Nonconformal Distortion and Local Orientation Reversal in the Fourier Circuit of a Modular-Addition Transformer

arXiv cs.AINovember 3, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2611.00414v1 Announce Type: new Abstract: We study the local differential geometry of a Fourier-based modular-addition circuit in a one-layer transformer whose algorithm has previously been reverse-engineered. For each of the five key Fourier frequencies, we restrict the model's multilayer perceptron (MLP) contribution to a corresponding Fourier input plane and readout, and measure its directional Beltrami coefficient under continuous input perturbations. Whereas nondegenerate restrictions of ideal complex multiplication are conformal, the trained maps exhibit nonconformal distortion (median $|\mu|=0.304$--$0.446$), spatial organization in the Beltrami argument, and regions of local or

This is a short summary published by AI Global Wire. The full article is owned and hosted by arXiv cs.AI — open it there to read it in full.

• Forskning