diff options
| -rw-r--r-- | learn_torch/grad/01_sigmoid.ipynb | 700 | ||||
| -rw-r--r-- | rl/basics/exp.py | 10 |
2 files changed, 710 insertions, 0 deletions
diff --git a/learn_torch/grad/01_sigmoid.ipynb b/learn_torch/grad/01_sigmoid.ipynb new file mode 100644 index 0000000..568b259 --- /dev/null +++ b/learn_torch/grad/01_sigmoid.ipynb @@ -0,0 +1,700 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 11, + "id": "3e0fd009", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:18:25.694270Z", + "start_time": "2022-12-21T14:18:25.689308Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import torch\n", + "from torch import nn" + ] + }, + { + "cell_type": "markdown", + "id": "19752d02", + "metadata": {}, + "source": [ + "## 1. sigmoid" + ] + }, + { + "cell_type": "markdown", + "id": "61c39ff9", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{equation}\n", + "\\begin{split}\n", + "\\sigma(x)=&\\frac{1}{1+\\exp(-x)}\\\\\n", + "\\sigma'(x)=&\\frac{1}{1+\\exp(-x)}\\cdot\\left(\\frac{\\exp(-x)}{1+\\exp(-x)}\\right)\\\\\n", + "=&\\sigma(x)\\cdot(1-\\sigma(x))\n", + "\\end{split}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "712ada20", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:18:56.364919Z", + "start_time": "2022-12-21T14:18:56.361697Z" + } + }, + "outputs": [], + "source": [ + "x = torch.tensor(1., requires_grad=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "b59eb7b2", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:18:58.039226Z", + "start_time": "2022-12-21T14:18:58.033116Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(1., requires_grad=True)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "2954b719", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:19:03.135490Z", + "start_time": "2022-12-21T14:19:03.132685Z" + } + }, + "outputs": [], + "source": [ + "x.grad" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "52f8345a", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:17:13.664355Z", + "start_time": "2022-12-21T14:17:13.661315Z" + } + }, + "outputs": [], + "source": [ + "y = x.sigmoid()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "11834af2", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:17:16.692371Z", + "start_time": "2022-12-21T14:17:16.685271Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.7311, grad_fn=<SigmoidBackward0>)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "85058642", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:17:24.778205Z", + "start_time": "2022-12-21T14:17:24.772897Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7310585786300049" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1/(1+np.exp(-1))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "aee2b514", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:17:42.045216Z", + "start_time": "2022-12-21T14:17:42.041184Z" + } + }, + "outputs": [], + "source": [ + "y.backward()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "1db231de", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:17:45.510450Z", + "start_time": "2022-12-21T14:17:45.504834Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.1966)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x.grad" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "752f7c65", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:18:10.236761Z", + "start_time": "2022-12-21T14:18:10.230619Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.1966, grad_fn=<MulBackward0>)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x.sigmoid()*(1-x.sigmoid())" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "de599e8a", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:18:31.682109Z", + "start_time": "2022-12-21T14:18:31.679012Z" + } + }, + "outputs": [], + "source": [ + "sigmoid = nn.Sigmoid()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "4aeb6c11", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:18:42.674460Z", + "start_time": "2022-12-21T14:18:42.667354Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.1966, grad_fn=<MulBackward0>)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sigmoid(x)*(1-sigmoid(x))" + ] + }, + { + "cell_type": "markdown", + "id": "0d705c70", + "metadata": {}, + "source": [ + "### 1.1 multi variables 多元形式" + ] + }, + { + "cell_type": "markdown", + "id": "1f78cda0", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{split}\n", + "&y: \\mathbb R^n \\rightarrow \\mathbb R\\\\\n", + "&y=\\sum_i\\sigma(x_i)=\\sigma(x_1)+\\sigma(x_2)+\\sigma(x_3)+\\cdots\\\\\n", + "&\\frac{\\partial y}{\\partial x_1}=\\frac{\\partial y}{\\partial \\sigma(x_1)}\\cdot\\frac{\\partial \\sigma(x_1)}{\\partial x_1}=1\\cdot \\sigma'(x_1)=\\sigma(x_1)\\cdot(1-\\sigma(x_1))\\\\\n", + "&\\frac{\\partial y}{\\partial x_2}=\\frac{\\partial y}{\\partial \\sigma(x_2)}\\cdot\\frac{\\partial \\sigma(x_2)}{\\partial x_2}=1\\cdot \\sigma'(x_2)=\\sigma(x_2)\\cdot(1-\\sigma(x_2))\n", + "\\end{split}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "a170b4f2", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:21:16.930507Z", + "start_time": "2022-12-21T14:21:16.927246Z" + } + }, + "outputs": [], + "source": [ + "x = torch.tensor([1., 2., 