Does anyone else feel weird when he says Thank You at the end? He just gave me a free, high-quality, understandable lecture on neural networks. Man, thank *you*!
@@resinsmp Now that's an interesting thought haha. "Since user searched this type of topic, it must already be aware of some other certain type of topics." Simply marvelous!
steve brunton idk who u r before watching this. but this presentation style of a glass whiteboard w/ image superimposed is the best way ive ever seen someone teach tbh. thank u at least for that. but more importantly this actually helped me understand the beast of neural nets a little more and hopefully be more prepared when our new ai overlords enslave us at least we will know how they think
This was massively helpful as an intro! When my question is just "yes but how does this ACTUALLY work", you either get pointlessly high level metaphors about it being like your brain, or jumping straight into gradient descent and all the math behind training. A+ video, thanks.
Steve, you are the first person I have ever seen describe an overview of neural networks without paralyzing the consciousness of the average person. I look forward to more of your lectures, focused in depth on particular aspects of deep learning. It is not hard to get an AI toolkit for experimentation. It is hard to get a toolkit and know what to do with it. My personal interest is in NLR (natural language recognition) and NLP (natural language programming) as applied to formal language sources such as dictionaries and encyclopedias. I look forward to lectures covering extant NLP AI toolkits. Sincerely, John
Important note about the function operating on a node. If the functions of two adjacent layers are linear, then they can be equivalently represented as a single layer (compositions of linear transforms is itself a linear transformation and thus could just be its own layer). So, nonlinear transformations are -necessary- for deep networks (not just neural networks). That isn't to say you can't have a composition of linear transformations to compose an overall linear transformation, if there's nonlinear constraints for each operator.
Thank you, I've always seen the term neural networks generalized and always thought of it as probably a bunch of matrix operations. But now I know that there are diverse variations and use cases for them
Very nice. I like the autoencoders. That is basically just understanding. Intelligence is basically just a compression algorithm. The more you understand the less data you have to save. You can extract information from your understanding. That's basically what the autoencoder is about. For instance, if you want to save an image of a circle you can store all the pixels in the image, or store the radius, position and color of it. Which one takes up more space? Well, storing the pixels. We can use our understanding of the image containing a circle in order to compress it. Our understanding IS the compression. The compression IS the understanding. It's the same.
I dig that perspective. I do think that compression can have some downsides. I feel like my emotional reactions to things are a sort of "compression". I can't keep track of everything I've read about a potentially political topic, but I can remember how it made me feel.
I started to learn NNs in good old early 2000-s. No internet, no collegues, nor even friends to share my excitement about NNs. But even then it was obvious that the future lies with them, though I had to concentrate on more essential skills for my living. And only now, after so many years have passed, I tend to come back to NNs, cause I'm still very excited about them and it is much-much-much easier now at least ot play with them (much more powerful computers, extensive online knowlegde base, community, whatever), not speaking about career opportunities. I'm glad YT somehow guessed I'm interested in NNs, though I haven't yet searched for it AFAIR. It gives me another impetus to start learning them again. Thanks for the video! Liked and sub-ed.
Thank you for your video! Seeing your example for principal values decomposition made neural networks much clearer to me than anything else I had seen till now. It allowed me to connect this to SVD-based linear modeling I used almost 10 years ago to create simplified models of visual features seen in fluid dynamics. I did not expect how much easier this suddenly seemed when it connected to what I already knew.
once you get hold of the back propagation and how to do the chain rule derivatives, you understand that was not the goal! you merely opened the door, and this video is the way to your goal!
Thank you so much for the video! The way you teach makes learning so much fun:) If you were born in ancient time, you alone would have shot the literacy rate by over 20%
I've been studying machine learning models and got to neural networks, and it was a bit intimidating. This excellent lecture took the "scary" right out of it.
Hey I just wanted to say thank you for making this video. I found it really helpful! I particularly enjoyed your presentation format, and the digestible length. About to watch a whole bunch more of you videos! :)
One of the most effective and useful introductory lectures on neural networks you can attend. It provides basic terminology and enables a good foundation for other lectures. HIGHLY RECOMMENDED. It would be helpful, Mr. Bunton, to say a little bit more about Neurons. Is a neuron strictly a LOGICAL function point in a process (my simple excel cell doing a logical function qualifies as a neuron with your definition), is it a PHYSICAL function point like a server, or is it both? Was there a reason you did not mention restricted Boltzmann motors? Thank you again, Sir, for the quality of this lecture.
