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For my greedy layer-wise pre-training using sparse autoencoder, the first layer training seems to be okay since it can fairly reconstruct my test set.

However, because I use "sparse" autoencoder, the activation in the hidden layer is generally very low (0.01 on average) and a few hidden nodes activate at around 0.3 occasionally.

The problem occur when I have to do the second layer pre-training on top of those sparse hidden activation. I cannot whiten the data as I did directly to the raw input in the first layer.

What is a good way to deal with this problem?

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This isn't specific to autoencoders, but a number of papers suggest procedures for initializing weights such that the outputs of each layer maintain a desired distribution. The motivation is similar to that of normalizing the inputs. Of course, the right procedure depends on the activation function.

Here are a few:

Glorot and Bengio (2010). Understanding the difficulty of training deep feedforward neural networks.

He et al. (2015). Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification.

LeCun et al. (1998). Efficient BackProp.

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