diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..c724764 --- /dev/null +++ b/.gitignore @@ -0,0 +1,118 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +.python-version + +# celery beat schedule file +celerybeat-schedule + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ + +# VSCode project +.vscode/ diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..ee14e76 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2018 davidtvs + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..b664b6f --- /dev/null +++ b/README.md @@ -0,0 +1,53 @@ +# PyTorch learning rate finder + +A PyTorch implementation of the learning rate range test detailed in [Cyclical Learning Rates for Training Neural Networks](https://arxiv.org/abs/1506.01186) by Leslie N. Smith and the tweaked version used by [fastai](https://github.com/fastai/fastai). + +The learning rate range test is a test that provides valuable information about the optimal learning rate. During a pre-training run, the learning rate is increased linearly or exponentially between two boundaries. The low initial learning rate allows the network to start converging and as the learning rate is increased it will eventually be too large and the network will diverge. + +Typically, a good static learning rate can be found half-way on the descending loss curve. In the plot below that would be `lr = 0.002`. + +For cyclical learning rates (also detailed in Leslie Smith's paper) where the learning rate is cycled between two boundaries `(base_lr, max_lr)`, the author advises the point at which the loss starts descending and the point at which the loss stops descending or becomes ragged for `base_lr` and `max_lr` respectively. In the plot below, `base_lr = 0.0002` and `max_lr=0.2`. + +![Learning rate range test](images/lr_finder_cifar10.png.png) + +## Requirements + +- Python 2.7 and above +- pip +- see `requirements.txt` + +## Implementation details and usage + +### Tweaked version from fastai + +Increases the learning rate in an exponential manner and computes the training loss for each learning rate. `lr_finder.plot()` plots the training loss versus logarithmic learning rate. + +```python +model = ... +criterion = nn.CrossEntropyLoss() +optimizer = optim.Adam(net.parameters(), lr=1e-7, weight_decay=1e-2) +lr_finder = LRFinder(net, optimizer, criterion, device="cuda") +lr_finder.range_test(trainloader, end_lr=100, num_iter=100) +lr_finder.plot() +``` + +### Leslie Smith's approach + +Increases the learning rate linearly and computes the evaluation loss for each learning rate. `lr_finder.plot()` plots the evaluation loss versus learning rate. +This approach typically produces more precise curves because the evaluation loss is more susceptible to divergence but it takes significantly longer to perform the test, especially if the evaluation dataset is large. + +```python +model = ... +criterion = nn.CrossEntropyLoss() +optimizer = optim.Adam(net.parameters(), lr=0.1, weight_decay=1e-2) +lr_finder = LRFinder(net, optimizer, criterion, device="cuda") +lr_finder.range_test(trainloader, end_lr=1, num_iter=100, step_mode="linear") +lr_finder.plot(log_lr=False) +``` + +### Notes + +- Examples for CIFAR10 and MNIST can be found in the examples folder. +- `LRFinder.range_test()` will change the model weights and the optimizer parameters. If you want to avoid this use: `model = copy.deepcopy(original_model)` +- The learning rate and loss history can be accessed through `lr_finder.history`. This will return a dictionary with `lr` and `loss` keys. +- When using `step_mode="linear"` the learning rate range should be within the same order of magnitude. diff --git a/examples/cifar10_resnet.py b/examples/cifar10_resnet.py new file mode 100644 index 0000000..102550a --- /dev/null +++ b/examples/cifar10_resnet.py @@ -0,0 +1,143 @@ +import torch.nn as nn + + +__all__ = ["Cifar10ResNet", "resnet20", "resnet32", "resnet44", "resnet56", "resnet101"] + + +def conv3x3(in_planes, out_planes, stride=1): + """3x3 convolution with padding""" + return nn.Conv2d( + in_planes, out_planes, kernel_size=3, stride=stride, padding=1, bias=False + ) + + +def conv1x1(in_planes, out_planes, stride=1): + """1x1 convolution""" + return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False) + + +class BasicBlock(nn.Module): + expansion = 1 + + def __init__(self, inplanes, planes, stride=1, downsample=None): + super(BasicBlock, self).