用矩阵自由能正则化，让自编码器生成更像高斯分布的编码。
Matricial Free Energy as a Gaussianizing Regularizer: Enhancing Autoencoders for Gaussian Code Generation
- 基于代码矩阵奇异值设计可微损失函数
- 训练后代码分布逼近高斯随机矩阵特征
- 适合需要稳定高斯编码的逆问题应用
我们提出一种基于矩阵自由能的自编码器正则化新方法。该方法通过代码矩阵（维度×批量大小）的奇异值定义可微损失函数。依据自由概率论与随机矩阵理论，当代码矩阵的奇异值分布与具有独立同分布高斯元素的随机度量相匹配时，该损失取得最小值。实验表明，通过标准随机梯度训练最小化负矩阵自由能，可获得类高斯分布的编码，并在训练集和测试集上均表现良好。在此基础上，我们构建了最大化矩阵自由能的自编码器，能可靠生成高斯编码，并应用于欠定逆问题中。
原文摘要 · Abstract (English)
We introduce a novel regularization scheme for autoencoders based on matricial free energy. Our approach defines a differentiable loss function in terms of the singular values of the code matrix (code dimension x batch size). From the standpoint of free probability an d random matrix theory, this loss achieves its minimum when the singular value distribution of the code matrix coincides with that of an appropriately sculpted random metric with i.i.d. Gaussian entries. Empirical simulations demonstrate that minimizing the negative matricial free energy through standard stochastic gradient-based training yields Gaussian-like codes that generalize across training and test sets. Building on this foundation, we propose a matricidal free energy maximizing autoencoder that reliably produces Gaussian codes and show its application to underdetermined inverse problems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。