{"ID":2864459,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24076","arxiv_id":"2509.24076","title":"A Family of Kernelized Matrix Costs for Multiple-Output Mixture Neural Networks","abstract":"Pairwise distance-based costs are crucial for self-supervised and contrastive feature learning. Mixture Density Networks (MDNs) are a widely used approach for generative models and density approximation, using neural networks to produce multiple centers that define a Gaussian mixture. By combining MDNs with contrastive costs, this paper proposes data density approximation using four types of kernelized matrix costs in the Hilbert space: the scalar cost, the vector-matrix cost, the matrix-matrix cost (the trace of Schur complement), and the SVD cost (the nuclear norm), for learning multiple centers required to define a mixture density.","short_abstract":"Pairwise distance-based costs are crucial for self-supervised and contrastive feature learning. Mixture Density Networks (MDNs) are a widely used approach for generative models and density approximation, using neural networks to produce multiple centers that define a Gaussian mixture. By combining MDNs with contrastive...","url_abs":"https://arxiv.org/abs/2509.24076","url_pdf":"https://arxiv.org/pdf/2509.24076v4","authors":"[\"Bo Hu\",\"José C. Príncipe\"]","published":"2025-09-28T21:23:11Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}