Parity, Sensitivity, and Transformers

ArXi:2602.05896v2 Announce Type: replace Understanding what neural architectures can and cannot compute is a central challenge in the theory of AI. One of the fundamental problems in this context is the PARITY task, which asks whether the number of 1s in a binary input sequence is even or odd. PARITY is one of the central tasks studied in the theory of computation, yet it remains surprisingly unclear under which conditions transformers can or cannot solve it. In this paper, we show that the minimal number of layers a transformer needs to compute PARITY is two.