recAMPLIFY: Large-Scale Pretraining of Recursive Protein Language Models

Protein language models (pLMs) are powerful tools for protein annotation and mutation-effect prediction, but progress has largely depended on scaling model size and data, making them expensive and prone to memorization. Test-time scaling offers a complementary path, but methods developed for autoregressive LLMs do not transfer directly: masked encoders lack a generation loop, and amino acids do not verbalize in a reasoning language. Instead, we adapt recursive pretraining to masked pLMs, where a weight-tied Transformer core refines residue-aligned hidden states over an adjustable number of cycles. We instantiate this recipe as recAMPLIFY, a pLM with $155$M unique parameters trained on the same $2$T tokens as AMPLIFY-$350$M. Despite $56$% fewer parameters, it improves CASP contact recovery and three out of four supervised tasks, notably raising fold accuracy by $22.8$%. Because optimal depth for recAMPLIFY varies across tasks and assays, we then introduce *Gated Mixture Recurrence* (GMR), a framework that decodes each protein from a probability-weighted mixture of hidden states visited during recursion. GMR employs a learned residual gate at scalar, low-rank, or per-dimension resolution to control how much of each cycle's proposed update is accepted into the state. This unifies halting and gating into a single adaptive computation objective while recovering PonderNet-style halting as a special case without gates. Layered on top of recAMPLIFY, GMR further reduces expected layer depth by up to $37$%, although the accuracy trade-off varies by task. Mechanistic analyses show that residual gating controls recurrence stability beyond the trained depth and that halt depth tracks biological properties.