Weibull Distribution Framework Reveals Consistent Weight Patterns Across Transformer Architectures
Researchers applied Weibull distribution analysis to weight distributions in transformer neural networks, finding that certain weight matrices (FFN modules and attention output projections) cluster in a narrow, consistent range across different model families and sizes. The framework enables fine-grained diagnostics of training dynamics by treating the Weibull shape parameter k as an architecture-independent measure of weight distribution evolution. This work provides a principled mathematical tool for understanding and comparing transformer internals across diverse architectural designs.
A new preprint proposes using the two-parameter Weibull distribution from extreme-value theory as a diagnostic framework for analyzing weight magnitude distributions in transformer models. The researchers calibrated their approach using the theoretical anchor that randomly initialized Gaussian weights follow a HalfNormal distribution (k ≈ 1.20), then applied this framework to 12 large language models spanning 7 architectural families including Pythia, OLMo, LLaMA-3, Mistral, and Qwen. They discovered three main findings: (1) certain weight matrices—termed the "Transmission Class" (FFN modules and attention output projections)—maintain remarkably consistent Weibull shape parameters (k ∈ [1.186, 1.204]) across all tested models regardless of activation function, normalization placement, or model size; (2) attention input projections (the "Selection Class") deviate from Weibull behavior in ways that correlate with architectural choices like grouped query attention; and (3) the Weibull scale parameter lambda grows during training and scales predictably with learning rate and weight decay. The authors released open-source code and a database to enable further investigation.
What's missing
The preprint does not discuss potential limitations of the Weibull framework for weight distributions that may deviate significantly from the assumed functional form, nor does it address whether the observed patterns hold for other model types (vision transformers, multimodal models) or training regimes (different optimizers, data distributions). The practical implications for model design, training, or interpretability are not explored.
What different sources said
- arXiv stat.MLCenter
A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions
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