From ffc825bccbf759531f64b4847c65c2a1f708d29d Mon Sep 17 00:00:00 2001 From: liuxinwei Date: Tue, 21 Nov 2023 13:48:33 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- doc/recipes/index.md | 2 +- tests/quant/images/compare_output.png | Bin 0 -> 27076 bytes tests/quant/images/compare_output_ns.png | Bin 0 -> 27076 bytes tests/quant/images/compare_stub.png | Bin 0 -> 22859 bytes tests/quant/images/ptq-flowchart.svg | 16 + tests/quant/images/ptq-qat.png | Bin 0 -> 79694 bytes tests/quant/images/qat-fake-quantization.png | Bin 0 -> 33592 bytes tests/quant/images/qat-flowchart.svg | 16 + .../quant/images/quantization-flowchart2.png | Bin 0 -> 2708250 bytes tests/quant/images/shadow.png | Bin 0 -> 15597 bytes .../sphx_glr_numeric_suite_tutorial_001.png | Bin 0 -> 14103 bytes tests/quant/images/tensor-quantization.png | Bin 0 -> 36247 bytes tests/quant/ns.ipynb | 872 ++++++++++++ tests/quant/practice.ipynb | 1242 +++++++++++++++++ tests/quant/sigmoid-fx/.gitignore | 3 + tests/quant/sigmoid-fx/cifar10-resnet18.ipynb | 230 +++ tests/quant/sigmoid-fx/fixed_sigmoid.py | 42 + tests/quant/sigmoid-fx/index.md | 6 + tests/quant/sigmoid-fx/observer.py | 9 + tests/quant/sigmoid-fx/sigmoid.ipynb | 490 +++++++ tests/quant/utils/sigmoid.py | 32 + tests/tanh.ipynb | 168 +++ tests/taylor.ipynb | 453 ++++++ 23 files changed, 3580 insertions(+), 1 deletion(-) create mode 100644 tests/quant/images/compare_output.png create mode 100644 tests/quant/images/compare_output_ns.png create mode 100644 tests/quant/images/compare_stub.png create mode 100644 tests/quant/images/ptq-flowchart.svg create mode 100644 tests/quant/images/ptq-qat.png create mode 100644 tests/quant/images/qat-fake-quantization.png create mode 100644 tests/quant/images/qat-flowchart.svg create mode 100644 tests/quant/images/quantization-flowchart2.png create mode 100644 tests/quant/images/shadow.png create mode 100644 tests/quant/images/sphx_glr_numeric_suite_tutorial_001.png create mode 100644 tests/quant/images/tensor-quantization.png create mode 100644 tests/quant/ns.ipynb create mode 100644 tests/quant/practice.ipynb create mode 100644 tests/quant/sigmoid-fx/.gitignore create mode 100644 tests/quant/sigmoid-fx/cifar10-resnet18.ipynb create mode 100644 tests/quant/sigmoid-fx/fixed_sigmoid.py create mode 100644 tests/quant/sigmoid-fx/index.md create mode 100644 tests/quant/sigmoid-fx/observer.py create mode 100644 tests/quant/sigmoid-fx/sigmoid.ipynb create mode 100644 tests/quant/utils/sigmoid.py create mode 100644 tests/tanh.ipynb create mode 100644 tests/taylor.ipynb diff --git a/doc/recipes/index.md b/doc/recipes/index.md index 4a099fc..11e5cbe 100644 --- a/doc/recipes/index.md +++ b/doc/recipes/index.md @@ -1,4 +1,4 @@ -# 技巧 +# 指南 ```{toctree} benchmark diff --git a/tests/quant/images/compare_output.png b/tests/quant/images/compare_output.png new file mode 100644 index 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zy#m}-7qC*KSV8<<->c@=9&KT)faK8Y0=*b{OqiM<=sZLvKqzg1L^Tm)K;A!%{P>a2 z{xx8tf&b*x=>}rYqnKxtIvYA>t?ugXpCTdzOZf!_1?S-Zz;Ip>I#adS?B*_Wj6|L} zz8HUQ7Q_T`Af*Vl^N^SKi)66uNT2&)*FB^{p>5VM$WxWB{YAG)^px5ruCTN-;*J=r zn3z%NDTuIv{(CaHE6?J(D){U6|DO5if9WKe`tb1xA;zb|FLbH23$zJQl2dzLB4hsU Fe*p0w)6@U} literal 0 HcmV?d00001 diff --git a/tests/quant/ns.ipynb b/tests/quant/ns.ipynb new file mode 100644 index 0000000..39e4a44 --- /dev/null +++ b/tests/quant/ns.ipynb @@ -0,0 +1,872 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Pytorch 数值套件教程\n", + "\n", + "当它工作时,量化是好的,但很难知道什么是错误的,当它不满足我们期望的准确性。量化精度问题的调试并不容易,且耗时较长。\n", + "\n", + "调试的一个重要步骤是度量浮点模型及其相应量化模型的统计量,以了解它们的最大差异在哪里。PyTorch 量化中构建了一套名为 PyTorch Numeric Suite 的数值工具,以支持量化模块和浮点模块之间的统计量的度量,从而支持量化调试工作。即使对于精度较高的量化模型,PyTorch Numeric Suite 仍然可以作为剖析工具,更好地理解模型内部的量化误差,并为进一步优化提供指导。\n", + "\n", + "PyTorch Numeric Suite 目前支持通过统一的 API 的静态量化和动态量化来量化模型。\n", + "\n", + "在本教程中,首先使用 ResNet18 作为一个例子来展示如何使用 PyTorch Numeric Suite 来度量静态量化模型和浮点模型之间的统计信息。然后将以基于 LSTM 的序列模型为例,展示 PyTorch Numeric Suite 在动态量化模型中的应用。\n", + "\n", + "\n", + "## 数值套件之静态量化\n", + "\n", + "```{rubric} 设置\n", + "```\n", + "\n", + "从必要的导入开始:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from __future__ import print_function, division, absolute_import\n", + "# import numpy as np\n", + "import torch\n", + "import torch.nn as nn\n", + "import torchvision\n", + "# from torchvision import datasets\n", + "# import torchvision.transforms as transforms\n", + "# import os\n", + "import torch.quantization\n", + "import torch.quantization._numeric_suite as ns\n", + "from torch.quantization import (\n", + " default_eval_fn,\n", + " default_qconfig,\n", + " quantize,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "然后加载预训练的浮点 ResNet18 模型,将其量化为 `qmodel`。我们不能比较两个任意的模型,只能比较一个浮点模型和它派生的量化模型。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "float_model = torchvision.models.quantization.resnet18(pretrained=True,\n", + " quantize=False)\n", + "float_model.to('cpu')\n", + "float_model.eval()\n", + "float_model.fuse_model()\n", + "float_model.qconfig = default_qconfig\n", + "img_data = [(torch.rand(2, 3, 10, 10, dtype=torch.float),\n", + " torch.randint(0, 1, (2,), dtype=torch.long)) for _ in range(2)]\n", + "qmodel = quantize(float_model, default_eval_fn, [img_data], inplace=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1. 比较浮点模型和量化模型的权重\n", + "\n", + "首先要比较的是量化模型和浮点模型的权值。可以从 PyTorch Numeric Suite 调用 ``compare_weights()`` 来获得字典 ``wt_compare_dict``,其键对应于模块名,每个条目都是一个字典,有两个键 `'float'` 和 `'quantized'`,包含 float 和 quantized 权重。``compare_weights()`` 接受浮点和量化状态字典并返回一个字典,与浮点权值对应的键和值是浮点和量化权值的字典:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "`wt_compare_dict` 键:\n", + "dict_keys(['conv1.weight', 'layer1.0.conv1.weight', 'layer1.0.conv2.weight', 'layer1.1.conv1.weight', 'layer1.1.conv2.weight', 'layer2.0.conv1.weight', 'layer2.0.conv2.weight', 'layer2.0.downsample.0.weight', 'layer2.1.conv1.weight', 'layer2.1.conv2.weight', 'layer3.0.conv1.weight', 'layer3.0.conv2.weight', 'layer3.0.downsample.0.weight', 'layer3.1.conv1.weight', 'layer3.1.conv2.weight', 'layer4.0.conv1.weight', 'layer4.0.conv2.weight', 'layer4.0.downsample.0.weight', 'layer4.1.conv1.weight', 'layer4.1.conv2.weight', 'fc._packed_params._packed_params'])\n", + "\n", + "`wt_compare_dict` 条目中 conv1 的权值:\n", + "dict_keys(['float', 'quantized'])\n", + "torch.Size([64, 3, 7, 7])\n", + "torch.Size([64, 3, 7, 7])\n" + ] + } + ], + "source": [ + "wt_compare_dict = ns.compare_weights(float_model.state_dict(),\n", + " qmodel.state_dict())\n", + "\n", + "print('`wt_compare_dict` 键:')\n", + "print(wt_compare_dict.keys())\n", + "\n", + "print(\"\\n`wt_compare_dict` 条目中 conv1 的权值:\")\n", + "print(wt_compare_dict['conv1.weight'].keys())\n", + "print(wt_compare_dict['conv1.weight']['float'].shape)\n", + "print(wt_compare_dict['conv1.weight']['quantized'].shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "一旦获得 ``wt_compare_dict``,用户就可以以任何他们想要的方式处理这个字典。以 float 和量化模型权值的量化误差为例,计算如下。\n", + "\n", + "计算量化张量 ``y`` 的信噪比(Signal-to-Quantization-Noise Ratio,简称 SQNR),它反映了最大标称(nominal)信号强度与量化中引入的量化误差之间的关系。更高的 SQNR 对应更低的量化误差。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "conv1.weight tensor(31.6638)\n", + "layer1.0.conv1.weight tensor(30.6450)\n", + "layer1.0.conv2.weight tensor(31.1528)\n", + "layer1.1.conv1.weight tensor(32.1438)\n", + "layer1.1.conv2.weight tensor(31.2477)\n", + "layer2.0.conv1.weight tensor(30.9890)\n", + "layer2.0.conv2.weight tensor(28.8233)\n", + "layer2.0.downsample.0.weight tensor(31.5558)\n", + "layer2.1.conv1.weight tensor(30.7668)\n", + "layer2.1.conv2.weight tensor(28.4516)\n", + "layer3.0.conv1.weight tensor(30.9247)\n", + "layer3.0.conv2.weight tensor(26.6841)\n", + "layer3.0.downsample.0.weight tensor(28.7825)\n", + "layer3.1.conv1.weight tensor(28.9707)\n", + "layer3.1.conv2.weight tensor(25.6785)\n", + "layer4.0.conv1.weight tensor(26.8496)\n", + "layer4.0.conv2.weight tensor(25.8396)\n", + "layer4.0.downsample.0.weight tensor(28.6355)\n", + "layer4.1.conv1.weight tensor(26.8759)\n", + "layer4.1.conv2.weight tensor(28.4319)\n", + "fc._packed_params._packed_params tensor(32.6506)\n" + ] + } + ], + "source": [ + "def compute_error(x, y):\n", + " Ps = torch.norm(x)\n", + " Pn = torch.norm(x-y)\n", + " return 20*torch.log10(Ps/Pn)\n", + "\n", + "\n", + "for key in wt_compare_dict:\n", + " print(key,\n", + " compute_error(wt_compare_dict[key]['float'],\n", + " wt_compare_dict[key]['quantized'].dequantize()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "另一个例子 ``wt_compare_dict`` 也可以用来绘制浮点和量化模型的权值直方图。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from matplotlib import pyplot as plt\n", + "\n", + "f = wt_compare_dict['conv1.weight']['float'].flatten()\n", + "plt.hist(f, bins = 100)\n", + "plt.title(\"Floating point model weights of conv1\")\n", + "plt.show()\n", + "\n", + "q = wt_compare_dict['conv1.weight']['quantized'].flatten().dequantize()\n", + "plt.hist(q, bins = 100)\n", + "plt.title(\"Quantized model weights of conv1\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2. 比较浮点和量化模型在相应的位置\n", + "\n", + "第二个工具允许对相同输入在相应位置上的浮点模型和量化模型之间的权重和激活进行比较,如下图所示。红色箭头表示比较的位置。\n", + "\n", + "```{figure} images/compare_output.png\n", + "```\n", + "\n", + "我们从 PyTorch Numeric Suite 调用 ``compare_model_outputs()`` 来获取给定输入数据对应位置的浮点模型和量化模型中的激活。这个 API 返回一个字典,其中模块名为键。每个条目本身是一个字典,有两个包含激活的键 'float' 和 'quantized'。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = img_data[0][0]\n", + "\n", + "# 接受浮点和量化模型以及输入数据,并返回一个字典,其键对应于量化模块名称,\n", + "# 每个条目是一个字典,有两个键'float'和'quantized',包含匹配位置上的浮点和量化模型的激活。