tsalib 0.1.1.0

TSAlib: Support for Tensor Shape Annotations

Tensor Shape Annotations Library (tsalib)

Writing deep learning programs which manipulate multi-dimensional tensors (numpy, pytorch, keras, tensorflow, ...) requires you to carefully keep track of shapes of matrices/tensors. The Tensor Shape Annotation (TSA) library enables you to write first-class, library-independent, shape expressions over dimension variables to model matrix/tensor variable shapes. TSAs enable us to label and verify tensor variables shapes as well as write more fluent shape transformations and tensor operations. Using TSAs enhances code clarity, accelerates debugging and improves overall developer productivity when writing tensor programs. Detailed article here.

See updates here.

Introduction

Carrying around the tensor shapes in your head gets increasingly hard as programs become more complex, e.g., reshaping before a matmult, examining/modifying deep pre-trained architectures (resnet, densenet, elmo), designing new kinds of attention mechanisms (multi-head attention) or when creating a new RNN cell. There is no principled way of shape specification and tracking inside code -- most developers resort to writing adhoc comments embedded in code to keep track of tensor shapes (see code from google-research/bert).

tsalib comes to our rescue here. It allows you to write shape expressions over dimension variables describing the shape of tensor variables. These expressions can be used in multiple ways:

• as first-class annotations of tensor variables,
• to write symbolic shape assertions and tensor constructors
• to specify shape transformations (reshape, permute, expand) or tensor product operations (matmult) succinctly.

TSAs expose the typically invisible tensor shape types, leading to improved productivity across the board.

Dimension Variables

Tensor shape annotations (TSAs) are constructed using dimension variables --B (Batch), C (Channels), D (EmbedDim) -- and arithmetic expressions (B*2, C+D) over them. Using tsalib, you can define dimension variables customized to your architecture/program.

TSAs may be be represented as

• a tuple (B,H,D) [long form]
• a string 'b,h,d' (compact notation) (or simply 'bhd')

Here is an example snippet which uses TSAs in a pytorch program to define, transform and verify tensor shapes. TSAs work seamlessly with arbitrary tensor libraries: numpy, pytorch, keras, tensorflow, mxnet, etc.

from tsalib import dim_vars as dvs
from tsalib import view_transform as vt, permute_transform as pt

#declare dimension variables
B, C, H, W = dvs('Batch:32 Channels:3 Height:256 Width:256') 
...
#create tensors using dimension variables
x: (B, C, H, W) = torch.randn(B, C, H, W) 
#perform tensor transformations
x: (B, C, H // 2, W // 2) = maxpool(x) 
#check symbolic assertions over TSAs, without knowing concrete shapes
assert x.size() == (B, C, H // 2, W // 2)

#reshape/permute using shorthand (einsum-like) notation with placeholders
x = x.view(vt('_,_,k,l', '_,_,k*l', x.size()))
assert x.size() == (B, C, (H//2)*(W//2))

Shape annotations/assertions turn out to be useful in many ways.

• They help us to quickly verify the variable shapes when writing new transformations or modifying existing modules.
• Assertions and annotations remain the same even if the concrete dimension lengths change.
• Faster debugging: if you annotate-as-you-go, the tensor variable shapes are explicit in code, readily available for a quick inspection. No more adhoc shape printing when investigating obscure shape errors.
• Do shape transformations using shorthand notation and avoid unwanted shape surgeries.
• Use TSAs to improve code clarity everywhere, even in your machine learning data pipelines.
• They serve as useful documentation to help others understand or extend your module.

Installation

pip install tsalib

Getting Started

See tests/test.py and tests/test_ext.py for complete examples of basic and extended usage.

from tsalib import dim_var as dv, dim_vars as dvs
import numpy as np

Declare Dimension Variables, Expressions over them

B, C, D, H, W = dv('Batch'), dv('Channels'), dv('EmbedDim'), dv('Height'), dv('Width')
#or
B, C, D, H, W = dvs('Batch Channels EmbedDim Height Width')
#or declare dim vars with default integer values (optional)
B, C, D, H, W = dvs('Batch:48 Channels:3 EmbedDim:300 Height Width')
#or provide *shorthand* names for dim vars
B, C, D, H, W = dvs('Batch(b):48 Channels(c):3 EmbedDim(d):300 Height(h) Width(w)')

# TSAs are tuples over dimension variables
S1 = (B, C, D)
# we can always verify TSAs against concrete shapes
assert S1 == (48, 3, 300)

Use Dimension Variables to declare Tensors

Instead of scalar variables batch_size, embed_dim, use dimension variables B, D uniformly throughout your code.

