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How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents

Research Efficiency & Systems

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TL;DR - This paper shows that transformer model growth, recursive depth, and boundary operators can improve pre-training scaling exponents rather than merely deliver fixed efficiency gains. A 7.4B growth architecture matches GPT-3 13B on CORE with roughly 20Ă— less compute, with gains increasing at larger scales.

  • Growing models during training, with or without shared weights, produces the largest changes in scaling exponents.
  • Boundary operators that normalize and inject an earlier block also yield increasing compute-efficiency gains, though smaller than model growth.
  • In data-constrained multi-epoch training, looping acts as a regularizer, and the compute-optimal loop count increases with scale.
  • The results suggest that increasing usable computational depth within a fixed compute budget can improve scaling behavior.

Sources (1)

How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents

arXiv cs.LG Zixi Chen, Akshay Vegesna, Samip Dahal, Andrew Gordon Wilson 2026-09-16 arXiv:2609.19107
Public signals Hugging Face upvotes 1
Providers: Hugging Face · Upvotes 1 OpenAlex · N/A Publisher · N/A Semantic Scholar · N/A X · N/A Fetched 2026-09-25 14:18:58.166590 UTC

TL;DR - This paper shows that transformer model growth, recursive depth, and boundary operators can improve pre-training scaling exponents rather than merely deliver fixed efficiency gains. A 7.4B growth architecture matches GPT-3 13B on CORE with roughly 20Ă— less compute, with gains increasing at larger scales.

  • Growing models during training, with or without shared weights, produces the largest changes in scaling exponents.
  • Boundary operators that normalize and inject an earlier block also yield increasing compute-efficiency gains, though smaller than model growth.
  • In data-constrained multi-epoch training, looping acts as a regularizer, and the compute-optimal loop count increases with scale.
  • The results suggest that increasing usable computational depth within a fixed compute budget can improve scaling behavior.
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