Learning to Compute Is Not Learning to Retain or Reuse in Looped Transformers

Peilong Zhou, Hongtao Zhang, Yulong Huang, Cangyuan Li, Mingyu Chen +1

Looped transformers compute by applying one block repeatedly, so they can run for more loops than they were trained with. Recurrent reasoners are known to overthink: iterating past the trained depth can turn a correct answer into a wrong one. Such a late error can reflect failed computation, loss of retention, or a state that later computation cannot reuse. We separate these cases in in-context Mealy-machine execution, where a simulator supplies intermediate targets and exact counterfactuals for hidden-state interventions. Models trained to answer at loop 32 are fully correct there but keep only 22% of these answers at loop 64. Retention depends on what training asks for: supervising one randomly chosen position per example, instead of always the last, keeps 99.8%, and randomizing the number of training loops also helps; truncating gradients, as in progressive training against overthinking, does not. The computation itself is exact: position $k$ is computed at loop $k$, and swapping its loop-$k$ hidden vector for the one from another input redirects every later position to that input's exact continuation (237/237 pairs in each of ten models). Retention, however, is not reuse.…