A neuron is pure software, a computational unit that mimics the basic functions of a biological neuron. While software relies on specific hardware for execution, a neuron is not a simple server. Unlike an Excel cell, which takes a single input and produces a straightforward output, a neuron receives multiple inputs from other neurons, processes them, and generates an output based on the combined information. Each input to a neuron is multiplied by a weight, a numerical value that represents the strength of the connection between the neurons. These weighted inputs are then summed together, and a bias value, representing an inherent offset, is added to the result. The resulting value is then passed through an activation function, which introduces non-linearity into the network's decision-making process. Activation functions, such as sigmoid and ReLU, transform the weighted input into the neuron's output, allowing the network to capture complex patterns and relationships in the data. ReLU is often used as an activation function because it requires less computational power compared to other activation functions, such as the sigmoid function. Through a process called learning, artificial neurons adjust their weights over time, enabling the network to improve its performance on a given task. Algorithms like back propagation guide this learning process, allowing the network to minimize errors and optimize its decision-making capabilities. Hope this helps.
Liked that the approach was direct and simplistic; and of course you can write your code in this manner too. So that you're not overwhelmed. Say four or five layers being coded, then you have outboard functions that handle the input and out put arrays. This last might take up most of the landscape of a program. Isn't this fellow clever? Dang. He's gotta be a Professor somewhere. Many thanks. The computer training that I had gotten was very rudimentary, first in the 60s and then another drop in the mid 90s. Luckily there's YT where you can catch up. And after a while the 'training' starts to remind you of subliminal sorts of stuff. Maybe?
Loved neural nets since 1998 when I read a book which showed how 3 layer nets can solve difficult problems. In the 21st century the neural nets are magnificent and a credit to the brains of the human race. I am using a 21st century neural net myself and it's great. Hahahaha. Great video
Steve: nice talk,... many questions come up, I'll ask a few 1)Do you distinguish planar vs non-planar networks? 2)Do RNN(s) become unstable? They look like control system time dependent processes. 3)Has anyone applied Monte Carlo toward selection of topology of a NN, or toward the activation function selection,...? Fascinating area to study.
He Steve, thank you a lot for all your brilliant videos! One request on the topic, could you please cover how all this works with shift/rotation/scale of the image? Nobody on youtube covers this tricky part of the neuron networks used for image recognition. I keep fingers crossed that you the one who could clarify this.
Oh wow I've been educated by your channel for a while now but did not realise you have published a textbook until your remark. Only A$80 here in Aus. Done! purchased..
Thank you too great video would they be building a quantum computer to be a single one of those dots to read internet transaction logs based on web page dynamics to filter and feed data across apps ?
I guess neurones can be thought of a functions that call other functions if a certain variable has a sufficient value. And the main difference between an ANN and our biological neural network is that ANN has a fixed set of functions with fixed connections, only changing the conditions triggering the next callback, whereas brains can grow new neurones and even disconnect and rewire connections. The question then becomes: Can we write a function that writes a new function? Or a function that modifies the content of an existing function so as to change its callback to call a different function? If this holds true, we could get even closer to natural neural networks. I’m also debating myself when to use “artificial” vs “synthetic”. I guess an [A]NN can’t rewire/reprogram itself, whereas a real one can? In which case if we produce a neural network that indeed can change its own inner structure, we could promote it from “artificial” to “synthetic”? Great video. Definitely earned yourself a subscriber. :)
@@Eigensteve OMG it's my honor😯. I didn't expect you would read my comment lol. I hope I could get in to UW this fall so that I could be in your class in person.
Hi! I am medical doctor with little background on computing studies or mathematics but great interest in data and its use for medical research and patient's care. I am now drafting a booklet on Machine Learning for health care workers with no previous coding background and found this video extremely clear and helpful. Would you allow me to add a link to this video in the booklet?
Can I use your mathematical apparatus, to investigate the physical processes of Metaphysics?? I am looking for a mathematical apparatus capable of working with metaphysical phenomena, i.e. metamathematics!!
