Pith. sign in

Therefore, equation 17 becomes: V ol= p det(G) = p 1 − cos2(θ) = q sin2(θ) = sin(θ)

The Gram matrix G is given by: G = ⟨v⊤ 1 v1⟩ ⟨v⊤ 1 v2⟩ ⟨v⊤ 2 v1⟩ ⟨v⊤ 2 v2⟩ (14) Then, compute the determinant of the Gram matrix: det(G) =⟨v⊤ 1 v1⟩⟨v⊤ 2 v2⟩ − ⟨v⊤ 1 v2⟩2 (15) The volume of the k-dimensional parallelotope spanned by the moda · 2016

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Gramian Multimodal Representation Learning and Alignment

cs.CV · 2024-12-16 · conditional · novelty 6.0

GRAM replaces cosine similarity with the Gramian volume of the parallelotope formed by multiple modality embeddings, and a volume-based contrastive loss improves multimodal retrieval and classification.

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  • Gramian Multimodal Representation Learning and Alignment cs.CV · 2024-12-16 · conditional · none · ref 1

    GRAM replaces cosine similarity with the Gramian volume of the parallelotope formed by multiple modality embeddings, and a volume-based contrastive loss improves multimodal retrieval and classification.