Neural network visualization techniques mark image locations by their relevancy to the networks classification. Existing methods are effective in highlighting the regions that affect the resulting classification the most. However, as we show, these methods are limited in their ability to identify the support for alternative classifications, an effect we name {em the saliency bias} hypothesis. In this work, we integrate two lines of research: gradient-based methods and attribution-based methods, and develop an algorithm that provides per-class explainability. The algorithm back-projects the per pixel local influence, in a manner that is guided by the local attributions, while correcting for salient features that would otherwise bias the explanation. In an extensive battery of experiments, we demonstrate the ability of our methods to class-specific visualization, and not just the predicted label. Remarkably, the method obtains state of the art results in benchmarks that are commonly applied to gradient-based methods as well as in those that are employed mostly for evaluating attribution methods. Using a new unsupervised procedure, our method is also successful in demonstrating that self-supervised methods learn semantic information.