Transport Instability Coordinates for Early-Warning Tests of Training Loss Spikes

Loss spikes in neural-network training are typically detected only after probe loss has entered an unstable regime. We frame future spike detection as a sequential testing problem in which row-wise, causal features act as test statistics for a finite non-NaN probe-loss spike event in a future lead window. Standard diagnostics such as loss trends, gradient norms, update norms, and adaptive-moment statistics measure scalar or parameter-space quantities, but they do not directly measure how the current stochastic optimizer transition moves the model’s representations. We introduce Transport Instability Coordinates (TIC), a causal feature-space diagnostic based on ghost updates from a frozen optimizer state. At each measured step, TIC samples ghost microbatches, applies the corresponding temporary AdamW transitions, and records the induced changes in a fixed probe representation and probe loss. These measurements define trace, log-moment, whitened, modal-concentration, and loss-directed transport coordinates, which we use in a discrete-time hazard model for future non-NaN probe-loss spikes. In dense critical-learning-rate Transformer experiments, TIC improves over time, loss-trend, gradient-norm, update-norm, Adam-mismatch, trace-only, and raw-tabular baselines at a fixed false-alert budget. A secondary PolyPythias-410M audit shows that the same coordinates decompose known outlier windows into coordinate-specific transport expansion. The results support feature-space transport as an early-warning statistic for imminent training instability.