LOCAL TARGET CONTRAST UNDER CONDITIONAL UNCERTAINTY

Local contrastive losses for regression use target differences to choose which nearby representations to separate. These differences can contain irreducible noise. We analyze a quadratic margin loss by conditioning on the input batch, including the dependence introduced by a target-gap median. Its preferred pair distance is proportional to the conditional probability of a push label, which need not measure a difference in conditional means. When the loss acts directly on scalar predictions, we give a sufficient condition under which the Bayes predictor is not a local minimum of the combined population objective. An exact example has positive excess squared risk for every positive loss weight. For nonconstant means, a finite-design analysis identifies net pair forces; incompatible edge pref- erences can cancel. Intermediate geometry can instead use prediction-insensitive directions, but independent activation changes need not correspond to a shared encoder update. We test this distinction using separate fitting, protection, diag- nostic and evaluation inputs. The tested shared updates show a tradeoff between geometry descent and protection of predictions on independent inputs. On the re- lated red and white Wine Quality tasks, MLP and Transformer comparisons show small, mixed effects. The results separate a condition for objective bias from a general ranking of loss locations in training.