![[P] algebra-de-grok: Visualizing hidden geometric phase transition in modular arithmetic networks](https://www.tweakedgeek.com/wp-content/uploads/2025/12/featured-article-6498-300x171.png)
A lightweight visualization tool has been developed to track the emergence of algebraic structures within neural networks training on modular arithmetic, highlighting the transition from memorization to generalization, known as "grokking." This tool uses real-time geometry to plot embedding constellations, transitioning from random noise to ordered algebraic groups, and employs metric-based detection to flag grokking onset well before validation accuracy spikes. It operates with minimal dependencies and visualizes the Fourier spectrum of neuron activations, turning a black-box phase transition into a visible geometric event. While tuned for algorithmic datasets and running on CPU, it provides a valuable tool for understanding network generalization on algorithmic tasks, with an open and adaptable codebase for further exploration. This matters because it offers insights into the internal reorganization of neural networks, enhancing our understanding of how they generalize beyond traditional loss metrics.
