Training-free LoopCD decoding lifts AIME accuracy 61.9%→73.3%, cuts FLOPs up to 48%

kastnerkyle · x · 2026-10-03

The paper "Decoding Looped Transformers Better for (Almost) Free" introduces LoopCD, a training-free contrastive decoding framework that turns a looped transformer's own intermediate recurrent states into guidance signals.

Core idea: Looped transformers save parameters by reusing a shared block, and each recurrent loop yields a decodable intermediate representation that standard decoding discards. LoopCD treats an early loop as a rough draft and the final loop as the refined answer, contrasting the two — in logit space (LoopCD-Logits, one extra output pass) or hidden-state space (LoopCD-Hidden, zero output overhead) — to push predictions in the direction the model was already improving.

Key results:

Ouro-2.6B-Thinking's AIME 2024 pass@1 jumps from 61.88% to 73.33%
Huginn's HumanEval pass@1 rises from 22.56% to 31.71%
With only half the recurrent loops, performance still matches or beats full-depth baselines, cutting forward FLOPs by 22.5%–48.2%

Consistent gains across four looped transformer families show intermediate recurrent states can serve as effective decoding guidance at no training cost.

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Training-free LoopCD decoding lifts AIME accuracy 61.9%→73.3%, cuts FLOPs up to 48%

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