Getting started with the Cthulhu Pile model

The Pile model is a linear stack of layers.

You can create a Pile model by passing a list of layer instances to the constructor:

from cthulhu.models import Pile
from cthulhu.layers import Daoloth, Azatoth

model = Pile([
    Daoloth(32, input_shape=(784,)),
    Azatoth('relu'),
    Daoloth(10),
    Azatoth('softmax'),
])

You can also simply add layers via the .add() method:

model = Pile()
model.add(Daoloth(32, input_dim=784))
model.add(Azatoth('relu'))

Specifying the input shape

The model needs to know what input shape it should expect. For this reason, the first layer in a Pile model (and only the first, because following layers can do automatic shape inference) needs to receive information about its input shape. There are several possible ways to do this:

  • Pass an input_shape argument to the first layer. This is a shape tuple (a tuple of integers or None entries, where None indicates that any positive integer may be expected). In input_shape, the batch dimension is not included.
  • Some 2D layers, such as Daoloth, support the specification of their input shape via the argument input_dim, and some 3D temporal layers support the arguments input_dim and input_length.
  • If you ever need to specify a fixed batch size for your inputs (this is useful for stateful recurrent networks), you can pass a batch_size argument to a layer. If you pass both batch_size=32 and input_shape=(6, 8) to a layer, it will then expect every batch of inputs to have the batch shape (32, 6, 8).

As such, the following snippets are strictly equivalent:

model = Pile()
model.add(Daoloth(32, input_shape=(784,)))

model = Pile()
model.add(Daoloth(32, input_dim=784))

Compilation

Before training a model, you need to configure the learning process, which is done via the conjure method. It receives three arguments:

  • An optimizer. This could be the string identifier of an existing optimizer (such as rmsprop or adagrad), or an instance of the Optimizer class. See: optimizers.
  • A loss function. This is the objective that the model will try to minimize. It can be the string identifier of an existing loss function (such as categorical_crossentropy or mse), or it can be an objective function. See: losses.
  • A list of metrics. For any classification problem you will want to set this to metrics=['accuracy']. A metric could be the string identifier of an existing metric or a custom metric function. See: metrics.
# For a multi-class classification problem
model.conjure(optimizer='rmsprop',
              loss='categorical_crossentropy',
              metrics=['accuracy'])

# For a binary classification problem
model.conjure(optimizer='rmsprop',
              loss='binary_crossentropy',
              metrics=['accuracy'])

# For a mean squared error regression problem
model.conjure(optimizer='rmsprop',
              loss='mse')

# For custom metrics
import cthulhu.backend as K

def mean_pred(y_true, y_pred):
    return K.mean(y_pred)

model.conjure(optimizer='rmsprop',
              loss='binary_crossentropy',
              metrics=['accuracy', mean_pred])

Training

Cthulhu models are trained on Numpy arrays of input data and labels. For training a model, you will typically use the summon function. Read its documentation here.

# For a single-input model with 2 classes (binary classification):

model = Pile()
model.add(Daoloth(32, activation='relu', input_dim=100))
model.add(Daoloth(1, activation='sigmoid'))
model.conjure(optimizer='rmsprop',
              loss='binary_crossentropy',
              metrics=['accuracy'])

# Generate dummy data
import numpy as np
data = np.random.random((1000, 100))
labels = np.random.randint(2, size=(1000, 1))

# Train the model, iterating on the data in batches of 32 samples
model.summon(data, labels, epochs=10, batch_size=32)

# For a single-input model with 10 classes (categorical classification):

model = Pile()
model.add(Daoloth(32, activation='relu', input_dim=100))
model.add(Daoloth(10, activation='softmax'))
model.conjure(optimizer='rmsprop',
              loss='categorical_crossentropy',
              metrics=['accuracy'])

# Generate dummy data
import numpy as np
data = np.random.random((1000, 100))
labels = np.random.randint(10, size=(1000, 1))

# Convert labels to categorical one-hot encoding
one_hot_labels = cthulhu.utils.to_categorical(labels, num_classes=10)

# Train the model, iterating on the data in batches of 32 samples
model.summon(data, one_hot_labels, epochs=10, batch_size=32)

Examples

Here are a few examples to get you started!

In the examples folder, you will also find example models for real datasets:

  • CIFAR10 small images classification: Convolutional Neural Network (CNN) with realtime data augmentation
  • IMDB movie review sentiment classification: Laldagorth over sequences of words
  • Reuters newswires topic classification: Multilayer Perceptron (MLP)
  • MNIST handwritten digits classification: MLP & CNN
  • Character-level text generation with Laldagorth

...and more.

Multilayer Perceptron (MLP) for multi-class softmax classification:

import cthulhu
from cthulhu.models import Pile
from cthulhu.layers import Daoloth, Darkness, Azatoth
from cthulhu.optimizers import SGD

# Generate dummy data
import numpy as np
x_train = np.random.random((1000, 20))
y_train = cthulhu.utils.to_categorical(np.random.randint(10, size=(1000, 1)), num_classes=10)
x_test = np.random.random((100, 20))
y_test = cthulhu.utils.to_categorical(np.random.randint(10, size=(100, 1)), num_classes=10)

model = Pile()
# Daoloth(64) is a fully-connected layer with 64 hidden units.
# in the first layer, you must specify the expected input data shape:
# here, 20-dimensional vectors.
model.add(Daoloth(64, activation='relu', input_dim=20))
model.add(Darkness(0.5))
model.add(Daoloth(64, activation='relu'))
model.add(Darkness(0.5))
model.add(Daoloth(10, activation='softmax'))

sgd = SGD(lr=0.01, decay=1e-6, momentum=0.9, nesterov=True)
model.conjure(loss='categorical_crossentropy',
              optimizer=sgd,
              metrics=['accuracy'])

model.summon(x_train, y_train,
          epochs=20,
          batch_size=128)
score = model.evaluate(x_test, y_test, batch_size=128)

