Weak Learning Failure Alone is not Gradient Starvation

Gradient starvation describes competition in which learning one predictive feature suppresses learning another. Yet a weak response alone cannot establish suppression: the same feature may remain poorly learned without the competing cue. We develop a controlled approach using matched training runs with an informative cue, an uninformative cue, and no cue. Our criterion requires both reference runs to reach a learning target within a fixed budget and measures the informative-cue deficit at each reference's first target crossing and across training. Across four model families, comparisons with uninformative cues show why negative differences alone are insufficient evidence. We derive an exact gradient-flow decomposition that tracks how differences in output loss gradients and response sensitivities, together with weight decay, change weak-feature learning. In a noiseless two-layer linear model under unregularized logistic gradient flow, we prove that a perfectly reliable cue can sustain a relative learning deficit indefinitely, even as both runs continue learning. We also rigorously verify finite-time suppression bounds against cue-free training in small networks through validated numerical integration. In CIFAR-10, removing or randomizing the cue during training improves cue-free accuracy by about 7.6 percentage points relative to retaining it, measured using a fresh linear classifier fitted to frozen features. On pretrained Waterbirds models, poor worst-group accuracy coexists with small measured core-feature deficits. Together, these results distinguish cue-induced suppression from weak learning shared across training conditions and show why poor robustness need not imply a substantial feature-learning deficit. Code is available at https://anonymous.4open.science/r/gradient_starvation-C646/.