Stable Image Regression via Adaptive Aggregation of Noisy Predictions and Input-Gradient-Regularized Fine-Tuning

Image regression models may exhibit substantial output variation under small input perturbations, which can reduce their reliability in applications requiring continuous predictions. This study investigates whether adaptive aggregation of noise-perturbed predictions, combined with explicit control of model sensitivity, can jointly improve local stability and predictive accuracy. The proposed method fine-tunes a base regressor using input-gradient regularization and learns a permutation-invariant, data-dependent aggregation operator. The aggregator uses a smooth quantile-like parameterization that adapts to the distribution of noisy predictions. A first-order decomposition defines the score B(x), which is used as a practical diagnostic rather than a formal robustness certificate. Its numerical value depends on the initialization and number of ascent steps used for its estimation. The method is evaluated on three image regression tasks: image quality assessment, facial age estimation, and crowd counting. Compared with fixed mean, trimmed-mean, and median aggregation, the proposed approach provides a more favorable accuracy–stability trade-off across the evaluated tasks and perturbation settings. Ablation and transfer analyses further distinguish the effects of learned aggregation and model fine-tuning and examine their dependence on smoothing parameters, tasks, and architectures. The results indicate that adaptive aggregation and sensitivity-controlled fine-tuning constitute a practical approach for improving the empirical local stability of image regression systems.