Potto is a differentiable programming language that has an integral primitive and supports separate compilation. This repository contains the core library implementation, while the applications can be found at https://github.com/divicomp/potto_applications. The applications include differentiating a ray tracing renderer.

This is experimental research code. The goal of this repo is to validate the ideas in the paper.

Potto requires Python 3.10+. To install Potto, run:

gh repo clone martinjm97/potto
cd potto
pip install -e .

We present the example depicted in Figure 1 of the paper:

,

which is the derivative of the integral of a jump discontinuity that is 1 if x <= t and 0 otherwise.

At t=0.5, the correct answer is 1. However, discretizing before computing the derivative as is standard in differentiable programming languages (e.g., PyTorch and TensorFlow) results in a derivative of 0.

In Potto, we can implement this example with:

from potto import Const, Var, TegVar, IfElse, FlipShift, Int, BoundedLebesgue
from potto import deriv, evaluate, VarVal

# Declare the variable of integration, variable, and infinitesimal
x, t, dt = TegVar("x"), Var("t"), Var("dt")

# integral from 0 to 1 of (if t - x >= 0 then 1 else 0) dx
integrand = IfElse(FlipShift((t,), (x,)), Const(1), Const(0))
mu = BoundedLebesgue(0, 1, x)
expr = deriv(Int(integrand, mu), {t.name: dt.name})

# Evaluate the derivative of the integral at t = 0.5, dt = 1
ctx = VarVal({t.name: 0.5, dt.name: 1})
print("Dₜ∫₀¹ [x ≤ t] dx at t=0.5 is", evaluate(expr, ctx))

The potto folder contains the core implementation. We break the implementation into pieces:

• ir contains the code for an IR lowering that we do to abstract diffeomorphisms outside of Dirac deltas and conditionals, as well as add more information to diffeomorphisms to make evaluation easier.
• lang contains the core language implementation such as the grammar, evaluator, and derivative code.
• libs contains useful libraries for diffeomorphisms, measures, and math operators.
• tests contains the tests for Potto.

You can reproduce Figures 2 and 3 by running case_study/plot_normal.py and case_study/figure3.py --plot. You can rerun the experiment in Figure 3 by running case_study/figure3.py --run.

@article{Michel2024Potto,
    title     = {Distributions for Compositionally Differentiating Parametric Discontinuities},
    author    = {Michel, Jesse and Mu, Kevin and Yang, Xuanda and Bangaru, Sai and Collins, Elias Rojas and Bernstein, Gilbert and Ragan-Kelley, Jonathan and Carbin, Michael and Li, Tzu-Mao},
    booktitle = {Object-Oriented Programming, Systems, Languages & Applications},
    year      = {2024}
}