The Loss Defines the Target: What a Model Actually Learns from Error

A loss function does more than penalize inaccurate predictions: it defines the statistical target that the learning process treats as optimal. Consequently, a model can minimize its stated objective correctly while learning a quantity that is misaligned with the evaluation metric, operational cost, or decision for which it will ultimately be used. This paper introduces the Loss Validity Map, a seven-level framework connecting target validity, error geometry, robustness, optimization, metric alignment, decision alignment, and transport. Its central rule is that successful numerical optimization does not establish that the learned target is valid for the intended decision. The framework is evaluated using 392 vehicles from the UCI Auto MPG dataset. Model years 1970–1979, comprising 307 vehicles, form the development period, while model years 1980–1982, comprising 85 vehicles, serve as a temporally separated final benchmark. The predictor class, 29-term pairwise feature representation, preprocessing pipeline, Ridge regularization strength, and evaluation protocol remain fixed so that the principal experimental change is the geometry of the training loss. Seven objectives are compared: mean squared error, mean absolute error, Huber loss, log-cosh loss, and quantile losses at τ = 0.25, 0.50, and 0.75. Their behavior is examined both on the original data and under controlled response contamination. The contamination study modifies only development labels, never the temporal benchmark, and contains 1,680 model fits across contamination rates, perturbation magnitudes, and repeated random draws. On the uncontaminated temporal benchmark, Huber records an MAE of 3.378 mpg and log-cosh records 3.388 mpg, compared with 3.794 mpg for mean squared error. A paired bootstrap with 10,000 resamples estimates the Huber-minus-log-cosh MAE difference at −0.0094 mpg, with a 95% interval from −0.0493 to +0.0309 mpg. Because this interval contains zero, Huber and log-cosh are interpreted as a competitive set rather than as a resolved ranking. Under 10% response contamination with perturbations of 20 mpg, mean squared error reaches an average temporal MAE of 4.374 mpg and exhibits substantially greater coefficient displacement. Huber remains at 3.421 mpg, while log-cosh reaches 3.433 mpg. These results demonstrate the greater sensitivity of quadratic loss to large residuals under the prespecified contamination design. The Huber threshold δ = 1.35 is treated as a prespecified threshold expressed directly in mpg, not as a test-optimized value or an automatic application of the conventional 1.345 constant for standardized residuals. A sensitivity analysis performed exclusively within the 1970–1979 development period evaluates δ values of 0.5, 1.0, 1.35, 2.0, and 3.0. The results show that 1.35 is not a unique or demonstrably optimal threshold; several nearby values produce similar expanding-temporal development performance. The quantile models preserve their expected ordering on the final benchmark, with a quantile crossing rate of 0%. The interval formed by the 0.25 and 0.75 conditional quantile estimates covers 47.1% of temporal test observations, near its nominal marginal coverage of 50%. This marginal result is not interpreted as a guarantee of conditional calibration. The findings do not establish a universally superior loss function. Instead, they show that each objective defines a different estimand, influence structure, and decision geometry. Robust objectives can reduce sensitivity to response contamination, while quantile objectives can remain valid even when they perform poorly under symmetric metrics that do not represent their intended target. The record includes a complete reproducibility package containing source code, data, protocol specifications, contamination results, bootstrap outputs, Huber-threshold sensitivity results, predictions, figures, structured outputs, integrity manifests, and checksums.