einops
Flexible and powerful tensor operations for readable and reliable code. Supports numpy, pytorch, tensorflow, and. Examples:
Tutorial / Documentation
Tutorial is the most convenient way to see einops
in action (and right now works as a documentation)
- part 1: einops fundamentals
- part 2: einops for deep learning
- part 3: TBD
Installation
Plain and simple:
pip install einops
einops
has no mandatory dependencies (code examples also require jupyter, pillow + backends). To obtain the latest github version
pip install https://github.com/arogozhnikov/einops/archive/master.zip
API
einops
has minimalistic and powerful API.
Two operations provided (see einops tutorial for examples)
from einops import rearrange, reduce # 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)
And two corresponding layers ( einops
keeps separate version for each framework) with the same API.
from einops.layers.chainer import Rearrange, Reduce from einops.layers.gluon import Rearrange, Reduce from einops.layers.keras import Rearrange, Reduce from einops.layers.torch import Rearrange, Reduce
Layers behave similarly to operations and have same parameters (for the exception of first argument, which is passed during call)
layer = Rearrange(pattern, **axes_lengths) layer = Reduce(pattern, reduction, **axes_lengths) # apply created layer to a tensor / variable x = layer(x)
Example of using layers within a model:
# example given for pytorch, but code in other frameworks is almost identical from torch.nn import Sequential, Conv2d, MaxPool2d, Linear, ReLU from einops.layers.torch import Reduce model = Sequential( Conv2d(3, 6, kernel_size=5), MaxPool2d(kernel_size=2), Conv2d(6, 16, kernel_size=5), MaxPool2d(kernel_size=2), # flattening Rearrange('b c h w -> b (c h w)'), Linear(16*5*5, 120), ReLU(), Linear(120, 10), )
Additionally two auxiliary functions provided
from einops import asnumpy, parse_shape # einops.asnumpy converts tensors of imperative frameworks to numpy numpy_tensor = asnumpy(input_tensor) # einops.parse_shape gives a shape of axes of interest parse_shape(input_tensor, 'batch _ h w') # e.g {'batch': 64, 'h': 128, 'w': 160}
Naming and terminology
einops
stays 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 by numpy.einsum
operation).
- Terms
tensor
andndarray
are equivalently used and refer to multidimensional array - Terms
axis
anddimension
are also equivalent
Why using einops
notation
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 in some context, second one provides information about input and output. In other words, einops
focuses on interface: what is input and output , not how output is computed.
The next operation looks similar:
y = rearrange(x, 'time c h w -> time (c h w)')
But it gives reader a hint: this is not an independent batch of images we are processing, but rather a sequence (video).
Semantic information makes code easier to read and maintain.
More 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)')
second line checks that input has four dimensions, but you can also specify particular dimensions. That's opposed to just writing comments about shapes since comments don't work as we know
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 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, since usually it makes no difference, but it can make a big difference (e.g. if you use grouped convolutions on 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 dx) -> b c x y', 'max', dx=2, dy=3) reduce(x, 'b c (x dx) (y dx) (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 all are defined in a uniform way.
Space-to-depth and depth-to space are defined in many frameworks. But how about width-to-height?
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)
Suppose x
shape was (3, 4, 5)
, then y
has shape ...
(60,) (3, 20)
Supported frameworks
Einops works with ...
- numpy
- pytorch
- tensorflow eager
- cupy
- chainer
- gluon
- tensorflow
- mxnet (experimental)
- and keras (experimental)
Contributing
Best ways to contribute are
- spread the word about
einops
- prepare a guide/post/tutorial for your favorite deep learning framework
- translating examples in languages other than English is also a good idea
- use
einops
notation in your papers to strictly define used operations
Supported python versions
einops
works with python 3.5 or later.
There is nothing specific to python 3 in the code, we simply need to move further and I decided not to support python 2.