What does the number of filters in a convolution layer convey?
How does this number effect the performance or quality of the architecture?
I mean should we always opt for a higher numbers of filters? whats good of them? and How does people assign diffrent number of filters for different layers ?
I mean looking at this question : How to determine the number of convolutional operators in CNN?
The answer specified 3 convolution layer with different numbers of filters and size,
Again in this question : number of feature maps in convolutional neural networks
you can see from the picture that, we have 28*28*6 filters for the first layer and 10*10*16 filter for the second conv layer.
How do they come up with these numbers, Is this through trial and error?
Thanks in advance
Solved – the significance of the number of convolution filters in a convolutional network
conv-neural-networkdeep learning
Related Solutions
I'm assuming that when you say 11x11x10 you mean that you have a layer with 10, 11x11 filters. So the number of convolutions that you'll be doing is simply 10, 2D discrete convolution per filter in your filter bank. So, let's say that you have a network:
480x480x1 # your input image of 1 channel
11x11x10 # your first filter bank of 10, 11x11 filters
5x5x20 # your second filter bank of 20, 5x5 filters
4x4x100 # your final filter bank of 100, 4x4 filters
You're going to be doing: $10 + 20 + 100 = 130$ multi channel 2D convolutions each with a depth of 1, 10, and 20 respectively. As you can see, the depth of each convolution is going to change as a function of the depth of the input volume from the previous layer.
But I assumed that you're trying to figure out how to compare this to a single channel 2D convolution. Well, you could just multiply the depth of each input volume by the number of filters in each layer and add them together. In your case: $10 + 200 + 2000 = 2,210$.
Now this only tells you how many single channel 2D convolutions you're doing, not how computationally intensive each convolution is, the computational intensity of each convolution will depend on a variety of parameters including image_size, image_depth, filter_size, your stride (how far you step between each individual filter calculation), the number of pooling layers you have, etc.
The second convolutional neural network (CNN) architecture you posted comes from this paper. In the paper the authors give a description of what happens between layers S2 and C3. Their explanation is not very clear though. I'd say that this CNN architecture is not 'standard', and it can be quite confusing as a first example for CNNs.
First of all, a clarification is needed on how feature maps are produced and what their relationship with filters is. A feature map is the result of the convolution of a filter with a feature map. Let's take the layers INPUT and C1 as an example. In the most common case, to get 6 feature maps of size $28 \times 28$ in layer C1 you need 6 filters of size $5 \times 5$ (the result of a 'valid' convolution of an image of size $M \times M$ with a filter of size $N \times N$, assuming $M \geq N$, has size $(M-N+1) \times (M-N+1)$. You could, however, produce 6 feature maps by combining feature maps produced by more or less than 6 filters (e.g. by summing them up). In the paper, nothing of the sort is implied though for layer C1.
What happens between layer S2 and layer C3 is the following. There are 16 feature maps in layer C3 produced from 6 feature maps in layer S2. The number of filters in layer C3 is indeed not obvious. In fact, from the architecture diagram only, one cannot judge what the exact number of filters that produce those 16 feature maps is. The authors of the paper provide the following table (page 8):
With the table they provide the following explanation (bottom of page 7):
Layer C3 is a convolutional layer with 16 feature maps. Each unit in each feature map is connected to several $5 \times 5$ neighborhoods at identical locations in a subset of S2's feature maps.
In the table the authors show that every feature map in layer C3 is produced by combining 3 or more feature maps (page 8):
The first six C3 feature maps take inputs from every contiguous subsets of three feature maps in S2. The next six take input from every contiguous subset of four. The next three take input from some discontinuous subsets of four. Finally, the last one takes input from all S2 feature maps.
Now, how many filters are there in layer C3? Unfortunately, they do not explain this. The two simplest possibilities would be:
- There is one filter per S2 feature map per C3 feature map, i.e. there is no filter sharing between S2 feature maps associated with the same C3 feature map.
- There is one filter per C3 feature map, which is shared across the (3 or more) feature maps of layer S2 that are combined.
In both cases, to 'combine' would mean that the results of convolution per S2 feature map group, would need to be combined to produced C3 feature maps. The authors do not specify how this is done, but addition is a common choice (see for example the animated gif near the middle of this page.
The authors give some additional information though, which can help us decipher the architecture. They say that 'layer C3 has 1,516 trainable parameters' (page 8). We can use this information to decide between cases (1) and (2) above.
In case (1) we have $(6 \times 3) + (9 \times 4) + (1 \times 6) = 60$ filters. The filter size is $(14-10+1) \times (14-10+1) = 5 \times 5$. The number of trainable parameters in this case would be $5 \times 5 \times 60 = 1,500$ trainable parameters. If we assume one bias unit per C3 feature map, we get $1,500 + 16 = 1,516$ parameters, which is what the authors say. For completeness, in case (2) we would have $(5 \times 5 \times 16) + 16 = 416$ parameters, which is not the case.
Therefore, if we look again at Table I above, there are 10 distinct C3 filters associated with each S2 feature map (thus 60 distinct filters in total).
The authors explain this type of choice:
Different feature maps [in layer C3] are forced to extract different (hopefully complementary) features because they get different sets of inputs.
I hope this clarifies the situation.
Best Answer
What does the number of filters in a convolution layer convey? - I usually like to think of filters as feature detectors. Although it depends on the problem domain, the significance # of feature detectors intuitively is the number of features (like edges, lines, object parts etc...) that the network can potentially learn. Also note that each filter generates a feature map. Feature maps allow you to learn the explanatory factors within the image, so the more # filters means the more the network learns (not necessarily good all the time - saturation and convergence matter the most)
How does this number affect the performance or quality of the architecture? - I don't think you will find a good answer for these types of question since we are still trying to formalize what is going on inside DL black box. Intuitively once again you will learn a more robust non-linear function the more filter banks you have however the performance is going to depend on the type of task and the data characteristics. You typically want to know what kind of data you are dealing with to determine the # parameters in your architecture (including filter). How many filters do I need? is more like asking how complex (specially) are the images in my dataset. There isn't any formal notion that relates # filters to performance. Its all experimental and iterative. Lots of trail and error forsure.