[P] algebra-de-grok: Visualizing hidden geometric phase transition in modular arithmetic networks
Analysis
This project presents a novel approach to understanding "grokking" in neural networks by visualizing the internal geometric structures that emerge during training. The tool allows users to observe the transition from memorization to generalization in real-time by tracking the arrangement of embeddings and monitoring structural coherence. The key innovation lies in using geometric and spectral analysis, rather than solely relying on loss metrics, to detect the onset of grokking. By visualizing the Fourier spectrum of neuron activations, the tool reveals the shift from noisy memorization to sparse, structured generalization. This provides a more intuitive and insightful understanding of the internal dynamics of neural networks during training, potentially leading to improved training strategies and network architectures. The minimalist design and clear implementation make it accessible for researchers and practitioners to integrate into their own workflows.
Key Takeaways
- •Visualizes the geometric phase transition during grokking.
- •Uses spectral entropy to detect grokking earlier than validation accuracy.
- •Provides a minimalist and easily integrable PyTorch tool.
“It exposes the exact moment a network switches from memorization to generalization ("grokking") by monitoring the geometric arrangement of embeddings in real-time.”