__init__() + self.conv1 = conv3x3(inplanes, planes, stride) + self.bn1 = nn.BatchNorm2d(planes) + self.relu = nn.ReLU(inplace=True) + self.conv2 = conv3x3(planes, planes) + self.bn2 = nn.BatchNorm2d(planes) + self.downsample = downsample + self.stride = stride + + def forward(self, x): + residual = x + + out = self.conv1(x) + out = self.bn1(out) + out = self.relu(out) + + out = self.conv2(out) + out = self.bn2(out) + + if self.downsample is not None: + residual = self.downsample(x) + + out += residual + out = self.relu(out) + + return out + + +class Cifar10ResNet(nn.Module): + def __init__(self, block, layers, num_classes=10, ch_width=2): + super(Cifar10ResNet, self).__init__() + width = [16, 16 * ch_width, 16 * ch_width * ch_width] + self.inplanes = 16 + self.conv1 = nn.Conv2d( + 3, width[0], kernel_size=3, stride=1, padding=1, bias=False + ) + self.bn1 = nn.BatchNorm2d(width[0]) + self.relu = nn.ReLU(inplace=True) + self.layer1 = self._make_layer(block, width[0], layers[0]) + self.layer2 = self._make_layer(block, width[1], layers[1], stride=2) + self.layer3 = self._make_layer(block, width[2], layers[2], stride=2) + self.avgpool = nn.AdaptiveAvgPool2d((1, 1)) + self.fc = nn.Linear(width[2] * block.expansion, num_classes) + + for m in self.modules(): + if isinstance(m, nn.Conv2d): + nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu") + elif isinstance(m, nn.BatchNorm2d): + nn.init.constant_(m.weight, 1) + nn.init.constant_(m.bias, 0) + + def _make_layer(self, block, planes, blocks, stride=1): + downsample = None + if stride != 1 or self.inplanes != planes * block.expansion: + downsample = nn.Sequential( + conv1x1(self.inplanes, planes * block.expansion, stride), + nn.BatchNorm2d(planes * block.expansion), + ) + + layers = [] + layers.append(block(self.inplanes, planes, stride, downsample)) + self.inplanes = planes * block.expansion + for _ in range(1, blocks): + layers.append(block(self.inplanes, planes)) + + return nn.Sequential(*layers) + + def forward(self, x): + x = self.conv1(x) + x = self.bn1(x) + x = self.relu(x) + + x = self.layer1(x) + x = self.layer2(x) + x = self.layer3(x) + + x = self.avgpool(x) + x = x.view(x.size(0), -1) + x = self.fc(x) + + return x + + +def resnet20(num_classes=10, ch_width=2): + """Constructs a ResNet-20 model. + """ + return Cifar10ResNet( + BasicBlock, [3, 3, 3], num_classes=num_classes, ch_width=ch_width + ) + + +def resnet32(num_classes=10, ch_width=2): + """Constructs a ResNet-32 model. + """ + return Cifar10ResNet( + BasicBlock, [5, 5, 5], num_classes=num_classes, ch_width=ch_width + ) + + +def resnet44(num_classes=10, ch_width=2): + """Constructs a ResNet-44 model. + """ + return Cifar10ResNet( + BasicBlock, [7, 7, 7], num_classes=num_classes, ch_width=ch_width + ) + + +def resnet56(num_classes=10, ch_width=2): + """Constructs a ResNet-56 model. + """ + return Cifar10ResNet( + BasicBlock, [9, 9, 9], num_classes=num_classes, ch_width=ch_width + ) + + +def resnet101(num_classes=10, ch_width=2): + """Constructs a ResNet-101 model. + """ + return Cifar10ResNet( + BasicBlock, [18, 18, 18], num_classes=num_classes, ch_width=ch_width + ) diff --git a/examples/lrfinder_cifar10.ipynb b/examples/lrfinder_cifar10.ipynb new file mode 100644 index 0000000..0767875 --- /dev/null +++ b/examples/lrfinder_cifar10.ipynb @@ -0,0 +1,282 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CIFAR10 example with ResNet56\n", + "\n", + "This example demonstrates the usage of `LRFinder` with a ResNet56 on the Cifar10 dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/davidtvs/datascience/pytorch/pytorch-lr-finder/python2/env/local/lib/python2.7/site-packages/tqdm/autonotebook/__init__.py:14: TqdmExperimentalWarning: Using `tqdm.autonotebook.tqdm` in notebook mode. Use `tqdm.tqdm` instead to force console mode (e.g. in jupyter console)\n", + " \" (e.g. in jupyter console)\", TqdmExperimentalWarning)\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "from copy import deepcopy\n", + "import torch.nn as nn\n", + "import torch.optim as optim\n", + "import torchvision.transforms as transforms\n", + "from torch.utils.data import DataLoader\n", + "from torchvision.datasets import CIFAR10\n", + "import cifar10_resnet as rc10\n", + "\n", + "import sys\n", + "sys.path.append('..')