Determine the generality of Neural Dimensional Analysis

Determine whether the empirical behavior and benefits of Neural Dimensional Analysis generalize beyond the evaluated FineWeb-Edu language-model settings, decoder-only Transformer families, two vision benchmarks, and two physics-informed neural-network problems, including at further corpora, model scales, and architectures.

Background

The paper develops Neural Dimensional Analysis (NDA) as a graph-level framework for scale consistency and evaluates the Gauge-Canonical Transformer (GCT) primarily on decoder-only LLMs from 51M to 1B parameters. Additional experiments cover two vision benchmarks and two physics-informed neural-network problems, but these evaluations do not establish generality across broader datasets, model families, or computational scales.

The unresolved issue is whether the observed stability, rescaling invariance, transfer behavior, and quantization robustness are properties of NDA more broadly or are specific to the controlled settings studied.