Abstract: A problem by Feichtinger, Heil, and Larson asks whether a positive-definite integral operator with M1 kernel admits a symmetric rank-one decomposition which is strongly square-summable with respect to the M1 norm. In conjunction with a concurrent result by Bandeira-Mixon-Steinerberger, we provide a negative answer to the problem and study special cases where such factorization is possible. We also discuss an application of the results to the semidefinite relaxation of a quadratic program. Algorithms that solve the first problem can be used to solve special cases of the Blind Source Separation problem. Joint work with Fushuai (Black) Jiang: https://arxiv.org/abs/2409.20372
Abstract: Neural network quantization is a branch of neural network compression that aims to replace high-precision parameters (such as 32-bit or 64-bit weights) with lower-bit representations while maintaining the model’s architecture and performance. In this talk, I will begin by introducing the basic concepts of neural network quantization and highlighting several interesting quantization methods. I will then present my paper Frame Quantization of Neural Networks—a joint work with Professor Wojciech Czaja—recently published in the Journal of Fourier Analysis and Applications. Finally, I will discuss several open questions related to neural network quantization and low-bit representations of neural networks.
Abstract: Neural network training is a challenging nonconvex optimization to analyze its convergence. While many studies focus on proving the linear convergence of the empirical risk, the analysis of the population risk is limited. In this talk, I will present my paper, Curse of Dimensionality in Neural Network Optimization, which addresses this problem regarding the target function's regularity. I will start with a brief overview of the neural network optimization literature and introduce Barron spaces, which are crucial for explaining the training convergence of shallow neural networks in the mean-field regime. This is a joint work with Professor Haizhao Yang (UMD).
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