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Teg

Teg is a differentiable programming language that includes an integral primitive, which allows for soundly optimizing integrals with discontinuous integrands. This is a research artifact for the paper: Systematically Differentiating Parametric Discontinuities. This repository contains the core library implementation, while the applications can be found at https://github.com/ChezJrk/teg_applications. The applications include image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs.

Installation Instructions

Teg requires Python 3.6+. To install Teg run:

git clone https://github.com/ChezJrk/Teg.git
cd Teg
pip install -e .

Illustrative Example

A minimal illustrative example is:

\frac{d}{dt} \int_{x = 0}^1 [x < t]

This is the integral of a step discontinuity that jumps from 1 to 0 at . If we set , then the result is 1, but discretizing before computing the derivative as is standard in differentiable programming languages (e.g., PyTorch and TensorFlow) results in a derivative of 0. Our language correctly models the interaction between the integral and the parametric discontinuity. In our language the implementation for this simple function is:

from teg import TegVar, Var, Teg, IfElse
from teg.derivs import FwdDeriv
from teg.eval.numpy_eval import evaluate

x, t = TegVar('x'), Var('t', 0.5)
expr = Teg(0, 1, IfElse(x < t, 1, 0), x)
deriv_expr = FwdDeriv(expr, [(t, 1)])
print(evaluate(deriv_expr))  # prints 1

Code Structure

Our implementation is in the teg folder:

  • derivs has the implementation of the source-to-source derivative including code for computing the forward and reverse derivatives in fwd_deriv.py and reverse_deriv.py respectively. Supported discontinuous functions are in the edge folder.
  • eval and include have all of the code for evaluating expressions either by interpreting locally in Python or compiling to C.
  • ir includes an intermediate representation useful in compiling code down to C.
  • lang includes the main language primitives with the base language in base.py and teg.py and the extended language (that has the Dirac delta function) is in extended.py.
  • maps and math specifies basic math libraries.
  • passes includes source-to-source compilation passes. Notably, reduce.py has the lowering code from the external language to the internal language.

We have a test folder with all of the systems tests.

Compiling to C

It is possible to compile Teg programs to C using python3 -m teg --compile --target C [[FILE NAME]].py. See teg/__main__.py for more options. To specify C compilation flags, use python3 -m teg --include-options.

Citation

@article{BangaruMichel2021DiscontinuousAutodiff,
  title = {Systematically Differentiating Parametric Discontinuities},
  author = {Bangaru, Sai and Michel, Jesse and Mu, Kevin and Bernstein, Gilbert and Li, Tzu-Mao and Ragan-Kelley, Jonathan},
  journal = {ACM Trans. Graph.},
  volume = {40},
  number = {107}, 
  pages = {107:1-107:17},
  year = {2021},
  publisher = {ACM},
}