I have a neural network in a synthetic experiment I am doing where scale matters and I do not wish to remove it & where my initial network is **initialized with a prior that is non-zero and equal everywhere**.

How do I add noise appropriately so that it trains well with the gradient descent rule?

I was thinking of adding the noise from xavier to my constant weight NN. So I create a new NN with xavier init or standard pytorch init and then to all weights add the constant value I need.

Would that work?

cross-posted:

- Quora: https://www.quora.com/unanswered/How-do-I-add-appropriate-noise-to-a-neural-network-with-constant-weights-so-that-back-propagation-training-works
- SO: https://stats.stackexchange.com/questions/483809/how-to-add-appropriate-noise-to-a-neural-network-with-constant-weights-so-that-b
- pytorch: How to add appropriate noise to a neural network with constant weights so that back propagation training works?