{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "FhGuhbZ6M5tl" }, "source": [ "##### Copyright 2022 The TensorFlow Authors." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "cellView": "form", "execution": { "iopub.execute_input": "2022-12-14T21:34:37.743300Z", "iopub.status.busy": "2022-12-14T21:34:37.742805Z", "iopub.status.idle": "2022-12-14T21:34:37.746966Z", "shell.execute_reply": "2022-12-14T21:34:37.746421Z" }, "id": "AwOEIRJC6Une" }, "outputs": [], "source": [ "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n", "# you may not use this file except in compliance with the License.\n", "# You may obtain a copy of the License at\n", "#\n", "# https://www.apache.org/licenses/LICENSE-2.0\n", "#\n", "# Unless required by applicable law or agreed to in writing, software\n", "# distributed under the License is distributed on an \"AS IS\" BASIS,\n", "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", "# See the License for the specific language governing permissions and\n", "# limitations under the License." ] }, { "cell_type": "markdown", "metadata": { "id": "EIdT9iu_Z4Rb" }, "source": [ "# Core API를 사용하는 옵티마이저" ] }, { "cell_type": "markdown", "metadata": { "id": "bBIlTPscrIT9" }, "source": [ "\n", " \n", " \n", " \n", " \n", "
TensorFlow.org에서 보기\n", " Google Colab에서 실행하기\n", "GitHub에서 소스 보기노트북 다운로드하기
" ] }, { "cell_type": "markdown", "metadata": { "id": "SjAxxRpBzVYg" }, "source": [ "## 소개\n", "\n", "이 노트북은 [TensorFlow Core 하위 수준 API](https://www.tensorflow.org/guide/core)를 사용하여 사용자 정의 옵티마이저 프로그램을 만드는 프로세스를 소개합니다. TensorFlow Core 및 기본 사용 사례에 대해 자세히 알아보려면 [Core API 개요](https://www.tensorflow.org/guide/core)를 방문하세요.\n", "\n", "[Keras 옵티마이저](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers) 모듈은 다양한 일반 훈련 목적에 사용할 것이 권장되는 최적화 도구입니다. 여기에는 미리 빌드한 다양한 옵티마이저 도구와 사용자 정의 설정에 사용하는 하위 클래스 기능이 포함됩니다. Keras 옵티마이저는 Core API로 빌드한 사용자 정의 레이어, 모델 및 훈련 루프와도 호환됩니다. 이러한 사전 구축 및 사용자 정의 가능한 옵티마이저 프로그램은 대부분의 경우에 적합하지만 Core API를 사용하면 최적화 프로세스를 완벽하게 제어할 수 있습니다. 예를 들어, SAM(선명도 인식 최소화)과 같은 기술을 사용하려면 모델과 옵티마이저를 결합해야 하는데, 이는 ML 옵티마이저의 기존 정의에 맞지 않습니다. 이 가이드는 Core API를 사용하여 처음부터 사용자 정의 옵티마이저를 구축하는 프로세스를 안내하고 옵티마이저의 구조, 구현 및 동작을 완전히 제어할 수 있는 권한을 제공합니다." ] }, { "cell_type": "markdown", "metadata": { "id": "nBmqYyodNRd_" }, "source": [ "## 옵티마이저 개요\n", "\n", "옵티마이저는 모델의 훈련 가능한 매개변수와 관련된 손실 함수를 최소화하는 데 사용하는 알고리즘입니다. 가장 간단한 최적화 기술은 손실 함수의 가장 가파른 하강 방향으로 단계를 진행하며 모델의 매개변수를 반복적으로 업데이트하는 경사 하강입니다. 단계 크기는 그래디언트 크기에 정비례하며, 그래디언트가 너무 크거나 작으면 문제가 될 수 있습니다. Adam, Adagrad 및 RMSprop과 같은 다른 많은 그래디언트 기반 옵티마이저는 메모리 효율성과 빠른 수렴을 위해 그래디언트의 다양한 수학적 속성을 활용합니다." ] }, { "cell_type": "markdown", "metadata": { "id": "nchsZfwEVtVs" }, "source": [ "## 설치하기" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:37.750509Z", "iopub.status.busy": "2022-12-14T21:34:37.750017Z", "iopub.status.idle": "2022-12-14T21:34:38.166186Z", "shell.execute_reply": "2022-12-14T21:34:38.165466Z" }, "id": "d9idwpXCltUl" }, "outputs": [], "source": [ "import matplotlib\n", "from matplotlib import pyplot as plt\n", "# Preset Matplotlib figure sizes.