To be precise, the distillation mentioned in this paper is not the distillation used by other model companies. In the one mentioned in the paper, your teacher and student model typically have similar architectures - and you typically need access to the full logits. What happens here instead is motivated by the fact that these companies don't have access to the training data and compute that anthropic/openai have. The distillation they do basically amounts to using traces from ant/oai models trained on much more data with a lot more compute (in many cases including the hidden intermediate tokens! turns out there were many ways to coax it out) and then either directly training on it or using it in many ways in post training pipelines. It falls under imitation learning, IMO.