Counting Like Transformers: Compiling Temporal Counting Logic Into Softmax Transformers

arXiv:2404.04393v1 Announce Type: cross
Abstract: Deriving formal bounds on the expressivity of transformers, as well as studying transformers that are constructed to implement known algorithms, are both effective methods for better understanding the computational power of transformers. Towards both ends, we introduce the temporal counting logic $\textbf{K}_\text{t}$[#] alongside the RASP variant $\textbf{C-RASP}$. We show they are equivalent to each other, and that together they are the best-known lower bound on the formal expressivity of future-masked soft attention transformers with unbounded …

abstract algorithms arxiv compiling computational cs.cl cs.fl cs.lg cs.lo logic power softmax studying temporal text transformers type understanding