Backpropagation in Convolutional Neural Networks (CNNs)
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- Опубліковано 31 лип 2024
- In this video we are looking at the backpropagation in a convolutional neural network (CNN). We use a simple CNN with zero padding (padding = 0) and a stride of two (stride = 2).
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---------- Content ----------
00:00 - Introduction
00:51 - The Forward propagation
02:23 - The BackPropagation
03:31 - (Intuition) Setting up Formula for Partial Derivatives
06:07 - Simplifying Formula for Partial Derivatives
07:05 - Finding Similarities
08:55 - Putting it All together
---------- Contributions ----------
Background music: pixabay.com/users/balancebay-...
#computervision #convolutionalneuralnetwork #ai #neuralnetwork #deeplearning #neuralnetworksformachinelearning #neuralnetworksexplained #neuralnetworkstutorial #neuralnetworksdemystified #computervisionandai #backpropagation
great video, but i don't understand how we can find the value of the dL/dzi terms. At 7:20 you make it seem like dL/dzi = zi, is that correct?
No, they come from the loss function. I explain this at 4:17.
It might be a bit unclear so I’ll highly reccomend you watch the video from 3blue1brown: ua-cam.com/video/tIeHLnjs5U8/v-deo.htmlsi=Z6asTm87XWcW1bVn 😃
I'm with @louissimion, you show how dL/dw1 is related to dz1/dw1+... (etc), but you never show/expain where dL/dz1 (etc) comes from. Poof - miracle occurs here. Having a numerical example would help a lot. This "theory/symbology" only post is therefore incomplete/useless from a learing/understanding standpoint.
@@rtpubtubeIt's quite literally what he wrote. He hasn't defined a loss function so that's just what it is from the chain rule. If you're asking how the actual value of dL/dz1 is computed, the last layer has its own set of weights besides the ones shown in the video, in addition to an activation function. You use that and a defined loss function to compute dL/dzi. It's similar to what you see in standard NNs. If you studied neural networks, you should know this. This is a video about CNNs not an intro to NNs. Go study that before this. It's not his job to point out every little thing.
Why is this channel so underrated? You deserve more subscribers and views.
Perhaps developers use ad blockers, and as a result, UA-cam needs to ensure revenue by not promoting these types of videos (that's my opinion)
Been trying to understand backpropogation in CNN for years until today! Thanks a ton mate!
it was obvious primitive algo dude... people like you are being called "data scientists" now, which is really sad...
This channel is a hidden gem. Thank you for your content
really clear explanation and good pacing. I felt I understood the math behind back propagation for the first time after watching this video!
Fantastic explanation!! Very clear and detailed, thumbs up!
Really intuitive and great animations.
This was really helpful....Thank you so much for the vizualization...Keep up the good work...Looking forward to your future uploads.
Very well explanation, I search many videos but no body explained regarding change in filter's weight. Thank you so much for this animated simple explanation.
great stuff man, crystal clear!
great job. this explanation is really intuitive
Great Explanation, helped me understand the background working
great explanation, clear direct and understandable, sub!
I have seen few videos before, this one is by far the best one. It breaks down each concept and answers all the questions that comes in the mind. The progression, the explanation is best
Thank you! 🔥
excellent. the exact video i was looking for.
great video, underrated channel , please keep it up with CNN videos!
Amazing!
I was looking for some material like this a long time ago and only found it here, beautiful :D
Thank you my brother 🔥
the animations were super useful, thanks!
your channel is a Hidden Gem..My suggestion is to start a discord and get some crowd functing and one on ones for people who want to learn from you..youa re gifted in teaching.
Best video to understand what is going on the under the hood of CNN.
Great explanation with cool visual. Thanks a lot.
Thank you my friend 😃
really beautiful, thanks.
Couldn’t explain it better myself … absolutely amazing and comprehensible presentation!
what i was looking for. well explained
Masterpiece 💕💕
Thank you so much!!! This video is so so so well done!
Thank you. Hope you got some value out of this! 💯
What a masterpiece.
Nicely put, thank you so much.
amazing video thanks!
Best explanation
Please do not stop making these videos!!!
I won’t let you down Joker 🔥🤝
Great explanation and visualization
Thank you my friend 🔥🚀
You are a great example of fluidity of thought and words..great explanation
Thank you my friend. Hope you got some value! :)
@@far1din sure did
Thanks a lot!
please continue your videos !!
Thanks for sharing!
Great example thanks a lot
great explanation
thanku you so much for this
Well done.
fab video! help me a lot
Glad to hear that you got some value out of this video! :D
Amazing
This is a topic which is rarely explained online, but it was very clearly explained here. Well done.