\n", "matplotlib.rcParams['figure.figsize'] = [9, 6]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:38.170269Z", "iopub.status.busy": "2022-12-14T21:34:38.169722Z", "iopub.status.idle": "2022-12-14T21:34:40.034813Z", "shell.execute_reply": "2022-12-14T21:34:40.034140Z" }, "id": "9xQKvCJ85kCQ" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2022-12-14 21:34:39.037395: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory\n", "2022-12-14 21:34:39.037520: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory\n", "2022-12-14 21:34:39.037530: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2.11.0\n" ] } ], "source": [ "import tensorflow as tf\n", "print(tf.__version__)\n", "# set random seed for reproducible results \n", "tf.random.set_seed(22)" ] }, { "cell_type": "markdown", "metadata": { "id": "0UmF5aU3MnwX" }, "source": [ "## 경사 하강\n", "\n", "기본 옵티마이저 클래스에는 그래디언트 목록을 제공한 변수 목록을 업데이트하는 초기화 메서드와 함수가 있어야 합니다. 학습율에 따라 조정된 그래디언트를 빼서 각 변수를 업데이트하는 기본 경사 하강 옵티마이저를 구현하는 것으로 시작합니다." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:40.038382Z", "iopub.status.busy": "2022-12-14T21:34:40.037954Z", "iopub.status.idle": "2022-12-14T21:34:40.042447Z", "shell.execute_reply": "2022-12-14T21:34:40.041854Z" }, "id": "MWjmUmeOQFFN" }, "outputs": [], "source": [ "class GradientDescent(tf.Module):\n", "\n", " def __init__(self, learning_rate=1e-3):\n", " # Initialize parameters\n", " self.learning_rate = learning_rate\n", " self.title = f\"Gradient descent optimizer: learning rate={self.learning_rate}\"\n", "\n", " def apply_gradients(self, grads, vars):\n", " # Update variables\n", " for grad, var in zip(grads, vars):\n", " var.assign_sub(self.learning_rate*grad)" ] }, { "cell_type": "markdown", "metadata": { "id": "ZSekgBHDRzmp" }, "source": [ "이 옵티마이저를 테스트하려면 단일 변수 $x$를 최소화하는 샘플 손실 함수를 생성해야 합니다. 매개변수 값을 최소화하기 위해 다음과 같이 그래디언트 함수를 계산하고 풀이합니다.\n", "\n", "$$L = 2x^4 + 3x^3 + 2$$\n", "\n", "$$\\frac{dL}{dx} = 8x^3 + 9x^2$$\n", "\n", "$\\frac{dL}{dx}$는 안장점이 $x = 0$이고 전역 최솟값이 $x = - \\frac{9}{8}$일 때 0 입니다. 따라서 손실 함수는 $x^\\star = - \\frac{9}{8}$일 때 최적화됩니다." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:40.045736Z", "iopub.status.busy": "2022-12-14T21:34:40.045114Z", "iopub.status.idle": "2022-12-14T21:34:43.662983Z", "shell.execute_reply": "2022-12-14T21:34:43.662364Z" }, "id": "VCtJaUo6Ry8V" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_vals = tf.linspace(-2, 2, 201)\n", "x_vals = tf.cast(x_vals, tf.float32)\n", "\n", "def loss(x):\n", " return 2*(x**4) + 3*(x**3) + 2\n", "\n", "def grad(f, x):\n", " with tf.GradientTape() as tape:\n", " tape.watch(x)\n", " result = f(x)\n", " return tape.gradient(result, x)\n", "\n", "plt.plot(x_vals, loss(x_vals), c='k', label = \"Loss function\")\n", "plt.plot(x_vals, grad(loss, x_vals), c='tab:blue', label = \"Gradient function\")\n", "plt.plot(0, loss(0), marker=\"o\", c='g', label = \"Inflection point\")\n", "plt.plot(-9/8, loss(-9/8), marker=\"o\", c='r', label = \"Global minimum\")\n", "plt.legend()\n", "plt.ylim(0,5)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"loss\")\n", "plt.title(\"Sample loss function and gradient\");" ] }, { "cell_type": "markdown", "metadata": { "id": "fLlIBJ9yuwhE" }, "source": [ "단일 변수 손실 함수를 사용하여 옵티마이저의 수렴을 테스트하는 함수를 작성합니다. 