\n", + "act_compare_dict = ns.compare_model_outputs(float_model, qmodel, data)\n", + "\n", + "print('keys of act_compare_dict:')\n", + "print(act_compare_dict.keys())\n", + "\n", + "print(\"\\nkeys of act_compare_dict entry for conv1's output:\")\n", + "print(act_compare_dict['conv1.stats'].keys())\n", + "print(act_compare_dict['conv1.stats']['float'][0].shape)\n", + "print(act_compare_dict['conv1.stats']['quantized'][0].shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "该字典可用于比较和计算 float 和量化模型激活的量化误差,如下所示。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for key in act_compare_dict:\n", + " print(key,\n", + " compute_error(act_compare_dict[key]['float'][0],\n", + " act_compare_dict[key]['quantized'][0].dequantize()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "如果希望对多个输入数据进行比较,可以执行以下操作。通过将 logger 附加到浮点模块和量化模块(如果它们在 ``white_list`` 中)来准备模型。默认的 logger 为 ``OutputLogger``,默认的 ``white_list`` 为 ``DEFAULT_NUMERIC_SUITE_COMPARE_MODEL_OUTPUT_WHITE_LIST``。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ns.prepare_model_outputs(float_model, qmodel)\n", + "\n", + "for data in img_data:\n", + " float_model(data[0])\n", + " qmodel(data[0])\n", + "\n", + "# 查找浮点和量化模块之间的匹配激活,并返回一个字典,其键对应于量化模块名称,\n", + "# 每个条目是一个字典,有两个键'float'和'quantized',包含由记录器记录的匹配浮点和量化激活\n", + "act_compare_dict = ns.get_matching_activations(float_model, qmodel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "上述 API 中使用的默认 logger 是 ``OutputLogger``,用于 log 模块的输出。我们可以继承基类 ``Logger``,并创建自己的 logger 来执行不同的功能。例如,我们可以创建一个新的 ``MyOutputLogger`` 类,如下所示。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class MyOutputLogger(ns.Logger):\n", + " r\"\"\"Customized logger class\n", + " \"\"\"\n", + "\n", + " def __init__(self):\n", + " super(MyOutputLogger, self).__init__()\n", + "\n", + " def forward(self, x):\n", + " # Custom functionalities\n", + " # ...\n", + " return x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "然后我们可以把这个记录器传递到上面的 API 中,比如:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = img_data[0][0]\n", + "act_compare_dict = ns.compare_model_outputs(float_model,\n", + " qmodel, data,\n", + " logger_cls=MyOutputLogger)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "或者:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ns.prepare_model_outputs(float_model, qmodel, MyOutputLogger)\n", + "for data in img_data:\n", + " float_model(data[0])\n", + " qmodel(data[0])\n", + "act_compare_dict = ns.get_matching_activations(float_model, qmodel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3. 使用相同的输入数据,将量化模型中的模块与等效的浮点模块进行比较\n", + "\n", + "第三个工具允许比较模型中的量化模块和对应的浮点模块,为它们提供相同的输入,并比较它们的输出,如下所示。\n", + "\n", + "```{figure} images/compare_stub.png\n", + "```\n", + "\n", + "在实践中,我们调用 `prepare_model_with_stub()` 来交换我们想要比较的量化模块与 `Shadow` 模块,如下所示:\n", + "\n", + "```{figure} images/shadow.png\n", + "```\n", + "\n", + "``Shadow`` 模块以量化模块、浮点模块和 logger 作为输入,并在其中创建 forward 路径,使浮点模块与 shadow 量化模块共享同输入张量。\n", + "\n", + "logger 可以自定义,默认的记录器是 ``ShadowLogger``,它将保存量化模块和浮点模块的输出,用于计算模块级量化误差。\n", + "\n", + "注意,在每次调用 ``compare_model_outputs()`` 和 ``compare_model_stub()`` 之前,我们需要有干净的浮点和量化模型。这是因为 ``compare_model_outputs()`` 和 ``compare_model_stub()`` 对 float 和量化模型进行了原地修改,如果一个接一个地调用,将导致意想不到的结果。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "float_model = torchvision.models.quantization.resnet18(pretrained=True, quantize=False)\n", + "float_model.to('cpu')\n", + "float_model.eval()\n", + "float_model.fuse_model()\n", + "float_model.qconfig = torch.quantization.default_qconfig\n", + "img_data = [(torch.rand(2, 3, 10, 10, dtype=torch.float), torch.randint(0, 1, (2,), dtype=torch.long)) for _ in range(2)]\n", + "qmodel = quantize(float_model, default_eval_fn, [img_data], inplace=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在下面的例子中,我们调用 PyTorch 数值套件中的 ``compare_model_stub()`` 来比较 ``QuantizableBasicBlock`` 模块和它的浮点数等效值。这个 API 返回字典,其键对应于模块名,每个条目都是一个字典,有两个键 'float' 和 'quantized',包含 quantized 及其匹配的浮点阴影模块的输出张量。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = img_data[0][0]\n", + "module_swap_list = [torchvision.models.quantization.resnet.QuantizableBasicBlock]\n", + "\n", + "# Takes in floating point and quantized model as well as input data, and returns a dict with key\n", + "# corresponding to module names and each entry being a dictionary with two keys 'float' and\n", + "# 'quantized', containing the output tensors of quantized module and its matching floating point shadow module.\n", + "ob_dict = ns.compare_model_stub(float_model, qmodel, module_swap_list, data)\n", + "\n", + "print('keys of ob_dict:')\n", + "print(ob_dict.keys())\n", + "\n", + "print(\"\\nkeys of ob_dict entry for layer1.0's output:\")\n", + "print(ob_dict['layer1.0.stats'].keys())\n", + "print(ob_dict['layer1.0.stats']['float'][0].shape)\n", + "print(ob_dict['layer1.0.stats']['quantized'][0].shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这个字典可以用来比较和计算模块级量化误差。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for key in ob_dict:\n", + " print(key, compute_error(ob_dict[key]['float'][0], ob_dict[key]['quantized'][0].dequantize()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "如果希望对多个输入数据进行比较,可以执行以下操作。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ns.prepare_model_with_stubs(float_model, qmodel, module_swap_list, ns.ShadowLogger)\n", + "for data in img_data:\n", + " qmodel(data[0])\n", + "ob_dict = ns.get_logger_dict(qmodel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在上述 API 中使用的默认记录器是 ``ShadowLogger``,用于记录量化模块及其匹配的浮动阴影模块的输出。我们可以继承基类 ``Logger``,并创建自己的 Logger 来执行不同的功能。例如,我们可以创建新的 ``MyShadowLogger`` 类,如下所示。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class MyShadowLogger(ns.Logger):\n", + " r\"\"\"Customized logger class\n", + " \"\"\"\n", + "\n", + " def __init__(self):\n", + " super(MyShadowLogger, self).__init__()\n", + "\n", + " def forward(self, x, y):\n", + " # Custom functionalities\n", + " # ...\n", + " return x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "然后我们可以把这个记录器传递到上面的 API 中,比如:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = img_data[0][0]\n", + "ob_dict = ns.compare_model_stub(float_model, qmodel, module_swap_list, data, logger_cls=MyShadowLogger)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "或者:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ns.prepare_model_with_stubs(float_model, qmodel, module_swap_list, MyShadowLogger)\n", + "for data in img_data:\n", + " qmodel(data[0])\n", + "ob_dict = ns.get_logger_dict(qmodel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Numeric Suite 之动态量化\n", + "\n", + "Numeric Suite APIs are designed in such as way that they work for both dynamic quantized model and static quantized model. We will use a model with both LSTM and Linear modules to demonstrate the usage of Numeric Suite on dynamic quantized model. This model is the same one used in the tutorial of dynamic quantization on LSTM word language model [^1].\n", + "\n", + "[^1]: [DYNAMIC QUANTIZATION ON AN LSTM WORD LANGUAGE MODEL](https://pytorch.org/tutorials/advanced/dynamic_quantization_tutorial.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 设置\n", + "\n", + "First we define the model as below. Notice that within this model only ``nn.LSTM`` and ``nn.Linear`` modules will be quantized dynamically and ``nn.Embedding`` will remain as floating point module after quantization.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class LSTMModel(nn.Module):\n", + " \"\"\"Container module with an encoder, a recurrent module, and a decoder.\"\"\"\n", + "\n", + " def __init__(self, ntoken, ninp, nhid, nlayers, dropout=0.5):\n", + " super(LSTMModel, self).__init__()\n", + " self.encoder = nn.Embedding(ntoken, ninp)\n", + " self.rnn = nn.LSTM(ninp, nhid, nlayers, dropout=dropout)\n", + " self.decoder = nn.Linear(nhid, ntoken)\n", + "\n", + " self.init_weights()\n", + "\n", + " self.nhid = nhid\n", + " self.nlayers = nlayers\n", + "\n", + " def init_weights(self):\n", + " initrange = 0.1\n", + " self.encoder.weight.data.uniform_(-initrange, initrange)\n", + " self.decoder.bias.data.zero_()\n", + " self.decoder.weight.data.uniform_(-initrange, initrange)\n", + "\n", + " def forward(self, input, hidden):\n", + " emb = self.encoder(input)\n", + " output, hidden = self.rnn(emb, hidden)\n", + " decoded = self.decoder(output)\n", + " return decoded, hidden\n", + "\n", + " def init_hidden(self, bsz):\n", + " weight = next(self.parameters())\n", + " return (weight.new_zeros(self.nlayers, bsz, self.nhid),\n", + " weight.new_zeros(self.nlayers, bsz, self.nhid))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we create the ``float_model`` and quantize it into qmodel.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ntokens = 10\n", + "\n", + "float_model = LSTMModel(\n", + " ntoken = ntokens,\n", + " ninp = 512,\n", + " nhid = 256,\n", + " nlayers = 5,\n", + ")\n", + "\n", + "float_model.eval()\n", + "\n", + "qmodel = torch.quantization.quantize_dynamic(\n", + " float_model, {nn.LSTM, nn.Linear}, dtype=torch.qint8\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1. Compare the weights of float and quantized models\n", + "\n", + "We first call ``compare_weights()`` from PyTorch Numeric Suite to get a dictionary ``wt_compare_dict`` with key corresponding to module names and each entry is a dictionary with two keys 'float' and 'quantized', containing the float and quantized weights." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "wt_compare_dict = ns.compare_weights(float_model.state_dict(), qmodel.state_dict())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we get ``wt_compare_dict``, it can be used to compare and compute the quantization error of the weights of float and quantized models as following.