merrill-2022-saturated-transformers-threshold-circuits

Summary

Transformers that use ReLU activations can only perform a very limited kind of computation, roughly equivalent to a shallow, fixed-depth circuit of threshold gates, meaning they hit a hard ceiling on how much in-context reasoning they can do no matter how many layers you stack. This matters because it sets a theoretical upper bound on what a standard transformer architecture can accomplish internally, pointing to where more expressive or iterative mechanisms would be needed to go beyond that limit.