Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics
Building on a two-parameter Weibull framework, this paper analyzes why the Weibull weight-scale parameter λ grows, overshoots, and relaxes during AdamW training. A three-force decomposition (alignment, injection, decay) is derived, showing alignment dominates the rise phase (88-94%). Near saturation, alignment and decay balance. A spline displacement method recovers alignment from sparse checkpoints with ~92-94% accuracy. Peak λ varies with training-data coherence, suggesting a data-dependent component.
[2606.19367] Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics
[Submitted on 11 Jun 2026]
Title:Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics
View a PDF of the paper titled Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics, by Tiexin Ding
View PDF HTML (experimental)
Abstract:Building on a two-parameter Weibull framework for diagnosing transformer weight distributions, we study why the Weibull weight-scale parameter $\lambda$ grows, overshoots, and then relaxes during AdamW training. We derive a leading-order three-force decomposition of the squared weight norm from the AdamW update: an alignment force measuring the correlation between weights and the adaptive update direction, an injection force from adaptive step magnitude, and a decay force from decoupled weight decay. On self-trained Pythia-70M models with ground-truth optimizer moments, alignment dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds and remaining robust to super-weight removal. Near saturation, alignment and decay approach balance, explaining the transition from weight-scale growth to relaxation. These force dynamics directly govern the squared-norm component underlying $\lambda(t)$; the remaining RMS-to-Weibull reconstruction offset is measurable and decomposes into bridge and integration components, totaling approximately 5-6% in densely sampled regions. To extend the analysis to real models where optimizer moments are unavailable, we introduce a spline displacement method that recovers the alignment force from sparse checkpoints with approximately 92-94% accuracy, about twice the naive two-point baseline. We further observe that the peak value of $\lambda(t)$ varies with training-data coherence in our experiments, suggesting a data-dependent component of weight-scale growth that we leave to a controlled follow-up study. Code and data are available at this https URL.
Comments: 21 pages, 14 figures
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2606.19367 [cs.LG]
(or arXiv:2606.19367v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.19367
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Tiexin Ding [view email] [v1] Thu, 11 Jun 2026 03:50:14 UTC (1,632 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics, by Tiexin Ding
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-06
Change to browse by:
cs
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?)