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Parameter Symmetry and Noise Equilibrium of Stochastic Gradient Descent Liu Ziyin Massachusetts Institute of Technology, NTT Research

Neural Information Processing Systems

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries - a broad subclass of continuous symmetries present in the model architecture or loss function - interplay with stochastic gradient descent (SGD). We first prove that gradient noise creates a systematic motion (a "Noether flow") of the parameters θ along the degenerate direction to a unique initialization-independent fixed point θ


Mitigating the Popularity Bias of Graph Collaborative Filtering: A Dimensional Collapse Perspective

Neural Information Processing Systems

Graph Collaborative Filtering (GCF) is widely used in personalized recommendation systems. However, GCF suffers from a fundamental problem where features tend to occupy the embedding space inefficiently (by spanning only a low-dimensional subspace).