UpLoop trains looped Transformers by upcycling, matching a dense baseline's parameter count, tokens and FLOPs
AspireAI community · arXiv (cs.LG, cs.CL)
Looped language models improve reasoning by running the same weights more than once, but each extra pass costs training FLOPs. UpLoop is a pretraining schedule that reaches that capability without extra compute: it starts from a shallow Transformer, progressively grows depth by copying learned layers, and spends the compute saved early on repeated execution of a shared middle block later in training. The authors report matching a standard dense baseline exactly in final parameter count, total training tokens and training FLOPs, with the average score across 22 downstream tasks rising from 22.99 to 27.52 at 1.3B parameters, and gains extending to mathematical reasoning after supervised fine-tuning. The comparison is at the 1.3B scale, so whether the same trade holds for frontier-size models is untested.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.