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20 papers in the last four weeks, up 300% on the four weeks before. 0.2% of all new papers.

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On the Effectiveness of the z-Transform Method in Quadratic Optimization
Jul 4, 2025Francis BachMomentum Stochastic Gradient Descent Convergence
SIERRA · Inria - Ecole Normale Sup´erieure · PSL Research University
Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential
Feb 26, 2025Shijun Zhang, Hongkai Zhao, Yimin Zhong +1Two-Layer Neural Networks Neural Network
Department of Applied Mathematics Hong Kong Polytechnic University · Department of Mathematics Duke University · Department of Mathematics and Statistics Auburn University +1
Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture Models
Apr 19, 2024Xinyu Liu, Hai ZhangGaussian Mixture Models Optimal Sample Complexity
Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay, Hong Kong SAR, China
FP8 is All You Need (Part 2): Full-FP64 3-D FFT on FP8-Generation Tensor CoresThe Integer-Epilogue Wall and the Minimal Hardware That Would Remove It
Date pendingSatoshi MatsuokaFp8 Nvidia
Director, RIKEN Center for Computational Science (R-CCS), Kobe, Hyogo, Japan
FreeTransformSR: Efficient Lightweight Image Super-Resolution via Free Low-Rank Learnable Transform
Date pendingHongji Li, Yunhui LiReal-World Image Super-Resolution Fourier
Chinese Academy of Sciences Changchun Institute of Optics Fine Mechanics and Physics, Changchun, Jilin 130033, China · University of the Chinese Academy of Sciences, Beijing 100049, China

Jul 4, 2025, cs.LGJ/K move · Enter open · S save

On the Effectiveness of the z-Transform Method in Quadratic Optimization

Francis Bach

SIERRA · Inria - Ecole Normale Sup´erieure · PSL Research University

Momentum Stochastic Gradient Descent Convergence Stochastic Gradient Descent Fourier Kernel Hilbert Spaces

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The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can be equivalently defined on the original sequence and its

z

-transform. In particular, the z-transform method focuses on asymptotic behaviors and allows the use of Taylor expansions. We present a sequence of results of increasing significance and difficulty for linear models and optimization algorithms, demonstrating the effectiveness and versatility of the z-transform method in deriving new asymptotic results. Starting from the simplest gradient descent iterations in an infinite-dimensional Hilbert space, we show how the spectral dimension characterizes the convergence behavior. We then extend the analysis to Nesterov acceleration, averaging techniques, and stochastic gradient descent.

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Latest papers 125

On the Effectiveness of the z-Transform Method in Quadratic Optimization

Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential

Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture Models

FP8 is All You Need (Part 2): Full-FP64 3-D FFT on FP8-Generation Tensor CoresThe Integer-Epilogue Wall and the Minimal Hardware That Would Remove It

FreeTransformSR: Efficient Lightweight Image Super-Resolution via Free Low-Rank Learnable Transform