Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scaling

arXiv:2508.16745v2 Announce Type: replace-cross Abstract: Reasoning is a core capability of large language models, yet how multi-step reasoning is learned and executed remains unclear. We study this question in a controlled cellular-automata (1dCA) framework that excludes memorisation by using disjoint training and test rules. Given a short state sequence, the model is required to infer the hidden local rule and then chain it to predict multiple future steps. Our evaluation shows that LLMs large