Stacking convolutional RBMs

Hello!

I am implementing the Convolutional Deep Belief Network described in the paper "Convolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical Representations" by H. Lee et al., ICML 2009.

I managed to implement the Convolutional RBM, but I am not sure on how to do the stacking part. In the paper it is said that after training the first layer, its weights are frozen and its activations are used as input to the next layer.

Let's say my inputs are real valued grayscale images. If I am training k filters for the first layer, that means I will have k feature maps at the end of the first layer. How do I now use these feature maps, or their pooled versions to be more precise, as the input to the next layer?

Do I now use each of the k maps as an input on its own and train k_2 filters (with dimensions filter_width * filter_height) for every map (k_2 is the number of filters I want to learn for the second layer), which results in k * k_2 feature maps at the end of the second layer, or do I learn k_2 3D filters (of dimensions filter_width * filter_height * k) which results in k_2 feature maps at the end of layer 2? Or do I have to somehow combine the feature maps from the first layer to get a single input for the next layer?

In the paper "Gradient-based Learning Applied To Document Recognition" by LeCun et al., where convolutional neural networks are described, multiple feature maps from one layer are combined in a defined way (Table 1 in the paper I mentioned) before they are used as input to the next layer.

I wasn't able to find the way how they did it in the Convolutional DBN paper. Can someone explain what is the correct way of doing the stacking?

The other question I have is about the types of units I should use in higher layers of the DBN. In my first layer the visual layer consists of real valued units and the units in the hidden layer are binary. After I do the pooling, the units in the pooling layer are also binary and they should be used as input in the second layer. Should the input units of my second layer be binary, or do I use the probabilities of the pooled layer units being turned on and have Gaussian units in the input of my next layer?

Thank you for your help!