타임스텝 $t$에서 업데이트된 매개변수의 값이 타임스텝 $t-1$에서 유지된 값과 같으면 수렴을 달성했다고 가정합니다. 설정한 반복 횟수를 완료하면 테스트를 종료하고 프로세스 중에 폭주하는 그래디언트를 추적합니다. 최적화 알고리즘을 제대로 활용하려면 매개변수를 나쁘게 초기화해야 합니다. 위의 예제에서 $x = 2$는 가파른 그래디언트를 포함하고 있고 변곡점으로 이어지기 때문에 좋은 선택입니다." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:43.667429Z", "iopub.status.busy": "2022-12-14T21:34:43.666814Z", "iopub.status.idle": "2022-12-14T21:34:43.672092Z", "shell.execute_reply": "2022-12-14T21:34:43.671538Z" }, "id": "SLQTc41ouv0F" }, "outputs": [], "source": [ "def convergence_test(optimizer, loss_fn, grad_fn=grad, init_val=2., max_iters=2000):\n", " # Function for optimizer convergence test\n", " print(optimizer.title)\n", " print(\"-------------------------------\")\n", " # Initializing variables and structures\n", " x_star = tf.Variable(init_val)\n", " param_path = []\n", " converged = False\n", "\n", " for iter in range(1, max_iters + 1):\n", " x_grad = grad_fn(loss_fn, x_star)\n", "\n", " # Case for exploding gradient\n", " if tf.math.is_nan(x_grad):\n", " print(f\"Gradient exploded at iteration {iter}\\n\")\n", " return []\n", "\n", " # Updating the variable and storing its old-version\n", " x_old = x_star.numpy()\n", " optimizer.apply_gradients([x_grad], [x_star])\n", " param_path.append(x_star.numpy())\n", "\n", " # Checking for convergence\n", " if x_star == x_old:\n", " print(f\"Converged in {iter} iterations\\n\")\n", " converged = True\n", " break\n", " \n", " # Print early termination message\n", " if not converged:\n", " print(f\"Exceeded maximum of {max_iters} iterations. Test terminated.\\n\")\n", " return param_path" ] }, { "cell_type": "markdown", "metadata": { "id": "vK-7_TsmyAgI" }, "source": [ "1e-3, 1e-2, 1e-1 학습률에 대한 경사 하강 옵티마이저의 수렴을 테스트합니다." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:43.675450Z", "iopub.status.busy": "2022-12-14T21:34:43.674690Z", "iopub.status.idle": "2022-12-14T21:34:55.597127Z", "shell.execute_reply": "2022-12-14T21:34:55.596380Z" }, "id": "lWRn8c91mqB0" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gradient descent optimizer: learning rate=0.001\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exceeded maximum of 2000 iterations. Test terminated.\n", "\n", "Gradient descent optimizer: learning rate=0.01\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exceeded maximum of 2000 iterations. Test terminated.\n", "\n", "Gradient descent optimizer: learning rate=0.1\n", "-------------------------------\n", "Gradient exploded at iteration 6\n", "\n" ] } ], "source": [ "param_map_gd = {}\n", "learning_rates = [1e-3, 1e-2, 1e-1]\n", "for learning_rate in learning_rates:\n", " param_map_gd[learning_rate] = (convergence_test(\n", " GradientDescent(learning_rate=learning_rate), loss_fn=loss))" ] }, { "cell_type": "markdown", "metadata": { "id": "TydrGHF5y6iI" }, "source": [ "손실 함수의 등고선도에서 매개변수의 경로를 시각화합니다." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:55.600742Z", "iopub.status.busy": "2022-12-14T21:34:55.600490Z", "iopub.status.idle": "2022-12-14T21:34:55.606498Z", "shell.execute_reply": "2022-12-14T21:34:55.605805Z" }, "id": "piffzGHI_u5G" }, "outputs": [], "source": [ "def viz_paths(param_map, x_vals, loss_fn, title, max_iters=2000):\n", " # Creating a controur plot of the loss function\n", " t_vals = tf.range(1., max_iters + 100.)\n", " t_grid, x_grid = tf.meshgrid(t_vals, x_vals)\n", " loss_grid = tf.math.log(loss_fn(x_grid))\n", " plt.pcolormesh(t_vals, x_vals, loss_grid, vmin=0, shading='nearest')\n", " colors = ['r', 'w', 'c']\n", " # Plotting the parameter paths over the contour plot\n", " for i, learning_rate in enumerate(param_map):\n", " param_path = param_map[learning_rate]\n", " if len(param_path) > 0:\n", " x_star = param_path[-1]\n", " plt.plot(t_vals[:len(param_path)], param_path, c=colors[i])\n", " plt.plot(len(param_path), x_star, marker='o', c=colors[i], \n", " label = f\"x*: learning rate={learning_rate}\")\n", " plt.xlabel(\"Iterations\")\n", " plt.ylabel(\"Parameter value\")\n", " plt.legend()\n", " plt.title(f\"{title} parameter paths\")" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:55.609653Z", "iopub.status.busy": "2022-12-14T21:34:55.609147Z", "iopub.status.idle": "2022-12-14T21:34:58.372039Z", "shell.execute_reply": "2022-12-14T21:34:58.371388Z" }, "id": "Ssyj2sO4BcNY" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "viz_paths(param_map_gd, x_vals, loss, \"Gradient descent\")" ] }, { "cell_type": "markdown", "metadata": { "id": "MmM-5eDLFnmC" }, "source": [ "더 작은 학습률을 사용하면 경사 하강이 변곡점에서 멈춘 것처럼 보입니다. 훈련 속도를 높이면 더 큰 단계 크기로 인해 고원 영역 주변에서 더 빠르게 이동할 수도 있습니다. 다만 손실 함수가 극도로 가파른 경우 초기 반복에서 그래디언트가 폭주할 위험이 있습니다." ] }, { "cell_type": "markdown", "metadata": { "id": "m5CDeXN8S1SF" }, "source": [ "## 모멘텀이 있는 경사 하강\n", "\n", "모멘텀이 있는 경사 하강은 그래디언트를 사용하여 변수를 업데이트할 뿐만 아니라 이전 업데이트를 기반으로 하는 변수 위치 변경도 포함합니다. 모멘텀 매개변수는 타임스텝 $t-1$의 업데이트가 타임스텝 $t$의 업데이트에 미치는 영향 수준을 결정합니다. 모멘텀을 누적하면 기본 경사 하강보다 빠르게 고원 영역을 지나도록 변수를 이동할 수 있습니다. 모멘텀 업데이트 규칙은 다음과 같습니다.\n", "\n", "$$\\Delta_x^{[t]} = lr \\cdot L^\\prime(x^{[t]}) + p \\cdot \\Delta_x^{[t-1]}$$\n", "\n", "$$x^{[t]} = x^{[t-1]} - \\Delta_x^{[t]}$$\n", "\n", "여기서,\n", "\n", "- $x$: 최적화하는 변수\n", "- $\\Delta_x$: $x$에서 변경\n", "- $lr$: 학습률\n", "- $L^\\prime(x)$: x에 대한 손실 함수의 그래디언트\n", "- $p$: 모멘텀 매개변수" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:58.375956Z", "iopub.status.busy": "2022-12-14T21:34:58.375441Z", "iopub.status.idle": "2022-12-14T21:34:58.380241Z", "shell.execute_reply": "2022-12-14T21:34:58.379655Z" }, "id": "rOBY8Tz4S0dX" }, "outputs": [], "source": [ "class Momentum(tf.Module):\n", "\n", " def __init__(self, learning_rate=1e-3, momentum=0.7):\n", " # Initialize parameters\n", " self.learning_rate = learning_rate\n", " self.momentum = momentum\n", " self.change = 0.