Well explained now I need to code it my self
Haha, that’s the hard part
@@far1din I think I came up with a solution Here
def backward(self, output_gradient, learning_rate):
kernels_gradient = np.zeros(self.kernels_shape)
input_gradient = np.zeros(self.input_shape)
for i in range(self.depth):
for j in range(self.input_depth):
kernels_gradient[i, j] = convolve2d(self.input[j], output_gradient[i], "valid")
input_gradient[j] += convolve2d(output_gradient[i], self.kernels[i, j], "same")
self.kernels -= learning_rate * kernels_gradient
self.biases -= learning_rate * output_gradient
return input_gradient
First i initialized the kernel gradient as an array of zeros with the kernel shape
then I iterated through the depth of the kernels the the depth of the input then for each gradient withe respect to the kernel
I did the same to compute the input gradients
Your vid helped me understand the backward method better
So I have to say thank you sooo much for it
@@far1din I'll document the solution and but it here when I do please pin the comment
@@SolathPrime That’s great my friend. Will pin 💯
Thanks.
+1 sub, excellent video
Thank you! 😃
tks u very much for this video, but it's probably more helpful if you also add a max pooling layer.
Great video!! Your explanation is the best I have found.
Could you please tell me what software you use for the animations ?
I use manim 😃
www.manim.community
thx
What is the loss function here, and how are the values in the flattened z matrix used to compute yhat ?
perfect, one suggestion make videos a little longer 20-30 is a good number
Haha, most people don't like these kind of videos too long. Average watchtime for this video is about 3minutes :P
@@far1dinoh shii! 3 minutes, that was very unexpected, maybe it's because people revisit the video to revise specific topic.
Must be 💯
Great explanation. Can you please tell which tool do you use for making these videos.
Thank you my friend! I use manim 😃
www.manim.community
1:15 why do you iterate in steps of 2? If you iterated by 1 then you could generate a 3x3 layer image. Is that just to save on computation time/complexity or is there something other reason for it?
The reason why I used a stride of two (iterations in steps of two) in this video is partially random and partially because I wanted to highlight that the stride when performing backpropagation should be the same as when performing the forward propagation. In most learning materials I have seen, they usually use a stride of one, hence a stride of one for the backpropagation. This could lead to confusion when operating with larger strides.
The stride could technically be whatever you like (as long as you keep it within the dimensions of the image/matrix). I could have chosen another number for the stride as you suggested. In that case, with a stride of one, the output would be a 3 x 3 matrix/image. Some will say that a shorter stride will encapsulate more information than a larger one, but this becomes “less true” as the size of the kernel increases. As far as I know there are no “rules” for when to use larger strides and not. Please let me know if this notion has changed as everything changes so quickly in this field! 🙂
@@far1din I never considered how stride length could change depending on kernel size. I guess that makes sense, the larger kernel could cover the same data as a small kernel, just in fewer steps/iterations. I also figured you intentionally generated a 2x2 image since that’s a lot simpler than a 3x3 and this an educational video. Thanks for the feedback, that was really insightful!
Is the stride only along the rows, and not along columns? Is is common or just simplified?
I've had no trouble learning about the 'vanilla' neural networks. Although your videos are great, I can't seem to find resources that delve a little deeper into the explanations of how CNNs work. Are there any resources you would recommend ?
5:24
does this just mean we divide z1 by w1 and ultiply by L divided by z1 and do that for all z'S to get the partial derivative of L in respect to w1?
It’s not that simple. Doing the actual calculations is a bit more tricky. Given no activation function, Z1 = w1*pixel1 + w2*pixel2 + w3*pixel3… you now have to take the derivative of this with respect to w1, then y = z1*w21 + z2*w22… take the derivative of y with respect to z1 etc. The calculus can be a bit too heavy for a comment like this.
I’ll highly reccomend you watch the video by 3blue1brown: ua-cam.com/video/tIeHLnjs5U8/v-deo.htmlsi=Z6asTm87XWcW1bVn 😃
What about the weights of the fully connected layer
No point in adding it to this video since that's something you should know from neural networks. That's why he just leaves it as dL/dzi.
dL/dzi = ??
I explain the term at 4:17.
It might be a bit unclear so I’ll highly reccomend you watch the video from 3blue1brown: ua-cam.com/video/tIeHLnjs5U8/v-deo.htmlsi=Z6asTm87XWcW1bVn 😃
You have nices videos, that helped me better understand the concept of CNN. But, from this video, it is not really obvious that matrix dL/dw - is convolution of image matrix and dL/dz matrix, as showed here ua-cam.com/video/Pn7RK7tofPg/v-deo.html. The stride of two is also a little bit confusing
Thank you for the comment! I believe he is doing the exact same thing (?)
I chose to have a stride of two in order to highlight that the stride should be similar to the stride used during the forward propagation. Most examples stick with a stride of one. I now realize it might have caused some confusion :p
Hello well explained. I need your presentation
Just download it 😂
w^* is an abuse of math notation, but it's convenient.
I think it's spelled "Convolution"
Haha thank you! 🚀