Neural Dimensional Analysis: Foundations of Dimensionless and Scale-Consistent Computation
Modern Transformers rely on many scale-control mechanisms, including normalization, residual scaling, attention temperatures, loss weighting, and adaptive updates. To explain how these mechanisms maintain scale consistency, we introduce Neural Dimensional Analysis (NDA), a unified framework based on dimensional consistency. We define neural units that specify how tensors rescale and which quantities can be added, just as physical units do in physics. Our rules match residual units, nondimensionalize attention and gate inputs, combine losses across units, and convert gradient units into parameter units. We implement NDA through dimensionless Unit Violation Indices (UVI) for diagnosing scal...
| Authors | Bum Jun Kim, Makoto Kawano, Yusuke Iwasawa et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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