Unraveling the Hessian: A Key to Smooth Convergence in Loss Function Landscapes
Provides insights into neural loss landscape geometry for researchers developing sample size determination techniques.
The paper investigates how neural network loss landscapes change with increasing sample size, deriving theoretical upper bounds for loss function differences when adding new data points and empirically confirming convergence on image classification datasets.
The loss landscape of neural networks is a critical aspect of their training, and understanding its properties is essential for improving their performance. In this paper, we investigate how the loss surface changes when the sample size increases, a previously unexplored issue. We theoretically analyze the convergence of the loss landscape in a fully connected neural network and derive upper bounds for the difference in loss function values when adding a new object to the sample. Our empirical study confirms these results on various datasets, demonstrating the convergence of the loss function surface for image classification tasks. Our findings provide insights into the local geometry of neural loss landscapes and have implications for the development of sample size determination techniques.