Submitted by neuralbeans t3_10puvih in deeplearning
I'd like to train a neural network where the softmax output has a minimum possible probability. During training, none of the probabilities should go below this minimum. Basically I want to avoid the logits from becoming too different from each other so that none of the output categories are ever completely excluded in a prediction, a sort of smoothing. What's the best way to do this during training?
That will just make the model learn larger logits to undo the effect of the temperature.
max[softmax, lowest accepted probability]
Use composite loss, i.e. add extra terms in the loss function to make the optimizer force the logits to stay within a fixed range.
For example, if current min logit = m and allowed minimum = u, current max logit = n and allowed maximum = v, then the following loss function should help:
Overall loss = CrossEntropy loss + lambda1 * max(u - m, 0) and lambda2 * max(n - v, 0)
The max terms ensure that no loss is added when the logits are all within the allowed range. Use lamba1 and lambda2 to scale each term so that they roughly match the CE loss in strength.
It needs to remain a valid softmax distribution.
I would scale logits before softmax, like it’s been done in self attention.Actually that scaling in self attn is to make the final dist of the attention weights to be smooth.
What's this about del attention?
Sorry, dictionary issue. I meant Self Attention (I ve edited previous answer)
yeah true, you can implement that by factoring everything back to the sum of 1 though
If the goal is to keep all predictions above a floor, the easiest way is to make the activation into floor + (1 - floor * num_logits) * softmax(logits). This doesn't have any material impact on the model, but it imposes a floor.
If the goal is to actually change something about how the predictions are made, then adding a floor isn't going to be the solution though. You could modify the activation function some other way (e.g. by scaling the logits, normalising them, etc.), or you could impose a loss penalty for the difference between the logits or the final predictions.
I want the output to remain a proper distribution.
Taking a leaf out of RL, you can add an additional entropy loss.
Alternatively, clip the logits but apply STE (copy gradients) on backprop
My proposed function does that. Let's say you have two outputs, and don't want either to go below 0.25. Your minimum value already adds up to 0.5, so you rescale the softmax to add up to 0.5 as well, giving you a sum of 1 and a valid distribution.
I am curious why do you want to do that? You can always post process the logits but forcing the Network to learn it will cause harm to the underlying representation imo
It's for reinforcement learning to keep the model exploring possibilities.
No, it would make the logits be closer to one another and the overall model a bit less confident in its probabilities.
like_a_tensor t1_j6mcv1v wrote
I'm not sure how to fix a minimum probability, but you could try softmax with a high temperature.