New framework analyzes gradient descent convergence in neural networks

Researchers have developed a new framework to analyze the convergence of gradient descent in neural networks, extending beyond the traditional neural tangent kernel (NTK) regime. This framework applies to a broad range of architectures, including pre-normalized multi-layer transformers, and proves that gradient descent converges to a stationary point under mild assumptions and specific initializations. The analysis establishes Lipschitz smoothness along the gradient descent trajectory and reveals that learning rate scaling depends on network depth and bottleneck dimensions rather than width, with implications for residual connections and function composition. AI

IMPACT Provides a theoretical foundation for understanding and potentially improving the training of complex neural network architectures.

RANK_REASON The cluster contains a single academic paper detailing a new theoretical framework for analyzing neural network training dynamics. [lever_c_demoted from research: ic=1 ai=1.0]

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• gradient descent
• multi-layer transformers
• Neural tangent kernel
• Residual Connections
• Xavier initialization

• paper
• other

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