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} }, "cell_type": "markdown", "id": "1dd8730c-ab92-43f9-b2ff-c894b1dc7ea5", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# correctionlib-gradients @ AGC Demo Day 30/11/2023\n", "\n", "### Enrico Guiraud with help from Nick Smith and Lukas Heinrich\n", "\n", "![image.png](attachment:2aae49a8-aafb-4212-b2d2-ab45603a896b.png)" ] }, { "cell_type": "markdown", "id": "478c5a98-b143-4619-9e01-c39b0b6c71d0", "metadata": { "editable": true, "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "## What\n", "\n", "A [JAX](https://jax.readthedocs.io)-friendly, autodifferentiable, Python-only implementation of a subset of [correctionlib](https://github.com/cms-nanoAOD/correctionlib) correction evaluations.\n", "\n", "If you don't know what these terms mean, for the purposes of this presentation:\n", "- automatic differentiation aka autodiff is a method to compute gradients of numerical functions: `f(x) -> df/dx(x)`\n", "- [JAX](https://jax.readthedocs.io) is (among other things) a Python tool to make functions that operate on arrays autodifferentiable\n", "- [correctionlib](https://github.com/cms-nanoAOD/correctionlib) is a JSON-based schema for HEP corrections as well as the reference implementation for the evaluation of those corrections, by Nick Smith\n", "\n", "As an exercise, I tried to follow recommendations from https://learn.scientific-python.org as closely as possible when working on the project." ] }, { "cell_type": "markdown", "id": "346436dd-5a95-4634-8d23-30b3f6ab9ed1", "metadata": { "editable": true, "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "## Why\n", "\n", "To enable autodifferentiation of full HEP analysis pipelines, we need to make each component of the pipeline autodifferentiable.\n", "\n", "This project makes one more piece of the pipeline autodifferentiable, namely correction evaluation." ] }, { "cell_type": "markdown", "id": "48277513-8874-4db5-ba2b-d4b834812cd4", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Installation\n", "\n", "```console\n", "pip install correctionlib-gradients\n", "```" ] }, { "cell_type": "markdown", "id": "71b00eab-55c7-4c2b-ab60-f48bea6f5114", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Example usage" ] }, { "cell_type": "code", "execution_count": 1, "id": "08ede0d6-dcb6-4b7e-82a3-c5ad2c8cea17", "metadata": { "editable": true, "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "import jax\n", "\n", "from correctionlib import schemav2\n", "from correctionlib_gradients import CorrectionWithGradient" ] }, { "cell_type": "markdown", "id": "27e0cd9f-571a-471e-b5d4-6396edc03b47", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Given a correctionlib schema (which can be deserialized from JSON using correctionlib)..." ] }, { "cell_type": "code", "execution_count": 2, "id": "4f208dcd-fea1-40bd-be03-5d9eac20c354", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "formula_schema = schemav2.Correction(\n", " name=\"RMS of x and y\",\n", " version=2,\n", " inputs=[schemav2.Variable(name=\"x\", type=\"real\"), schemav2.Variable(name=\"y\", type=\"real\")],\n", " output=schemav2.Variable(name=\"a scale\", type=\"real\"),\n", " data=schemav2.Formula(\n", " nodetype=\"formula\",\n", " expression=\"sqrt((x * x + pow(y, 2)) / 2)\",\n", " parser=\"TFormula\",\n", " variables=[\"x\", \"y\"],\n", " ),\n", ")" ] }, { "cell_type": "markdown", "id": "da442dd1-68ab-4745-a5e9-ed683d42cae1", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "...construct a `CorrectionWithGradient` object and you are done:" ] }, { "cell_type": "code", "execution_count": 3, "id": "6b463ead-1677-46b2-9cf0-4a0acf66b6d2", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "corr = CorrectionWithGradient(formula_schema)" ] }, { "cell_type": "markdown", "id": "4d41ac6e-c2a5-4e20-b5a5-c1aa426820c5", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "You can use c.evaluate as a JAX-friendly, auto-differentiable function that composes with any other JAX-friendly operation:" ] }, { "cell_type": "code", "execution_count": 4, "id": "15d73f61-3424-403f-9f05-c93d7cf09603", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "value = Array(0.70710677, dtype=float32, weak_type=True)\n", "df/dx = 0.0\n", "df/dy = 0.7071067690849304\n" ] } ], "source": [ "df = jax.value_and_grad(corr.evaluate, argnums=[0, 1])\n", "\n", "value, grad = df(0.0, 1.0)\n", "print(f\"{value = }\\ndf/dx = {grad[0]}\\ndf/dy = {grad[1]}\")" ] }, { "cell_type": "markdown", "id": "1701207a-57f0-4401-a429-b10637bbba8c", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "`jax.jit` works too (for Formulas; WIP on