationships. The authors provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy and demonstrate consistent performance gains when integrated into mixed‑curvature learning tasks like graph anomaly detection, node classification, and multimodal learning.
Learning informative representations of mechanical Triply Periodic Minimal Surface (TPMS) metamaterials is important for mechanics analysis and structural design, yet existing methods have rarely expl...
arXiv:2606. 16990v1 Announce Type: new Abstract: While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered by high dimensionality and the ``varying length'' problem across different filtration scales.
arXiv:2607. 08337v1 Announce Type: new Abstract: Diffusion unlearning is essential for mitigating the generation of harmful or copyrighted content in text-to-image models.
arXiv:2602. 23665v5 Announce Type: replace-cross Abstract: We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search.