B, D = dvs('Batch:48 EmbedDim:300')
#declare a 2-D tensor of shape(48, 300)
x = torch.randn(B, D)
#assertions over dimension variables (not exact values)
assert x.size() == (B, D)

Use TSAs to annotate variables on-the-go (Python 3)

a: (B, D) = np.array([[1., 2., 3.], [10., 9., 8.]]) #(Batch, EmbedDim): (2, 3)

b: (2, B, D) = np.stack([a, a]) #(2, Batch, EmbedDim): (2, 2, 3)

Arithmetic over dimension variables is supported. This enables easy tracking of shape changes across neural network layers.

v: (B, C, H, W) = torch.randn(B, C, h, w)
x : (B, C * 2, H//2, W//2) = torch.nn.conv2D(C, C*2, ...)(v) 

Use TSAs to make matrix operations compact and explicit

Avoid explicit shape computations for reshaping. Use tsalib.view_transform to specify view changes declaratively.

    x = np.ones((B, T, D))
    new_shape = view_transform(src=(B,T,D), to=(B,T,4,D//4), in_shape=x.shape)
    x = x.reshape(new_shape) #(20, 10, 300) -> (20, 10, 4, 75)

    from tsalib import view_transform as vt
    #or, compact form:
    x = x.reshape(vt('btd', 'b,t,4,d//4', x.shape))
    #or, super-compact, using dimension placeholders:
    x = x.reshape(vt(',,d', ',,4,d//4', x.shape))

Similarly, use tsalib.permute_transform to compute permutation index order (no manual guess-n-check) from a declarative spec.

    perm_indices = permute_transform(src=(B,T,D,K), to=(D,T,B,K)) #(2, 1, 0, 3)
    x = x.transpose(perm_indices) #(10, 50, 300, 30) -> (300, 50, 10, 30)

    from tsalib import permute_transform as pt
    #or, compactly:
    x = x.transpose(pt('btdk', 'dtbk'))
    #or, super-compact:
    x = x.transpose(pt('b_d_', 'd_b_'))

Use dimension names instead of cryptic indices.

ax = (2, B, D).index(B) #ax = 1
c: (2, D) = np.mean(b, axis=ax) 
print(f'after mean along axis {B}={ax}: {(2,D)}: {c.shape}') #... axis Batch=1: (2, EmbedDim): (2, 3)

See tests/test.py and tests/test_ext.py for complete examples of basic and extended usage.

Examples

The examples directory contains TS annotations of a few well-known, complex neural architectures: Resnet, OpenAI Transformer. With TSAs, we can gain deeper and immediate insight into how the module works by scanning through the forward function.

Dependencies

sympy. A library for building symbolic expressions in Python.

Tested with Python 3.6. For writing type annotations inline, Python >= 3.5 is required.

Python >= 3.5 allows optional type annotations for variables. These annotations do not affect the program performance in any way.

Documentation

Full docs coming soon!

References

• Blog article introducing TSA.
• A proposal for designing a tensor library with named dimensions from ground-up. The TSA library takes care of some use cases, without requiring any change in the tensor libraries.
• Pytorch Issue on Names Axes here.
• Using einsum for tensor operations improves productivity and code readability. blog
• The Tile DSL uses indices ranging over dimension variables to write compact, library-independent tensor operations.
• The datashape library introduces a generic type system and grammar for structure data. tsalib focuses on shapes of homogeneous tensor data types only, with arithmetic support.

Contributors

Nishant Sinha, OffNote Labs. @medium, @twitter

Change Log

• [9 Nov 2018] Support for shorthand notation in view/permute/expand transforms.
• [9 Nov 2018] Support for using TSA in assertions and tensor constructors (cast to integers).
• [25 Oct 2018] Initial Release