methods / Representation Alignment / Triangle-area tri-modal similarity
Triangle-area tri-modal similarity
Replaces pairwise cosine similarity in a contrastive loss with the exact area of the triangle spanned by three unit-norm modality embeddings, computed directly in the shared high-dimensional embedding space via a Gram-determinant (Heron-style) formula -- a single scalar that jointly measures three-way alignment without an anchor modality, a fusion layer, or any pairwise decomposition.