\n", + "from lr_finder import LRFinder" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loading CIFAR10" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "cifar_pwd = \"../../data\"\n", + "batch_size=256" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Files already downloaded and verified\n", + "Files already downloaded and verified\n" + ] + } + ], + "source": [ + "transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))])\n", + "\n", + "trainset = CIFAR10(root=cifar_pwd, train=True, download=True, transform=transform)\n", + "trainloader = DataLoader(trainset, batch_size=batch_size, shuffle=True, num_workers=0)\n", + "\n", + "testset = CIFAR10(root=cifar_pwd, train=False, download=True, transform=transform)\n", + "testloader = DataLoader(testset, batch_size=batch_size * 2, shuffle=False, num_workers=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "model = rc10.resnet56()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Training loss (fastai)\n", + "\n", + "This learning rate test range follows the same procedure used by fastai. The model is trained for `num_iter` iterations while the learning rate is increased from its initial value specified by the optimizer algorithm to `end_lr`. The increase can be linear (`step_mode=\"linear\"`) or exponential (`step_mode=\"exp\"`); linear provides good results for small ranges while exponential is recommended for larger ranges." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "0d037366991346d9a1d1d296f73ab134", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(IntProgress(value=0), HTML(value=u'')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Stopping early, the loss has diverged\n", + "Learning rate search finished. See the graph with {finder_name}.plot()\n" + ] + } + ], + "source": [ + "# Deepcopy the original model to avoid changing it\n", + "net = deepcopy(model)\n", + "criterion = nn.CrossEntropyLoss()\n", + "optimizer = optim.Adam(net.parameters(), lr=1e-7, weight_decay=1e-2)\n", + "lr_finder = LRFinder(net, optimizer, criterion, device=\"cuda\")\n", + "lr_finder.range_test(trainloader, end_lr=100, num_iter=100, step_mode=\"exp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the loss in the loss vs. learning rate plot is the **training** loss." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lr_finder.plot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Validation loss (Leslie N. Smith)\n", + "\n", + "If a dataloader is passed to `LRFinder.range_test()` through the `val_loader` parameter the model is evaluated on that dataset after each iteration. The evaluation loss is more sensitive to instability therefore it provides a more precise view of when the divergence occurs. The disadvantage is that it takes significantly longer to run.\n", + "\n", + "This version of the learning rate range test is described in [Cyclical Learning Rates for Training Neural Networks by Leslie N. Smith](https://arxiv.org/abs/1506.01186)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "e6263893c6f64df58540d8433fdb40ee", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(IntProgress(value=0), HTML(value=u'')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Stopping early, the loss has diverged\n", + "Learning rate search finished. See the graph with {finder_name}.plot()\n" + ] + } + ], + "source": [ + "# Deepcopy the original model to avoid changing it\n", + "net = deepcopy(model)\n", + "criterion = nn.CrossEntropyLoss()\n", + "optimizer = optim.Adam(net.parameters(), lr=1e-7, weight_decay=1e-2)\n", + "lr_finder = LRFinder(net, optimizer, criterion, device=\"cuda\")\n", + "lr_finder.range_test(trainloader, val_loader=testloader, end_lr=100, num_iter=100, step_mode=\"exp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the loss in the loss vs. learning rate plot is the **evaluation** loss." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lr_finder.plot(skip_end=0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "lr-finder (p2)", + "language": "python", + "name": "lr-finder-p2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/lrfinder_mnist.ipynb b/examples/lrfinder_mnist.ipynb new file mode 100644 index 0000000..b8f292a --- /dev/null +++ b/examples/lrfinder_mnist.ipynb @@ -0,0 +1,293 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# MNIST example with 3-conv. layer network\n", + "\n", + "This example demonstrates the usage of `LRFinder` with a 3-conv. layer network on the MNIST dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/davidtvs/datascience/pytorch/pytorch-lr-finder/python2/env/local/lib/python2.7/site-packages/tqdm/autonotebook/__init__.py:14: TqdmExperimentalWarning: Using `tqdm.autonotebook.tqdm` in notebook mode. Use `tqdm.tqdm` instead to force console mode (e.g. in jupyter console)\n", + " \" (e.g. in jupyter console)\", TqdmExperimentalWarning)\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "from copy import deepcopy\n", + "import torch.nn as nn\n", + "import torch.nn.functional as F\n", + "import torch.optim as optim\n", + "import torchvision.transforms as transforms\n", + "from torch.utils.data import DataLoader\n", + "from torchvision.datasets import MNIST\n", + "\n", + "import sys\n", + "sys.path.append('..')\n", + "from lr_finder import LRFinder" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loading MNIST" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "mnist_pwd = \"../../data\"\n", + "batch_size=256" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))])\n", + "\n", + "trainset = MNIST(mnist_pwd, train=True, download=True, transform=transform)\n", + "trainloader = DataLoader(trainset, batch_size=batch_size, shuffle=True, num_workers=0)\n", + "\n", + "testset = MNIST(mnist_pwd, train=False, download=True, transform=transform)\n", + "testloader = DataLoader(testset, batch_size=batch_size * 2, shuffle=False, num_workers=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "class Net(nn.Module):\n", + " def __init__(self):\n", + " super(Net, self).__init__()\n", + " self.conv1 = nn.Conv2d(1, 10, kernel_size=5)\n", + " self.conv2 = nn.Conv2d(10, 20, kernel_size=5)\n", + " self.conv2_drop = nn.Dropout2d()\n", + " self.fc1 = nn.Linear(320, 50)\n", + " self.fc2 = nn.Linear(50, 10)\n", + "\n", + " def forward(self, x):\n", + " x = F.relu(F.max_pool2d(self.conv1(x), 2))\n", + " x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))\n", + " x = x.view(-1, 320)\n", + " x = F.relu(self.fc1(x))\n", + " x = F.dropout(x, training=self.training)\n", + " x = self.fc2(x)\n", + " return F.log_softmax(x, dim=1)\n", + " \n", + "model = Net()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Training loss (fastai)\n", + "\n", + "This learning rate test range follows the same procedure used by fastai. The model is trained for `num_iter` iterations while the learning rate is increased from its initial value specified by the optimizer algorithm to `end_lr`. The increase can be linear (`step_mode=\"linear\"`) or exponential (`step_mode=\"exp\"`); linear provides good results for small ranges while exponential is recommended for larger ranges." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "553c47fb9e8b4fff9c16a7f4b81f7389", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(IntProgress(value=0), HTML(value=u'')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Learning rate search finished. See the graph with {finder_name}.plot()\n" + ] + } + ], + "source": [ + "# Deepcopy the original model to avoid changing it\n", + "net = deepcopy(model)\n", + "criterion = nn.NLLLoss()\n", + "optimizer = optim.SGD(net.parameters(), lr=0.001, momentum=0.5)\n", + "lr_finder = LRFinder(net, optimizer, criterion, device=\"cuda\")\n", + "lr_finder.range_test(trainloader, end_lr=10, num_iter=100, step_mode=\"exp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the loss in the loss vs. learning rate plot is the **training** loss." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lr_finder.plot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Validation loss (Leslie N. Smith)\n", + "\n", + "If a dataloader is passed to `LRFinder.range_test()` through the `val_loader` parameter the model is evaluated on that dataset after each iteration. The evaluation loss is more sensitive to instability therefore it provides a more precise view of when the divergence occurs. The disadvantage is that it takes significantly longer to run.\n", + "\n", + "This version of the learning rate range test is described in [Cyclical Learning Rates for Training Neural Networks by Leslie N. Smith](https://arxiv.org/abs/1506.01186)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "ae59483bc91c4f659c67cee9c326cd30", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(IntProgress(value=0), HTML(value=u'')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Learning rate search finished. See the graph with {finder_name}.plot()\n" + ] + } + ], + "source": [ + "# Deepcopy the original model to avoid changing it\n", + "net = deepcopy(model)\n", + "criterion = nn.NLLLoss()\n", + "optimizer = optim.SGD(net.parameters(), lr=0.001, momentum=0.5)\n", + "lr_finder = LRFinder(net, optimizer, criterion, device=\"cuda\")\n", + "lr_finder.range_test(trainloader, val_loader=testloader, end_lr=10, num_iter=100, step_mode=\"exp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the loss in the loss vs. learning rate plot is the **evaluation** loss." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lr_finder.plot(skip_end=1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "lr-finder (p2)", + "language": "python", + "name": "lr-finder-p2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/images/lr_finder_cifar10.png b/images/lr_finder_cifar10.png new file mode 100644 index 0000000..b253a0b Binary files /dev/null and b/images/lr_finder_cifar10.png differ diff --git a/lr_finder.py b/lr_finder.py new file mode 100644 index 0000000..678a72f --- /dev/null +++ b/lr_finder.py @@ -0,0 +1,249 @@ +from __future__ import print_function, with_statement, division +import torch +from tqdm.autonotebook import tqdm +from torch.optim.lr_scheduler import _LRScheduler +import matplotlib.pyplot as plt + + +class LRFinder(object): + """Learning rate range test. + + The learning rate range test increases the learning rate in a pre-training run + between two boundaries in a linear or exponential manner. It provides valuable + information on how well the network can be trained over a range of learning rates + and what is the optimal learning rate. + + Arguments: + model (torch.nn.Module): wrapped model. + optimizer (torch.optim.Optimizer): wrapped optimizer where the defined learning + is assumed to be the lower boundary of the range test. + criterion (torch.nn.Module): wrapped loss function. + device (str or torch.device, optional): a string ("cpu" or "cuda") with an + optional ordinal for the device type (e.g. "cuda:X", where is the ordinal). + Alternatively, can be an object representing the device on which the + computation will take place. Default: None, uses the same device as `model`. + + Example: + >>> lr_finder = LRFinder(net, optimizer, criterion, device="cuda") + >>> lr_finder.range_test(dataloader, end_lr=100, num_iter=100) + + Cyclical Learning Rates for Training Neural Networks: https://arxiv.org/abs/1506.01186 + fastai/lr_find: https://github.com/fastai/fastai + + """ + + def __init__(self, model, optimizer, criterion, device=None): + self.model = model + self.optimizer = optimizer + self.criterion = criterion + self.history = {"lr": [], "loss": []} + self.best_loss = None + + # If device is None, use the same as the model + if device is None: + self.device = next(self.model.parameters()).device + else: + self.device = device + model = self.model.to(self.device) + + def range_test( + self, + train_loader, + val_loader=None, + end_lr=10, + num_iter=100, + step_mode="exp", + smooth_f=0.05, + diverge_th=5, + ): + """Performs the learning rate range test. + + Arguments: + train_loader (torch.utils.data.DataLoader): the training set data laoder. + val_loader (torch.utils.data.DataLoader, optional): if `None` the range test + will only use the training loss. When given a data loader, the model is + evaluated after each iteration on that dataset and the evaluation loss + is used. Note that in this mode the test takes significantly longer but + generally produces more precise results. Default: None. + end_lr (float, optional): the initial learning rate which is the lower + boundary of the test. Default: 10. + num_iter (int, optional): the number of iterations over which the test + occurs. Default: 100. + step_mode (str, optional): one of the available learning rate policies, + linear or exponential ("linear", "exp"). Default: "exp". + smooth_f (float, optional): the loss smoothing factor within the [0, 1[ + interval. Disabled if set to 0, otherwise the loss is smoothed using + exponential smoothing. Default: 0.05. + diverge_th (int, optional): the test is stopped when the loss surpasses the + threshold: diverge_th * best_loss. Default: 5. + + """ + + if step_mode.lower() == "exp": + lr_schedule = ExponentialLR(self.optimizer, end_lr, num_iter) + elif step_mode.lower() == "linear": + lr_schedule = LinearLR(self.optimizer, end_lr, num_iter) + else: + raise ValueError("expected one of (exp, linear), got {}".format(step_mode)) + + if smooth_f < 0 or smooth_f >= 1: + raise ValueError("smooth_f is outside the range [0, 1[") + + # Create an iterator to get data batch by batch + iterator = iter(train_loader) + for iteration in tqdm(range(num_iter)): + # Get a new set of inputs and labels + try: + inputs, labels = next(iterator) + except StopIteration: + iterator = iter(train_loader) + inputs, labels = next(iterator) + + # Train on batch and retrieve loss + loss = self._train_batch(inputs, labels) + if val_loader: + loss = self._validate(val_loader) + + # Update the learning rate + lr_schedule.step() + self.history["lr"].append(lr_schedule.get_lr()[0]) + + # Track