einops_video.mp4

einops

Flexible and powerful tensor operations for readable and reliable code.
Supports numpy, pytorch, tensorflow, jax, andothers.

Recent updates:

• 0.8.0: tinygrad backend added, small fixes
• 0.7.0: no-hassletorch pile,support ofarray api standardand more
• 10'000🎉: github reports that more than 10k project use einops
• einops 0.6.1: paddle backend added
• einops 0.6 introducespacking and unpacking
• einops 0.5: einsum is now a part of einops
• Einops paperis accepted for oral presentation at ICLR 2022 (yes, it worth reading). Talk recordings areavailable

Previous updates

- flax and oneflow backend added - torch.jit.script is supported for pytorch layers - powerful EinMix added to einops. [Einmix tutorial notebook](https://github /arogozhnikov/einops/blob/master/docs/3-einmix-layer.ipynb)

Tweets

In case you need convincing arguments for setting aside time to learn about einsum and einops... Tim Rocktäschel

Writing better code with PyTorch and einops 👌 Andrej Karpathy

Slowly but surely, einops is seeping in to every nook and cranny of my code. If you find yourself shuffling around bazillion dimensional tensors, this might change your life Nasim Rahaman

More testimonials

Contents

• Installation
• Documentation
• Tutorial
• API micro-reference
• Why use einops
• Supported frameworks
• Citing
• Repositoryanddiscussions

Installation

Plain and simple:

pip install einops

Tutorials

Tutorials are the most convenient way to seeeinopsin action

• part 1:einops fundamentals
• part 2:einops for deep learning
• part 3:packing and unpacking
• part 4:improve pytorch code with einops

Kapil Sachdeva recorded a smallintro to einops.

API

einopshas a minimalistic yet powerful API.

Three core operations provided (einops tutorial shows those cover stacking, reshape, transposition, squeeze/unsqueeze, repeat, tile, concatenate, view and numerous reductions)

fromeinopsimportrearrange,reduce,repeat
# rearrange elements according to the pattern
output_tensor=rearrange(input_tensor,'t b c -> b c t')
# combine rearrangement and reduction
output_tensor=reduce(input_tensor,'b c (h h2) (w w2) -> b h w c','mean',h2=2,w2=2)
# copy along a new axis
output_tensor=repeat(input_tensor,'h w -> h w c',c=3)

Later additions to the family arepackandunpackfunctions (better than stack/split/concatenate):

fromeinopsimportpack,unpack
# pack and unpack allow reversibly 'packing' multiple tensors into one.
# Packed tensors may be of different dimensionality:
packed,ps=pack([class_token_bc,image_tokens_bhwc,text_tokens_btc],'b * c')
class_emb_bc,image_emb_bhwc,text_emb_btc=unpack(transformer(packed),ps,'b * c')

Finally, einops provides einsum with a support of multi-lettered names:

fromeinopsimporteinsum,pack,unpack
# einsum is like... einsum, generic and flexible dot-product
# but 1) axes can be multi-lettered 2) pattern goes last 3) works with multiple frameworks
C=einsum(A,B,'b t1 head c, b t2 head c -> b head t1 t2')

EinMix

EinMixis a generic linear layer, perfect for MLP Mixers and similar architectures.

Layers

Einops provides layers (einopskeeps a separate version for each framework) that reflect corresponding functions

fromeinops.layers.torchimportRearrange,Reduce
fromeinops.layers.tensorflowimportRearrange,Reduce
fromeinops.layers.flaximportRearrange,Reduce
fromeinops.layers.paddleimportRearrange,Reduce
fromeinops.layers.chainerimportRearrange,Reduce

Example of using layers within a pytorch model

Example given for pytorch, but code in other frameworks is almost identical

fromtorch.nnimportSequential,Conv2d,MaxPool2d,Linear,ReLU
fromeinops.layers.torchimportRearrange

model=Sequential(
...,
Conv2d(6,16,kernel_size=5),
MaxPool2d(kernel_size=2),
# flattening without need to write forward
Rearrange('b c h w -> b (c h w)'),
Linear(16*5*5,120),
ReLU(),
Linear(120,10),
)

No more flatten needed!

Additionally, torch users will benefit from layers as those are script-able and compile-able.

