Weibull Distribution Framework Reveals Consistent Weight Patterns Across Transformer Architectures
A new study applies the two-parameter Weibull distribution from extreme-value theory as a diagnostic tool for analyzing weight magnitude distributions in transformer neural networks. Testing across 12 models spanning 7 architectural families—including Pythia, LLaMA-3, Mistral, and Qwen—the framework identifies distinct behavioral classes among weight matrices and tracks training dynamics. The approach offers a principled, architecture-independent method for monitoring how individual components of large language models evolve during training.
Researchers have introduced a diagnostic framework using the Weibull distribution to characterize element-wise weight magnitude distributions in transformer models, with the shape parameter k serving as an architecture-independent benchmark. At initialization, Gaussian weights produce a known k value of approximately 1.20, providing a stable anchor against which deviations during training can be measured. The study finds that feed-forward network modules and the attention output projection consistently converge to a narrow k band (median terminal k between 1.186 and 1.204) across diverse architectures and scales from 70M to 14B parameters, forming what the authors call the 'Transmission Class.' In contrast, query and key attention projections—the 'Selection Class'—depart from Weibull behavior, with the severity of departure depending on how Q/K weights are stored (separately vs. grouped-query attention). The scale parameter lambda was found to grow during training and correlate strongly with the square root of the learning rate-to-weight-decay ratio (Pearson r = 0.94), suggesting the two parameters encode independent information about functional role and training progress respectively. The authors release an accompanying Python library (npm-weibull-py v0.4) and a benchmark database to support further research.
What's missing
The study is a preprint and has not yet undergone peer review. The framework is primarily descriptive and diagnostic; the authors do not demonstrate that Weibull-based monitoring leads to improved training outcomes or model performance. The causal mechanisms explaining why certain weight classes converge to the observed k values remain unestablished. The correlation between lambda and training hyperparameters is shown within the Pythia family only, and generalizability to other architectural families is not fully validated.
What different sources said
- arXiv stat.MLCenter
A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions
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