Einsum Is All You Need: NumPy, PyTorch and TensorFlow 

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

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

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

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

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

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.

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

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

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 .

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

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

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

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

Insane brother, excellent just excellent

nice explanation, very clear! thanks!

Thanks, a perfect explanation.

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.

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

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

Thanks a lot. it saves my day

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]

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 ->.

Great video thanks :)

Helt otroligt

einsum to rule them all, indeed.

What a nice video !

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

will einsen work for model parallelism in keras models?

Great explanation! click

awesome

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

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

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

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

cool

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

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

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

Does einsum mess the auto-differentiation of TensorFlow

are you considering doing an another video on advanced einsum?

thanks for awesome explanation

Thanx! This one is very useful!

Thank you for sharing this!

nicely done

Very cool!

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