翻訳待ち：Data Predictability Shapes Weibull Weight-Scale Growth in Transformer Training
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。ソース概要：arXiv:2608.23573v1 Announce Type: new Abstract: A trained transformer's weight magnitudes can be summarized by a two-parameter Weibull distribution whose shape $k \approx 1.2$ is stable across layers and models, so the scale $\lambda$ carries most training-induced movement. What corpus property sets how much $\lambda$ grows? Using the bigram conditional entropy $D = H(\text{next} \mid \text{prev})$, a training-free statistic computed before training, we find across controlled corruption families a learning-rate-conditioned law, $\lambda^2 - \lambda_0^2 = C_0(\eta) + C_1(\eta)(H_r - D)^{0.59}$, where $H_r$ is a matched-budget shuffle baseline. The convex exponent is inherited from an independently measured data-side saturation relation rather than fitted directly to the growth curve. After removing the two per-$\eta$ coefficients, 23 runs spanning an order of magnitude in learning rate collapse onto $(H_r - D)^{0.59}$ with unit slope ($R^2 = 0.941$; direct per-$\eta$ fits are weaker, $R^2 \approx 0.82$). Because $D$ is computed before training, the law is a forward predictor: an end-to-end self-validation recovers held-out within-family weight growth with 5.7% relative error. The readout holds at model and per-layer resolutions and across two tested architectures, with the functional form preserved and only the coefficients changing. It also marks its boundary: cross-corpus prediction over-predicts code, implicating redundancy as a second axis of a broader $\Phi(D,R,A,H)$ data-to-weight framework.
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。
--> [Submitted on 27 Jun 2026] Title:Data Predictability Shapes Weibull Weight-Scale Growth in Transformer Training View a PDF of the paper titled Data Predictability Shapes Weibull Weight-Scale Growth in Transformer Training, by Tiexin Ding View PDF HTML (experimental) Abstract:A trained transformer's weight magnitudes can be summarized by a two-parameter Weibull distribution whose shape $k \approx 1.2$ is stable across layers and models, so the scale $\lambda$ carries most training-induced movement. What corpus property sets how much $\lambda$ grows? Using the bigram conditional entropy $D = H(\text{next} \mid \text{prev})$, a training-free statistic computed before training, we find across controlled corruption families a learning-rate-conditioned law, $\lambda^2 - \lambda_0^2 = C_0(\eta) + C_1(\eta)(H_r - D)^{0.59}$, where $H_r$ is a matched-budget shuffle baseline. The convex exponent is inherited from an independently measured data-side saturation relation rather than fitted directly to the growth curve. After removing the two per-$\eta$ coefficients, 23 runs spanning an order of magnitude in learning rate collapse onto $(H_r - D)^{0.59}$ with unit slope ($R^2 = 0.941$; direct per-$\eta$ fits are weaker, $R^2 \approx 0.82$). Because $D$ is computed before training, the law is a forward predictor: an end-to-end self-validation recovers held-out within-family weight growth with 5.7% relative error. The readout holds at model and per-layer resolutions and across two tested architectures, with the functional form preserved and only the coefficients changing. It also marks its boundary: cross-corpus prediction over-predicts code, implicating redundancy as a second axis of a broader $\Phi(D,R,A,H)$ data-to-weight framework. Comments: 27 pages, 14 figures, 5 tables. Code and data: this https URL Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2608.23573 [cs.LG] (or arXiv:2608.23573v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.23573 arXiv-issued DOI via DataCite Submission history From: Tiexin Ding [view email] [v1] Sat, 27 Jun 2026 12:26:39 UTC (2,360 KB) Full-text links: Access Paper: View a PDF of the paper titled Data Predictability Shapes Weibull Weight-Scale Growth in Transformer Training, by Tiexin Ding View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-08 Change to browse by: cs stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: 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?)