neural_networks_tutorial.ipynb

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        "%matplotlib inline"
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        "\nNeural Networks\n===============\n\nNeural networks can be constructed using the ``torch.nn`` package.\n\nNow that you had a glimpse of ``autograd``, ``nn`` depends on\n``autograd`` to define models and differentiate them.\nAn ``nn.Module`` contains layers, and a method ``forward(input)``\\ that\nreturns the ``output``.\n\nFor example, look at this network that classifies digit images:\n\n.. figure:: /_static/img/mnist.png\n   :alt: convnet\n\n   convnet\n\nIt is a simple feed-forward network. It takes the input, feeds it\nthrough several layers one after the other, and then finally gives the\noutput.\n\nA typical training procedure for a neural network is as follows:\n\n- Define the neural network that has some learnable parameters (or\n  weights)\n- Iterate over a dataset of inputs\n- Process input through the network\n- Compute the loss (how far is the output from being correct)\n- Propagate gradients back into the network\u2019s parameters\n- Update the weights of the network, typically using a simple update rule:\n  ``weight = weight - learning_rate * gradient``\n\nDefine the network\n------------------\n\nLet\u2019s define this network:\n\n"
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        "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\n\n\nclass Net(nn.Module):\n\n    def __init__(self):\n        super(Net, self).__init__()\n        # 1 input image channel, 6 output channels, 5x5 square convolution\n        # kernel\n        self.conv1 = nn.Conv2d(1, 6, 5)\n        self.conv2 = nn.Conv2d(6, 16, 5)\n        # an affine operation: y = Wx + b\n        self.fc1 = nn.Linear(16 * 5 * 5, 120)\n        self.fc2 = nn.Linear(120, 84)\n        self.fc3 = nn.Linear(84, 10)\n\n    def forward(self, x):\n        # Max pooling over a (2, 2) window\n        x = F.max_pool2d(F.relu(self.conv1(x)), (2, 2))\n        # If the size is a square you can only specify a single number\n        x = F.max_pool2d(F.relu(self.conv2(x)), 2)\n        x = x.view(-1, self.num_flat_features(x))\n        x = F.relu(self.fc1(x))\n        x = F.relu(self.fc2(x))\n        x = self.fc3(x)\n        return x\n\n    def num_flat_features(self, x):\n        size = x.size()[1:]  # all dimensions except the batch dimension\n        num_features = 1\n        for s in size:\n            num_features *= s\n        return num_features\n\n\nnet = Net()\nprint(net)"
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        "You just have to define the ``forward`` function, and the ``backward``\nfunction (where gradients are computed) is automatically defined for you\nusing ``autograd``.\nYou can use any of the Tensor operations in the ``forward`` function.\n\nThe learnable parameters of a model are returned by ``net.parameters()``\n\n"
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        "params = list(net.parameters())\nprint(len(params))\nprint(params[0].size())  # conv1's .weight"
      ]
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      "source": [
        "Let try a random 32x32 input.\nNote: expected input size of this net (LeNet) is 32x32. To use this net on\nMNIST dataset, please resize the images from the dataset to 32x32.\n\n"
      ]
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      "source": [
        "input = torch.randn(1, 1, 32, 32)\nout = net(input)\nprint(out)"
      ]
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        "Zero the gradient buffers of all parameters and backprops with random\ngradients:\n\n"
      ]
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      "source": [
        "net.zero_grad()\nout.backward(torch.randn(1, 10))"
      ]
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      "source": [
        "<div class=\"alert alert-info\"><h4>Note</h4><p>``torch.nn`` only supports mini-batches. The entire ``torch.nn``\n    package only supports inputs that are a mini-batch of samples, and not\n    a single sample.\n\n    For example, ``nn.Conv2d`` will take in a 4D Tensor of\n    ``nSamples x nChannels x Height x Width``.\n\n    If you have a single sample, just use ``input.unsqueeze(0)`` to add\n    a fake batch dimension.</p></div>\n\nBefore proceeding further, let's recap all the classes you\u2019ve seen so far.\n\n**Recap:**\n  -  ``torch.Tensor`` - A *multi-dimensional array* with support for autograd\n     operations like ``backward()``. Also *holds the gradient* w.r.t. the\n     tensor.\n  -  ``nn.Module`` - Neural network module. *Convenient way of\n     encapsulating parameters*, with helpers for moving them to GPU,\n     exporting, loading, etc.