Fractal Dimension Generalization Measure

基于数据依赖分形维数的泛化界

Generalization Bounds with Data-dependent Fractal Dimensions

本文提出一种数据依赖分形维数，在不依赖 Lipschitz 假设的情况下证明神经网络泛化界，并引入几何稳定性概念及与拓扑数据分析的联系，通过实验验证理论有效性。

论分形维数作为泛化度量的局限性

On the Limitations of Fractal Dimension as a Measure of Generalization

该研究针对基于分形维数的神经网络泛化度量开展实证评估，发现超参数混杂效应、差初始化下预测失效及拓扑度量的双下降现象，为相关因果关系研究奠定基础。

Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms

Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account in order to obtain meaningful generalization bounds, it is still theoretically not clear which properties of the data and the algorithm determine the generalization performance. In this study, we approach this problem from a dynamical systems theory perspective and represent stochastic optimization algorithms as random iterated function systems (IFS). Well …

傅里叶分形维数预测深度神经网络的泛化能力

Fourier fractal dimension to predict the generalization of deep neural networks

提出基于权重变化的傅里叶分形维数作为泛化度量，并设计傅里叶优化器正则化该维数，在CIFAR-10等数据集上实现与泛化差距的高相关性。

通过算法相关Rademacher复杂度获得泛化保证

Generalization Guarantees via Algorithm-dependent Rademacher Complexity

本文提出基于算法相关且数据相关的经验Rademacher复杂度来刻画泛化误差，据此得到有限分形维数新界、简化随机梯度下降的维数无关泛化界证明，并恢复VC类与压缩方案的结果。

Rate-Distortion Theoretic Generalization Bounds for Stochastic Learning Algorithms

Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting different complexity notions such as the mutual information between the data sample and the algorithm output, compressibility of the hypothesis space, and the fractal dimension of the hypothesis space. While these bounds have illuminated the problem at hand from different angles, their suggested complexity notions might appear seemingly unrelated, thereby res…