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for key in wt_compare_dict:\n", + " if wt_compare_dict[key]['quantized'].is_quantized:\n", + " print(key, compute_error(wt_compare_dict[key]['float'], wt_compare_dict[key]['quantized'].dequantize()))\n", + " else:\n", + " print(key, compute_error(wt_compare_dict[key]['float'], wt_compare_dict[key]['quantized']))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Inf value in ``encoder.weight`` entry above is because encoder module is not quantized and the weights are the same in both floating point and quantized models.\n", + "\n", + "### 2. Compare float point and quantized models at corresponding locations\n", + "\n", + "Then we call ``compare_model_outputs()`` from PyTorch Numeric Suite to get the activations in float model and quantized model at corresponding locations for the given input data. This API returns a dict with module names being keys. Each entry is itself a dict with two keys 'float' and 'quantized' containing the activations. Notice that this sequence model has two inputs, and we can pass both inputs into ``compare_model_outputs()`` and ``compare_model_stub()``.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "input_ = torch.randint(ntokens, (1, 1), dtype=torch.long)\n", + "hidden = float_model.init_hidden(1)\n", + "\n", + "act_compare_dict = ns.compare_model_outputs(float_model, qmodel, input_, hidden)\n", + "print(act_compare_dict.keys())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This dict can be used to compare and compute the quantization error of the activations of float and quantized models as following. The LSTM module in this model has two outputs, in this example we compute the error of the first output.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for key in act_compare_dict:\n", + " print(key, compute_error(act_compare_dict[key]['float'][0][0], act_compare_dict[key]['quantized'][0][0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3. Compare a module in a quantized model with its float point equivalent, with the same input data\n", + "\n", + "Next we call ``compare_model_stub()`` from PyTorch Numeric Suite to compare LSTM and Linear module with its float point equivalent. This API returns a dict with key corresponding to module names and each entry being a dictionary with two keys 'float' and 'quantized', containing the output tensors of quantized and its matching float shadow module.\n", + "\n", + "We reset the model first.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "float_model = LSTMModel(\n", + " ntoken = ntokens,\n", + " ninp = 512,\n", + " nhid = 256,\n", + " nlayers = 5,\n", + ")\n", + "float_model.eval()\n", + "\n", + "qmodel = torch.quantization.quantize_dynamic(\n", + " float_model, {nn.LSTM, nn.Linear}, dtype=torch.qint8\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we call ``compare_model_stub()`` from PyTorch Numeric Suite to compare LSTM and Linear module with its float point equivalent. This API returns a dict with key corresponding to module names and each entry being a dictionary with two keys 'float' and 'quantized', containing the output tensors of quantized and its matching float shadow module.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "module_swap_list = [nn.Linear, nn.LSTM]\n", + "ob_dict = ns.compare_model_stub(float_model, qmodel, module_swap_list, input_, hidden)\n", + "print(ob_dict.keys())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This dict can be then used to compare and compute the module level quantization error.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for key in ob_dict:\n", + " print(key, compute_error(ob_dict[key]['float'][0], ob_dict[key]['quantized'][0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "40db 的 SQNR 是很高的,在这种情况下,我们在浮点和量化模型之间有很好的数值对齐。\n", + "\n", + "## 结论\n", + "\n", + "在本教程中,我们演示了如何使用 PyTorch Numeric Suite 来度量量化模型和浮点模型之间的统计数据,并使用用于静态量化和动态量化的统一 API 在即时模式下进行比较。\n", + "感谢你的阅读!一如既往,我们欢迎任何反馈,所以如果您有任何问题,请创建 [issue](https://github.com/pytorch/pytorch/issues)。" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.10.4 ('tvmx': conda)", + "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": "3.10.4" + }, + "vscode": { + "interpreter": { + "hash": "e579259ee6098e2b9319de590d145b4b096774fe457bdf04260e3ba5c171e887" + } + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/tests/quant/practice.ipynb b/tests/quant/practice.ipynb new file mode 100644 index 0000000..9d79bfc --- /dev/null +++ b/tests/quant/practice.ipynb @@ -0,0 +1,1242 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 量化实践\n", + "\n", + "参考:[Practical Quantization in PyTorch](https://pytorch.org/blog/quantization-in-practice/)\n", + "\n", + "{guilabel}`NN 量化目标`:运行更快、内存需求更低。\n", + "\n", + "- 量化源于信息压缩;在深度神经网络中,它指的是降低其权重和/或激活的数值精度。\n", + "- 过度参数化的 DNN 有更多的 **自由度**,这使它们成为信息压缩的良好候选对象 {cite:ps}`gholami2021survey`。\n", + "\n", + "当量化模型时,通常会发生两件事——模型变得更小,运行效率更高。硬件供应商明确地允许更快地处理 8 位数据(而不是 32 位数据),从而获得更高的 **吞吐量** (throughput)。更小的模型具有更低的内存占用和功耗 {cite:ps}`krishnamoorthi2018quantizing`,这对于边缘部署至关重要。\n", + "\n", + "## 量化背景知识\n", + "\n", + "### 映射函数\n", + "\n", + "映射函数:将值从浮点数映射到整数空间的函数。常用的映射函数是由 $Q(r) = \\operatorname{round}(r/S + Z)$ 给出的线性变换,其中为 $r$ 为输入,$S, Z$ 为量化参数(quantization parameters)。为了重新变换为浮点空间,反函数由 $\\overline{r} = (Q(r) - Z) \\cdot S$ 给出(被称为 **反量化**,即 dequantization)。\n", + "\n", + "```{note}\n", + "$\\overline{r} \\neq r$,它们之间的差异构成了量化误差。\n", + "```\n", + "\n", + "### 量化参数\n", + "\n", + "映射函数由缩放因子 $S$ 和零点 $Z$ 所参数化。$S$ 仅仅是输入范围与输出范围的比值 $S = \\frac {\\beta - \\alpha}{\\beta_q - \\alpha_q}$。这里 $[\\alpha, \\beta]$ 是输入的裁剪(clipping)范围,即允许输入的边界。$[\\alpha_q, \\beta_q]$ 是它被映射到的量化输出空间的范围。对于 8 位量化,输出范围 $0 \\leq \\beta_q - \\alpha_q \\leq 2^8 -1$。$Z = -(\\frac {\\alpha}{S} - \\alpha_q)$ 作为偏置,以确保输入空间中的 $0$ 完全映射到量化空间中的 $0$。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 校准\n", + "\n", + "选择输入裁剪范围的过程称为 **校准** (calibration)。最简单的方法(也是 PyTorch 中的默认方法)是记录正在运行的最小值和最大值,并将它们赋值给 $\\alpha$ 和 $\\beta$。[TensorRT](https://docs.nvidia.com/deeplearning/tensorrt/pytorch-quantization-toolkit/docs/calib.html) 使用熵最小化(KL 散度),均方误差最小化,或输入范围的百分位数。\n", + "\n", + "在 PyTorch 中,{class}`Observer ` 模块收集关于输入值的统计信息并计算 `qparams` $S, Z$。不同的校准方案会产生不同的量化输出,最好通过经验验证哪种方案最适合您的应用程序和体系结构。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{admonition} 观测器基类\n", + "{class}`~torch.ao.quantization.observer.ObserverBase` 是观测器(observer)模块的基类。在 {func}`forward` 中,将更新观测张量的统计信息。观测器应该提供用于收集的统计信息并计算量化参数的 `calculate_qparams` 函数。\n", + "```\n", + "\n", + "### 均匀量化\n", + "\n", + "````{admonition} 均匀量化的观测器基类\n", + "{class}`~torch.ao.quantization.observer.UniformQuantizationObserverBase` 是所有使用均匀量化(uniform quantization,{cite:p}`UniformQuantizers21`)来计算 `scale` 和 `zero_point` 的观测器基类。\n", + "\n", + "参数:\n", + "- `dtype`:量化后的数据类型。\n", + "- `qscheme`:量化方案。\n", + "- `reduce_range`:使用 1 bit 归约量化数据类型的范围。这有时是为了避免指令溢出所必需的。\n", + "- `quant_min`:最小量化值。如果未指定,它将遵循 8 bit 设置。\n", + "- `quant_max`:最大量化值。如果未指定,它将遵循 8 bit 设置。\n", + "- `eps`:float32 的 $\\epsilon$ 值,默认为 {data}`torch.finfo(torch.float32).eps`。\n", + "\n", + "```{warning}\n", + "1. {attr}`dtype` 仅支持 ``torch.qint8`` 或者 ``torch.quint8``。\n", + "2. {attr}`qscheme` 有:\n", + "\n", + " - ``torch.per_tensor_affine``\n", + " - ``torch.per_tensor_symmetric``\n", + " - ``torch.per_channel_affine``\n", + " - ``torch.per_channel_symmetric``\n", + "```\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} MinMaxObserver\n", + "{class}`~torch.ao.quantization.observer.MinMaxObserver` 观测器模块,根据运行的最小值和最大值计算量化参数。\n", + "\n", + "此观测器使用张量最小/最大统计量来计算量化参数。该模块记录传入张量的运行最小值和最大值,并利用该统计量计算量化参数。\n", + "\n", + "记作 running min/max 为 {math}`x_{\\min}` 和 {math}`x_{\\max}`;`scale` 和零点为 {math}`s`,{math}`z`,则:\n", + "\n", + "$$\n", + "\\begin{array}{ll}\n", + "x_\\text{min} &= \\begin{cases}\n", + " \\min(X) & \\text{if~}x_\\text{min} = \\text{None} \\\\\n", + " \\min\\left(x_\\text{min}, \\min(X)\\right) & \\text{otherwise}\n", + "\\end{cases}\\\\\n", + "x_\\text{max} &= \\begin{cases}\n", + " \\max(X) & \\text{if~}x_\\text{max} = \\text{None} \\\\\n", + " \\max\\left(x_\\text{max}, \\max(X)\\right) & \\text{otherwise}\n", + "\\end{cases}\\\\\n", + "\\end{array}\n", + "$$\n", + "\n", + "其中 $X$ 是被观测张量。\n", + "\n", + "为:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\text{if 对称:}&\\\\\n", + "&s = 2 \\max(|x_\\text{min}|, x_\\text{max}) /\n", + " \\left( Q_\\text{max} - Q_\\text{min} \\right) \\\\\n", + "&z = \\begin{cases}\n", + " 0 & \\text{if dtype is qint8} \\\\\n", + " 128 & \\text{otherwise}\n", + "\\end{cases}\\\\\n", + "\\text{else:}&\\\\\n", + " &s = \\left( x_\\text{max} - x_\\text{min} \\right ) /\n", + " \\left( Q_\\text{max} - Q_\\text{min} \\right ) \\\\\n", + " &z = Q_\\text{min} - \\text{round}(x_\\text{min} / s)\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "这里 $Q_{\\min}$ 和 $Q_{\\max}$ 量化的数据类型的最小最大值。\n", + "\n", + "如果 running 最小值等于 running 最大值,则 `scale` 和 `zero_point` 设置为 $1.0$ 和 $0$。\n", + "\n", + "````{admonition} MovingAverageMinMaxObserver\n", + "{class}`~torch.ao.quantization.observer.MovingAverageMinMaxObserver` 是 {class}`~torch.ao.quantization.observer.MinMaxObserver` 的子类,它是基于最小值和最大值的滑动平均值计算量化参数的观测器模块。\n", + "\n", + "此观测器根据传入张量的极小值和极大值的滑动\n", + "\n", + "平均值计算量化参数。该模块记录传入张量的平均最小值和最大值,并利用该统计量计算量化参数。\n", + "\n", + "$$\n", + "\\begin{array}{ll}\n", + " x_\\text{min} = \\begin{cases}\n", + " \\min(X) & \\text{if~}x_\\text{min} = \\text{None} \\\\\n", + " (1 - c) x_\\text{min} + c \\min(X) & \\text{otherwise}\n", + " \\end{cases}\\\\\n", + " x_\\text{max} = \\begin{cases}\n", + " \\max(X) & \\text{if~}x_\\text{max} = \\text{None} \\\\\n", + " (1 - c) x_\\text{max} + c \\max(X) & \\text{otherwise}\n", + " \\end{cases}\\\\\n", + "\\end{array}\n", + "$$\n", + "\n", + "其中 $c$ 是 ``averaging_constant``。