用于多模态对齐的双曲 Gramian 体积
Hyperbolic Gramian Volumes for Multimodal Alignment
把多模态对齐中的 Gramian 体积从欧氏空间搬到洛伦兹双曲模型，并用可学习混合保留欧氏判别性，可直接替换视频-文本对比学习中的相似度/对齐损失，提升零样本跨类别判别与语义敏感度。
原文依据 HyperGRAM, a hybrid geometry framework that combines Euclidean discriminative stability with hyperbolic semantic variance through learnable mixing
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论多模态对比学习通常依赖成对相似度进行对齐，但近期工作表明 Gramian 体积能够捕捉跨模态的高阶相关性。然而，欧氏 Gramian 体积在 L2 归一化下会出现体积坍缩，数值集中于 1 附近，判别性方差极小。双曲几何的指数体积增长通过保持方差自然地解决了这一问题，这促使我们将 Gramian 对齐推广到双曲空间。然而初步实验表明，仅使用纯双曲几何并不充分：它虽然保持了方差，但在跨类别判别上不如欧氏基线。我们提出 HyperGRAM，一个混合几何框架，通过可学习混合将欧氏的判别稳定性与双曲的语义方差结合起来。借助数值稳定的洛伦兹模型，HyperGRAM 使体积承担双重角色：既区分匹配与不匹配的三元组，又在匹配对内部保持反映解释空间（即有效多模态实现构成的集合）的语义敏感度。在四个视频-文本基准上的评估表明，混合几何一致优于纯欧氏与纯双曲变体，取得显著的零样本提升，且跨数据集的语义敏感度呈现出对比性的相关模式。
英文原文摘要 1416 字符
Multimodal contrastive learning typically relies on pairwise similarities for alignment, but recent work has shown that Gramian volumes can capture higher-order correlations across modalities. However, Euclidean Gramian volumes suffer from volume collapse under L2 normalization, concentrating near unity with minimal discriminative variance. Hyperbolic geometry's exponential volume growth naturally addresses this via variance preservation, motivating us to extend Gramian alignment to hyperbolic space. Yet preliminary experiments reveal that pure hyperbolic geometry alone is insufficient: while it preserves variance, it underperforms Euclidean baselines on cross-category discrimination. We introduce HyperGRAM, a hybrid geometry framework that combines Euclidean discriminative stability with hyperbolic semantic variance through learnable mixing. Using the numerically stable Lorentz model, HyperGRAM enables volumes to serve dual roles: discriminating matched from mismatched triplets while preserving semantic sensitivity within matched pairs that reflects interpretation spaces (the set of valid multimodal realizations). Evaluation across four video-text benchmarks demonstrates that hybrid geometry consistently outperforms both pure Euclidean and pure hyperbolic variants, achieving significant zero-shot improvements with cross-dataset semantic sensitivity exhibiting contrasting correlation patterns.