3.], requires_grad=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "28ad92b0", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:21:20.400132Z", + "start_time": "2022-12-21T14:21:20.394956Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([1., 2., 3.], requires_grad=True)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "207aed3d", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:21:33.866170Z", + "start_time": "2022-12-21T14:21:33.863052Z" + } + }, + "outputs": [], + "source": [ + "y = x.sigmoid().sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "aae94138", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:21:37.659070Z", + "start_time": "2022-12-21T14:21:37.653139Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(2.5644, grad_fn=<SumBackward0>)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "768fc89e", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:21:58.365597Z", + "start_time": "2022-12-21T14:21:58.362737Z" + } + }, + "outputs": [], + "source": [ + "x.grad" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "66ada1a0", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:22:04.651730Z", + "start_time": "2022-12-21T14:22:04.648331Z" + } + }, + "outputs": [], + "source": [ + "y.backward()" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "6106351f", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:22:15.633303Z", + "start_time": "2022-12-21T14:22:15.627301Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.1966, 0.1050, 0.0452])" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x.grad" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "7c8fb8e2", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:22:52.283229Z", + "start_time": "2022-12-21T14:22:52.277048Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.1966, 0.1050, 0.0452], grad_fn=<MulBackward0>)" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x.sigmoid() * (1-x.sigmoid())" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "752e44c8", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:23:04.923198Z", + "start_time": "2022-12-21T14:23:04.920210Z" + } + }, + "outputs": [], + "source": [ + "sigmoid = nn.Sigmoid()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "67c3ec8e", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:23:14.293035Z", + "start_time": "2022-12-21T14:23:14.287461Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor([0.1966, 0.1050, 0.0452], grad_fn=<MulBackward0>)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sigmoid(x)*(1-sigmoid(x))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "07ace81a", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "5d320185", + "metadata": {}, + "source": [ + "### 1.2 自定义函数" + ] + }, + { + "cell_type": "markdown", + "id": "5f7bccd6", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{split}\n", + "&y=\\sigma^2(x)\\\\\n", + "&y'=2\\sigma(x)\\cdot(\\sigma'(x))=2\\sigma(x)\\cdot(\\sigma(x)(1-\\sigma(x)))\n", + "\\end{split}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "8f933296", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:23:49.314325Z", + "start_time": "2022-12-21T14:23:49.311149Z" + } + }, + "outputs": [], + "source": [ + "x = torch.tensor(2., requires_grad=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "41f93718", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:23:57.314962Z", + "start_time": "2022-12-21T14:23:57.311915Z" + } + }, + "outputs": [], + "source": [ + "y = x.sigmoid()*x.sigmoid()" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "7e776d6d", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:23:58.838686Z", + "start_time": "2022-12-21T14:23:58.833639Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.7758, grad_fn=<MulBackward0>)" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "44cff663", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:24:24.895720Z", + "start_time": "2022-12-21T14:24:24.893088Z" + } + }, + "outputs": [], + "source": [ + "x.grad" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "1adcff5a", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:24:28.985525Z", + "start_time": "2022-12-21T14:24:28.981695Z" + } + }, + "outputs": [], + "source": [ + "y.backward()" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "0d02d2e6", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:24:31.996468Z", + "start_time": "2022-12-21T14:24:31.989945Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.1850)" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x.grad" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "0b75dad1", + "metadata": { + "ExecuteTime": { + "end_time": "2022-12-21T14:24:55.668346Z", + "start_time": "2022-12-21T14:24:55.661259Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "tensor(0.1850, grad_fn=<MulBackward0>)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "2*x.sigmoid()*(x.sigmoid() * (1-x.sigmoid()))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d5af58cb", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/rl/basics/exp.py b/rl/basics/exp.py new file mode 100644 index 0000000..739562d --- /dev/null +++ b/rl/basics/exp.py @@ -0,0 +1,10 @@ + + +import matplotlib.pyplot as plt +import numpy as np + +x = np.linspace(-4, 8, 100) + +plt.plot(x, np.exp(x)) + +plt.show()
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