I really really really like the way you present- could you help me understand your set up? There's a see-through glass that you draw on, there's a projector (i think) that's allowing you to see which part of the presentation you're in. Plus the dark shirt enables me to just focus on your face, and your hands. It's a very intuitive interface for learning. Your hand gestures easily capture my eyes' attention. Do please elaborate. Thanks!
Thanks for your explanation in the video. have learned a lot. Am doing research in speech emotion recognition. Can you pls tell me the best Deep learning algorithms that will work?
Could you please do a follow up on this? I basically came here for the "many many more" you mentioned towards the end. LSTMs and other architectures that are useful for time series processing. It would be nice if you could do an overview video about that class of networks.
@@jvsonyt Hardly. It's just a trigger. Person A with a high number of followers shares a video -> They then go watch the video -> The video view number increases -> IF video has increase in X views THEN bump video ranking in reccomendations by Y amount -> You now get it in your reccomendations.
I don’t like the traditional sigmoid function as much. I did a performance test on both speed, loss, & accuracy on image classification, and tanh performed better on all three metrics compared to sigmoid (and ReLU ended up being better than tanh).
5:34 What about Spiking Recurrent Neural Networks generally SNN outperform RNN When it comes to problems that are changing times Although SNN He suffers from a weight problem, but isn't Spiking Recurrent Neural Networks It will be a better solution
Does anyone else feel weird when he says Thank You at the end? He just gave me a free, high-quality, understandable lecture on neural networks. Man, thank *you*!
:) People watching and enjoying these videos makes it so much more fun to make them. So indeed, thanks for watching!
@@Eigensteve ..being happy to see other people making progress. Man, you have a great heart..!
Steve, we should be thanking "you"
Presenter with true class 👏
😁😍
I don't know why youtube decided I needed that little course, but I'm glad that it did now.
This video has common variables with other videos you watch!
Sounds like you’ve been autoencoded
That's why the CF algorithm did
same thing
TH-cam also uses neural networks
TH-cam's recommendation algorithm is becoming self-aware...
It was TH-cam's turn in the introduction round
I hope Jus relu and sigmoid
@@GowthamRaghavanR those are the safe ones
Imagine for a second also what the algorithm never recommended to you, because it already knew you were aware.
@@resinsmp Now that's an interesting thought haha. "Since user searched this type of topic, it must already be aware of some other certain type of topics." Simply marvelous!
I am addicted to your series of lectures for the last three months. your "welcome back" intro looks like a chorus to me. thank you!
steve brunton idk who u r before watching this. but this presentation style of a glass whiteboard w/ image superimposed is the best way ive ever seen someone teach tbh. thank u at least for that. but more importantly this actually helped me understand the beast of neural nets a little more and hopefully be more prepared when our new ai overlords enslave us at least we will know how they think
This was massively helpful as an intro! When my question is just "yes but how does this ACTUALLY work", you either get pointlessly high level metaphors about it being like your brain, or jumping straight into gradient descent and all the math behind training. A+ video, thanks.
Steve, you are the first person I have ever seen describe an overview of neural networks without paralyzing the consciousness of the average person.
I look forward to more of your lectures, focused in depth on particular aspects of deep learning.
It is not hard to get an AI toolkit for experimentation. It is hard to get a toolkit and know what to do with it.
My personal interest is in NLR (natural language recognition) and NLP (natural language programming) as applied to formal language sources such as dictionaries and encyclopedias.
I look forward to lectures covering extant NLP AI toolkits.
Sincerely,
John
John, I recommend Stanford's course on recurrent neural networks. Free on TH-cam. It's a playlist with over 20 lectures
th-cam.com/play/PLoROMvodv4rOhcuXMZkNm7j3fVwBBY42z.html
You really simplify the stuff in a way that has me feel enthusiastic to learn it. Thank you.
Important note about the function operating on a node. If the functions of two adjacent layers are linear, then they can be equivalently represented as a single layer (compositions of linear transforms is itself a linear transformation and thus could just be its own layer). So, nonlinear transformations are -necessary- for deep networks (not just neural networks). That isn't to say you can't have a composition of linear transformations to compose an overall linear transformation, if there's nonlinear constraints for each operator.
