def fizzbuzz_accuracy(low: int, hi: int, net: Layer) -> float:
num_correct = 0
for n in range(low, hi):
x = binary_encode(n)
predicted = argmax(net.forward(x))
actual = argmax(fizz_buzz_encode(n))
if predicted == actual:
num_correct += 1
return num_correct / (hi - low)
self.tanh, gradient)
class Relu(Layer):
def forward(self, input: Tensor) -> Tensor:
self.input = input
return tensor_apply(lambda x: max(x,0), input)
def backward(self, gradient: Tensor) -> Tensor:
return tensor_combine(lambda x, grad: grad if x > 0 else 0,
self.input,
gradient)
from neural_networks import binary_encode, fizz_buzz_encode, argmax
xs = [binary_encode(n) for n in range(101, 1024)]
ys = [fizz_buzz_encode(n) for n in range(101, 1024)]
NUM_HIDDEN = 25
random.seed(0)
net = Sequential([
Linear(input_dim = 10, output_dim = NUM_HIDDEN, init = 'uniform'),
Tanh(),
Linear(input_dim = NUM_HIDDEN, output_dim = 4, init = 'uniform'),
Sigmoid()
])
def fizzbuzz_accuracy(low: int, hi: int, net: Layer) -> float:
def main():
# XOR revisited
# training data
xs = [[0., 0], [0., 1], [1., 0], [1., 1]]
ys = [[0.], [1.], [1.], [0.]]
random.seed(0)
net = Sequential([
Linear(input_dim=2, output_dim=2),
Sigmoid(),
Linear(input_dim=2, output_dim=1)
])
import tqdm
optimizer = GradientDescent(learning_rate=0.1)
loss = SSE()
with tqdm.trange(3000) as t:
for epoch in t:
epoch_loss = 0.0
for x, y in zip(xs, ys):
predicted = net.forward(x)
epoch_loss += loss.loss(predicted, y)
gradient = loss.gradient(predicted, y)
net.backward(gradient)
optimizer.step(net)
t.set_description(f"xor loss {epoch_loss:.3f}")
for param in net.params():
print(param)
# FizzBuzz Revisited
from neural_networks import binary_encode, fizz_buzz_encode, argmax
xs = [binary_encode(n) for n in range(101, 1024)]
ys = [fizz_buzz_encode(n) for n in range(101, 1024)]
NUM_HIDDEN = 25
random.seed(0)
net = Sequential([
Linear(input_dim=10, output_dim=NUM_HIDDEN, init='uniform'),
Tanh(),
Linear(input_dim=NUM_HIDDEN, output_dim=4, init='uniform'),
Sigmoid()
])
def fizzbuzz_accuracy(low: int, hi: int, net: Layer) -> float:
num_correct = 0
for n in range(low, hi):
x = binary_encode(n)
predicted = argmax(net.forward(x))
actual = argmax(fizz_buzz_encode(n))
if predicted == actual:
num_correct += 1
return num_correct / (hi - low)
optimizer = Momentum(learning_rate=0.1, momentum=0.9)
loss = SSE()
with tqdm.trange(1000) as t:
for epoch in t:
epoch_loss = 0.0
for x, y in zip(xs, ys):
predicted = net.forward(x)
epoch_loss += loss.loss(predicted, y)
gradient = loss.gradient(predicted, y)
net.backward(gradient)
optimizer.step(net)
accuracy = fizzbuzz_accuracy(101, 1024, net)
t.set_description(f"fb loss: {epoch_loss:.2f} acc: {accuracy:.2f}")
# Now check results on the test set
print("test results", fizzbuzz_accuracy(1, 101, net))
random.seed(0)
net = Sequential([
Linear(input_dim=10, output_dim=NUM_HIDDEN, init='uniform'),
Tanh(),
Linear(input_dim=NUM_HIDDEN, output_dim=4, init='uniform')
# No final sigmoid layer now
])
optimizer = Momentum(learning_rate=0.1, momentum=0.9)
loss = SoftmaxCrossEntropy()
with tqdm.trange(100) as t:
for epoch in t:
epoch_loss = 0.0
for x, y in zip(xs, ys):
predicted = net.forward(x)
epoch_loss += loss.loss(predicted, y)
gradient = loss.gradient(predicted, y)
net.backward(gradient)
optimizer.step(net)
accuracy = fizzbuzz_accuracy(101, 1024, net)
t.set_description(f"fb loss: {epoch_loss:.3f} acc: {accuracy:.2f}")
# Again check results on the test set
print("test results", fizzbuzz_accuracy(1, 101, net))
