  This paper delves into the critical area of deep learning robustness,
challenging the conventional belief that classification robustness and
explanation robustness in image classification systems are inherently
correlated. Through a novel evaluation approach leveraging clustering for
efficient assessment of explanation robustness, we demonstrate that enhancing
explanation robustness does not necessarily flatten the input loss landscape
with respect to explanation loss - contrary to flattened loss landscapes
indicating better classification robustness. To deeply investigate this
contradiction, a groundbreaking training method designed to adjust the loss
landscape with respect to explanation loss is proposed. Through the new
training method, we uncover that although such adjustments can impact the
robustness of explanations, they do not have an influence on the robustness of
classification. These findings not only challenge the prevailing assumption of
a strong correlation between the two forms of robustness but also pave new
pathways for understanding relationship between loss landscape and explanation
loss.
