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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).


Robust low-rank training via approximate orthonormal constraints

Neural Information Processing Systems

By modeling robustness in terms of the condition number of the neural network, we argue that this loss of robustness is due to the exploding singular values of the low-rank weight matrices.



Block Broyden's Methods for Solving Nonlinear Equations

Neural Information Processing Systems

This paper studies quasi-Newton methods for solving nonlinear equations. We propose block variants of both good and bad Broyden's methods, which enjoy explicit local superlinear convergence rates. Our block good Broyden's method has a faster condition-number-free convergence rate than existing Broyden's methods because it takes the advantage of multiple rank modification on Jacobian estimator. On the other hand, our block bad Broyden's method directly estimates the inverse of the Jacobian provably, which reduces the computational cost of the iteration. Our theoretical results provide some new insights on why good Broyden's method outperforms bad Broyden's method in most of the cases. The empirical results also demonstrate the superiority of our methods and validate our theoretical analysis.