Binning):" ] }, { "cell_type": "code", "execution_count": 5, "id": "9f1207a8-a3df-4379-955e-7b1dc99211ee", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "value = Array(0.70710677, dtype=float32, weak_type=True)\n", "df/dx = 0.0\n", "df/dy = 0.7071067690849304\n" ] } ], "source": [ "jitted_df = jax.jit(jax.value_and_grad(corr.evaluate, argnums=[0, 1]))\n", "\n", "value, grad = jitted_df(0.0, 1.0)\n", "print(f\"{value = }\\ndf/dx = {grad[0]}\\ndf/dy = {grad[1]}\")" ] }, { "cell_type": "markdown", "id": "51cb097d-5c87-4507-9388-ca9fbbd41ccc", "metadata": {}, "source": [ "`jax.vmap` can be used to vectorize the evaluation over multiple rows of inputs:" ] }, { "cell_type": "code", "execution_count": 6, "id": "20dcc6a5-cb2d-4ed4-8a89-2fb51ff66179", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "value = Array([0.70710677, 0.70710677], dtype=float32)\n", "df/dx = [0. 0.70710677]\n", "df/dy = [0.70710677 0. ]\n" ] } ], "source": [ "xs = jax.numpy.array([0.0, 1.0])\n", "ys = jax.numpy.array([1.0, 0.0])\n", "\n", "vec_df = jax.vmap(jax.jit(jax.value_and_grad(corr.evaluate, argnums=[0, 1])))\n", "\n", "value, grad = vec_df(xs, ys)\n", "\n", "print(f\"{value = }\\ndf/dx = {grad[0]}\\ndf/dy = {grad[1]}\")" ] }, { "cell_type": "markdown", "id": "ac52f046-c9b6-4d44-a97e-f65b0c1988b5", "metadata": { "editable": true, "jp-MarkdownHeadingCollapsed": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Supported types of corrections\n", "\n", "Currently the following corrections from `correctionlib.schemav2` are supported:\n", "\n", "- `Formula`, including parametrical formulas\n", "- `Binning` with uniform or non-uniform bin edges and `flow=\"clamp\"`; bin contents can be either:\n", " - all scalar values\n", " - all `Formula` or `FormulaRef`\n", "- scalar constants" ] }, { "cell_type": "markdown", "id": "ff2ccdf9-63be-4a54-9d09-f9b43e572230", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Open questions\n", "\n", "- what are other types of corrections that definitely need support? `MultiBinning`?\n", "- what is the \"right\" differentiable relaxation of a histogram? [more discussion in #gradhep](https://iris-hep.slack.com/archives/C0155BGPGE4/p1699120426133849)\n", "- what is the \"right\" way to differentiate a composition of `Binning` and `Formula`s (i.e. formulas defined piece-wise)?\n", "- several operations are not JAX-traceable (`jax.grad` works with them but not `jax.jit`, `jax.vmap` etc.). can we do better?\n", " - scipy's cubic splines, that we use as a differentiable approximation of a 1D histogram profile, are not JAX-traceable\n", " - bin look-ups, that we perform in case of a `Formula` inside a `Binning`, are not JAX-traceable\n", "- further development: I am moving on soon. I plan to add a few obvious improvements, but I won't be there to develop this in the years to come" ] }, { "attachments": { "6641f60c-1892-4c2b-84ae-856906c996f2.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "fb6a10bb-8221-454f-a60c-c698a227c947", "metadata": {}, "source": [ "### An example histogram (blue) with one possible differentiable relaxation (orange)\n", "\n", "![image.png](attachment:6641f60c-1892-4c2b-84ae-856906c996f2.png)\n", "\n", "What is the \"right\" relaxation?" ] }, { "attachments": { "a60ab5fe-632b-4de6-a001-7076f21cd9bd.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "ddd741f5-591f-4ae2-b87a-d5193c812294", "metadata": {}, "source": [ "### An example compound histogram (some bins contain Formulas)\n", "\n", "![image.png](attachment:a60ab5fe-632b-4de6-a001-7076f21cd9bd.png)\n", "\n", "What is the \"right\" relaxation?" ] }, { "cell_type": "markdown", "id": "8ed77d04-96c9-4abc-a098-fd3ef2ff0d8f", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Bonus: what about C++?\n", "\n", "- autodifferentiable analyses are mostly a Python R&D topic, not a lot of interest in end-to-end differentiable analyses in C++ in the community\n", "- via Python+JAX we can make fast progress, learn about the problem, the solution space, the technical hurdles, and then go for a C++ implementation in the future if needed\n", "- at the time of writing I do not know of a C++ library that can autodifferentiate a compute graph evaluation the same way JAX does in this package (and implementing such a C++ library is a project of a larger scope than we feel like tackling at this point)\n", "- I think the best option for C++ is implementing a code generator that produces code that evaluates a given correction, then pass the generated correction evaluation code through [enzyme](https://enzyme.mit.edu) or [clad](https://github.com/vgvassilev/clad)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }