FunFact: Build Your Own Tensor Decomposition Model in a Breeze

FunFact is a Python package that aims to simplify the design of matrix and tensor factorization algorithms. It features a powerful programming interface that augments the NumPy API with Einstein notations for writing concise tensor expressions. Given an arbitrary forward calculation scheme, the package will solve the corresponding inverse problem using stochastic gradient descent, automatic differentiation, and multi-replica vectorization. Its application areas include quantum circuit synthesis, tensor decomposition, and neural network compression. It is GPU- and parallelization-ready thanks to modern numerical linear algebra backends such as JAX/TensorFlow and PyTorch.

Installation

• To use FunFact with the JAX backend:

  pip install "funfact[jax]"
  

• To use FunFact with the PyTorch backend:

  pip install "funfact[torch]"
  

Running the command as above will install the version of the respective packages hosted on PyPI. Please refer to the installation page for more details on installation options.

FunFact can also be installed with the NumPy backend, which only supports forward calculations. The NumPy backend doesn't support automatic differentiation and is not able to optimize tensor expressions for methods such as funfact.factorize.

pip install -U funfact  # does not install JAX or PyTorch

Quick start example: semi-nonnegative CP decomposition

Package import:

import funfact as ff
import numpy as np

Create target tensor:

T = np.arange(60, dtype=np.float32).reshape(3, 4, 5); T

Define abstract tensors and indices:

R = 2
a = ff.tensor('a', T.shape[0], R, prefer=ff.conditions.NonNegative())
b = ff.tensor('b', T.shape[1], R)
c = ff.tensor('c', T.shape[2], R)
i, j, k, r = ff.indices('i, j, k, r')

Create a tensor expression (only specifies the algebra but does not carry out the computation immediately):

tsrex = (a[i, ~r] * b[j, r]) * c[k, r]; tsrex

Find rank-2 approximation:

>>> fac = ff.factorize(tsrex, T, max_steps=1000, vec_size=8, penalty_weight=10)
>>> fac.factors
100%|██████████| 1000/1000 [00:03<00:00, 304.00it/s]
<'data' fields of tensors a, b, c>

Reconstruction:

>>> fac()
DeviceArray([[[-0.234,  0.885,  2.004,  3.123,  4.243],
              [ 4.955,  5.979,  7.002,  8.025,  9.049],
              [10.145, 11.072, 12.   , 12.927, 13.855],
              [15.335, 16.167, 16.998, 17.83 , 18.661]],

             [[20.025, 21.014, 22.003, 22.992, 23.981],
              [25.019, 26.01 , 27.001, 27.992, 28.983],
              [30.013, 31.006, 31.999, 32.992, 33.985],
              [35.007, 36.002, 36.997, 37.992, 38.987]],

             [[40.281, 41.14 , 41.999, 42.858, 43.716],
              [45.082, 46.04 , 46.999, 47.958, 48.917],
              [49.882, 50.941, 51.999, 53.058, 54.117],
              [54.682, 55.841, 56.999, 58.158, 59.316]]], dtype=float32)

Examine factors:

>>> fac['a']
DeviceArray([[1.788, 1.156],
             [3.007, 0.582],
             [4.226, 0.008]], dtype=float32)

>>> fac['b']
DeviceArray([[-2.923, -4.333],
             [-3.268, -3.541],
             [-3.614, -2.749],
             [-3.959, -1.957]], dtype=float32)

>>> fac['c']
DeviceArray([[-3.271,  3.461],
             [-3.341,  3.309],
             [-3.41 ,  3.158],
             [-3.479,  3.006],
             [-3.548,  2.855]], dtype=float32)

How to cite

If you use this package for a publication (either in-paper or electronically), please cite it using the following DOI: https://doi.org/10.11578/dc.20210922.1

Contributors

Current developers:

• Yu-Hang "Maxin" Tang
• Daan Camps

Previou contributors:

• Elizaveta Rebrova

Copyright

FunFact Copyright (c) 2021, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from the U.S. Dept. of Energy). All rights reserved.

If you have questions about your rights to use or distribute this software, please contact Berkeley Lab's Intellectual Property Office at [email protected].

NOTICE. This Software was developed under funding from the U.S. Department of Energy and the U.S. Government consequently retains certain rights. As such, the U.S. Government has been granted for itself and others acting on its behalf a paid-up, nonexclusive, irrevocable, worldwide license in the Software to reproduce, distribute copies to the public, prepare derivative works, and perform publicly and display publicly, and to permit others to do so.

Funding Acknowledgment

This work was supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under U.S. Department of Energy Contract No. DE-AC02-05CH11231.