\n", + "\n", + "```{note}\n", + "仅用于 ``torch.per_tensor_affine`` 量化方案。\n", + "```\n", + "````\n", + "`````\n", + "\n", + "`````{admonition} PerChannelMinMaxObserver\n", + "{class}`~torch.ao.quantization.observer.PerChannelMinMaxObserver` 观测器模块,根据逐通道运行的最小值和最大值计算量化参数。\n", + "\n", + "此观测器使用张量最小/最大统计量来逐通道计算量化参数。该模块记录传入张量的运行最小值和最大值,并使用该统计量计算量化\n", + "参数。\n", + "\n", + "参数:\n", + "\n", + "- `ch_axis`:通道的轴。\n", + "\n", + "量化参数的计算方法与 {class}`~torch.ao.quantization.observer.MinMaxObserver` 相同,区别在于运行的最小/最大值存储在每个通道上。\n", + "\n", + "此观测器 存在子类 {class}`~torch.ao.quantization.observer.MovingAveragePerChannelMinMaxObserver`。\n", + "`````\n", + "\n", + "````{admonition} HistogramObserver\n", + "{class}`~torch.ao.quantization.observer.HistogramObserver` 记录张量值的运行直方图(histogram)以及最小/最大值。\n", + "\n", + "参数:\n", + "\n", + "- `bins`:用于直方图的箱的数量。\n", + "- `upsample_rate`:直方图上采样的因子,这用于插值直方图与不同的观测范围。\n", + "\n", + "`scale` 和零点计算方式如下:\n", + "\n", + "1. 创建传入输入的直方图:直方图的计算是连续的,每个 bin 的范围随着观测到的每个新张量而变化。\n", + "2. 搜索直方图中的分布,寻找最佳的最小/最大值:对最小/最大值的搜索确保了相对于浮点模型的量化误差的最小化。\n", + "3. 计算`scale` 和零点的方法同 {class}`~torch.ao.quantization.observer.MinMaxObserver`。\n", + "````" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[tensor([[-0.8635, 1.4422],\n", + " [-0.1421, -1.5490],\n", + " [ 0.6654, -0.6494]]),\n", + " tensor([[ 0.0805, -0.4340],\n", + " [ 0.2766, 0.5731],\n", + " [ 1.1772, -0.7429]])]" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import torch\n", + "from torch.ao.quantization.observer import MinMaxObserver, MovingAverageMinMaxObserver, HistogramObserver\n", + "\n", + "# 设置输入\n", + "C, L = 3, 2\n", + "normal = torch.distributions.normal.Normal(0, 1)\n", + "\n", + "inputs = [normal.sample((C, L)),\n", + " normal.sample((C, L))]\n", + "inputs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "设置观测:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "observers = [MinMaxObserver(),\n", + " MovingAverageMinMaxObserver(),\n", + " HistogramObserver()]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "计算并查看量化参数:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MinMaxObserver (tensor([0.0117]), tensor([132], dtype=torch.int32))\n", + "MovingAverageMinMaxObserver (tensor([0.0117]), tensor([132], dtype=torch.int32))\n", + "HistogramObserver (tensor([0.0090]), tensor([150], dtype=torch.int32))\n" + ] + } + ], + "source": [ + "for obs in observers:\n", + " for x in inputs:\n", + " obs(x)\n", + " print(obs.__class__.__name__, obs.calculate_qparams())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 仿射和对称量化方案\n", + "\n", + "仿射(affine)或非对称量化(asymmetric quantization)方案分配输入范围的最小和最大观测值。仿射方案通常提供更小的剪切范围,并且对于量化非负激活非常有用(如果你的输入张量永远都不是负的,你就不需要输入范围包含负值)。计算范围为 $\\alpha=\\min(r), \\beta = \\max(r)$。当用于权值张量 {cite:ps}`wu2020integer` 时,仿射量化会导致更昂贵的计算推理。\n", + "\n", + "对称量化(Symmetric quantization)方案将输入范围集中在 $0$ 附近,消除了计算零点偏置的需要。计算范围为 $-\\alpha=\\beta=\\max(|\\max(r)|,|\\min(r)|)$。\n", + "\n", + "对于倾斜的信号(如非负激活),这可能会导致糟糕的量化分辨率(quantization resolution),因为剪辑范围包括从未在输入中出现的值(参见下面的 pyplot)。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "from matplotlib import pyplot as plt\n", + "import numpy as np\n", + "\n", + "\n", + "def get_symmetric_range(x):\n", + " '''获取对称范围'''\n", + " beta = torch.max(x.max(), x.min().abs())\n", + " return -beta.item(), beta.item()\n", + "\n", + "\n", + "def get_affine_range(x):\n", + " '''获取仿射范围'''\n", + " return x.min().item(), x.max().item()\n", + "\n", + "\n", + "def plot(plt, data, scheme):\n", + " '''画出不同方案的分布'''\n", + " boundaries = get_affine_range(data) if scheme == 'affine' \\\n", + " else get_symmetric_range(data)\n", + " a, _, _ = plt.hist(data, density=True, bins=100, histtype='stepfilled')\n", + " ymin, ymax = np.quantile(a[a > 0], [0.25, 0.95])\n", + " plt.vlines(x=boundaries, ls='--', colors='purple', ymin=ymin, ymax=ymax)\n", + "\n", + "\n", + "# 模拟激活和权重\n", + "act = torch.distributions.pareto.Pareto(1, 10).sample((1, 1024))\n", + "weights = torch.distributions.normal.Normal(0, 0.14).sample((3, 64, 7, 7)).flatten()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(2, 2, figsize=(10, 8))\n", + "plot(axs[0, 0], act, 'affine')\n", + "axs[0, 0].set_title(\"Activation, Affine-Quantized\")\n", + "plot(axs[0, 1], act, 'symmetric')\n", + "axs[0, 1].set_title(\"Activation, Symmetric-Quantized\")\n", + "plot(axs[1, 0], weights, 'affine')\n", + "axs[1, 0].set_title(\"Weights, Affine-Quantized\")\n", + "plot(axs[1, 1], weights, 'symmetric')\n", + "axs[1, 1].set_title(\"Weights, Symmetric-Quantized\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在 PyTorch 中,你可以在初始化 `Observer` 时指定仿射或对称模式。注意,并非所有 `observer` 都支持这两种方案。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Qscheme: torch.per_tensor_affine | (tensor([0.0117]), tensor([132], dtype=torch.int32))\n", + "Qscheme: torch.per_tensor_symmetric | (tensor([0.0121]), tensor([128]))\n" + ] + } + ], + "source": [ + "for qscheme in [torch.per_tensor_affine, torch.per_tensor_symmetric]:\n", + " obs = MovingAverageMinMaxObserver(qscheme=qscheme)\n", + " for x in inputs:\n", + " obs(x)\n", + " print(f\"Qscheme: {qscheme} | {obs.calculate_qparams()}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 逐张量和逐通道量化方案\n", + "\n", + "量化参数可以作为整体计算层的整个权值张量,也可以单独计算每个通道的权值张量。在每张量中,对层中的所有通道应用相同的剪切范围:\n", + "\n", + "![](images/tensor-quantization.png)\n", + "\n", + "对于权值量化,逐通道(Per-Channel)对称量化提供了更好的精度;逐张量(Per-Tensor)量化的性能很差,这可能是由于不同通道之间的转换权值与批量范数折叠(batchnorm folding) {cite:ps}`wu2020integer` 差异很大。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(tensor([0.0090, 0.0060, 0.0052]), tensor([ 96, 255, 126], dtype=torch.int32))\n" + ] + } + ], + "source": [ + "from torch.ao.quantization.observer import MovingAveragePerChannelMinMaxObserver\n", + "# 计算全部 `C` 通道的 qparams\n", + "obs = MovingAveragePerChannelMinMaxObserver(ch_axis=0)\n", + "for x in inputs:\n", + " obs(x)\n", + "print(obs.calculate_qparams())" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(tensor([0.0060, 0.0117]), tensor([143, 132], dtype=torch.int32))\n" + ] + } + ], + "source": [ + "obs = MovingAveragePerChannelMinMaxObserver(ch_axis=1)\n", + "for x in inputs:\n", + " obs(x)\n", + "print(obs.calculate_qparams())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 后端引擎\n", + "\n", + "目前,量化算子通过 [FBGEMM 后端](https://github.com/pytorch/FBGEMM) 在 x86 机器上运行,或者在 ARM 机器上使用 [QNNPACK](https://github.com/pytorch/QNNPACK) 原语。服务器 GPU 的后端支持(通过 TensorRT 和 cuDNN)即将推出。了解更多关于将量化扩展到自定义后端:[RFC-0019](https://github.com/pytorch/rfcs/blob/master/RFC-0019-Extending-PyTorch-Quantization-to-Custom-Backends.md)。" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "from torch.ao.quantization.qconfig import get_default_qconfig\n", + "backend = 'fbgemm' # if x86 else 'qnnpack'\n", + "qconfig = get_default_qconfig(backend)\n", + "torch.backends.quantized.engine = backend" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## `QConfig`\n", + "\n", + "{class}`~torch.ao.quantization.qconfig.QConfig` NamedTuple 存储用于量化激活和权重的 Observer 和量化方案。\n", + "\n", + "一定要传递 `Observer` 类(而不是实例),或者可以返回 `Observer` 实例的可调用对象。使用 {func}`with_args` 覆盖默认参数。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "QConfig(activation=functools.partial(, qscheme=torch.per_tensor_affine){}, weight=functools.partial(, qscheme=torch.qint8){})" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from torch.ao.quantization.qconfig import QConfig\n", + "\n", + "my_qconfig = QConfig(\n", + " activation=MovingAverageMinMaxObserver.with_args(\n", + " qscheme=torch.per_tensor_affine),\n", + " weight=MovingAveragePerChannelMinMaxObserver.with_args(qscheme=torch.qint8)\n", + ")\n", + "my_qconfig" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 在 PyTorch 中\n", + "\n", + "PyTorch 允许您使用几种不同的方式来量化您的模型:\n", + "\n", + "- Eager 模式 v/s FX Graph 模式:如果你更喜欢灵活但手动的,或受限的自动过程\n", + "- 静态 v/s 动态:如果量化激活(层的输出)的 `qparams` 为所有输入预先计算,或对每个输入重新计算,\n", + "- 量化感知训练(quantization-aware training) v/s 训练后量化(post-training quantization):如果 `qparams` 是在有或没有重新训练的情况下计算的\n", + "\n", + "FX Graph Mode 自动融合符合条件的模块,插入 Quant/DeQuant stub,校准模型并返回量化模块——所有这些都是在两个方法调用中进行的——但仅适用于 [可符号跟踪](https://pytorch.org/docs/stable/fx.html#torch.fx.symbolic_trace) 的网络。 \n", + "\n", + "在 DNN 中,量化的合适候选对象是 FP32 权值(层参数)和激活(层输出)。量化权值可以减少模型的大小。量化激活通常会导致更快的推理。\n", + "\n", + "例如,50 层 ResNet 网络有近 2600 万个权值参数,在正向传程中计算近 1600 万个激活。\n", + "\n", + "### Post-Training Dynamic/Weight-only Quantization\n", + "\n", + "这里模型的权值是预量化的;在推理期间,激活是动态量化的。这是所有方法中最简单的一种,它在 {func}`~torch.ao.quantization.quantize.quantize_dynamic` 中有一行 API 调用。目前只支持线性和循环(LSTM、GRU、RNN)层进行动态量化。\n", + "\n", + "- 可以导致更高的精度,因为每个输入的裁剪范围是精确校准的\n", + "- 对于像 LSTM 和 Transformer 这样的模型,动态量化是首选的,因为从内存中写入/检索模型的权值会受制于带宽\n", + "- 在运行时对每个层的激活进行校准和量化会增加计算开销。" