用四种核化矩阵损失，提升多输出混合神经网络的密度建模能力
A Family of Kernelized Matrix Costs for Multiple-Output Mixture Neural Networks
- 提出四种基于希尔伯特空间的核化矩阵损失函数
- 在多中心混合密度模型中显著优化特征分布拟合效果
- 适合做自监督学习和生成建模的研究者参考
基于成对距离的损失函数在自监督与对比学习中至关重要。混合密度网络（MDNs）是广泛用于生成模型和密度逼近的方法，通过神经网络输出多个中心以定义高斯混合模型。本文将MDNs与对比损失结合，提出四种在希尔伯特空间中的核化矩阵损失：标量损失、向量-矩阵损失、矩阵-矩阵损失（即Schur补的迹）以及SVD损失（即核范数），用于学习定义混合密度所需的多个中心。
原文摘要 · Abstract (English)
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.
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