Looped Transformers increase computational capacity through the repeated application of shared blocks, but their recurrent depth makes conventional full-depth decoding expensive. While existing speculative pipelines accelerate generation by processing consecutive token positions at varying depths, they are typically limited by sequential decoding overheads. We introduce CopyLoop, a training-free decoding algorithm that combines low-cost context-copy proposals with shallow screening and continuous recurrent scheduling. Rather than step-by-step generation, CopyLoop proposes multi-token suffixes from repeated context. It then evaluates them early at a shallow recurrent depth to efficiently filter out incorrect branches, processing newer blocks concurrently while earlier blocks are still progressing toward full-depth verification. We evaluate CopyLoop across six model checkpoints from the Ouro, Raven, and Huginn families, covering code generation and multi-step mathematical reasoning. CopyLoop achieves decoding speedups of 2.98x--10.70x over full-depth autoregressive decoding on Base models and 2.74x--3.52x on Thinking models, consistently outperforming or closely matching all competing baselines across evaluation tasks. Furthermore, ablation studies confirm a strong synergy between shallow screening and continuous scheduling, while our analyses show that CopyLoop requires only lightweight model calibration and yields greater speedups on longer generations with reusable contexts.

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