the best loss and smooth it if smooth_f is specified + if iteration == 0: + self.best_loss = loss + else: + if smooth_f > 0: + loss = smooth_f * loss + (1 - smooth_f) * self.history["loss"][-1] + if loss < self.best_loss: + self.best_loss = loss + + # Check if the loss has diverged; if it has, stop the test + self.history["loss"].append(loss) + if loss > diverge_th * self.best_loss: + print("Stopping early, the loss has diverged") + break + + print("Learning rate search finished. See the graph with {finder_name}.plot()") + + def _train_batch(self, inputs, labels): + # Set model to training mode + self.model.train() + + # Move data to the correct device + inputs = inputs.to(self.device) + labels = labels.to(self.device) + + # Forward pass + self.optimizer.zero_grad() + outputs = self.model(inputs) + loss = self.criterion(outputs, labels) + + # Backward pass + loss.backward() + self.optimizer.step() + + return loss.item() + + def _validate(self, dataloader): + # Set model to evaluation mode and disable gradient computation + running_loss = 0 + self.model.eval() + with torch.no_grad(): + for inputs, labels in dataloader: + # Move data to the correct device + inputs = inputs.to(self.device) + labels = labels.to(self.device) + + # Forward pass and loss computation + outputs = self.model(inputs) + loss = self.criterion(outputs, labels) + running_loss += loss.item() * inputs.size(0) + + return running_loss / len(dataloader.dataset) + + def plot(self, skip_start=10, skip_end=5, log_lr=True): + """Plots the learning rate range test. + + Arguments: + skip_start (int, optional): number of batches to trim from the start. + Default: 10. + skip_end (int, optional): number of batches to trim from the start. + Default: 5. + log_lr (bool, optional): True to plot the learning rate in a logarithmic + scale; otherwise, plotted in a linear scale. Default: True. + + """ + + if skip_start < 0: + raise ValueError("skip_start cannot be negative") + if skip_end < 0: + raise ValueError("skip_end cannot be negative") + + # Get the data to plot from the history dictionary. Also, handle skip_end=0 + # properly so the behaviour is the expected + lrs = self.history["lr"] + losses = self.history["loss"] + if skip_end == 0: + lrs = lrs[skip_start:] + losses = losses[skip_start:] + else: + lrs = lrs[skip_start:-skip_end] + losses = losses[skip_start:-skip_end] + + # Plot loss as a function of the learning rate + plt.plot(lrs, losses) + if log_lr: + plt.xscale("log") + plt.xlabel("Learning rate") + plt.ylabel("Loss") + plt.show() + + +class LinearLR(_LRScheduler): + """Linearly increases the learning rate between two boundaries over a number of + iterations. + + Arguments: + optimizer (torch.optim.Optimizer): wrapped optimizer. + end_lr (float, optional): the initial learning rate which is the lower + boundary of the test. Default: 10. + num_iter (int, optional): the number of iterations over which the test + occurs. Default: 100. + last_epoch (int): the index of last epoch. Default: -1. + + """ + + def __init__(self, optimizer, end_lr, num_iter, last_epoch=-1): + self.end_lr = end_lr + self.num_iter = num_iter + super(LinearLR, self).__init__(optimizer, last_epoch) + + def get_lr(self): + curr_iter = self.last_epoch + 1 + r = curr_iter / self.num_iter + return [base_lr + r * (self.end_lr - base_lr) for base_lr in self.base_lrs] + + +class ExponentialLR(_LRScheduler): + """Exponentially increases the learning rate between two boundaries over a number of + iterations. + + Arguments: + optimizer (torch.optim.Optimizer): wrapped optimizer. + end_lr (float, optional): the initial learning rate which is the lower + boundary of the test. Default: 10. + num_iter (int, optional): the number of iterations over which the test + occurs. Default: 100. + last_epoch (int): the index of last epoch. Default: -1. + + """ + + def __init__(self, optimizer, end_lr, num_iter, last_epoch=-1): + self.end_lr = end_lr + self.num_iter = num_iter + super(ExponentialLR, self).__init__(optimizer, last_epoch) + + def get_lr(self): + curr_iter = self.last_epoch + 1 + r = curr_iter / self.num_iter + return [base_lr * (self.end_lr / base_lr) ** r for base_lr in self.base_lrs] diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..11a00ac --- /dev/null +++ b/requirements.txt @@ -0,0 +1,12 @@ +cycler==0.10.0 +kiwisolver==1.0.1 +matplotlib==3.0.2 +numpy==1.15.4 +Pillow==5.3.0 +pkg-resources==0.0.0 +pyparsing==2.3.0 +python-dateutil==2.7.5 +six==1.11.0 +torch==0.4.1 +torchvision==0.2.1 +tqdm==4.28.1