\n", " self.title = f\"Gradient descent optimizer: learning rate={self.learning_rate}\"\n", "\n", " def apply_gradients(self, grads, vars):\n", " # Update variables \n", " for grad, var in zip(grads, vars):\n", " curr_change = self.learning_rate*grad + self.momentum*self.change\n", " var.assign_sub(curr_change)\n", " self.change = curr_change" ] }, { "cell_type": "markdown", "metadata": { "id": "t_nDu38gW6Fu" }, "source": [ "1e-3, 1e-2, 1e-1 학습률에 대한 모멘텀 옵티마이저의 수렴을 테스트합니다." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:34:58.383756Z", "iopub.status.busy": "2022-12-14T21:34:58.383270Z", "iopub.status.idle": "2022-12-14T21:35:04.971187Z", "shell.execute_reply": "2022-12-14T21:35:04.970517Z" }, "id": "tA6oQL-sW2xg" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gradient descent optimizer: learning rate=0.001\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exceeded maximum of 2000 iterations. Test terminated.\n", "\n", "Gradient descent optimizer: learning rate=0.01\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Converged in 80 iterations\n", "\n", "Gradient descent optimizer: learning rate=0.1\n", "-------------------------------\n", "Gradient exploded at iteration 6\n", "\n" ] } ], "source": [ "param_map_mtm = {}\n", "learning_rates = [1e-3, 1e-2, 1e-1]\n", "for learning_rate in learning_rates:\n", " param_map_mtm[learning_rate] = (convergence_test(\n", " Momentum(learning_rate=learning_rate),\n", " loss_fn=loss, grad_fn=grad))" ] }, { "cell_type": "markdown", "metadata": { "id": "wz_LV0EPYE6k" }, "source": [ "손실 함수의 등고선도에서 매개변수의 경로를 시각화합니다." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:35:04.974680Z", "iopub.status.busy": "2022-12-14T21:35:04.974434Z", "iopub.status.idle": "2022-12-14T21:35:07.959988Z", "shell.execute_reply": "2022-12-14T21:35:07.959228Z" }, "id": "qbW1eEKaX3T9" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "viz_paths(param_map_mtm, x_vals, loss, \"Momentum\")" ] }, { "cell_type": "markdown", "metadata": { "id": "4bEFnhPRTBXh" }, "source": [ "## Adam(적응적 모멘트 추정)\n", "\n", "Adam(적응적 모멘트 추정) 알고리즘은 모멘텀과 RMSprop(제곱평균제곱근 전파)의 두 가지 주요 경사 하강을 활용하는 효율적이고 고도로 일반화할 수 있는 최적화 기술입니다. 모멘텀은 감소 매개변수와 함께 첫 번째 모멘트(그래디언트의 합계)를 사용하여 경사 하강을 가속화하는 데 도움이 됩니다. RMSprop도 비슷하지만 RMSprop은 두 번째 모멘트(그래디언트 제곱의 합)를 활용합니다.\n", "\n", "Adam 알고리즘은 첫 번째 모멘트와 두 번째 모멘트를 모두 결합하여 보다 일반화할 수 있는 업데이트 규칙을 제공합니다. 변수 $x$의 부호는 $\\frac{x}{\\sqrt{x^2}}$를 계산하여 결정할 수 있습니다. Adam 옵티마이저는 이러한 사실을 사용하여 효과적으로 평활화한 부호인 업데이트 단계를 계산합니다. 