标题： 无矩阵自由能作为高斯化正则化器：增强自编码器以生成高斯代码 显示英文标题

标题： Matricial Free Energy as a Gaussianizing Regularizer: Enhancing Autoencoders for Gaussian Code Generation

摘要： 我们引入了一种基于矩阵自由能的自编码器新颖正则化方案。 我们的方法在代码矩阵（代码维度 x 批量大小）的奇异值方面定义了一个可微损失函数。 从自由概率和随机矩阵理论的角度来看，当代码矩阵的奇异值分布与具有独立同分布高斯条目的适当雕刻随机度量的奇异值分布一致时，该损失达到最小值。 实证模拟表明，通过标准基于随机梯度的训练最小化负矩阵自由能会产生类似高斯的代码，这些代码在训练集和测试集之间具有泛化能力。 在此基础上，我们提出了一种矩阵自由能最大化自编码器，该编码器能够可靠地生成高斯代码，并展示了其在欠定逆问题中的应用。 显示英文摘要

摘要： 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.