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Image classification models often encounter objects in diverse and unpredictable contexts at test time, which may differ substantially from those seen during training. This phenomenon, termed context shift, exposes a key fragility in neural networks: when models rely on non-causal contextual cues for prediction, shifts in context can lead to significant performance degradation. In this paper, we propose a novel training framework to improve the robustness of convolutional neural networks under context shift. Our approach leverages spatial feature attribution to guide models toward making predictions that rely less on contextual regions and more on object-relevant features. As a first step, recognizing a theoretical limitation of existing feature attribution methods we introduce a new variant, ContrastiveCAMs, which produces more faithful attribution maps of model predictions. Building on ContrastiveCAMs, we further propose Context-Regularized Cross-Entropy (CR-CE), a modification of the standard cross-entropy loss that regularizes the model's attention by suppressing the influence of contextual regions, thereby improving robustness to context shift. We evaluate the effectiveness of our approach on several medium-to-large scale datasets (Waterbirds, Spawrious, ImageNet/ImageNet-BG, Hard-ImageNet), and report consistent improvements in context-shift robustness.