Naming

einopsstands for Einstein-Inspired Notation for operations (though "Einstein operations" is more attractive and easier to remember).

Notation was loosely inspired by Einstein summation (in particular bynumpy.einsumoperation).

Why useeinopsnotation?!

Semantic information (being verbose in expectations)

y=x.view(x.shape[0],-1)
y=rearrange(x,'b c h w -> b (c h w)')

While these two lines are doing the same job insomecontext, the second one provides information about the input and output. In other words,einopsfocuses on interface:what is the input and output,nothowthe output is computed.

The next operation looks similar:

y=rearrange(x,'time c h w -> time (c h w)')

but it gives the reader a hint: this is not an independent batch of images we are processing, but rather a sequence (video).

Semantic information makes the code easier to read and maintain.

Convenient checks

Reconsider the same example:

y=x.view(x.shape[0],-1)# x: (batch, 256, 19, 19)
y=rearrange(x,'b c h w -> b (c h w)')

The second line checks that the input has four dimensions, but you can also specify particular dimensions. That's opposed to just writing comments about shapes since comments don't prevent mistakes, not tested, and without code review tend to be outdated

y=x.view(x.shape[0],-1)# x: (batch, 256, 19, 19)
y=rearrange(x,'b c h w -> b (c h w)',c=256,h=19,w=19)

Result is strictly determined

Below we have at least two ways to define the depth-to-space operation

# depth-to-space
rearrange(x,'b c (h h2) (w w2) -> b (c h2 w2) h w',h2=2,w2=2)
rearrange(x,'b c (h h2) (w w2) -> b (h2 w2 c) h w',h2=2,w2=2)

There are at least four more ways to do it. Which one is used by the framework?

These details are ignored, sinceusuallyit makes no difference, but it can make a big difference (e.g. if you use grouped convolutions in the next stage), and you'd like to specify this in your code.

Uniformity

reduce(x,'b c (x dx) -> b c x','max',dx=2)
reduce(x,'b c (x dx) (y dy) -> b c x y','max',dx=2,dy=3)
reduce(x,'b c (x dx) (y dy) (z dz) -> b c x y z','max',dx=2,dy=3,dz=4)

These examples demonstrated that we don't use separate operations for 1d/2d/3d pooling, those are all defined in a uniform way.

Space-to-depth and depth-to space are defined in many frameworks but how about width-to-height? Here you go:

rearrange(x,'b c h (w w2) -> b c (h w2) w',w2=2)

Framework independent behavior

Even simple functions are defined differently by different frameworks

y=x.flatten()# or flatten(x)

Supposex's shape was(3, 4, 5),thenyhas shape...

• numpy, pytorch, cupy, chainer:(60,)
• keras, tensorflow.layers, gluon:(3, 20)

einopsworks the same way in all frameworks.

Independence of framework terminology

Example:tilevsrepeatcauses lots of confusion. To copy image along width:

np.tile(image,(1,2))# in numpy
image.repeat(1,2)# pytorch's repeat ~ numpy's tile

With einops you don't need to decipher which axis was repeated:

repeat(image,'h w -> h (tile w)',tile=2)# in numpy
repeat(image,'h w -> h (tile w)',tile=2)# in pytorch
repeat(image,'h w -> h (tile w)',tile=2)# in tf
repeat(image,'h w -> h (tile w)',tile=2)# in jax
repeat(image,'h w -> h (tile w)',tile=2)# in cupy
... (etc.)

Testimonialsprovide users' perspective on the same question.

Supported frameworks

Einops works with...

• numpy
• pytorch
• tensorflow
• jax
• cupy
• chainer
• tf.keras
• flax(experimental)
• paddle(experimental)
• oneflow(community)
• tinygrad(community)

Additionally, starting from einops 0.7.0 einops can be used with any framework that supportsPython array API standard,which includes

• numpy>=2.0
• MLX,afterml-explore/mlx#1289

Citing einops

Please use the following bibtex record

@inproceedings{
rogozhnikov2022einops,
title={Einops: Clear and Reliable Tensor Manipulations with Einstein-like Notation},
author={Alex Rogozhnikov},
booktitle={International Conference on Learning Representations},
year={2022},
url={https://openreview.net/forum?id=oapKSVM2bcj}
}

Supported Python versions

einopsworks with Python 3.8 or later.