A completely uniform transformer for parity
This addresses a theoretical problem in formal language modeling for researchers in computational linguistics and machine learning, but it is incremental as it builds on existing work.
The authors tackled the problem of constructing a transformer that recognizes the parity language without input-length-dependent parameters, achieving a 3-layer constant-dimension transformer with uniform positional encoding, improving upon a prior 2-layer construction that required length-dependent encoding.
We construct a 3-layer constant-dimension transformer, recognizing the parity language, where neither parameter matrices nor the positional encoding depend on the input length. This improves upon a construction of Chiang and Cholak who use a positional encoding, depending on the input length (but their construction has 2 layers).