\n  -  ``nn.Parameter`` - A kind of Tensor, that is *automatically\n     registered as a parameter when assigned as an attribute to a*\n     ``Module``.\n  -  ``autograd.Function`` - Implements *forward and backward definitions\n     of an autograd operation*. Every ``Tensor`` operation creates at\n     least a single ``Function`` node that connects to functions that\n     created a ``Tensor`` and *encodes its history*.\n\n**At this point, we covered:**\n  -  Defining a neural network\n  -  Processing inputs and calling backward\n\n**Still Left:**\n  -  Computing the loss\n  -  Updating the weights of the network\n\nLoss Function\n-------------\nA loss function takes the (output, target) pair of inputs, and computes a\nvalue that estimates how far away the output is from the target.\n\nThere are several different\n`loss functions <https://pytorch.org/docs/nn.html#loss-functions>`_ under the\nnn package .\nA simple loss is: ``nn.MSELoss`` which computes the mean-squared error\nbetween the input and the target.\n\nFor example:\n\n"
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        "output = net(input)\ntarget = torch.randn(10)  # a dummy target, for example\ntarget = target.view(1, -1)  # make it the same shape as output\ncriterion = nn.MSELoss()\n\nloss = criterion(output, target)\nprint(loss)"
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        "Now, if you follow ``loss`` in the backward direction, using its\n``.grad_fn`` attribute, you will see a graph of computations that looks\nlike this:\n\n::\n\n    input -> conv2d -> relu -> maxpool2d -> conv2d -> relu -> maxpool2d\n          -> view -> linear -> relu -> linear -> relu -> linear\n          -> MSELoss\n          -> loss\n\nSo, when we call ``loss.backward()``, the whole graph is differentiated\nw.r.t. the loss, and all Tensors in the graph that has ``requires_grad=True``\nwill have their ``.grad`` Tensor accumulated with the gradient.\n\nFor illustration, let us follow a few steps backward:\n\n"
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        "print(loss.grad_fn)  # MSELoss\nprint(loss.grad_fn.next_functions[0][0])  # Linear\nprint(loss.grad_fn.next_functions[0][0].next_functions[0][0])  # ReLU"
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        "Backprop\n--------\nTo backpropagate the error all we have to do is to ``loss.backward()``.\nYou need to clear the existing gradients though, else gradients will be\naccumulated to existing gradients.\n\n\nNow we shall call ``loss.backward()``, and have a look at conv1's bias\ngradients before and after the backward.\n\n"
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        "net.zero_grad()     # zeroes the gradient buffers of all parameters\n\nprint('conv1.bias.grad before backward')\nprint(net.conv1.bias.grad)\n\nloss.backward()\n\nprint('conv1.bias.grad after backward')\nprint(net.conv1.bias.grad)"
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        "Now, we have seen how to use loss functions.\n\n**Read Later:**\n\n  The neural network package contains various modules and loss functions\n  that form the building blocks of deep neural networks. A full list with\n  documentation is `here <https://pytorch.org/docs/nn>`_.\n\n**The only thing left to learn is:**\n\n  - Updating the weights of the network\n\nUpdate the weights\n------------------\nThe simplest update rule used in practice is the Stochastic Gradient\nDescent (SGD):\n\n     ``weight = weight - learning_rate * gradient``\n\nWe can implement this using simple python code:\n\n.. code:: python\n\n    learning_rate = 0.01\n    for f in net.parameters():\n        f.data.sub_(f.grad.data * learning_rate)\n\nHowever, as you use neural networks, you want to use various different\nupdate rules such as SGD, Nesterov-SGD, Adam, RMSProp, etc.\nTo enable this, we built a small package: ``torch.optim`` that\nimplements all these methods. Using it is very simple:\n\n"
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      "cell_type": "code",
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      "source": [
        "import torch.optim as optim\n\n# create your optimizer\noptimizer = optim.SGD(net.parameters(), lr=0.01)\n\n# in your training loop:\noptimizer.zero_grad()   # zero the gradient buffers\noutput = net(input)\nloss = criterion(output, target)\nloss.backward()\noptimizer.step()    # Does the update"
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      "source": [
        ".. Note::\n\n      Observe how gradient buffers had to be manually set to zero using\n      ``optimizer.zero_grad()``. This is because gradients are accumulated\n      as explained in `Backprop`_ section.\n\n"
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