/// <summary>
/// A fully-connected ReLU network with one hidden layer, trained to predict y from
/// x by minimizing squared Euclidean distance.
///
/// This implementation uses the nn package from PyTorch to build the network.
/// PyTorch autograd makes it easy to define computational graphs and take gradients,
/// but raw autograd can be a bit too low-level for defining complex neural networks;
/// this is where the nn package can help. The nn package defines a set of Modules,
/// which you can think of as a neural network layer that has produces output from
/// input and may have some trainable weights.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
private static void LearnWithNnModules(Tensor x, Tensor y)
{
Console.WriteLine("Using NN Modules:");
// N is batch size; D_in is input dimension;
// H is hidden dimension; D_out is output dimension.
var(N, D_in, H, D_out) = (64, 1000, 100, 10);
var stopwatch = Stopwatch.StartNew();
// Use the nn package to define our model as a sequence of layers. nn.Sequential
// is a Module which contains other Modules, and applies them in sequence to
// produce its output. Each Linear Module computes output from input using a
// linear function, and holds internal Tensors for its weight and bias.
var model = new torch.nn.Sequential(
new torch.nn.Linear(D_in, H),
new torch.nn.ReLU(),
new torch.nn.Linear(H, D_out)
);
model.cuda(0);
// The nn package also contains definitions of popular loss functions; in this
// case we will use Mean Squared Error (MSE) as our loss function.
var loss_fn = new torch.nn.MSELoss(reduction: "sum");
loss_fn.cuda(0);
var learning_rate = 1.0e-4;
for (int t = 0; t <= 500; t++)
{
// Forward pass: compute predicted y by passing x to the model. Module objects
// override the __call__ operator so you can call them like functions. When
// doing so you pass a Tensor of input data to the Module and it produces
// a Tensor of output data.
var y_pred = model.Invoke(x).First();
// Compute and print loss. We pass Tensors containing the predicted and true
// values of y, and the loss function returns a Tensor containing the
// loss.
var loss = loss_fn.Invoke(y_pred, y).First();
if (t % 20 == 0)
{
Console.WriteLine($"\tstep {t}: {loss.item<double>():F4}");
}
// Zero the gradients before running the backward pass.
model.zero_grad();
// Backward pass: compute gradient of the loss with respect to all the learnable
// parameters of the model. Internally, the parameters of each Module are stored
// in Tensors with requires_grad=True, so this call will compute gradients for
// all learnable parameters in the model.
loss.backward();
// Update the weights using gradient descent. Each parameter is a Tensor, so
// we can access its gradients like we did before.
Py.With(torch.no_grad(), _ =>
{
foreach (var param in model.parameters())
{
param.isub(learning_rate * param.grad);
}
});
}
stopwatch.Stop();
Console.WriteLine($"\telapsed time: {stopwatch.Elapsed.TotalSeconds:F3} seconds\n");
}
/// <summary>
/// A fully-connected ReLU network with one hidden layer, trained to predict y from x by
/// minimizing squared Euclidean distance.
///
/// This implementation uses the nn package from PyTorch to build the network.
///
/// Rather than manually updating the weights of the model as we have been doing, we
/// use the optim package to define an Optimizer that will update the weights for us. The
/// optim package defines many optimization algorithms that are commonly used for deep
/// learning, including SGD+momentum, RMSProp, Adam, etc.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
private static void LearnWithOptimizer(Tensor x, Tensor y)
{
Console.WriteLine("Using NN Modules:");
// N is batch size; D_in is input dimension;
// H is hidden dimension; D_out is output dimension.
var(N, D_in, H, D_out) = (64, 1000, 100, 10);
var stopwatch = Stopwatch.StartNew();
// Use the nn package to define our model as a sequence of layers. nn.Sequential
// is a Module which contains other Modules, and applies them in sequence to
// produce its output. Each Linear Module computes output from input using a
// linear function, and holds internal Tensors for its weight and bias.
var model = new torch.nn.Sequential(
new torch.nn.Linear(D_in, H),
new torch.nn.ReLU(),
new torch.nn.Linear(H, D_out)
);
model.cuda(0);
// The nn package also contains definitions of popular loss functions; in this
// case we will use Mean Squared Error (MSE) as our loss function.
var loss_fn = new torch.nn.MSELoss(reduction: "sum");
loss_fn.cuda(0);
var learning_rate = 1.0e-4;
var optimizer = torch.optim.Adam(model.parameters(), lr: learning_rate);
for (int t = 0; t <= 500; t++)
{
// Forward pass: compute predicted y by passing x to the model.
var y_pred = model.Invoke(x).First();
// Compute and print loss. We pass Tensors containing the predicted and true
// values of y, and the loss function returns a Tensor containing the
// loss.
var loss = loss_fn.Invoke(y_pred, y).First();
if (t % 20 == 0)
{
Console.WriteLine($"\tstep {t}: {loss.item<double>():F4}");
}
// Before the backward pass, use the optimizer object to zero all of the
// gradients for the variables it will update (which are the learnable
// weights of the model). This is because by default, gradients are
// accumulated in buffers( i.e, not overwritten) whenever .backward()
// is called. Checkout docs of torch.autograd.backward for more details.
optimizer.zero_grad();
// Backward pass: compute gradient of the loss with respect to model
// parameters
loss.backward();
// Calling the step function on an Optimizer makes an update to its
// parameters
optimizer.step();
}
stopwatch.Stop();
Console.WriteLine($"\telapsed time: {stopwatch.Elapsed.TotalSeconds:F3} seconds\n");
}