Improving Generalization of Deep Neural Networks by Optimum Shifting

Recent studies showed that the generalization of neural networks is correlated with the sharpness of the loss landscape and flat minima suggests a better generalization ability than sharp minima. In this paper, we propose a novel method called optimum shifting, which changes the parameters of a neural network from a sharp minimum to a flatter one while maintaining the same training loss value. Our method is based on the observation that when the input and output of a neural network are fixed, the matrix multiplications within the network can be treated as systems of under-determined linear equations, enabling adjustment of parameters in the solution space, which can be simply accomplished by solving a constrained optimization problem. Furthermore, we introduce a practical stochastic optimum shifting technique utilizing the neural collapse theory to reduce computational costs and provide more degrees of freedom for optimum shifting. Extensive experiments with various deep neural network architectures on benchmark datasets demonstrate the effectiveness of our method.