"Accelerating Grokking"

"The grokking phenomenon\u2014where neural networks suddenly generalize after extensive training\u2014remains poorly understood and computationally expensive to achieve. We intro duce a novel layer-dependent spectral analysis framework that accelerates grokking by up to 21% across mathematical tasks while improving accuracy to 99.97%. Our approach dynamically adjusts attention head weights based on frequency domain characteristics, demonstrating that different transformer layers require distinct spectral processing strategies. Through rigorous ablation studies, we established that early layers benefit from focusing on low-frequency patterns while deeper layers require high-frequency details, with layer-specific processing providing 34.3% performance improvement. This framework offers both practical training efficiency for resource-constrained environ ments and theoretical insights into neural network generalization mechanisms. Beyond accelerating grokking, our findings suggest a fundamental connection between frequency domain charac teristics and abstract rule learning, opening new avenues for understanding deep learning\u2019s generalization capabilities."