Thank you,
I've always seen the term neural networks generalized and always thought of it as probably a bunch of matrix operations. But now I know that there are diverse variations and use cases for them
Very nice. I like the autoencoders. That is basically just understanding. Intelligence is basically just a compression algorithm. The more you understand the less data you have to save. You can extract information from your understanding. That's basically what the autoencoder is about. For instance, if you want to save an image of a circle you can store all the pixels in the image, or store the radius, position and color of it. Which one takes up more space? Well, storing the pixels. We can use our understanding of the image containing a circle in order to compress it. Our understanding IS the compression. The compression IS the understanding. It's the same.
shut up
profound observation
Thank you for your comment, excellent observance!
I dig that perspective. I do think that compression can have some downsides. I feel like my emotional reactions to things are a sort of "compression". I can't keep track of everything I've read about a potentially political topic, but I can remember how it made me feel.
I like to think of autoencoder as an architect outputting a blueprint, then a construction company building that building
This is the best short intro to this topic I've seen. Thanks!
Sir your deep learning videos are the only ones on TH-cam I take seriously.
I just found your channel as a suggestion from a 3Blue1Brown video. I subscribed instantly, easily explained, thanks.
So cool! Which video?
@@EigensteveI was watching the playlist on NN from 3Blue1Brown, and then your video appeared on my suggestions, very glad and superb content, thanks.
I started to learn NNs in good old early 2000-s. No internet, no collegues, nor even friends to share my excitement about NNs. But even then it was obvious that the future lies with them, though I had to concentrate on more essential skills for my living. And only now, after so many years have passed, I tend to come back to NNs, cause I'm still very excited about them and it is much-much-much easier now at least ot play with them (much more powerful computers, extensive online knowlegde base, community, whatever), not speaking about career opportunities. I'm glad YT somehow guessed I'm interested in NNs, though I haven't yet searched for it AFAIR. It gives me another impetus to start learning them again. Thanks for the video! Liked and sub-ed.
These were most productive 9 minutes. Great explanation on the architectures.
Thank you for a good explanation. This is the quality of content we want to see! 10 folds better than Siraj Raval's channel, in my opinion.
Well, that makes sense given he's a renowned professor =)
Thank you for your video!
Seeing your example for principal values decomposition made neural networks much clearer to me than anything else I had seen till now.
It allowed me to connect this to SVD-based linear modeling I used almost 10 years ago to create simplified models of visual features seen in fluid dynamics.
I did not expect how much easier this suddenly seemed when it connected to what I already knew.
Great content for existing developers. Wow. Incredible. To say the least I am speechless. You didn’t waste my time and I appreciate that!!
once you get hold of the back propagation and how to do the chain rule derivatives, you understand that was not the goal! you merely opened the door, and this video is the way to your goal!
Thank you so much for the video! The way you teach makes learning so much fun:) If you were born in ancient time, you alone would have shot the literacy rate by over 20%
Amazing program... I love the thing he's drawing on that projects his diagrams.
I've been studying machine learning models and got to neural networks, and it was a bit intimidating. This excellent lecture took the "scary" right out of it.
Hey I just wanted to say thank you for making this video. I found it really helpful!
I particularly enjoyed your presentation format, and the digestible length. About to watch a whole bunch more of you videos! :)
One of the best introductions to AI I have seen.
YES. ☝️this
forget neural networks, this guy figured out that it's better if you stand behind what your presenting instead of in front of it. mind blown
Excellent overview on neural network architecture. Very interesting and worthwhile video.
Adore this free online schooling, thanks so much Steve!!
Glad you enjoy it! Thanks!
Gosh i needed this intro at the start of my seminar paper...
One of the most effective and useful introductory lectures on neural networks you can attend. It provides basic terminology and enables a good foundation for other lectures. HIGHLY RECOMMENDED. It would be helpful, Mr. Bunton, to say a little bit more about Neurons. Is a neuron strictly a LOGICAL function point in a process (my simple excel cell doing a logical function qualifies as a neuron with your definition), is it a PHYSICAL function point like a server, or is it both? Was there a reason you did not mention restricted Boltzmann motors? Thank you again, Sir, for the quality of this lecture.
A neuron is pure software, a computational unit that mimics the basic functions of a biological neuron. While software relies on specific hardware for execution, a neuron is not a simple server. Unlike an Excel cell, which takes a single input and produces a straightforward output, a neuron receives multiple inputs from other neurons, processes them, and generates an output based on the combined information.
