  Recent studies show that paddings in convolutional neural networks encode
absolute position information which can negatively affect the model performance
for certain tasks. However, existing metrics for quantifying the strength of
positional information remain unreliable and frequently lead to erroneous
results. To address this issue, we propose novel metrics for measuring (and
visualizing) the encoded positional information. We formally define the encoded
information as PPP (Position-information Pattern from Padding) and conduct a
series of experiments to study its properties as well as its formation. The
proposed metrics measure the presence of positional information more reliably
than the existing metrics based on PosENet and a test in F-Conv. We also
demonstrate that for any extant (and proposed) padding schemes, PPP is
primarily a learning artifact and is less dependent on the characteristics of
the underlying padding schemes.
