Numerical instability in neural network training is typically diagnosed only after it manifests as a non-finite loss, and is monitored through scalar quantities such as the loss value and gradient norm. We present Numerical Runtime Intelligence (NRI), a lightweight runtime-monitoring framework that observes the structural numerical health of transformer models during training and inference by computing interpretable signals from quantities the model already produces: the Shannon entropy of weight singular-value spectra and of attention distributions. Using a reproducible, multi-architecture failure-trace dataset spanning causal (GPT-style) and bidirectional (ViT-style) transformer blocks, we report two findings. First, real transformers equipped with LayerNorm, residual connections, and adaptive optimization absorb most injected structural damage without reaching numerical divergence: of four induced failure modes, only unbounded weight-norm growth reliably produced a non-finite value, while injected rank collapse, attention concentration, and unit death were largely absorbed. Second, and centrally, NRI's spectral signal registers structural degradation on these non-diverging runs even while loss-proxy and gradient-norm quantities remain within their healthy range — degradation that standard loss- and gradient-based monitoring cannot, by construction, observe. We characterize where the signal is sensitive (unit death, rank collapse) and where it is blind (attention concentration absorbed by the architecture), and release the dataset and analysis code for reproducibility. This preprint extends and supersedes the author's prior release (v0.4.0, doi.org/10.5281/zenodo.20573423). The present version (v0.5.0) adds the multi-architecture failure dataset, held-out-calibrated validation, and the silent-degradation finding. This work concerns the observability and classification layer only. Mechanisms that act on or stabilize training in response to a signal are outside the scope of this work.
Ahlem Makhebi (Sat,) studied this question.