Latent Algorithmic Structure Precedes Grokking: A Mechanistic Study of ReLU MLPs on Modular Arithmetic

Grokking-the phenomenon where validation accuracy of neural networks on modular addition of two integers rises long after training data has been memorized-has been characterized in previous works as producing sinusoidal input weight distributions in transformers and multi-layer perceptrons (MLPs). We find empirically that ReLU MLPs in our experimental setting instead learn near-binary square wave input weights, where intermediate-valued weights appear exclusively near sign-change boundaries, alongside output weight distributions whose dominant Fourier phases satisfy a phase-sum relation $φ_{\mathrm{out}} = φ_a + φ_b$; this relation holds even when the model is trained on noisy data and fa...

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