# Load the MNIST data
import mnist
# This will download the data, change this to where you want it.
# (Yes, it's a 0-argument function, that's what the library expects.)
# (Yes, I'm assigning a lambda to a variable, like I said never to do.)
mnist.temporary_dir = lambda: '/tmp'
# Each of these functions first downloads the data and returns a numpy array.
# We call .tolist() because our "tensors" are just lists.
train_images = mnist.train_images().tolist()
train_labels = mnist.train_labels().tolist()
assert shape(train_images) == [60000, 28, 28]
assert shape(train_labels) == [60000]
import matplotlib.pyplot as plt
fig, ax = plt.subplots(10, 10)
for i in range(10):
for j in range(10):
# Plot each image in black and white and hide the axes.
ax[i][j].imshow(train_images[10 * i + j], cmap='Greys')
ax[i][j].xaxis.set_visible(False)
ax[i][j].yaxis.set_visible(False)
# plt.show()
# Load the MNIST test data
test_images = mnist.test_images().tolist()
test_labels = mnist.test_labels().tolist()
assert shape(test_images) == [10000, 28, 28]
assert shape(test_labels) == [10000]
# Recenter the images
# Compute the average pixel value
avg = tensor_sum(train_images) / 60000 / 28 / 28
# Recenter, rescale, and flatten
train_images = [[(pixel - avg) / 256 for row in image for pixel in row]
for image in train_images]
test_images = [[(pixel - avg) / 256 for row in image for pixel in row]
for image in test_images]
assert shape(train_images) == [60000, 784], "images should be flattened"
assert shape(test_images) == [10000, 784], "images should be flattened"
# After centering, average pixel should be very close to 0
assert -0.0001 < tensor_sum(train_images) < 0.0001
# One-hot encode the test data
train_labels = [one_hot_encode(label) for label in train_labels]
test_labels = [one_hot_encode(label) for label in test_labels]
assert shape(train_labels) == [60000, 10]
assert shape(test_labels) == [10000, 10]
# Training loop
import tqdm
def loop(model: Layer,
images: List[Tensor],
labels: List[Tensor],
loss: Loss,
optimizer: Optimizer = None) -> None:
correct = 0 # Track number of correct predictions.
total_loss = 0.0 # Track total loss.
with tqdm.trange(len(images)) as t:
for i in t:
predicted = model.forward(images[i]) # Predict.
if argmax(predicted) == argmax(labels[i]): # Check for
correct += 1 # correctness.
total_loss += loss.loss(predicted, labels[i]) # Compute loss.
# If we're training, backpropagate gradient and update weights.
if optimizer is not None:
gradient = loss.gradient(predicted, labels[i])
model.backward(gradient)
optimizer.step(model)
# And update our metrics in the progress bar.
avg_loss = total_loss / (i + 1)
acc = correct / (i + 1)
t.set_description(f"mnist loss: {avg_loss:.3f} acc: {acc:.3f}")
# The logistic regression model for MNIST
random.seed(0)
# Logistic regression is just a linear layer followed by softmax
model = Linear(784, 10)
loss = SoftmaxCrossEntropy()
# This optimizer seems to work
optimizer = Momentum(learning_rate=0.01, momentum=0.99)
# Train on the training data
loop(model, train_images, train_labels, loss, optimizer)
# Test on the test data (no optimizer means just evaluate)
loop(model, test_images, test_labels, loss)
# A deep neural network for MNIST
random.seed(0)
# Name them so we can turn train on and off
dropout1 = Dropout(0.1)
dropout2 = Dropout(0.1)
model = Sequential([
Linear(784, 30), # Hidden layer 1: size 30
dropout1,
Tanh(),
Linear(30, 10), # Hidden layer 2: size 10
dropout2,
Tanh(),
Linear(10, 10) # Output layer: size 10
])
# Training the deep model for MNIST
optimizer = Momentum(learning_rate=0.01, momentum=0.99)
loss = SoftmaxCrossEntropy()
# Enable dropout and train (takes > 20 minutes on my laptop!)
dropout1.train = dropout2.train = True
loop(model, train_images, train_labels, loss, optimizer)
# Disable dropout and evaluate
dropout1.train = dropout2.train = False
loop(model, test_images, test_labels, loss)