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"\nPyTorch: nn\n-----------\n\nA third order polynomial, trained to predict $y=\\sin(x)$ from $-\\pi$\nto $pi$ by minimizing squared Euclidean distance.\n\nThis implementation uses the nn package from PyTorch to build the network.\nPyTorch autograd makes it easy to define computational graphs and take gradients,\nbut raw autograd can be a bit too low-level for defining complex neural networks;\nthis is where the nn package can help. The nn package defines a set of Modules,\nwhich you can think of as a neural network layer that has produces output from\ninput and may have some trainable weights.\n\n"
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"import torch\nimport math\n\n\n# Create Tensors to hold input and outputs.\nx = torch.linspace(-math.pi, math.pi, 2000)\ny = torch.sin(x)\n\n# For this example, the output y is a linear function of (x, x^2, x^3), so\n# we can consider it as a linear layer neural network. Let's prepare the\n# tensor (x, x^2, x^3).\np = torch.tensor([1, 2, 3])\nxx = x.unsqueeze(-1).pow(p)\n\n# In the above code, x.unsqueeze(-1) has shape (2000, 1), and p has shape\n# (3,), for this case, broadcasting semantics will apply to obtain a tensor\n# of shape (2000, 3) \n\n# Use the nn package to define our model as a sequence of layers. nn.Sequential\n# is a Module which contains other Modules, and applies them in sequence to\n# produce its output. The Linear Module computes output from input using a\n# linear function, and holds internal Tensors for its weight and bias.\n# The Flatten layer flatens the output of the linear layer to a 1D tensor,\n# to match the shape of `y`.\nmodel = torch.nn.Sequential(\n torch.nn.Linear(3, 1),\n torch.nn.Flatten(0, 1)\n)\n\n# The nn package also contains definitions of popular loss functions; in this\n# case we will use Mean Squared Error (MSE) as our loss function.\nloss_fn = torch.nn.MSELoss(reduction='sum')\n\nlearning_rate = 1e-6\nfor t in range(2000):\n\n # Forward pass: compute predicted y by passing x to the model. Module objects\n # override the __call__ operator so you can call them like functions. When\n # doing so you pass a Tensor of input data to the Module and it produces\n # a Tensor of output data.\n y_pred = model(xx)\n\n # Compute and print loss. We pass Tensors containing the predicted and true\n # values of y, and the loss function returns a Tensor containing the\n # loss.\n loss = loss_fn(y_pred, y)\n if t % 100 == 99:\n print(t, loss.item())\n\n # Zero the gradients before running the backward pass.\n model.zero_grad()\n\n # Backward pass: compute gradient of the loss with respect to all the learnable\n # parameters of the model. Internally, the parameters of each Module are stored\n # in Tensors with requires_grad=True, so this call will compute gradients for\n # all learnable parameters in the model.\n loss.backward()\n\n # Update the weights using gradient descent. Each parameter is a Tensor, so\n # we can access its gradients like we did before.\n with torch.no_grad():\n for param in model.parameters():\n param -= learning_rate * param.grad\n\n# You can access the first layer of `model` like accessing the first item of a list\nlinear_layer = model[0]\n\n# For linear layer, its parameters are stored as `weight` and `bias`.\nprint(f'Result: y = {linear_layer.bias.item()} + {linear_layer.weight[:, 0].item()} x + {linear_layer.weight[:, 1].item()} x^2 + {linear_layer.weight[:, 2].item()} x^3')"
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