Do Halting Heads Really Save Compute in Looped Language Models?

Looped language models run each token through the same layers several times, and each run is one iteration. To save compute, an extra layer, the halting head, gives after each iteration the probability that the token stops there, so that easy tokens can stop early. Pretraining models from scratch, up to 1.3B parameters, we find two problems. First, heads trained on a mix of all iterations predict that tokens need under half the iterations, yet under the standard stopping rule tokens run almost every iteration, because this training never scores the single iteration where a token stops. Scoring every iteration instead fixes this, but in our runs it works only with a strong penalty favoring early stops. Second, savings are commonly reported as an average number of iterations per token, but when sequences are generated in batches that run until their slowest token stops, a model without a head is almost as good at that cost. The reported average can therefore overstate the saving. We recommend reporting the iterations tokens actually run, with the stopping threshold and batch size, and give a test, run before training a head, that bounds its gain.