Abstract
Looped Transformers increase effective depth by repeatedly applying a shared block, offering a parameter-efficient approach to language modeling. However, most existing works directly reuse each loop's output as the next's input, which can lead to hidden-state scale growth and perturbation amplification as recurrence deepens. We propose Rectified Looped Transformer (RLT), which redesigns feedback between loops using an interpolation schedule inspired by flow-based modeling. At each loop, RLT forms the next input by linearly interpolating between the current state and its prediction. Such interpolation distributes state changes across loops, encouraging a smoother trajectory from the initial input to the final output. Theoretical analysis proves that, under appropriate assumptions, RLT keeps state magnitudes uniformly bounded across loops and reduces the worst-case perturbation amplification. We evaluate RLT on language modeling corpora and downstream benchmarks. At matched training and inference depths, RLT consistently achieves lower perplexity than a standard looped Transformer, while exhibiting greater robustness to input perturbations and variance in inference depth. Consistent with the theoretical results, latent trajectory analysis shows that RLT maintains more stable hidden-state norms across loops, which also facilitates extrapolation-based decoding strategies. Notably, RLT achieves these gains without requiring additional trainable parameters or extra recurrent block evaluations, thus providing a simple yet more stable feedback mechanism for looped Transformers.
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URL
https://arxiv.org/abs/2611.16265
