I've been reading about convolutional nets and I've programmed a few models myself. When I see visual diagrams of other models it shows each layer being smaller and deeper than the last ones. Layers have three dimensions like 256x256x32. What is this third number? I assume the first two numbers are the number of nodes but I don't know what the depth is.
TLDR; 256x256x32 refers to the layer's output shape rather than the layer itself.
There are many articles and posts out there explaining how convolution layers work. I'll try to answer your question without going into too many details, just focusing on shapes.
Assuming you are working with 2D convolution layers, your input and output will both be three-dimensional. That is, without considering the batch which would correspond to a 4th axis... Therefore, the shape of a convolution layer input will be (c, h, w) (or (h, w, c) depending on the framework) where c is the number of channels, h is the width of the input and w the width. You can see it as a c-channel hxw image.
The most intuitive example of such input is the input of the first convolution layer of your convolutional neural network: most likely an image of size hxw with c channels for example c=1 for greyscale or c=3 for RGB...
What's important is that for all pixels of that input, the values on each channel gives additional information on that pixel. Having three channels will give each pixel ('pixel' as in position in the 2D input space) a richer content than having a single. Since each pixel will be encoded with three values (three channels) vs. a single one (one channel). This kind of intuition about what channels represent can be extrapolated to a higher number of channels. As we said an input can have c channels.
Now going back to convolution layers, here is a good visualization. Imagine having a 5x5 1-channel input. And a convolution layer consisting of a single 3x3 filter (i.e. kernel_size=3)
input
filter
convolution
output
shape
(1, 5, 5)
(3, 3)
(3,3)
representation
Now keep in mind the dimension of the output will depend on the stride and padding of the convolution layer. Here the shape of the output is the same as the shape of the filter, it does not necessarily have to be! Take an input shape of (1, 5, 5), with the same convolution settings, you would end up with a shape of (4, 4) (which is different from the filter shape (3, 3).
Also, something to note is that if the input had more than one channel: shape (c, h, w), the filter would have to have the same number of channels. Each channel of the input would convolve with each channel of the filter and the results would be averaged into a single 2D feature map. So you would have an intermediate output of (c, 3, 3), which after averaging over the channels, would leave us with (1, 3, 3)=(3, 3). As a result, considering a convolution with a single filter, however many input channels there are, the output will always have a single channel.
From there what you can do is assemble multiple filters on the same layer. This means you define your layer as having k 3x3 filters. So a layer consists k filters. For the computation of the output, the idea is simple: one filter gives a (3, 3) feature map, so k filters will give k (3, 3) feature maps. These maps are then stacked into what will be the channel dimension. Ultimately, you're left with an output shape of... (k, 3, 3).
Let k_h and k_w, be the kernel height and kernel width respectively. And h', w' the height and width of one outputted feature map:
input
layer
output
shape
(c, h, w)
(k, c, k_h, k_w)
(k, h', w')
description
c-channel hxw feature map
k filters of shape (c, k_h, k_w)
k-channel h'xw' feature map
Back to your question:
Layers have 3 dimensions like 256x256x32. What is this third number? I assume the first two numbers are the number of nodes but I don't know what the depth is.
Convolution layers have four dimensions, but one of them is imposed by your input channel count. You can choose the size of your convolution kernel, and the number of filters. This number will determine is the number of channels of the output.
256x256 seems extremely high and you most likely correspond to the output shape of the feature map. On the other hand, 32 would be the number of channels of the output, which... as I tried to explain is the number of filters in that layer. Usually speaking the dimensions represented in visual diagrams for convolution networks correspond to the intermediate output shapes, not the layer shapes.
As an example, take the VGG neural network:
Very Deep Convolutional Networks for Large-Scale Image Recognition
Input shape for VGG is (3, 224, 224), knowing that the result of the first convolution has shape (64, 224, 224) you can determine there is a total of 64 filters in that layer.
As it turns out the kernel size in VGG is 3x3. So, here is a question for you: knowing there is a single bias parameter per filter, how many total parameters are in VGG's first convolution layer?
Sorry for the short answer, but when you have a digital image, you have 2 dimensions and then you often have 3 for the colors. The convolutional filter looks into parts of the picture with lower height/width dimensions and much more depth channels (in your case 32) to get more information. This is then fed into the neural network to learn.
I created the example in PyTorch to demonstrate the output you had:
import torch
import torch.nn as nn
bs=16
x = torch.randn(bs, 3, 256, 256)
c = nn.Conv2d(3,32,kernel_size=5,stride=1,padding=2)
out = c(x)
print(out.shape, out.shape[1])
Out:
torch.Size([16, 32, 256, 256]) 32
It's a real tensor inside. It may help.
You can play with a lot of convolution parameters.
