Help in understanding Convolution Network

[Arkadi Kagan]

Hello everybody,

I need a help in understanding Convolution Network.

I built Caffe and run Python sample from
http://nbviewer.jupyter.org/github/BVLC/caffe/blob/master/examples/00-classification.ipynb
The batch size is changed to 1 for simplicity.

After analyzing the cat picture, here is the content of the net:

>>> net.blobs['data'].data.shape
(1, 3, 227, 227)
>>> net.params['conv1'][0].data.shape
(96, 3, 11, 11)
>>> net.blobs['conv1'].data.shape
(1, 96, 55, 55)

That is, apply 96 kernels of size (3, 11, 11)
on a picture (3, 227, 227).

The layer 'conv1' is defined as
    num_output: 96
    kernel_size: 11
    stride: 4

Therefore, (4 * 55 + (11 - 4)) = 227.
That is, loop 96 given kernels
    for each (3, 11, 11) kernel, convolve the (3, 227, 227) picture
    with stride 4, i.e. skip 4 values on each step

Farther, if I do this loop, I get roughly the same numbers as in net.blobs['conv1'].data:

def convolve(kernels, pictures, stride):
    result = []
    for p in pictures:
        res1 = []
        for k in kernels:
            res2 = []
            for i in range(0, pictures.shape[2] - (kernels.shape[2] - stride), stride):
                res3 = []
                for j in range(0, pictures.shape[3] - (kernels.shape[3] - stride), stride):
                    m = p[:, i : i + kernels.shape[2], j : j + kernels.shape[3]] * k
                    res3 += [np.sum(m)]
                res2 += [res3]
            res1 += [res2]
        result += [res1]
    return np.array(result)

c1 = convolve(net.params['conv1'][0].data, net.blobs['data'].data, 4)
c1[c1 < 0] = 0 # prune negative

However, on the next convolution layer 'conv2', I don't understand this numbers:

>>> net.blobs['norm1'].data.shape
(1, 96, 27, 27)
>>> net.blobs['conv2'].data.shape
(1, 256, 27, 27)
>>> net.params['conv2'][0].data.shape
(256, 48, 5, 5)

The layer 'conv2' is defined as
    num_output: 256
    pad: 2
    kernel_size: 5
    group: 2

In this case the kernel size is twice smaller than the "picture"
  kernel of size (48, 5, 5)
  convolved on "picture" of size (96, 27, 27)
Stride is not defined, so I assume it's 1.
23 + (5 - 1) = 27, therefore there must be 23 steps in each direction to convolve 27x27 flat rectangle.
There are, evidently 27.
I don't undrestand where 256 comes too.

Any corrections, suggestions or useful links are greatly appreciated.

[Nam Vo]

It's because conv2 has:
group: 2

It is basically splitted, due to legacy reason (read AlexNet paper). These days nobody does that.

[Nam Vo]

256 is the number of filters, you specify that with
num_output: 256

[Arkadi Kagan]

Thanks for prompt reply.

I read again this "ImageNet Classification with Deep Convolutional Neural Networks":

The first convolutional layer filters the 224 x 224 x 3 input image with 96 kernels of size 11 x 11 x 3
with a stride of 4 pixels (this is the distance between the receptive field centers of neighboring

neurons in a kernel map). The second convolutional layer takes as input the (response-normalized
and pooled) output of the first convolutional layer and filters it with 256 kernels of size 5 x 5 x 48.

The dimensions fit to what I see, so I hope I am looking into the right paper.

> It is basically splitted, due to legacy reason (read AlexNet paper).

I did not found any mention of this split.
The resulting data is still (256, 48, 5, 5), therefore the two parts are merged back somehow.
I tried to convolve the two parts separately:

c2_1 = convolve(net.params['conv2'][0].data, net.blobs['norm1'].data[:,:48], 1)
c2_2 = convolve(net.params['conv2'][0].data, net.blobs['norm1'].data[:,48:], 1)
c2_1[c2_1 < 0] = 0 # prune negative
c2_2[c2_2 < 0] = 0 # prune negative

The result is too different from the original.
How do we merge them back?
How do I get definition of what "group" really means?

Another question: why do I get numbers different from the original even with "conv1", where my numbers are very close but not exact somehow?
Is it a round-up error?

Thanks,
Arkadi.

[Arkadi Kagan]

Answering part of my own question:
http://caffe.berkeleyvision.org/tutorial/layers.html

• group (g) [default 1]: If g > 1, we restrict the connectivity of each filter to a subset of the input. Specifically, the input and output channels are separated into g groups, and the i'th
output group channels will be only connected to the i'th input group channels.

I have to think about it yet.

[Nam Vo]

I think they split both the data and the filters, but who cares lol? If you do I'm afraid that you'll have to read their code.

[Arkadi Kagan]

It must be possible to train new network without "group > 1".

However, all pre-trained networks (https://github.com/BVLC/caffe/tree/master/models), except Google-Net, use it.

Unfortunately, I don't have capacity to train my own network.
Google-Net, at least on first glance, have even more parameters to hide the convolution itself.

Do you have a link into a pre-trained network without "group"?

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[Nam Vo]

Check caffe model zoo, all networks except alexnet/caffenet shouldn't have that group thing.