The Representations of Deep Neural Networks Trained on Dihedral Group Multiplication
Gavin McCracken ⋅ Sihui Wei ⋅ Gabriela Moisescu-Pareja ⋅ Harley Wiltzer ⋅ Irina Rish ⋅ Jonathan Love
Abstract
We find coset and approximate coset circuits play a key role in how multilayer perceptrons learn dihedral group multiplication, consistent with recent findings on modular addition. We identify that neural preactivations concentrate on (approximate) cosets, and visualize the manifolds distributed across neurons that correspond to the (approximate) coset representations.
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