Caffe conv layer weights and dimensions

Question

I came across this nice article which gives an intuitive explanation of how convnets work.

Now trying to understand what is going on exactly inside a caffe conv layer:

With input data of shape 1 x 13 x 19 x 19, and 128 filters conv layer:

layers {
  name: "conv1_7x7_128"
  type: CONVOLUTION
  blobs_lr: 1.
  blobs_lr: 2.
  bottom: "data"
  top: "conv2"
  convolution_param {
    num_output: 128
    kernel_size: 7
    pad: 3
    weight_filler {
      type: "xavier"
      }
      bias_filler {
      type: "constant"
      }
    }
}

Layer output shape is 1 x 128 x 19 x 19 if i understand correctly.

Looking at the layer's weights' shapes in net->layers()[1]->blobs() :

layer  1: type Convolution  'conv1_7x7_128'
  blob 0: 128 13 7 7
  blob 1: 128

Looks like blob 0 has all the weigths: one 7x7 matrix per plane (13) per filter (128).

Doing convolutions with blob 0 on 1 x 13 x 19 x 19 data, if i understand correctly we end up with 128 x 13 x 19 x 19 output (there's padding so each 7x7 matrix produces one number for each pixel)

• How does 128 x 13 x 19 x 19 turn into layer's 1 x 128 x 19 x 19 output ?

• What are the 128 weights in blob 1 ?

Bonus question: what is blobs_lr ?

Answer 1

You are quoting an older version of caffe's prototxt format. Adjusting to new format will give you

layer {  # layer and not layer*s*
  name: "conv1_7x7_128"
  type: "Convolution"  # tyoe as string
  param { lr_mult: 1. }  # instead of blobs_lr
  param { lr_mult: 2. }  # instead of blobs_lr 
  bottom: "data"
  top: "conv2"
  convolution_param {
    num_output: 128
    kernel_size: 7
    pad: 3
    weight_filler {
      type: "xavier"
      }
      bias_filler {
      type: "constant"
      }
    }
}

If you have input data of shape 1 x 13 x 19 x 19, means your batch_size is 1, you have 13 channels with spatial dimensions of 19 x 19.
Applying 128 filters of 7 x 7 (each filter is applied to all 13 input channels) means you have 128 filters of shape 13 x 7 x 7 (this is the shape of your first layer's parameter). Applying each filter results with a single output channel 1 x 1 x 19 x 19, since you have 128 such filters you end up with 1 x 128 x 19 x 19 output.

The second layer's parameter is the bias term - an additive scalar to the result of each filter. You can turn off the bias term by adding

bias_term: false

To the convolution_param of you layer.

You can read more about convolution layer here .

As for the bonus question, Eliethesaiyan already answered it well in his comment .