As mentioned above, both
tf.nn.conv2d with strides = 2
and
tf.nn.max_pool with 2x2 pooling
can reduce the size of input to half, and I know the output may be different, but what I don't know is that affect the final training result or not, any clue about this, thanks.
In both your examples assume we have a [height, width] kernel applied with strides [2,2]. That means we apply the kernel to a 2-D window of size [height, width] on the 2-D inputs to get an output value, and then slide the window over by 2 either up or down to get the next output value.
In both cases you end up with 4x fewer outputs than inputs (2x fewer in each dimension) assuming padding='SAME'
The difference is how the output values are computed for each window:
conv2d
the output is a linear combination of the input values times a weight for each cell in the [height, width] kernel
these weights become trainable parameters in your model
max_pool
the output is just selecting the maximum input value within the [height, width] window of input values
there is no weight and no trainable parameters introduced by this operation
The results of the final training could actually be different as the convolution multiplies the tensor by a filter, which you might not want to do as it takes up extra computational time and also can overfit your model as it will have more weights.
im trying to fit the data with the following shape to the pretrained keras vgg19 model.
image input shape is (32383, 96, 96, 3)
label shape is (32383, 17)
and I got this error
expected block5_pool to have 4 dimensions, but got array with shape (32383, 17)
at this line
model.fit(x = X_train, y= Y_train, validation_data=(X_valid, Y_valid),
batch_size=64,verbose=2, epochs=epochs,callbacks=callbacks,shuffle=True)
Here's how I define my model
model = VGG16(include_top=False, weights='imagenet', input_tensor=None, input_shape=(96,96,3),classes=17)
How did maxpool give me a 2d tensor but not a 4D tensor ? I'm using the original model from keras.applications.vgg16. How can I fix this error?
Your problem comes from VGG16(include_top=False,...) as this makes your solution to load only a convolutional part of VGG. This is why Keras is complaining that it got 2-dimensional output insted of 4-dimensional one (4 dimensions come from the fact that convolutional output has shape (nb_of_examples, width, height, channels)). In order to overcome this issue you need to either set include_top=True or add additional layers which will squash the convolutional part - to a 2d one (by e.g. using Flatten, GlobalMaxPooling2D, GlobalAveragePooling2D and a set of Dense layers - including a final one which should be a Dense with size of 17 and softmax activation function).
I'm new on neural networks. I follow some tutorials on a lot of platforms, but there is one thing than I don't understand.
In a simple multi layer perceptron :
We have the input layer, an hidden layer for this example (with the same number of neurons than the input layer) and an output layer with one unit.
We initialize the weights of the units in hidden layer randomly but in a range of small values.
Now, the input layer is fully connected with the hidden layer.
So each units in hidden layer are going to receive the same parameters. How are they going to extract different features from each other ?
Thanks for explanation!
We initialize the weights of the units in hidden layer randomly but in
a range of small values. Now, the input layer is fully connected with
the hidden layer. So each units in hidden layer are going to receive
the same parameters. How are they going to extract different features
from each other ?
Actually each neuron will not have the same value. To get to the activations of the hidden layer you use the matrix equation Wx + b In this case W is the weight matrix of shape (Hidden Size, Input Size). x is the input vector of the hidden layer of shape (Input Size) and b is the bias of shape (Hidden Size). This results in an activation of shape (Hidden Size). So while each hidden neuron would be "seeing" the same x vector it will be taking the dot product of x with its own random row vector and adding its own random bias which will give that neuron a different value. The values contained in the W matrix and b vector are what are trained and optimized. Since they have different starting points they will eventually learn different features through the gradient decent.
The Keras tutorial gives the following code example (with comments):
# apply a convolution 1d of length 3 to a sequence with 10 timesteps,
# with 64 output filters
model = Sequential()
model.add(Convolution1D(64, 3, border_mode='same', input_shape=(10, 32)))
# now model.output_shape == (None, 10, 64)
I am confused about the output size. Shouldn't it create 10 timesteps with a depth of 64 and a width of 32 (stride defaults to 1, no padding)? So (10,32,64) instead of (None,10,64)
In k-Dimensional convolution you will have a filters which will somehow preserve a structure of first k-dimensions and will squash the information from all other dimension by convoluting them with a filter weights. So basically every filter in your network will have a dimension (3x32) and all information from the last dimension (this one with size 32) will be squashed to a one real number with the first dimension preserved. This is the reason why you have a shape like this.
You could imagine a similar situation in 2-D case when you have a colour image. Your input will have then 3-dimensional structure (picture_length, picture_width, colour). When you apply the 2-D convolution with respect to your first two dimensions - all information about colours will be squashed by your filter and will no be preserved in your output structure. The same as here.