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "from torch import nn\n", + "\n", + "# 小 model\n", + "def create_model():\n", + " m = nn.Sequential(\n", + " nn.Conv2d(2, 64, (8,)),\n", + " nn.ReLU(),\n", + " nn.Linear(16, 10),\n", + " nn.LSTM(10, 10))\n", + " return m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{rubric} eager 模式\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): Conv2d(2, 64, kernel_size=(8,), stride=(1, 1))\n", + " (1): ReLU()\n", + " (2): DynamicQuantizedLinear(in_features=16, out_features=10, dtype=torch.qint8, qscheme=torch.per_tensor_affine)\n", + " (3): DynamicQuantizedLSTM(10, 10)\n", + ")" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from torch.ao.quantization.quantize import quantize_dynamic\n", + "\n", + "m = create_model()\n", + "m.eval()\n", + "model_quantized = quantize_dynamic(\n", + " model=m, qconfig_spec={nn.LSTM, nn.Linear}, dtype=torch.qint8, inplace=False\n", + ")\n", + "model_quantized" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{rubric} FX 模式\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/media/pc/data/4tb/lxw/libs/anaconda3/envs/tvmx/lib/python3.10/site-packages/torch/nn/quantized/_reference/modules/utils.py:25: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", + " torch.tensor(weight_qparams[\"scale\"], dtype=torch.float, device=device))\n", + "/media/pc/data/4tb/lxw/libs/anaconda3/envs/tvmx/lib/python3.10/site-packages/torch/nn/quantized/_reference/modules/utils.py:28: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", + " torch.tensor(weight_qparams[\"zero_point\"], dtype=zero_point_dtype, device=device))\n", + "/media/pc/data/4tb/lxw/libs/anaconda3/envs/tvmx/lib/python3.10/site-packages/torch/nn/quantized/_reference/modules/rnn.py:302: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", + " torch.tensor(weight_qparams[\"scale\"], dtype=torch.float, device=device))\n", + "/media/pc/data/4tb/lxw/libs/anaconda3/envs/tvmx/lib/python3.10/site-packages/torch/nn/quantized/_reference/modules/rnn.py:305: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n", + " torch.tensor(weight_qparams[\"zero_point\"], dtype=torch.int, device=device))\n" + ] + } + ], + "source": [ + "from torch.ao.quantization import quantize_fx\n", + "from torch.ao.quantization.qconfig import default_dynamic_qconfig\n", + "\n", + "m = create_model()\n", + "m.eval()\n", + "# 空键表示应用于所有模块的默认值\n", + "qconfig_dict = {\"\": default_dynamic_qconfig}\n", + "model_prepared = quantize_fx.prepare_fx(m, qconfig_dict)\n", + "model_quantized = quantize_fx.convert_fx(model_prepared)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Post-Training Static Quantization (PTQ)\n", + "\n", + "PTQ 也预量化模型权重,但不是动态校准激活,而是使用验证数据对剪切范围进行预校准和固定(“静态”)。在推理过程中,激活在运算之间保持量化精度。大约 100 个小批次的代表性数据就足以校准观测者。为了方便起见,下面的例子在校准中使用了随机数据——在应用程序中使用随机数据将导致错误的 `qparams`。\n", + "\n", + "![](images/ptq-flowchart.svg)\n", + "\n", + "[模块融合](https://pytorch.org/tutorials/recipes/fuse.html) 将多个顺序模块(如:`[Conv2d, BatchNorm, ReLU]`)组合成一个。融合模块意味着编译器只需要运行一个内核而不是多个;这可以通过减少量化误差来提高速度和准确性。\n", + "\n", + "- 静态量化比动态量化具有更快的推理速度,因为它消除了层之间的 float<->int 转换成本。\n", + "- 静态量化模型可能需要定期重新校准,以保持对分布漂移的鲁棒性。\n", + "\n", + "静态量化模型包括以下步骤:\n", + "\n", + "- 融合模块\n", + "- 插入 Quant/DeQuant 存根\n", + "- 准备融合模块(在层前和层后插入观察者)\n", + "- 校准准备好的模块(传递代表数据)\n", + "- 转换校准模块(替换为量化版本)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "from torch.quantization import quantize_fx\n", + "import torch\n", + "from torch import nn\n", + "\n", + "# 如果在ARM上运行,使用 `qnnpack`。\n", + "backend = \"fbgemm\" # 运行在 x86 CPU 上。\n", + "\n", + "\n", + "def create_model():\n", + " m = nn.Sequential(\n", + " nn.Conv2d(2, 64, 3),\n", + " nn.ReLU(),\n", + " nn.Conv2d(64, 128, 3),\n", + " nn.ReLU()\n", + " )\n", + " return m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 急切的模式\n", + "\n", + "**融合**:就地融合用所述融合模块替换所述序列中的第一个模块,其余用相同模块替换。" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): ConvReLU2d(\n", + " (0): Conv2d(2, 64, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " )\n", + " (1): Identity()\n", + " (2): ConvReLU2d(\n", + " (0): Conv2d(64, 128, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " )\n", + " (3): Identity()\n", + ")" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = create_model()\n", + "# fuse first Conv-ReLU pair\n", + "torch.quantization.fuse_modules(m, ['0', '1'], inplace=True)\n", + "# fuse second Conv-ReLU pair\n", + "torch.quantization.fuse_modules(m, ['2', '3'], inplace=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "插入 stub:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): QuantStub()\n", + " (1): ConvReLU2d(\n", + " (0): Conv2d(2, 64, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " )\n", + " (2): Identity()\n", + " (3): ConvReLU2d(\n", + " (0): Conv2d(64, 128, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " )\n", + " (4): Identity()\n", + " (5): DeQuantStub()\n", + ")" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = nn.Sequential(torch.quantization.QuantStub(),\n", + " *m,\n", + " torch.quantization.DeQuantStub())\n", + "m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "准备:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/media/pc/data/4tb/lxw/libs/anaconda3/envs/tvmx/lib/python3.10/site-packages/torch/ao/quantization/observer.py:176: UserWarning: Please use quant_min and quant_max to specify the range for observers. reduce_range will be deprecated in a future release of PyTorch.\n", + " warnings.warn(\n" + ] + }, + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): QuantStub(\n", + " (activation_post_process): HistogramObserver()\n", + " )\n", + " (1): ConvReLU2d(\n", + " (0): Conv2d(2, 64, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " (activation_post_process): HistogramObserver()\n", + " )\n", + " (2): Identity()\n", + " (3): ConvReLU2d(\n", + " (0): Conv2d(64, 128, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " (activation_post_process): HistogramObserver()\n", + " )\n", + " (4): Identity()\n", + " (5): DeQuantStub()\n", + ")" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from torch.ao.quantization.qconfig import get_default_qconfig\n", + "from torch.ao.quantization.quantize import prepare\n", + "\n", + "m.qconfig = get_default_qconfig(backend)\n", + "prepare(m, inplace=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**校准**:为了方便起见,这个例子使用了随机数据。使用代表性(验证)数据代替。" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "# with torch.inference_mode(): # PyTorch 1.9\n", + "with torch.no_grad():\n", + " for _ in range(10):\n", + " x = torch.rand(1, 2, 28, 28)\n", + " m(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "转换:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): Quantize(scale=tensor([0.0080]), zero_point=tensor([0]), dtype=torch.quint8)\n", + " (1): QuantizedConvReLU2d(2, 64, kernel_size=(3, 3), stride=(1, 1), scale=0.01072006206959486, zero_point=0)\n", + " (2): Identity()\n", + " (3): QuantizedConvReLU2d(64, 128, kernel_size=(3, 3), stride=(1, 1), scale=0.0029677667189389467, zero_point=0)\n", + " (4): Identity()\n", + " (5): DeQuantize()\n", + ")" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "torch.quantization.convert(m, inplace=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "检查:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n" + ] + } + ], + "source": [ + "# 1 字节,而不是 FP32 的 4 字节\n", + "print(m[1].weight().element_size())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### FX GRAPH 模式" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "from torch.ao.quantization.qconfig import get_default_qconfig\n", + "from torch.ao.quantization import quantize_fx\n", + "\n", + "\n", + "def calibrate(model, data_loader):\n", + " '''使用代表性(验证)数据来校准'''\n", + " model.eval()\n", + " # with torch.inference_mode():\n", + " with torch.no_grad():\n", + " for image, _ in data_loader:\n", + " model(image)\n", + "\n", + "\n", + "def ptq(float_model, sample_inference_data, backend='fbgemm'):\n", + " qconfig = get_default_qconfig(backend)\n", + " qconfig_dict = {\"\": qconfig}\n", + " float_model.eval()\n", + "\n", + " prepared_model = quantize_fx.prepare_fx(float_model, qconfig_dict)\n", + " # 运行校准\n", + " calibrate(prepared_model, sample_inference_data)\n", + " return prepared_model" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "from torch.ao.quantization.qconfig import get_default_qconfig\n", + "from torch.ao.quantization import quantize_fx\n", + "\n", + "def data_iter():\n", + " for _ in range(10):\n", + " yield torch.rand(1, 2, 28, 28), _\n", + "\n", + "m = create_model()\n", + "model_prepared = ptq(m, data_iter(), backend='fbgemm')\n", + "# 量化\n", + "model_quantized = quantize_fx.convert_fx(model_prepared)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Quantization-aware Training (QAT)\n", + "\n", + "![](images/qat-flowchart.svg)\n", + "\n", + "PTQ 方法对于大型模型非常好,但在较小的模型中准确性会受到影响。当然,这是由于将 FP32 的模型调整到 INT8 域时的数值精度损失。\n", + "\n", + "QAT 通过在训练损失中包含量化误差来解决这个问题,因此训练一个 INT8-first 模型。\n", + "\n", + "![](images/ptq-qat.png)\n", + "\n", + "所有的权重和偏置都存储在 FP32 中,反向传播照常发生。然而在正向传递中,量化是通过 `FakeQuantize` 模块进行内部模拟的。它们之所以被称为假的,是因为它们对数据进行量化和立即反量化,并添加与量化推理过程中可能遇到的类似的量化噪声。因此,最终的损失可以解释任何预期的量化误差。在此基础上进行优化,可以使模型在损失函数中识别出更宽的区域,并识别出 FP32 参数,这样量化到 INT8 不会显著影响精度。\n", + "\n", + "[![](images/qat-fake-quantization.png)](https://developer.nvidia.com/blog/achieving-fp32-accuracy-for-int8-inference-using-quantization-aware-training-with-tensorrt)\n", + "\n", + "- QAT 比 PTQ 具有更高的精度。\n", + "- Qparams 可以在模型训练期间学习,以获得更细粒度的准确性(参见 [LearnableFakeQuantize](https://github.com/pytorch/pytorch/blob/master/torch/ao/quantization/_learnable_fake_quantize.py))。\n", + "- 在 QAT 中,重新训练一个模型的计算成本可以达到几百个 epoch。{cite:ps}`gholami2021survey`\n", + "\n", + "除了在将模型实际转换为量化版本之前的训练循环之外,QAT 遵循与 PTQ 相同的步骤:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "from torch import nn\n", + "\n", + "# 运行在 x86 CPU 上。如果在 ARM 上运行,使用 \"qnnpack\"。