Revisiting Padded Transformer Expressivity: Which Architectural Choices Matter and Which Don't

arXiv:2605.30523v1 Announce Type: cross Abstract: Recent work describes what transformers can and cannot compute through connections to boolean circuits, but existing results lack exact characterizations and are sensitive to modeling choices. Padded transformers -- to whose input filler symbols such as ``...'' are appended -- emerge as a useful gadget for establishing equivalences to circuit classes by providing polynomial space for adaptive parallel computation. However, only a limited set of padded transformer idealizations has been studied, leaving open how robustly these equivalences hold under changes to attention type, model width, and uniformity. We find that, under practical assumptions, padded transformers are surprisingly robust to all of these, and identify numeric precision and model depth as the main factors affecting expressivity. Concretely, we prove that polynomially padded ext{L-uniform} constant-precision transformers are equivalent to ext{L-uniform AC}^0, while growing-precision ones achieve ext{L-uniform TC}^0 regardless of width. Furthermore, looping enables sequential processing analogous to circuits: log^d N-looped constant-precision transformers reach ext{FO-uniform AC}^d, and growing-precision ones reach ext{FO-uniform TC}^d. Interestingly, growing width or precision beyond logarithmic does not increase expressivity, and all our results hold for both softmax and average hard attention transformers.

Source: arXiv cs.AI | 2026-06-01