Researchers explore complex SGD and directional bias in kernel Hilbert spaces

Researchers have introduced a novel variant of Stochastic Gradient Descent (SGD) designed for complex-valued neural networks. This new method, termed complex SGD, offers convergence guarantees even without analyticity constraints, mirroring advancements in the real-valued setting. The study also demonstrates that directional bias properties observed in real-valued kernel regression problems extend to the complex domain. Empirical results showcase complex SGD's effectiveness in kernel regression tasks within complex reproducing kernel Hilbert spaces, enabling the recovery of specific functions like superoscillation functions and Blaschke products. AI

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IMPACT Introduces a new optimization technique for complex-valued neural networks, potentially improving performance in specific machine learning tasks.

RANK_REASON This is a research paper introducing a new variant of an optimization algorithm with theoretical guarantees and empirical validation.

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• Stochastic Gradient Descent
• SGD
• Gradient Descent
• GD
• kernel regression
• reproducing kernel Hilbert spaces
• Fock Space
• Hardy Space

• paper
• other