Numerical Fragility in Transformers: A Layer-wise Theory for Risk Estimation and Selective Stabilization

תקציר מקורי באנגליתarXiv:2510.21770v2 Announce Type: replace Abstract: Low-precision execution can induce substantial forward discrepancies in Transformers even for fixed weights and input, yet these discrepancies are usually monitored only at the output and lack a layer-wise theoretical account. We develop a first-order decomposition of output mismatch into layer-local attention, LayerNorm, and residual-transport terms, and derive from it a practical causal risk estimator and a budgeted controller, Bound-Guided Selective Stabilization (BGSS). Controlled sweeps verify the predicted local sign, monotonicity, and transport structure. On GPT-2, the transport-aware combined predictor is positively correlated with FP32-reference mismatch in all $18$ runs and improves over a no-transport ablation in $17/18$ runs.