Einsum Is All You Need: NumPy, PyTorch and TensorFlow

[@udbhavprasad3521]

Honestly, there is no channel that even compares to this level of quality

[@matt.jordan]

This is literally insane how well you explained this I instantly subbed you deserve so much more attention

[@AladdinPersson]

Wow thanks :)

[@qiguosun129]

This is literally the best and simplest explanation I ever had, thanks.

[@johngrabner]

Another perfect video. Most valuable because it provides a foundation for your other video. Can't wait for your next einsum video.

[@AladdinPersson]

Really appreciate your comment! :)

[@rajanalexander4949]

Excellent tutorial of a very useful but sometimes confusing feature in NumPy. I would only add that " . . . " is syntactic sugar for omitting a bunch of indices.

[@mayankkamboj4025]

Wow, I finally get einsum ! Thank you so much. And that lotr reference was good.

[@SantoshGupta-jn1wn]

One of the most important videos I've ever seen.

[@stacksmasherninja7266]

It almost felt like you implemented these functions yourself in those libraries ! Great video

[@iva1389]

i had to translate it to tensorflow :) very useful video for practice. thank you!

[@kenzhebektaniyev8180]

cool! tbh I didn't believe you could explain it but you did

[@CrazyProgrammer16]

Hey, but why does "i,j->ij" also have a product??? Here in the input nothing is repeating. Are there other rules?

[@rekeshwardhanani920]

Insane brother, excellent just excellent

[@thecros1076]

Learnt something new today❤️❤️, ...I always had a question how and were did you learn everything?

[@AladdinPersson]

I don't know all of this stuff. I research everything to try to make every video as good as I possible can so the process is usually that I learn something in depth and then decide to share it with you guys

[@thecros1076]

@@AladdinPersson ❤️❤️❤️loved all of your videos ... hardwork and talent is a deadly combination ....hope to see new project videos soon❤️

[@haideralishuvo4781]

Awesome , Your channel is so underrated . Was struggling for a good channel to learn about pytorch ,Thanksfully got yours :D Can you cover pix2pix , cycleGAN , RCNN's ? Would be greatful if you do .

[@AladdinPersson]

Appreciate you 👊 Many people have requested that so it's coming but can't promise when :)

[@iskhwa]

Thanks, a perfect explanation.

[@francesco_savi]

nice explanation, very clear! thanks!

[@johnj7883]

Thanks a lot. it saves my day

[@iva1389]

einsum to rule them all, indeed.

[@Han-ve8uh]

One thing that wasn't mentioned in the video that i realized halfway through is sometimes einsum is used on 1 operand while sometimes on 2. I tried "torch.einsum('ii->i', t,t)" and got "RuntimeError: einsum(): more operands were provided than specified in the equation". This tells me that the number of operands must correspond to the number of comma separated indexes on left hand side of ->.

[@ALVONIUM]

Helt otroligt

[@valeriusevanligasetiawan6967]

This is great, I just wanna know however, if I can do FFT of Green function using einsum. Note: been trying for a week to implement the code, never got the correct result.

[@cassenav]

Great video thanks :)

[@iva1389]

gives me error while matrix-vector multipication: torch.einsum("ij, kj->ik", x, v) einsum(): operands do not broadcast with remapped shapes [original->remapped]: [2, 5]->[2, 1, 5] [1, 3]->[1, 1, 3] same in tf Expected dimension 5 at axis 1 of the input shaped [1,3] but got dimension 3 [Op:Einsum]

[@Raghhuveer]

How does it compare in terms of performance and efficiency to standard numpy function calls?

[@danyalzia6958]

So, basically einsum is the DSL that is shared between these libraries, right?

[@Choiuksu]

What a nice video !

[@AladdinPersson]

Thank you so much :)

[@jeanchristophe15]

I am not sure the "Batch matrix multiplication" example is correct, because i is used twice.

[@gtg238s]

Great explanation! click

[@AladdinPersson]

Thank you so much! :)

[@SAINIVEDH]

can someone explain how matrix diagonal is "ii->i" ?

[@ericmink]

I think it's because if you wrote it as a nested loop, then you would loop over all rows with a variable `i`, and for the columns you would reuse the same variable (every entry at coordinates (i,i) is on the diagonal). Now for the result, if you left the `i` out it would sum the diagonal elements up. If you have it in there, it will create a list instead.

[@AlbertMunda]

awesome

[@alfahimmohammad]

will einsen work for model parallelism in keras models?

[@AladdinPersson]

I haven't tried that but I would imagine that it works

[@alfahimmohammad]

@@AladdinPersson I tried it. It wasn't good. I was better off with manually assigning each layer to each GPU in pytorch

[@hieunguyentrung8987]

np.einsum('ik,kj->ij', x,y) is actually much much slower than np.dot(x,y) when the matrix size gets larger Also tf.einsum is slightly slower than tf.matmul but torch.einsum is slightly faster than torch.matmul... Only from a perspective of the configuration of my laptop though

[@misabic1499]

Hi. Your model building from scratch tutorials are really helpful. Eagerly waiting for more tutorials to come. I really appreciate it!

[@AladdinPersson]

I appreciate the kind words! Any video in particular that you thought were good and do you have any specific suggestions for the future?

[@leonardmensahboante4308]

@@AladdinPersson Please do a video on python hooks, thus how to use pre-trained model as the encoder to the UNET architectures for image segmentation.

[@gauravmenghani4]

Lovely. I always found einsum non-intuitive. Learnt a lot! Thanks :)

[@ripsirwin1]

This is so difficult to understand I don't know if I'll ever get it.

[@AladdinPersson]

Sorry, maybe I didn't explain it good enough:/

[@ripsirwin1]

@@AladdinPersson no you're great. I just have to work at it

[@AndyLee-xq8wq]

cool

[@parasharchatterjee3223]

It's the Einstein summation convention that's used in physics very commonly, and just removes the clunky summation sign in pages long calculations!

[@epolat19]

Does einsum mess the auto-differentiation of TensorFlow

[@michaelmoran9020]

Are the "free indicies" part of standard einstein notation or something made up to allow you to exclude array dimensions from the einsum entirely?

[@javidhesenov7611]

thanks for awesome explanation

[@deoabhijit5935]

are you considering doing an another video on advanced einsum?

[@leofh1917]

Thanx! This one is very useful!

[@minma02262]

Thank you for sharing this!

[@rockapedra1130]

Very cool!

[@jamgplus334]

nicely done

[@MorisonMs]

3:37 (Outer product) there is no need to sum, simply M[i,j] = A[i,k]*B[k,j]

[@lewis2865]

It's matrix multiplication