模型增长、递归与边界算子如何影响 scaling 指数

Computer Science > Machine Learning arXiv:2609.19107v1 (cs) [Submitted on 16 Sep 2026] Title:How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents Authors:Zixi Chen, Akshay Vegesna, Samip Dahal, Andrew Gordon Wilson View a PDF of the paper titled How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents, by Zixi Chen and 3 other authors View PDF HTML (experimental) Abstract:Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to exponential improvements in performance with increases in computation. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly $20\times$ less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides increasing compute-efficiency gains, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2609.19107 [cs.LG] (or arXiv:2609.19107v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.19107 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zixi Chen [view email] [v1] Wed, 16 Sep 2026 17:36:13 UTC (1,275 KB) Full-text links: Access Paper: View a PDF of the paper titled How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents, by Zixi Chen and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)