# Looped Language Model

Decision models that answer fixed-option questions usually score every option in one forward pass, with a depth fixed at training time, so easy and hard questions cost the same. LEV swaps in a language-model backbone pretrained as a loop, reads the options after every step and trains all steps jointly, so one checkpoint answers at any depth; on JevBench the 2.6B model rises from 63.2% at depth one to 76.2% at depth four, mostly on hard questions. A small stopper sets depth per question with a threshold fitted on unlabelled requests, saving 15% to 24% of the computation at under one accuracy point.

Decision models that answer fixed-option questions usually score every option in one forward pass, with a depth fixed at training time, so easy and hard questions cost the same. LEV swaps in a language-model backbone pretrained as a loop, reads the options after every step and trains all steps jointly, so one checkpoint answers at any depth; on JevBench the 2.6B model rises from 63.2% at depth one to 76.2% at depth four, mostly on hard questions. A small stopper sets depth per question with a threshold fitted on unlabelled requests, saving 15% to 24% of the computation at under one accuracy point.

Typed decision models used to return option probabilities in a single forward pass, giving every decision a fixed amount of computation. SanSi turns a language model pre-trained to loop into a typed decision model, reading the option probabilities after every loop and training each with a proper scoring rule, so one model serves every budget from one loop to eight. On 10,027 test decisions from 59 sources it reaches 72.0% accuracy, 13.5 points above a non-looped model of the same shape trained with the same recipe and 1.8 points below a single-pass model with three times its parameters, at 7.7 times the GPU time of one pass.

Typed decision models used to return option probabilities in a single forward pass, giving every decision a fixed amount of computation. SanSi turns a language model pre-trained to loop into a typed decision model, reading the option probabilities after every loop and training each with a proper scoring rule, so one model serves every budget from one loop to eight. On 10,027 test decisions from 59 sources it reaches 72.0% accuracy, 13.5 points above a non-looped model of the same shape trained with the same recipe and 1.8 points below a single-pass model with three times its parameters, at 7.7 times the GPU time of one pass.