HyperSpectrum Geometry is proposed, a curvature metric-controlled hyperspherical manifold representation learning framework that combines a learnable global Riemannian metric tensor with normalized angular hyperspherical classification and suggests that learnable metric deformation constitutes a useful and underexplored component of interpretable semantic representation learning.
Hyperbolic neural networks introduce geometric operations that require explicit treatment in relevance propagation. Equivalent geometric realizations can produce different feature attributions, even when local relevance is conserved. We study this problem through Geometric Representation Invariance (GRI), a specializat...
Pin Xiong, Shang-Lin Li, Yi Ding et al.· 0 citations
A Semantic Manifold-Aware Similarity Learning (SMSL) framework, where the term "semantic manifold" is used in an operational sense to denote a topology-aware organization of textual semantic units induced from token/entity interactions, rather than a strict low-dimensional differentiable manifold.
A framework grounded in coarse geometry, the branch of mathematics studying metric spaces up to quasi-isometry is proposed: features are nonlinear functions of the distances from each point to a set of anchor points, so they read global geometry directly rather than through local aggregation.
K. Enakoutsa· Neural Processing Letters· 0 citations
CurvBi (Curvature-aware Bicomplex), a novel framework for multimodal knowledge graph completion that unifies modality alignment and relational modeling under a coherent mathematical foundation, is proposed.
Thanh Le, Vy Cao, Duong-Khang Au et al.· Data mining and knowledge di...· 0 citations
3D instance segmentation requires fine-grained geometric discrimination together with an effective representation of the hierarchical organization of real-world objects and scenes. Conventional transformer architectures, however, operate predominantly in Euclidean space, whose polynomial volume growth can be poorly mat...
Xiao-Yu Wei, A. Konushin· Neural Networks· 0 citations
Riemannian Geometry-Sensitive Quantization (RGSQ), which formulates quantization as a reconstruction problem under a unified Fisher-Riemannian metric, enabling standard unimodal PTQ methods to evaluate multimodal quantization error under their original assumptions.
Zhi-Ping Wu, Dong-Dong Ren, Yang Zhou et al.· 0 citations
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