There are a huge number of citations about looping on this Ouro page [1]. Ouro is an open looped LLM with a very instructive paper at [2] (also containing references to lots of helpful papers). Basically they get these four results from looping:
• Parameter efficiency. 1.4B and 2.6B parameter looping Ouro models match 4B and 8B transformers on most benchmarks.
• Adaptive computation. Looping is trained in a novel way to avoid exiting too early or too late.
• Reasons to use looping. Looping does not increase raw knowledge storage (approximately 2 bits per parameter for looped and non-looped models) but dramatically enhances knowledge manipulation capabilities.
• Improved safety and adherence. They find that safety and alignment of CoT to final output improves as recurrent steps increase.
• Parameter efficiency. 1.4B and 2.6B parameter looping Ouro models match 4B and 8B transformers on most benchmarks.
• Adaptive computation. Looping is trained in a novel way to avoid exiting too early or too late.
• Reasons to use looping. Looping does not increase raw knowledge storage (approximately 2 bits per parameter for looped and non-looped models) but dramatically enhances knowledge manipulation capabilities.
• Improved safety and adherence. They find that safety and alignment of CoT to final output improves as recurrent steps increase.
[1] https://ouro-llm.github.io
[2] https://arxiv.org/pdf/2510.25741