Grokking modular arithmetic

• URL: http://arxiv.org/abs/2301.02679v1
• Date: Fri, 6 Jan 2023 19:00:01 GMT
• Title: Grokking modular arithmetic
• Authors: Andrey Gromov
• Abstract summary: We present a simple neural network that can learn modular arithmetic tasks. We show that the network exhibits a sudden jump in generalization known as grokking''
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various modular arithmetic tasks under vanilla gradient descent with the MSE loss function in the absence of any regularization; (ii) evidence that grokking modular arithmetic corresponds to learning specific feature maps whose structure is determined by the task; (iii) analytic expressions for the weights -- and thus for the feature maps -- that solve a large class of modular arithmetic tasks; and (iv) evidence that these feature maps are also found by vanilla gradient descent as well as AdamW, thereby establishing complete interpretability of the representations learnt by the network.

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