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I agree with the discussions in this thread. Key problem is the norm can blow up leading to overconfidence and miscalibration. We discuss this in our recent paper on using angular measures for hardness https://arxiv.org/abs/1912.02279 @BeidiChen @animesh_garg @Anshumali_
We observe that angular alignment freezes early in training but norm grows exponentially. Angular measure has a stronger correlation with human selection frequency: a measure of inherent ambiguity. For self training, using angular measure for confidence boosts performance.pic.twitter.com/Pcg3T68Wt2
So in summary, the norm can blow up leading to miscalibration and angle is a more robust measure of uncertainty. However, training on angular loss is a more challenging optimization problem and it appears instead, we need stronger regularization to limit the norm
Label smoothing is another way to prevent the norm from blowing uppic.twitter.com/icTSESPB35
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