Leap+Verify: Regime-Adaptive Speculative Weight Prediction for Accelerating Neural Network Training

Applies speculative execution to accelerate neural network training. Decomposes training into three dynamically detected regimes — chaotic, transition, stable — using activation-space cosine similarity as a real-time Lyapunov proxy. Discovers a universal momentum catastrophe: Adam moment extrapolation performs 100–10,000x worse than actual weights at all scales. Finite-difference predictors succeed where momentum fails, achieving 67–90% strict acceptance at 7B scale in stable regimes. Demonstrated on GPT-2 124M, Qwen 2.5-1.5B, and Qwen 2.5-7B.