  Convolutional neural networks (CNNs) are commonly used for image
classification. Saliency methods are examples of approaches that can be used to
interpret CNNs post hoc, identifying the most relevant pixels for a prediction
following the gradients flow. Even though CNNs can correctly classify images,
the underlying saliency maps could be erroneous in many cases. This can result
in skepticism as to the validity of the model or its interpretation. We propose
a novel approach for training trustworthy CNNs by penalizing parameter choices
that result in inaccurate saliency maps generated during training. We add a
penalty term for inaccurate saliency maps produced when the predicted label is
correct, a penalty term for accurate saliency maps produced when the predicted
label is incorrect, and a regularization term penalizing overly confident
saliency maps. Experiments show increased classification performance, user
engagement, and trust.
