Good, but how many recursion rounds do I need? The optimal number of recursion rounds depends on the model size and training compute budget. Smaller models benefit more from RINS. Also, RINS helps more with long-training durations.

Besides, we also introduce *stochastic* RINS where we select the number of recursion rounds from a binomial distribution. This *improves* performance in SigLIP (despite also *saving* training flops). But in LM, there is a tradeoff between flexibility and maximum performance gain.

Question: what if we use infinite compute? Will the gap vanish? We did scaling analysis and found that RINS improves both the asymptotic performance limit (so the gap actually increases, not vanishes) and improves convergence speed (scaling exponent).

Our inspiration came from the study of self-similarity in language. If patterns are shared across scales, could scale-invariant decoding serve as a good inductive bias for processing language? It turns out that it does!

RINS is trivial to implement. After you pick your favorite model & fix your training budget: (1) partition the model into 2 equally-sized blocks, (2) apply recursion on the first and train for the same amount of compute you had planned -> meaning with *fewer* examples! That’s it!

Recursion is trending (e.g. MobileLLM). But recursion adds compute / example so to show that it helps, one must match training flops; otherwise we could’ve just trained the baseline longer. With this, RINS beats +60 other recursive methods. (2/n)

🔥Excited to introduce RINS - a technique that boosts model performance by recursively applying early layers during inference without increasing model size or training compute flops! Not only does it significantly improve LMs, but also multimodal systems like SigLIP.
(1/N)