\n", + "backend = \"fbgemm\"\n", + "\n", + "m = create_model()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "融合:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): ConvReLU2d(\n", + " (0): Conv2d(2, 64, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " )\n", + " (1): Identity()\n", + " (2): ConvReLU2d(\n", + " (0): Conv2d(64, 128, kernel_size=(3, 3), stride=(1, 1))\n", + " (1): ReLU()\n", + " )\n", + " (3): Identity()\n", + ")" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "torch.quantization.fuse_modules(m, ['0', '1'], inplace=True) # 融合第一对 Conv-ReLU\n", + "torch.quantization.fuse_modules(m, ['2', '3'], inplace=True) # 融合第二对 Conv-ReLU" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "插入存根(打桩):" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "m = nn.Sequential(torch.quantization.QuantStub(),\n", + " *m,\n", + " torch.quantization.DeQuantStub())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "准备:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): QuantStub(\n", + " (activation_post_process): HistogramObserver()\n", + " )\n", + " (1): ConvReLU2d(\n", + " 2, 64, kernel_size=(3, 3), stride=(1, 1)\n", + " (weight_fake_quant): PerChannelMinMaxObserver(min_val=tensor([]), max_val=tensor([]))\n", + " (activation_post_process): HistogramObserver()\n", + " )\n", + " (2): Identity()\n", + " (3): ConvReLU2d(\n", + " 64, 128, kernel_size=(3, 3), stride=(1, 1)\n", + " (weight_fake_quant): PerChannelMinMaxObserver(min_val=tensor([]), max_val=tensor([]))\n", + " (activation_post_process): HistogramObserver()\n", + " )\n", + " (4): Identity()\n", + " (5): DeQuantStub()\n", + ")" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m.train()\n", + "m.qconfig = torch.quantization.get_default_qconfig(backend)\n", + "torch.quantization.prepare_qat(m, inplace=True)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "循环训练:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "n_epochs = 10\n", + "opt = torch.optim.SGD(m.parameters(), lr=0.1)\n", + "def loss_fn(out, tgt): return torch.pow(tgt-out, 2).mean()\n", + "\n", + "\n", + "for epoch in range(n_epochs):\n", + " x = torch.rand(10, 2, 24, 24)\n", + " out = m(x)\n", + " loss = loss_fn(out, torch.rand_like(out))\n", + " opt.zero_grad()\n", + " loss.backward()\n", + " opt.step()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "转换:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Sequential(\n", + " (0): Quantize(scale=tensor([0.0079]), zero_point=tensor([0]), dtype=torch.quint8)\n", + " (1): QuantizedConvReLU2d(2, 64, kernel_size=(3, 3), stride=(1, 1), scale=0.009738738648593426, zero_point=0)\n", + " (2): Identity()\n", + " (3): QuantizedConvReLU2d(64, 128, kernel_size=(3, 3), stride=(1, 1), scale=0.004433792550116777, zero_point=0)\n", + " (4): Identity()\n", + " (5): DeQuantize()\n", + ")" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m.eval()\n", + "torch.quantization.convert(m, inplace=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 敏感性分析\n", + "\n", + "并不是所有层对量化的响应都是一样的,有些层对精度下降比其他层更敏感。确定最优的层组合以最小化精度下降是非常耗时的,因此 {cite:ps}`wu2020integer` 建议进行一次一次的灵敏度分析,以确定哪些层最敏感,并在这些层上保持 FP32 的精度。在他们的实验中,跳过 2 个 conv 层(在 MobileNet v1 的 28 个 conv 层中)使他们接近 FP32 的精度。使用 FX Graph 模式,可以创建自定义 `qconfigs` 来轻松做到这一点。\n", + "\n", + "```python\n", + "# ONE-AT-A-TIME SENSITIVITY ANALYSIS \n", + "\n", + "for quantized_layer, _ in model.named_modules():\n", + " print(\"Only quantizing layer: \", quantized_layer)\n", + "\n", + " # The module_name key allows module-specific qconfigs. \n", + " qconfig_dict = {\"\": None, \n", + " \"module_name\":[(quantized_layer, torch.quantization.get_default_qconfig(backend))]}\n", + "\n", + " model_prepared = quantize_fx.prepare_fx(model, qconfig_dict)\n", + " # calibrate\n", + " model_quantized = quantize_fx.convert_fx(model_prepared)\n", + " # evaluate(model)\n", + "```\n", + "\n", + "另一种方法是比较 FP32 和 INT8 层的统计数据;常用的度量有 SQNR(信号量化噪声比,即 Signal to Quantized Noise Ratio)和均方误差(Mean-Squre-Error)。这种比较分析也有助于指导进一步的优化。\n", + "\n", + "![](images/compare_output_ns.png)\n", + "\n", + "PyTorch 在数值套件下提供了帮助进行此分析的工具。从完整的教程中了解更多关于使用 [Numeric Suite](https://pytorch.org/tutorials/prototype/numeric_suite_tutorial.html) 的信息。\n", + "\n", + "```python\n", + "# extract from https://pytorch.org/tutorials/prototype/numeric_suite_tutorial.html\n", + "import torch.quantization._numeric_suite as ns\n", + "\n", + "def SQNR(x, y):\n", + " # Higher is better\n", + " Ps = torch.norm(x)\n", + " Pn = torch.norm(x-y)\n", + " return 20*torch.log10(Ps/Pn)\n", + "\n", + "wt_compare_dict = ns.compare_weights(fp32_model.state_dict(), int8_model.state_dict())\n", + "for key in wt_compare_dict:\n", + " print(key, compute_error(wt_compare_dict[key]['float'], wt_compare_dict[key]['quantized'].dequantize()))\n", + "\n", + "act_compare_dict = ns.compare_model_outputs(fp32_model, int8_model, input_data)\n", + "for key in act_compare_dict:\n", + " print(key, compute_error(act_compare_dict[key]['float'][0], act_compare_dict[key]['quantized'][0].dequantize()))\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 对您工作流程的建议\n", + "\n", + "![](images/quantization-flowchart2.png)\n", + "\n", + "要点:\n", + "\n", + "- 大(10M+ 参数)模型对量化误差更具鲁棒性。\n", + "- 从 FP32 检查点量化模型比从零开始训练 INT8 模型提供了更好的 accuracy。\n", + "- 分析模型运行时是可选的,但它可以帮助识别阻碍推理的层。\n", + "- 动态量化是一个简单的第一步,特别是当您的模型有许多线性或递归层时。\n", + "- 使用逐通道对称量化借由 `MinMax` 观测者量化权重。使用逐张量仿射量化借由 `MovingAverageMinMax` 观测者量化激活。\n", + "- 使用诸如 SQNR 之类的度量来确定哪些层最容易受到量化误差的影响。关闭这些层上的量化。\n", + "- 使用 QAT 对原始训练调度的大约 $10\\%$ 进行微调,退火学习率(annealing learning rate)调度从初始训练学习率的 $1\\%$ 开始。\n", + "- 如果上面的工作流程不适合你,我们想知道更多。发布一个包含你的代码细节的帖子(模型架构,准确性指标,尝试过的技术)。请抄送 [@suraj.pt](https://discuss.pytorch.org/u/suraj.pt/)。" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.10.4 ('tvmx': conda)", + "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": "3.10.4" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "e579259ee6098e2b9319de590d145b4b096774fe457bdf04260e3ba5c171e887" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tests/quant/sigmoid-fx/.gitignore b/tests/quant/sigmoid-fx/.gitignore new file mode 100644 index 0000000..304a2f5 --- /dev/null +++ b/tests/quant/sigmoid-fx/.gitignore @@ -0,0 +1,3 @@ +models/ +*copy* +draft/ \ No newline at end of file diff --git a/tests/quant/sigmoid-fx/cifar10-resnet18.ipynb b/tests/quant/sigmoid-fx/cifar10-resnet18.ipynb new file mode 100644 index 0000000..3e627fc --- /dev/null +++ b/tests/quant/sigmoid-fx/cifar10-resnet18.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Cifar10 上的 ReNet18 Sigmoid 线性化\n", + "\n", + "本文主要介绍在 cifar10 的试验 resnet18 的性能。\n", + "\n", + "导入一些必要包:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "from torch import nn, fx\n", + "from torchvision.models import resnet18, ResNet18_Weights\n", + "from torch_book.datasets.simple_vision import Cifar10\n", + "# from torch_book.tools import train, try_all_gpus, evaluate_accuracy\n", + "\n", + "torch.cuda.empty_cache() # 清空 GPU 缓存" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "创建模型:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def _create_model():\n", + " \"\"\"模型加载\"\"\"\n", + " model = resnet18(weights=ResNet18_Weights.DEFAULT)\n", + " model.conv1 = nn.Conv2d(model.conv1.in_channels, \n", + " model.conv1.out_channels, \n", + " 3, 1, 1)\n", + " model.maxpool = nn.Identity() #nn.Conv2d(64, 64, 1, 1, 1)\n", + " model.fc = nn.Linear(model.fc.in_features, 10)\n", + " return model" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "model = _create_model()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "加载数据:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "dataset = Cifar10(root=\"../data\", batch_size=64, num_workers=4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "relu_valid_acc = evaluate_accuracy(model, test_iter)\n", + "relu_valid_acc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 模块变换\n", + "\n", + "利用 FX 替换全部 {class}`~torch.nn.ReLU` 为 {func}`torch.sigmoid`。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def replace(model):\n", + " mod = fx.symbolic_trace(model)\n", + " # 遍历 Graph 中全部节点\n", + " for node in mod.graph.nodes:\n", + " # 如果匹配目标\n", + " if node.op == \"call_module\":\n", + " if \"relu\" in node.target:\n", + " # 设置插入点,添加新节点,用新节点替换所有 `node` 的用法\n", + " with mod.graph.inserting_after(node):\n", + " new_node = mod.graph.call_function(torch.sigmoid, node.args, node.kwargs)\n", + " node.replace_all_uses_with(new_node)\n", + " # 移除 graph 中旧的节点\n", + " mod.graph.erase_node(node)\n", + " mod.graph.lint()\n", + " # 不用忘记 recompile!\n", + " new_code = mod.recompile()\n", + " return mod" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mod = replace(model)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "valid_acc = evaluate_accuracy(mod, test_iter)\n", + "valid_acc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "微调:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def fine_tune(mod, num_epochs,\n", + " train_iter, test_iter,\n", + " devices=try_all_gpus(),\n", + " lr=0.0000142857,\n", + " lr_period=4,\n", + " lr_decay=0.0857142,\n", + " weight_decay=0.00857142,\n", + " momentum=0.857142):\n", + " optimizer = torch.optim.SGD(mod.parameters(),\n", + " lr=lr,\n", + " momentum=momentum, \n", + " weight_decay=weight_decay)\n", + " scheduler = torch.optim.lr_scheduler.StepLR(optimizer, \n", + " step_size=lr_period, \n", + " gamma=lr_decay)\n", + " train(mod, train_iter, test_iter,\n", + " num_epochs, devices,\n", + " optimizer, scheduler)\n", + " return mod" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mod = replace(model)\n", + "mod = fine_tune(mod, 100,\n", + " train_iter, test_iter, \n", + " try_all_gpus(),\n", + " lr=0.000142857,\n", + " lr_period=2,\n", + " lr_decay=0.857142,\n", + " weight_decay=0.00714285,\n", + " momentum=0.857142)\n", + "\n", + "torch.save(mod.state_dict(), \n", + " 'models/resnet18_cifar10_sigmoid_64_1.h5')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.10.4 ('tvmx': conda)", + "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": "3.10.9" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "e579259ee6098e2b9319de590d145b4b096774fe457bdf04260e3ba5c171e887" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tests/quant/sigmoid-fx/fixed_sigmoid.py b/tests/quant/sigmoid-fx/fixed_sigmoid.py new file mode 100644 index 0000000..c6a58fe --- /dev/null +++ b/tests/quant/sigmoid-fx/fixed_sigmoid.py @@ -0,0 +1,42 @@ +import logging +from sympy import interpolating_spline, symbols, exp +import torch +from torch import nn + +def sigmoid(x): + x = 1 + exp(-x) + return 1/x + +def get_nodes(indexes=[-6, -5, -3, -2, -1, 0, 1, 2, 3, 5, 6], + func=sigmoid): + """boundary 保证函数取得边界值""" + x = symbols("x") + if 0.0 not in indexes: + indexes.append(0.0) + indexes.sort() # 排序 + boundary = max(abs(indexes[-1]), abs(indexes[0])) + indexes[-1] = boundary + indexes[0] = - boundary + # simplify(sigmoid(1) + sigmoid(-1)) + logging.debug(f"值的范围:\n {indexes}") + sigmoid_sym = interpolating_spline(1, + x, + indexes, + [float(func(n)) for n in indexes]) + nodes = {} + for expr, set_pair in sigmoid_sym.as_expr_set_pairs(): + nodes[set_pair] = float(expr.diff()), float(expr.taylor_term(0, x)) + return nodes + +def linear_sigmoid(x, nodes): + y = torch.zeros_like(x) + for set_pair, (scale, zero_point) in nodes.items(): + start, end = [torch.tensor(k, dtype=torch.float32) + for k in set_pair.args[:2]] + scale, zero_point = [torch.tensor(k, dtype=torch.float32) + for k in [scale, zero_point]] + cond = (x >= start) * (x < end) + f = x * scale + zero_point + y += f * cond + y += torch.ones_like(x) * (x >= end) + return y #* (y <=1) * (y >= 0) diff --git a/tests/quant/sigmoid-fx/index.md b/tests/quant/sigmoid-fx/index.md new file mode 100644 index 0000000..7bc348b --- /dev/null +++ b/tests/quant/sigmoid-fx/index.md @@ -0,0 +1,6 @@ +# Sigmoid 量化 + +```{toctree} +sigmoid +cifar10-resnet18 +``` \ No newline at end of file diff --git a/tests/quant/sigmoid-fx/observer.py b/tests/quant/sigmoid-fx/observer.py new file mode 100644 index 0000000..a724982 --- /dev/null +++ b/tests/quant/sigmoid-fx/observer.py @@ -0,0 +1,9 @@ +# from torch.nn import functional as F +import torch +from torch import fx +from torch.ao.quantization.observer import HistogramObserver + +@fx.wrap +def histogram_observer(x): + observer = HistogramObserver(dtype=torch.quint8, qscheme=torch.per_tensor_affine) + return observer(x) \ No newline at end of file diff --git a/tests/quant/sigmoid-fx/sigmoid.ipynb b/tests/quant/sigmoid-fx/sigmoid.ipynb new file mode 100644 index 0000000..a2af84d --- /dev/null +++ b/tests/quant/sigmoid-fx/sigmoid.ipynb @@ -0,0 +1,490 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sigmoid 量化\n", + "\n", + "对于定义域 $\\mathbb{R}$ 中的输入,sigmoid 函数将输入变换为区间 $(0, 1)$ 上的输出。因此,sigmoid 通常称为挤压函数(squashing function):它将范围 $(- \\infty, \\infty)$ 中的任意输入压缩到区间 $(0, 1)$ 中的某个值,sigmoid 函数定义如下:\n", + "\n", + "$$\n", + "\\operatorname{sigmoid}(x) = \\frac{1}{1 + \\exp(-x)}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n \n \n \n \n 2022-11-03T17:02:52.612571\n image/svg+xml\n \n \n Matplotlib v3.5.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import torch\n", + "from torch_book import plotx\n", + "\n", + "x = torch.arange(-8.0, 8.0, 0.1, requires_grad=True)\n", + "y = torch.sigmoid(x)\n", + "plotx.plot(x.detach(), y.detach(), \n", + " 'x', 'sigmoid(x)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "sigmoid 函数特性:\n", + "\n", + "$$\n", + "\\operatorname{sigmoid}(x) + \\operatorname{sigmoid}(-x) = 1\n", + "$$\n", + "\n", + "sigmoid 函数的导数为下面的公式:\n", + "\n", + "$$\n", + "\\frac{\\operatorname{d}}{\\operatorname{d} x} \\operatorname{sigmoid}(x) = \\frac{\\exp(-x)}{(1 + \\exp(-x))^2} = \\operatorname{sigmoid}(x)\\left(1-\\operatorname{sigmoid}(x)\\right) = \\operatorname{sigmoid}(x)\\operatorname{sigmoid}(-x)\n", + "$$\n", + "\n", + "可视化导函数:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n \n \n \n \n 2022-11-03T17:02:52.838310\n image/svg+xml\n \n \n Matplotlib v3.5.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "y.backward(torch.ones_like(x), retain_graph=True)\n", + "plotx.plot(x.detach(), x.grad, \n", + " 'x', 'sigmoid 导函数')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\operatorname{g}(t) = \\int_{-\\infty}^t \\frac{\\operatorname{d}}{\\operatorname{d} x} \\operatorname{sigmoid}(x) \\operatorname{d} x\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n \n \n \n \n 2022-11-03T17:02:53.029792\n image/svg+xml\n \n \n Matplotlib v3.5.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x.grad.zero_()\n", + "y.backward(torch.ones_like(x), retain_graph=True)\n", + "p = x.grad.cumsum(dim=0) * 0.1\n", + "plotx.plot(x.detach(), p, \n", + " 'x', 'sigmoid 概率密度函数')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "sigmoid 函数于 $x_0$ 处的泰勒展示式:\n", + "\n", + "$$\n", + "\\operatorname{sigmoid}(x) = \\operatorname{sigmoid}(x_0)( 1 + \\operatorname{sigmoid}(-x_0) \\sum_{k=1}^{\\infty} \\cfrac{(x - x_0)^k}{k!})\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 区间分划\n", + "\n", + "由于 sigmoid 函数关于 $y = 0.5$ 对称,故仅仅考虑 $x > 0$ 的部分即可。\n", + "\n", + "由 sigmoid 及其导函数图像可以看出:$x \\in [-6, 6]$ 的函数值以及导数值变化剧烈。依此可以将此范围外的函数值直接设定为极限值即可。\n", + "\n", + "```{note}\n", + "对于 $n$ **分划**:\n", + "\n", + "$$\n", + "\\Delta: a=x_0 < x_1 < \\cdots < x_n =b \n", + "$$\n", + "\n", + "在每个子段 $[x_i, x_{i+1}]$ 构造插值多项式,并将其拼接起来,即 **分段插值**。\n", + "\n", + "若函数 $S_k(x)$ 在分划 $\\delta$ 的每个子段 $[x_i, x_{i+1}]$ 都是 $k$ 次多项式,则称 $S_k(x)$ 为具有分划 $\\delta$ 的 **分段 $k$ 次式**。点 $x_i$ ($i=0,1,\\cdots,n$)称作 $S_k(x)$ 的节点。\n", + "```\n", + "\n", + "为了提高量化精度,在 $[0, 6]$ 上考虑分段插值。取 $n=10$,依据 sigmoid 导函数的变化趋势可设定 $S_k(x)$ 的节点为:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "11" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nodes = 0, 0.25, 0.5, 0.75, 1, 2, 2.5, 3, 4, 5, 6\n", + "len(nodes)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.5000, 0.5622, 0.6225, 0.6792, 0.7311, 0.8808, 0.9241, 0.9526, 0.9820,\n", + " 0.9933, 0.9975], grad_fn=)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = torch.tensor(nodes, requires_grad=True)\n", + "y = torch.sigmoid(x)\n", + "y" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.2500, 0.2461, 0.2350, 0.2179, 0.1966, 0.1050, 0.0701, 0.0452, 0.0177,\n", + " 0.0066, 0.0025])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y.backward(torch.ones_like(x), retain_graph=True)\n", + "x.grad" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## uint8 量化\n", + "\n", + "先看看简单的方案:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def Qz(v, s):\n", + " k = s * v - np.floor(v * s)\n", + " o = k > 0.5\n", + " return o.astype(\"int\")\n", + "\n", + "def Q(v, s):\n", + " x = np.floor(v * s) + Qz(v, s)\n", + " return x/s" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "scale = (1 << 8) - 1\n", + "with torch.no_grad():\n", + " qy = Q(y.numpy(), scale)\n", + " qy = torch.from_numpy(qy)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "from torch.ao.quantization.observer import MinMaxObserver, MovingAverageMinMaxObserver, HistogramObserver\n", + "\n", + "\n", + "dtype = torch.quint8\n", + "qscheme = torch.per_tensor_affine\n", + "\n", + "config = {\n", + " \"dtype\": dtype,\n", + " \"qscheme\": qscheme\n", + "}\n", + "observers = [MinMaxObserver(**config),\n", + " MovingAverageMinMaxObserver(**config),\n", + " HistogramObserver(**config)]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MinMaxObserver tensor([0.0039]) tensor([0], dtype=torch.int32)\n", + "MovingAverageMinMaxObserver tensor([0.0039]) tensor([0], dtype=torch.int32)\n", + "HistogramObserver tensor([0.0039]) tensor([0], dtype=torch.int32)\n" + ] + } + ], + "source": [ + "for obs in observers:\n", + " obs(y)\n", + " s, z = obs.calculate_qparams()\n", + " print(obs.__class__.__name__, s, z)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.4967, 0.5593, 0.6218, 0.6766, 0.7274, 0.8800, 0.9230, 0.9504, 0.9816,\n", + " 0.9895, 0.9973])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "with torch.no_grad():\n", + " _y = (torch.floor(y/s) + z) * s\n", + "_y" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.4980, 0.5608, 0.6235, 0.6784, 0.7294, 0.8824, 0.9255, 0.9529, 0.9804,\n", + " 0.9922, 0.9961], dtype=torch.float64)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qy" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.5000, 0.5622, 0.6225, 0.6792, 0.7311, 0.8808, 0.9241, 0.9526, 0.9820,\n", + " 0.9933, 0.9975], grad_fn=)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sigmoid 观测器" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import interpolating_spline, symbols, exp, simplify, oo\n", + "\n", + "def sigmoid(x):\n", + " x = 1 + exp(-x)\n", + " return 1/x\n", + "\n", + "x = symbols(\"x\")\n", + "# simplify(sigmoid(1) + sigmoid(-1))\n", + "node_indexes = [-6, -5, -3, -2, -1, 0, 1, 2, 3, 5, 6]\n", + "sigmoid_sym = interpolating_spline(1,\n", + " x,\n", + " node_indexes,\n", + " [float(sigmoid(n)) for n in node_indexes])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\begin{cases} 0.00422022776765008 x + 0.0277939897625353 & \\text{for}\\: x \\geq -6 \\wedge x \\leq -5 \\\\0.020366511126641 x + 0.10852540655749 & \\text{for}\\: x \\geq -5 \\wedge x \\leq -3 \\\\0.0717770488445508 x + 0.262757019711219 & \\text{for}\\: x \\geq -3 \\wedge x \\leq -2 \\\\0.149738499347878 x + 0.418679920717873 & \\text{for}\\: x \\geq -2 \\wedge x \\leq -1 \\\\0.231058578630005 x + 0.5 & \\text{for}\\: \\left(x \\geq -1 \\vee x \\geq 0\\right) \\wedge \\left(x \\geq -1 \\vee x \\leq 1\\right) \\wedge \\left(x \\geq 0 \\vee x \\leq 0\\right) \\wedge \\left(x \\leq 0 \\vee x \\leq 1\\right) \\\\0.149738499347878 x + 0.581320079282127 & \\text{for}\\: x \\geq 1 \\wedge x \\leq 2 \\\\0.0717770488445508 x + 0.737242980288781 & \\text{for}\\: x \\geq 2 \\wedge x \\leq 3 \\\\0.020366511126641 x + 0.891474593442511 & \\text{for}\\: x \\geq 3 \\wedge x \\leq 5 \\\\0.00422022776765008 x + 0.972206010237465 & \\text{for}\\: x \\geq 5 \\wedge x \\leq 6 \\end{cases}$" + ], + "text/plain": [ + "Piecewise((0.00422022776765008*x + 0.0277939897625353, (x >= -6) & (x <= -5)), (0.020366511126641*x + 0.10852540655749, (x >= -5) & (x <= -3)), (0.0717770488445508*x + 0.262757019711219, (x >= -3) & (x <= -2)), (0.149738499347878*x + 0.418679920717873, (x >= -2) & (x <= -1)), (0.231058578630005*x + 0.5, ((x >= -1) | (x >= 0)) & ((x >= -1) | (x <= 1)) & ((x >= 0) | (x <= 0)) & ((x <= 0) | (x <= 1))), (0.149738499347878*x + 0.581320079282127, (x >= 1) & (x <= 2)), (0.0717770488445508*x + 0.737242980288781, (x >= 2) & (x <= 3)), (0.020366511126641*x + 0.891474593442511, (x >= 3) & (x <= 5)), (0.00422022776765008*x + 0.972206010237465, (x >= 5) & (x <= 6)))" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sigmoid_sym" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n \n \n \n \n 2022-11-03T17:03:01.121674\n image/svg+xml\n \n \n Matplotlib v3.5.