Hidden Minima in Two-Layer ReLU Networks

arXiv — stat.MLTuesday, December 9, 2025 at 5:00:00 AM
  • Recent research has identified two infinite families of spurious minima in two-layer ReLU networks, one with vanishing loss and another with loss bounded away from zero. The latter, although avoided by vanilla SGD, remains hidden, prompting an analysis of their distinguishing properties. The study reveals that the Hessian spectra of hidden and non-hidden minima align up to terms of order O(d^{-1/2}), leading to a focus on the structural differences of arcs from these minima.
  • Understanding the characteristics of hidden minima is crucial for optimizing two-layer ReLU networks, as it can influence the effectiveness of training algorithms like SGD. The findings may provide insights into improving convergence rates and performance in neural network training, which is vital for advancements in artificial intelligence applications.
  • This research contributes to ongoing discussions in the field of neural networks regarding optimization challenges and the behavior of various training algorithms. The exploration of hidden minima aligns with broader themes in machine learning, such as the quest for efficient training methods and the theoretical underpinnings of neural network performance, which are essential for developing more robust AI systems.
— via World Pulse Now AI Editorial System

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