옵티마이저는 $\\frac{x}{\\sqrt{x^2}}$를 계산하는 대신 각 변수 업데이트에 대해 $x$(첫 번째 모멘트) 및 $x^2$(두 번째 모멘트)의 평활화 버전을 계산합니다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "WjgyqRiZ7XhA" }, "source": [ "**Adam 알고리즘**\n", "\n", "$\\beta_1 \\gets 0.9 ; \\triangleright \\text{literature value}$\n", "\n", "$\\beta_2 \\gets 0.999 ; \\triangleright \\text{literature value}$\n", "\n", "$lr \\gets \\text{1e-3} ; \\triangleright \\text{configurable learning rate}$\n", "\n", "$\\epsilon \\gets \\text{1e-7} ; \\triangleright \\text{prevents divide by 0 error}$\n", "\n", "$V_{dv} \\gets \\vec {\\underset{n\\times1}{0}} ;\\triangleright \\text{stores momentum updates for each variable}$\n", "\n", "$S_{dv} \\gets \\vec {\\underset{n\\times1}{0}} ; \\triangleright \\text{stores RMSP updates for each variable}$\n", "\n", "$t \\gets 1$\n", "\n", "$\\text{On iteration } t:$\n", "\n", "$;;;; \\text{For} (\\frac{dL}{dv}, v) \\text{ in gradient variable pairs}:$\n", "\n", "$;;;;;;;; V_{dv_i} = \\beta_1V_{dv_i} + (1 - \\beta_1)\\frac{dL}{dv} ; \\triangleright \\text{momentum update}$\n", "\n", "$;;;;;;;; S_{dv_i} = \\beta_2V_{dv_i} + (1 - \\beta_2)(\\frac{dL}{dv})^2 ; \\triangleright \\text{RMSP update}$\n", "\n", "$;;;;;;;; v_{dv}^{bc} = \\frac{V_{dv_i}}{(1-\\beta_1)^t} ; \\triangleright \\text{momentum bias correction}$\n", "\n", "$;;;;;;;; s_{dv}^{bc} = \\frac{S_{dv_i}}{(1-\\beta_2)^t} ; \\triangleright \\text{RMSP bias correction}$\n", "\n", "$;;;;;;;; v = v - lr\\frac{v_{dv}^{bc}}{\\sqrt{s_{dv}^{bc}} + \\epsilon} ; \\triangleright \\text{parameter update}$\n", "\n", "$;;;;;;;; t = t + 1$\n", "\n", "**알고리즘의 끝**\n", "\n", "$V_{dv}$와 $S_{dv}$가 0으로 초기화되고 $\\beta_1$ 및 $\\beta_2$가 1에 가까운 경우 모멘텀과 RMSprop 업데이트는 자연스럽게 0으로 바이어스됩니다. 따라서 변수는 바이어스 수정으로 혜택을 받을 수 있습니다. 또한 바이어스 보정은 가중치가 전역 최솟값에 접근할 때 가중치의 진동을 제어하는 데 도움이 됩니다." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:35:07.964142Z", "iopub.status.busy": "2022-12-14T21:35:07.963419Z", "iopub.status.idle": "2022-12-14T21:35:07.970836Z", "shell.execute_reply": "2022-12-14T21:35:07.970274Z" }, "id": "hm5vffRJRsEc" }, "outputs": [], "source": [ "class Adam(tf.Module):\n", " \n", " def __init__(self, learning_rate=1e-3, beta_1=0.9, beta_2=0.999, ep=1e-7):\n", " # Initialize the Adam parameters\n", " self.beta_1 = beta_1\n", " self.beta_2 = beta_2\n", " self.learning_rate = learning_rate\n", " self.ep = ep\n", " self.t = 1.\n", " self.v_dvar, self.s_dvar = [], []\n", " self.title = f\"Adam: learning rate={self.learning_rate}\"\n", " self.built = False\n", "\n", " def apply_gradients(self, grads, vars):\n", " # Set up moment and RMSprop slots for each variable on the first call\n", " if not self.built:\n", " for var in vars:\n", " v = tf.Variable(tf.zeros(shape=var.shape))\n", " s = tf.Variable(tf.zeros(shape=var.shape))\n", " self.v_dvar.append(v)\n", " self.s_dvar.append(s)\n", " self.built = True\n", " # Perform Adam updates\n", " for i, (d_var, var) in enumerate(zip(grads, vars)):\n", " # Moment calculation\n", " self.v_dvar[i] = self.beta_1*self.v_dvar[i] + (1-self.beta_1)*d_var\n", " # RMSprop calculation\n", " self.s_dvar[i] = self.beta_2*self.s_dvar[i] + (1-self.beta_2)*tf.square(d_var)\n", " # Bias correction\n", " v_dvar_bc = self.v_dvar[i]/(1-(self.beta_1**self.t))\n", " s_dvar_bc = self.s_dvar[i]/(1-(self.beta_2**self.t))\n", " # Update model variables\n", " var.assign_sub(self.learning_rate*(v_dvar_bc/(tf.sqrt(s_dvar_bc) + self.ep)))\n", " # Increment the iteration counter\n", " self.t += 1." ] }, { "cell_type": "markdown", "metadata": { "id": "UWN4Qus7flUO" }, "source": [ "경사 하강 예제에 사용한 것과 동일한 학습률로 Adam 옵티마이저의 성능을 테스트합니다. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:35:07.974261Z", "iopub.status.busy": "2022-12-14T21:35:07.973616Z", "iopub.status.idle": "2022-12-14T21:35:28.169711Z", "shell.execute_reply": "2022-12-14T21:35:28.168936Z" }, "id": "GXHCxtemFBpR" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Adam: learning rate=0.001\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exceeded maximum of 2000 iterations. Test terminated.\n", "\n", "Adam: learning rate=0.01\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exceeded maximum of 2000 iterations. Test terminated.\n", "\n", "Adam: learning rate=0.1\n", "-------------------------------\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Converged in 1156 iterations\n", "\n" ] } ], "source": [ "param_map_adam = {}\n", "learning_rates = [1e-3, 1e-2, 1e-1]\n", "for learning_rate in learning_rates:\n", " param_map_adam[learning_rate] = (convergence_test(\n", " Adam(learning_rate=learning_rate), loss_fn=loss))" ] }, { "cell_type": "markdown", "metadata": { "id": "jgpUcs_xXEjX" }, "source": [ "손실 함수의 등고선도에서 매개변수의 경로를 시각화합니다." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2022-12-14T21:35:28.173545Z", "iopub.status.busy": "2022-12-14T21:35:28.173003Z", "iopub.status.idle": "2022-12-14T21:35:31.056427Z", "shell.execute_reply": "2022-12-14T21:35:31.055784Z" }, "id": "ctvOUmlzFK8s" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "viz_paths(param_map_adam, x_vals, loss, \"Adam\")" ] }, { "cell_type": "markdown", "metadata": { "id": "_oGScF8zJcY4" }, "source": [ "이 특별한 예제에서 Adam 옵티마이저는 작은 학습률을 사용할 때 기존의 경사 하강에 비해 수렴 속도가 느립니다. 그러나 알고리즘은 성공적으로 고원 영역을 지나며 학습률이 높을 때 전역 최솟값으로 수렴합니다. 대형 그래디언트가 발생해도 Adam 학습률의 동적 스케일링으로 인해 그래디언트 폭주가 더 이상 문제가 되지 않습니다." ] }, { "cell_type": "markdown", "metadata": { "id": "VFLfEH4ManbW" }, "source": [ "## 결론\n", "\n", "이 노트북에서는 [TensorFlow Core API](https://www.tensorflow.org/guide/core)를 사용하여 옵티마이저를 작성하고 비교하는 기본 내용을 소개했습니다. Adam과 같은 미리 빌드된 옵티마이저는 일반화할 수 있지만 경우에 따라 일부 모델 또는 데이터세트에서는 최선의 선택이 아닐 수도 있습니다. 최적화 프로세스를 세밀하게 제어하면 ML 훈련 워크플로를 간소화하고 전반적인 성능을 개선할 수도 있습니다. 사용자 정의 옵티마이저의 더 많은 예제는 다음 문서를 참조하세요.\n", "\n", "- 이 Adam 옵티마이저는 [멀티레이어 퍼셉트론](https://www.tensorflow.org/guide/core/mlp_core) 가이드 및 [분산 훈련]()에서 사용됩니다.\n", "- [Model Garden](https://blog.tensorflow.org/2020/03/introducing-model-garden-for-tensorflow-2.html)에는 Core API로 작성된 다양한 [사용자 정의 옵티마이저](https://github.com/tensorflow/models/tree/master/official/modeling/optimization)가 있습니다.\n" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "optimizers_core.ipynb", "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "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": "3.9.16" } }, "nbformat": 4, "nbformat_minor": 0 }