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sympy.plotting import plot\n", + "\n", + "plot(sigmoid_sym, ylabel=\"sigmoid(x)\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.10.4 ('tvmx': conda)", + "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": "3.10.4" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "e579259ee6098e2b9319de590d145b4b096774fe457bdf04260e3ba5c171e887" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tests/quant/utils/sigmoid.py b/tests/quant/utils/sigmoid.py new file mode 100644 index 0000000..9d30537 --- /dev/null +++ b/tests/quant/utils/sigmoid.py @@ -0,0 +1,32 @@ +from sympy import interpolating_spline, symbols, exp #, simplify +import torch +from torch.nn + +def sigmoid(x): + x = 1 + exp(-x) + return 1/x + +x = symbols("x") +# simplify(sigmoid(1) + sigmoid(-1)) +node_indexes = [-6, -5, -3, -2, -1, 0, 1, 2, 3, 5, 6] +sigmoid_sym = interpolating_spline(1, + x, + node_indexes, + [float(sigmoid(n)) for n in node_indexes]) + +nodes = {} +for expr, set_pair in sigmoid_sym.as_expr_set_pairs(): + nodes[set_pair] = float(expr.diff()), float(expr.taylor_term(0, x)) + +class Sigmoid(nn.Module): + def forward(self, x): + y = torch.zeros_like(x) + for set_pair, (scale, zero_point) in nodes.items(): + start, end = [torch.tensor(k, dtype=torch.float32) + for k in set_pair.args[:2]] + scale, zero_point = [torch.tensor(k, dtype=torch.float32) + for k in [scale, zero_point]] + cond = (x >= start) * (x < end) + f = x * scale + zero_point + y += f * cond + return y \ No newline at end of file diff --git a/tests/tanh.ipynb b/tests/tanh.ipynb new file mode 100644 index 0000000..36d6a50 --- /dev/null +++ b/tests/tanh.ipynb @@ -0,0 +1,168 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# tanh 量化\n", + "\n", + "对于定义域 $\\mathbb{R}$ 中的输入,tanh 函数将输入变换为区间 $(-1, 1)$ 上的输出。函数定义如下:\n", + "\n", + "$$\n", + "\\operatorname{tanh}(x) = \\frac{1 - \\exp(-2x)}{1 + \\exp(-2x)}.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n \n \n \n \n 2022-10-20T14:40:31.551499\n image/svg+xml\n \n \n Matplotlib v3.5.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "from matplotlib import pyplot as plt\n", + "import torch\n", + "from torch_book.visual.mp_plot import plot\n", + "\n", + "x = torch.arange(-8.0, 8.0, 0.1, requires_grad=True)\n", + "y = torch.tanh(x)\n", + "plot(x.detach(), y.detach(), 'x', 'tanh(x)', figsize=(5, 2.5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "tanh 函数特性:\n", + "\n", + "$$\n", + "\\operatorname{tanh}(x) + \\operatorname{tanh}(-x) = 0\n", + "$$\n", + "\n", + "tanh 函数的导数为下面的公式:\n", + "\n", + "$$\n", + "\\frac{\\operatorname{d}}{\\operatorname{d} x} \\operatorname{tanh}(x) = 1 - \\operatorname{tanh}^2(x).\n", + "$$\n", + "\n", + "可视化导函数:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n \n \n \n \n 2022-10-20T14:41:39.793065\n image/svg+xml\n \n \n Matplotlib v3.5.1, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "y.backward(torch.ones_like(x),retain_graph=True)\n", + "plot(x.detach(), x.grad, 'x', 'tanh 导函数', figsize=(5, 2.5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "tanh 函数的泰勒展示式:\n", + "\n", + "$$\n", + "\\operatorname{tanh}(x) = \\sum_{k=-\\infty}^{\\infty} \\frac{x^k}{k!}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.10.4 ('tvmx': conda)", + "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": "3.10.4" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "e579259ee6098e2b9319de590d145b4b096774fe457bdf04260e3ba5c171e887" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tests/taylor.ipynb b/tests/taylor.ipynb new file mode 100644 index 0000000..1c63482 --- /dev/null +++ b/tests/taylor.ipynb @@ -0,0 +1,453 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 泰勒公式与量化\n", + "\n", + "```{admonition} 定理\n", + "假设 $f(x)$ 在 $x_0 \\in [a, b]$ 内有直到 $n+1$ 阶导,则当 $x \\in [a, b]$ 时,泰勒多项式\n", + "\n", + "$$\n", + "p_n (x) = \\sum_{k=0}^n \\cfrac{f^{(k)}(x_0)}{k!} (x - x_0)^k\n", + "$$ (P1)\n", + "\n", + "满足\n", + "\n", + "$$\n", + "f(x) - p_n(x) = \\cfrac{f^{(n+1)}(\\xi)}{(n+1)!} (x - x_0)^{n+1}\n", + "$$ (P2)\n", + "\n", + "其中 $\\xi \\in [x_0, x]$,因而,$\\xi \\in [a, b]$。\n", + "```\n", + "\n", + "这样,可以使用 $p$ 进制数近似浮点数:\n", + "\n", + "$$\n", + "x = \\sum_{k=0}^{\\infty} x_k p^k \n", + "$$ (P3)\n", + "\n", + "其中 $x_k \\in Q$。\n", + "\n", + "这里 $Q$ 表示 $p$ 进制数的值域。\n", + "\n", + "比特(bit)是表示信息量的最小单位,可以用 $0$ (不存在)和 $1$ (存在)来度量。这样二进制数域 $\\{0, 1\\}$ 便可等价于信息量。\n", + "\n", + "```{note}\n", + "计算机中数据存储是以“字节”(Byte,简写为 B)为单位,数据传输大多是以“位”(bit,又名“比特”)为单位,且有 $1 \\text{B} = 8 \\text{bit}$,$1 \\text{bit}$ 表示 $0$ 与 $1$ 两种状态。\n", + "\n", + "计算机存储整数可能有 int8,uint8,int32,int64 等。\n", + "```\n", + "\n", + "如若限定 $k=8, p=2, x_k \\in \\{0, 1\\}$,则 $x \\in [0,2^8-1] \\cap \\mathbb{N} $。这种约束下的集合便是值域为 $[0, 255]$ 的 uint8 数据。" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(2, dtype=uint8)" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "a = np.array(2, dtype=\"uint8\")\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "查看数据占用字节数:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.itemsize # 1字节=8比特" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "可以存储两个 uint8 数据为一个块:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2, 7], dtype=uint8)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.array([2, 7], dtype=\"uint8\")\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "单个元素占用字节数:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.itemsize" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "全部数据集合占用字节数:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.nbytes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "单个 uint8 数据,图示:\n", + "\n", + "```{mermaid}\n", + "flowchart LR\n", + "subgraph uint8\n", + " x0[0或1]\n", + " x1[0或1]\n", + " x2[0或1] \n", + " x3[0或1]\n", + " x4[0或1] \n", + " x5[0或1] \n", + " x6[0或1] \n", + " x7[0或1]\n", + "end\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "其他数据类型可以类推。也可以对数据类型进行转换:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([300, 5, 100, -20], dtype=int32)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v = np.array([300, 5, 100, -20], dtype=\"int32\")\n", + "v" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "转换为 uint8 数据:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 44, 5, 100, 236], dtype=uint8)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q = v.astype(\"uint8\")\n", + "q" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "可见数据被截断了。" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 44, 5, 100, 236], dtype=int32)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v % 256" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量化数据" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def normalize(v):\n", + " \"\"\"将数据缩放到 [0, 1]\"\"\"\n", + " b = v.min() # \\alpha\n", + " a = v.max() - b # \\beta\n", + " v = v - b\n", + " return v/a" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "class Quant:\n", + " def __init__(self, x, dtype=\"uint8\"):\n", + " self.x = x\n", + " self.dtype = dtype\n", + " self.q = x.astype(self.dtype)\n", + " \n", + " @property \n", + " def scale(self):\n", + " a = self.x.max() - self.x.min()\n", + " b = self.q.max() - self.q.min()\n", + " return a/b\n", + " \n", + " @property\n", + " def zero_point(self):\n", + " return np.round(self.q.max() - self.x.max()/self.scale)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([300, 5, 100, -20], dtype=int32)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v = np.array([300, 5, 100, -20], dtype=\"int32\")\n", + "v" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "self = Quant(v)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1.3852813852813852, 19.0)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "self.scale, self.zero_point" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 34, -19, 112, 300], dtype=int32)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = (self.q - self.zero_point) * self.scale\n", + "x = x.astype(\"int32\")\n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([300, 5, 100, -20], dtype=int32)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.10.4 ('tvmx': conda)", + "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": "3.10.4" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "e579259ee6098e2b9319de590d145b4b096774fe457bdf04260e3ba5c171e887" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}

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