My implement of Rethinking Feature Distribution for Loss Functions in Image Classification using MXNet/Gluon

• In original paper, the L-GM-loss was formulated as $L_{GM} = L_{cls} + \lambda L_{lkd}$, where the regularization term $L_{lkd} = d_{z_{i}} + \frac{1}{2}log|\Lambda_{z_{i}}|$. But when i implement it i find that it's pretty hard to optimize this term beacuse the loss also lead to a small variance(much smaller than a identity matrix), so $\frac{1}{2}log|\Lambda_{z_{i}}|$ will decrease to -inf after several iterations and also make the loss Nan. I tried 2 ways to cover this problem

  1. Remove the regularization term and only optimize the classification loss
  2. Remove the $\frac{1}{2}log|\Lambda_{z_{i}}|$ and keep the regularization term

  this 2 solutions seem to fix the problem but since the regularization term is inferred from it's likelihood, simply removed is not a good way

• The L-GM-Loss layer has two paramters:mean,var. You can't use traditional init way like Xavier etc. to initialize the var because the variance of a distribution is non-negative, the negative variance will also lead to the Nan loss. In my implement, i use a constant value 1 to initialize the var

I plot the features distribution in my experiment, but as you can see below, there are quit different from the original paper, i will talk about the difference latter.

i set the $\alpha$ to 0.1, you can see the clear margin between classes, but some classes' distribution are extremely flat which means the variance of those distribution varies a lot in different dimemsions. I guess it's pretty tricky to optimize the variance, yet i dont have a good idea to fix this maybe i should reimplement it using customop that requires to implement the backward by myself, if you have any idea about that please tell me :)

still suffering from the variance problem 😢

the author released code is written in caffe and cuda, you can find it in here

By adding a lr_mult term to the variance(set a low learning rate) i fixed the problem, here is the result.