Each input to a neuron is multiplied by a weight, a numerical value that represents the strength of the connection between the neurons. These weighted inputs are then summed together, and a bias value, representing an inherent offset, is added to the result. The resulting value is then passed through an activation function, which introduces non-linearity into the network's decision-making process. Activation functions, such as sigmoid and ReLU, transform the weighted input into the neuron's output, allowing the network to capture complex patterns and relationships in the data. ReLU is often used as an activation function because it requires less computational power compared to other activation functions, such as the sigmoid function.
Through a process called learning, artificial neurons adjust their weights over time, enabling the network to improve its performance on a given task. Algorithms like back propagation guide this learning process, allowing the network to minimize errors and optimize its decision-making capabilities.
Hope this helps.
Awesome concise high level explanation! Thank you
Liked that the approach was direct and simplistic; and of course you can write your code in this manner too. So that you're not overwhelmed. Say four or five layers being coded, then you have outboard functions that handle the input and out put arrays. This last might take up most of the landscape of a program. Isn't this fellow clever? Dang. He's gotta be a Professor somewhere. Many thanks. The computer training that I had gotten was very rudimentary, first in the 60s and then another drop in the mid 90s. Luckily there's YT where you can catch up. And after a while the 'training' starts to remind you of subliminal sorts of stuff. Maybe?
So youtube know that i am currently learning neural network and this video is appear in my recommendation ,great
I have been looking for this content a really long time. Thanks so much.
Clear, simple, effective. Thank you!
Also loved the graphic style. We're the images projected on a screen in front of you? Great result, I wish more people showed info this way
Best. I love your lecture. It explains problem in a simple way. Thank you so much.
Amazing time spent to understand the Networks a little more.
Amazing video and explication , focusing on key points is very interesting for such sciences, thank you a lot and keep doing that !
Loved neural nets since 1998 when I read a book which showed how 3 layer nets can solve difficult problems. In the 21st century the neural nets are magnificent and a credit to the brains of the human race. I am using a 21st century neural net myself and it's great. Hahahaha. Great video
Steve: nice talk,... many questions come up, I'll ask a few
1)Do you distinguish planar vs non-planar networks?
2)Do RNN(s) become unstable? They look like control system time dependent processes.
3)Has anyone applied Monte Carlo toward selection of topology of a NN, or toward the activation function selection,...?
Fascinating area to study.
TH-cam is trying to teach us about itself.
Hahaha. Good.
It's becoming sentient!
Even worse, it's a teenager who just wants to be understood. XD
This is a perfectly compressed overview of neural networks. What autoencoder did you use to write this?
Human brain
@@bunderbah Bruman hain
@@MilaPronto Humain bran
one hot encoder. lols
@@mbonuchinedu2420 That's like a robot trying to be funny
I like the way of explaining by projecting on glass board....very very nice...
Clear and concise. Thanks for posting.
Simple perfect enjoyable expaining of DNNs. Thanks for sharing!
He Steve, thank you a lot for all your brilliant videos! One request on the topic, could you please cover how all this works with shift/rotation/scale of the image? Nobody on youtube covers this tricky part of the neuron networks used for image recognition. I keep fingers crossed that you the one who could clarify this.
Oh wow I've been educated by your channel for a while now but did not realise you have published a textbook until your remark. Only A$80 here in Aus. Done! purchased..
I need to watch all the videos of this channel.
Strangely enough. I needed this vid. Thank you YT ALGO
thank you. i somehow get inspiration from videos like these.
Thank you too great video would they be building a quantum computer to be a single one of those dots to read internet transaction logs based on web page dynamics to filter and feed data across apps ?
ty YT, is all joy your latest state of recomendations
I guess neurones can be thought of a functions that call other functions if a certain variable has a sufficient value. And the main difference between an ANN and our biological neural network is that ANN has a fixed set of functions with fixed connections, only changing the conditions triggering the next callback, whereas brains can grow new neurones and even disconnect and rewire connections.
The question then becomes: Can we write a function that writes a new function? Or a function that modifies the content of an existing function so as to change its callback to call a different function? If this holds true, we could get even closer to natural neural networks.
I’m also debating myself when to use “artificial” vs “synthetic”. I guess an [A]NN can’t rewire/reprogram itself, whereas a real one can? In which case if we produce a neural network that indeed can change its own inner structure, we could promote it from “artificial” to “synthetic”?
