Brain-inspired machine learning is gaining increasing consideration, particularly in computer vision. Several studies investigated the inclusion of top-down feedback connections in convolutional networks; however, it remains unclear how and when these connections are functionally helpful. Here we address this question in the context of object recognition under noisy conditions. We consider deep convolutional networks (CNNs) as models of feed-forward visual processing and implement Predictive Coding (PC) dynamics through feedback connections (predictive feedback) trained for reconstruction or classification of clean images. First, we show that the accuracy of the network implementing PC dynamics is significantly larger compared to its equivalent forward network. Importantly, to directly assess the computational role of predictive feedback in various experimental situations, we optimize and interpret the hyper-parameters controlling the network's recurrent dynamics. That is, we let the optimization process determine whether top-down connections and predictive coding dynamics are functionally beneficial. Across different model depths and architectures (3-layer CNN, ResNet18, and EfficientNetB0) and against various types of noise (CIFAR100-C), we find that the network increasingly relies on top-down predictions as the noise level increases; in deeper networks, this effect is most prominent at lower layers. All in all, our results provide novel insights relevant to Neuroscience by confirming the computational role of feedback connections in sensory systems, and to Machine Learning by revealing how these can improve the robustness of current vision models.