  We investigate the optimization target of Contrast-Consistent Search (CCS),
which aims to recover the internal representations of truth of a large language
model. We present a new loss function that we call the Midpoint-Displacement
(MD) loss function. We demonstrate that for a certain hyper-parameter value
this MD loss function leads to a prober with very similar weights to CCS. We
further show that this hyper-parameter is not optimal and that with a better
hyper-parameter the MD loss function attains a higher test accuracy than CCS.