Great video. Definitely earned yourself a subscriber. :)
I was actually actively looking for a video like this - it wasn’t just the Algorithm™️ 😂
I love this man. You are my role model.
Thanks so much!
@@Eigensteve OMG it's my honor😯.
I didn't expect you would read my comment lol. I hope I could get in to UW this fall so that I could be in your class in person.
Amazing good explanation and simple word for non english native speaker like me
Good overall neural net explanation!
Hi! I am medical doctor with little background on computing studies or mathematics but great interest in data and its use for medical research and patient's care. I am now drafting a booklet on Machine Learning for health care workers with no previous coding background and found this video extremely clear and helpful. Would you allow me to add a link to this video in the booklet?
Absolutely, that would be great!
Finally a good presentation
Thanks!
Love your videos and your book! Can't wait to start working through it actually!
Autoencoders are awesome because they don't require labeled data. The data is the label.
Glad I found this channel! Loved everything about this video.
Glad you enjoy it!
Thank you very much for this extraordinary way of teaching.
Thanks a lot to Steve and TH-cam for recommending this great video
Thanks for sharing Steve
Can I use your mathematical apparatus, to investigate the physical processes of Metaphysics??
I am looking for a mathematical apparatus capable of working with metaphysical phenomena, i.e. metamathematics!!
Great explanation. Thank you.
I really really really like the way you present- could you help me understand your set up?
There's a see-through glass that you draw on, there's a projector (i think) that's allowing you to see which part of the presentation you're in.
Plus the dark shirt enables me to just focus on your face, and your hands. It's a very intuitive interface for learning. Your hand gestures easily capture my eyes' attention.
Do please elaborate. Thanks!
Thanks for this explanation
Thank you is all I can say but it doesn't feel like enough for this
a fantastic overview thanks!!♥
Thank you for this beautiful explanation.. I really enjoy it.
Amazing video, thanks for the information
Really clear. Thanks for the vidéo !
simply great, thanks for this intro video
This video is brought to you by TH-cam’s great Neural M. Network.
Please upload a tutorial making of this video I will like to replicate your format for educational purposes
Great explanation. Thank you!
Thanks
Thanks for your explanation in the video. have learned a lot. Am doing research in speech emotion recognition. Can you pls tell me the best Deep learning algorithms that will work?
This was most helpful, very clear, thank you
Could you please do a follow up on this? I basically came here for the "many many more" you mentioned towards the end. LSTMs and other architectures that are useful for time series processing. It would be nice if you could do an overview video about that class of networks.
Great work on this video!
I really appreciate this talk, thank you.
A question. 3:20, what are f,g and h? I didn't see anything similar to these.
7:45 Can it be combined with a Decision Tree? I think it would be a good idea, and I have found some research that has a similar idea
Thank you so much! I needed this.
So youtube decided to make this 5 month old video famous? :D
all comments are max 2h old..
2 days later and I'm here haha
Could easily be that some person with alot of followers shared the video. Then it has more views which makes it a more reccomended video.
@@cyberneticbutterfly8506 so the WHOLE system is self aware?
@@jvsonyt Hardly. It's just a trigger. Person A with a high number of followers shares a video -> They then go watch the video -> The video view number increases -> IF video has increase in X views THEN bump video ranking in reccomendations by Y amount -> You now get it in your reccomendations.
@@cyberneticbutterfly8506 aliens
I don’t like the traditional sigmoid function as much. I did a performance test on both speed, loss, & accuracy on image classification, and tanh performed better on all three metrics compared to sigmoid (and ReLU ended up being better than tanh).
Me: Why am I watching a video on neural network architectures?
TH-cam: Start learning bitch
Such a great explanation, thank you
Great explanation Thank u Sir
Awesome 😎... well ☺️ i didn’t understand much but i think I could use as inspiration to Spinal Cord my Dark Matter.
5:34 What about Spiking Recurrent Neural Networks
generally SNN outperform RNN When it comes to problems that are changing times Although SNN He suffers from a weight problem, but isn't Spiking Recurrent Neural Networks It will be a better solution
love from India, sir.
Very nice explanation
TH-cam read my mind this was exactly what I was curious about
That encoder neural network could be used for encrypting data!
Yes ☺️
give lectures on the activation structures pls
TH-cam recommended it. But i love it.
4:00 How come some of those don't have output nodes?