aiqbench analysis
This research establishes the theoretical advantages of weight normalization within overparameterized matrix sensing, proving it enables linear convergence and exponential speedups compared to standard approaches. By leveraging Riemannian optimization, the study demonstrates that increasing model overparameterization polynomially reduces both iteration counts and sample complexity for signal recovery tasks. These findings provide a rigorous foundation for understanding how specific normalization techniques can accelerate deep learning dynamics in structured matrix problems.
On the Benefits of Weight Normalization for Overparameterized Matrix Sensing
arXiv:2510.01175v2 Announce Type: replace Abstract: While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized matrix sensing problem. We prove that WN with Riemannian optimization achieves linear convergence, yielding an exponential speedup over standard methods that do not use WN. Our analysis further demonstrates that both iteration and sample complexity improve polynomially as the level of overparameterization increases. To the best of our knowledge, this work provides the first characterization of how WN leverages overparameterization for faster convergence in matrix sensing.
Abstract:While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized matrix sensing problem. We prove that WN with Riemannian optimization achieves linear convergence, yielding an exponential speedup over standard methods that do not use WN. Our analysis further demonstrates that both iteration and sample complexity improve polynomially as the level of overparameterization increases. To the best of our knowledge, this work provides the first characterization of how WN leverages overparameterization for faster convergence in matrix sensing.
Machine Learning (cs.LG); Signal Processing (eess.SP); Optimization and Control (math.OC); Machine Learning (stat.ML)
arXiv:2510.01175 [cs.LG]
(or arXiv:2510.01175v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2510.01175 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 199 words
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