PyTorch: import torch
from torch import nn
from d2l import torch as d2l
n_train = 50
x_train, _ = torch.sort(torch.rand(n_train) * 5)
def f(x):
    return 2 * torch.sin(x) + x**0.8
y_train = f(x_train) + torch.normal(0.0, 0.5, (n_train,))
x_test = torch.arange(0, 5, 0.1)
y_truth = f(x_test)
n_test = len(x_test)
n_test
y_hat = torch.repeat_interleave(y_train.mean(), n_test)
plot_kernel_reg(y_hat)
X_repeat = x_test.repeat_interleave(n_train).reshape((-1, n_train))
attention_weights = nn.functional.softmax(-(X_repeat - x_train)**2 / 2, dim=1)
y_hat = torch.matmul(attention_weights, y_train)
plot_kernel_reg(y_hat)
d2l.show_heatmaps(attention_weights.unsqueeze(0).unsqueeze(0), xlabel='Sorted training inputs', ylabel='Sorted testing inputs')
X = torch.ones((2, 1, 4))
Y = torch.ones((2, 4, 6))
torch.bmm(X, Y).shape
weights = torch.ones((2, 10)) * 0.1
values = torch.arange(20.0).reshape((2, 10))
torch.bmm(weights.unsqueeze(1), values.unsqueeze(-1))
class NWKernelRegression(nn.Module):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        self.w = nn.Parameter(torch.rand((1,), requires_grad=True))
    def forward(self, queries, keys, values):
        queries = queries.repeat_interleave(keys.shape[1]).reshape((-1, keys.shape[1]))
        self.attention_weights = nn.functional.softmax(-((queries - keys) * self.w)**2 / 2, dim=1)
        return torch.bmm(self.attention_weights.unsqueeze(1), values.unsqueeze(-1)).reshape(-1)
X_tile = x_train.repeat((n_train, 1))
Y_tile = y_train.repeat((n_train, 1))
keys = X_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train, -1))
values = Y_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train, -1))
net = NWKernelRegression()
loss = nn.MSELoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=0.5)
animator = d2l.Animator(xlabel='epoch', ylabel='loss', xlim=[1, 5])
for epoch in range(5):
    trainer.zero_grad()
    l = loss(net(x_train, keys, values), y_train)
    l.sum().backward()
    trainer.step()
    animator.add(epoch + 1, float(l.sum()))
keys = x_train.repeat((n_test, 1))
values = y_train.repeat((n_test, 1))
y_hat = net(x_test, keys, values).unsqueeze(1).detach()
plot_kernel_reg(y_hat)
d2l.show_heatmaps(net.attention_weights.unsqueeze(0).unsqueeze(0), xlabel='Sorted training inputs', ylabel='Sorted testing inputs')

MXNet: from mxnet import autograd, gluon, np, npx
from mxnet.gluon import nn
from d2l import mxnet as d2l
npx.set_np()
n_train = 50
x_train = np.sort(np.random.rand(n_train) * 5)
def f(x):
    return 2 * np.sin(x) + x**0.8
y_train = f(x_train) + np.random.normal(0.0, 0.5, (n_train,))
x_test = np.arange(0, 5, 0.1)
y_truth = f(x_test)
n_test = len(x_test)
n_test
y_hat = y_train.mean().repeat(n_test)
plot_kernel_reg(y_hat)
X_repeat = x_test.repeat(n_train).reshape((-1, n_train))
attention_weights = npx.softmax(-(X_repeat - x_train)**2 / 2)
y_hat = np.dot(attention_weights, y_train)
plot_kernel_reg(y_hat)
d2l.show_heatmaps(np.expand_dims(np.expand_dims(attention_weights, 0), 0), xlabel='Sorted training inputs', ylabel='Sorted testing inputs')
X = np.ones((2, 1, 4))
Y = np.ones((2, 4, 6))
npx.batch_dot(X, Y).shape
weights = np.ones((2, 10)) * 0.1
values = np.arange(20).reshape((2, 10))
npx.batch_dot(np.expand_dims(weights, 1), np.expand_dims(values, -1))
class NWKernelRegression(nn.Block):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        self.w = self.params.get('w', shape=(1,))
    def forward(self, queries, keys, values):
        queries = queries.repeat(keys.shape[1]).reshape((-1, keys.shape[1]))
        self.attention_weights = npx.softmax(-((queries - keys) * self.w.data())**2 / 2)
        return npx.batch_dot(np.expand_dims(self.attention_weights, 1), np.expand_dims(values, -1)).reshape(-1)
X_tile = np.tile(x_train, (n_train, 1))
Y_tile = np.tile(y_train, (n_train, 1))
keys = X_tile[(1 - np.eye(n_train)).astype('bool')].reshape((n_train, -1))
values = Y_tile[(1 - np.eye(n_train)).astype('bool')].reshape((n_train, -1))
net = NWKernelRegression()
net.initialize()
loss = gluon.loss.L2Loss()
trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.5})
animator = d2l.Animator(xlabel='epoch', ylabel='loss', xlim=[1, 5])
for epoch in range(5):
    with autograd.record():
        l = loss(net(x_train, keys, values), y_train)
    l.backward()
    trainer.step(1)
    animator.add(epoch + 1, float(l.sum()))
keys = np.tile(x_train, (n_test, 1))
values = np.tile(y_train, (n_test, 1))
y_hat = net(x_test, keys, values)
plot_kernel_reg(y_hat)
d2l.show_heatmaps(np.expand_dims(np.expand_dims(net.attention_weights, 0), 0), xlabel='Sorted training inputs', ylabel='Sorted testing inputs')