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About this paper
Jing He, Hua Jiang, Cheng Li, Siqian Xin, Shuzhen Yang
He et al. developed a validation-set-free early stopping method for Transformer models by analyzing the spectral dynamics of the encoder's first self-attention Value (V) matrix using Random Matrix Theory. Their Power-Law based heavy-tailed metric identifies an optimal stopping point, reducing training time by over 50% while maintaining near-final model performance on machine translation tasks.
Key insights
- The spectral distribution of the Value (V) matrix, specifically `en.0.s.a.V`, reliably reflects the Transformer's implicit self-regularization and training dynamics more stably than Query or Key matrices.
- Transformer training progresses through three distinct spectral phases: structural exploration, heavy-tailed structure formation and stabilization (where implicit regularization is strong), and performance saturation and convergence plateau.
- The emergence and stabilization of heavy-tailed spectral structures within the `en.0.s.a.V` matrix, quantifiable by the PL-based KS metric, serve as an intrinsic signal for optimal model generalization and an effective early stopping point.
Summary by alphaXiv.
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