๐ ๐๐ก๐๐ญ ๐ข๐ ๐ฅ๐จ๐จ๐ฉ๐๐ ๐๐๐ฌ ๐๐จ๐ฎ๐ฅ๐ ๐ฎ๐ฌ๐ ๐ร ๐๐๐ฐ๐๐ซ ๐ฉ๐๐ซ๐๐ฆ๐๐ญ๐๐ซ๐ฌ ๐๐ง๐ ๐ ๐ร ๐ฌ๐ฆ๐๐ฅ๐ฅ๐๐ซ ๐๐ ๐๐๐๐ก๐ ๐๐ง๐ ๐ฌ๐ญ๐ข๐ฅ๐ฅ ๐๐ ๐๐จ๐ฆ๐ฉ๐๐ซ๐๐๐ฅ๐ ๐ญ๐จ ๐ ๐ฌ๐ญ๐๐ง๐๐๐ซ๐ ๐๐ซ๐๐ง๐ฌ๐๐จ๐ซ๐ฆ๐๐ซ?
Introducing ๐๐๐ญ๐ก๐ข๐ง๐ค๐ข๐ง๐ ๐๐ญ ๐
๐ข๐ฑ๐๐ ๐๐จ๐ข๐ง๐ญ๐ฌ. We argue that looped LMs don't have to pay for every loop. They can scale by adding FLOPs at constant memory.
The key is the fixed point of the loop. We introduce:
โ ๐
๐ข๐ฑ๐๐-๐๐จ๐ข๐ง๐ญ ๐๐ก๐จ๐ซ๐ญ๐๐ฎ๐ญ๐ฌ: what fixed points buy a looped model in training (pre-training, post-training) and inference (prefill, decoding)
โ A ๐ฅ๐๐๐ซ๐ง๐๐ ๐๐๐ฉ๐ญ๐ก ๐ฉ๐ซ๐ข๐จ๐ซ and ๐จ๐ซ๐ญ๐ก๐จ๐ ๐จ๐ง๐๐ฅ ๐ข๐ง๐ฃ๐๐๐ญ๐ข๐จ๐ง: two ways to shape those fixed points
๐งต Long thread ahead (0/n).
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