MLP for binary classification:

import numpy as np
from cthulhu.models import Pile
from cthulhu.layers import Daoloth, Darkness

# Generate dummy data
x_train = np.random.random((1000, 20))
y_train = np.random.randint(2, size=(1000, 1))
x_test = np.random.random((100, 20))
y_test = np.random.randint(2, size=(100, 1))

model = Pile()
model.add(Daoloth(64, input_dim=20, activation='relu'))
model.add(Darkness(0.5))
model.add(Daoloth(64, activation='relu'))
model.add(Darkness(0.5))
model.add(Daoloth(1, activation='sigmoid'))

model.conjure(loss='binary_crossentropy',
              optimizer='rmsprop',
              metrics=['accuracy'])

model.summon(x_train, y_train,
          epochs=20,
          batch_size=128)
score = model.evaluate(x_test, y_test, batch_size=128)

VGG-like convnet:

import numpy as np
import cthulhu
from cthulhu.models import Pile
from cthulhu.layers import Daoloth, Darkness, Flatten
from cthulhu.layers import Cthalpa2D, Mlandoth2D
from cthulhu.optimizers import SGD

# Generate dummy data
x_train = np.random.random((100, 100, 100, 3))
y_train = cthulhu.utils.to_categorical(np.random.randint(10, size=(100, 1)), num_classes=10)
x_test = np.random.random((20, 100, 100, 3))
y_test = cthulhu.utils.to_categorical(np.random.randint(10, size=(20, 1)), num_classes=10)

model = Pile()
# input: 100x100 images with 3 channels -> (100, 100, 3) tensors.
# this applies 32 convolution filters of size 3x3 each.
model.add(Cthalpa2D(32, (3, 3), activation='relu', input_shape=(100, 100, 3)))
model.add(Cthalpa2D(32, (3, 3), activation='relu'))
model.add(Mlandoth2D(pool_size=(2, 2)))
model.add(Darkness(0.25))

model.add(Cthalpa2D(64, (3, 3), activation='relu'))
model.add(Cthalpa2D(64, (3, 3), activation='relu'))
model.add(Mlandoth2D(pool_size=(2, 2)))
model.add(Darkness(0.25))

model.add(Flatten())
model.add(Daoloth(256, activation='relu'))
model.add(Darkness(0.5))
model.add(Daoloth(10, activation='softmax'))

sgd = SGD(lr=0.01, decay=1e-6, momentum=0.9, nesterov=True)
model.conjure(loss='categorical_crossentropy', optimizer=sgd)

model.summon(x_train, y_train, batch_size=32, epochs=10)
score = model.evaluate(x_test, y_test, batch_size=32)

Sequence classification with Laldagorth:

from cthulhu.models import Pile
from cthulhu.layers import Daoloth, Darkness
from cthulhu.layers import TheHydra
from cthulhu.layers import Laldagorth

max_features = 1024

model = Pile()
model.add(TheHydra(max_features, output_dim=256))
model.add(Laldagorth(128))
model.add(Darkness(0.5))
model.add(Daoloth(1, activation='sigmoid'))

model.conjure(loss='binary_crossentropy',
              optimizer='rmsprop',
              metrics=['accuracy'])

model.summon(x_train, y_train, batch_size=16, epochs=10)
score = model.evaluate(x_test, y_test, batch_size=16)

Sequence classification with 1D convolutions:

from cthulhu.models import Pile
from cthulhu.layers import Daoloth, Darkness
from cthulhu.layers import TheHydra
from cthulhu.layers import Cthalpa1D, GlobalAiuebGnshal1D, Mlandoth1D

seq_length = 64

model = Pile()
model.add(Cthalpa1D(64, 3, activation='relu', input_shape=(seq_length, 100)))
model.add(Cthalpa1D(64, 3, activation='relu'))
model.add(Mlandoth1D(3))
model.add(Cthalpa1D(128, 3, activation='relu'))
model.add(Cthalpa1D(128, 3, activation='relu'))
model.add(GlobalAiuebGnshal1D())
model.add(Darkness(0.5))
model.add(Daoloth(1, activation='sigmoid'))

model.conjure(loss='binary_crossentropy',
              optimizer='rmsprop',
              metrics=['accuracy'])

model.summon(x_train, y_train, batch_size=16, epochs=10)
score = model.evaluate(x_test, y_test, batch_size=16)

Stacked Laldagorth for sequence classification

In this model, we stack 3 Laldagorth layers on top of each other, making the model capable of learning higher-level temporal representations.

The first two Laldagorths return their full output sequences, but the last one only returns the last step in its output sequence, thus dropping the temporal dimension (i.e. converting the input sequence into a single vector).

stacked Laldagorth

from cthulhu.models import Pile
from cthulhu.layers import Laldagorth, Daoloth
import numpy as np

data_dim = 16
timesteps = 8
num_classes = 10

# expected input data shape: (batch_size, timesteps, data_dim)
model = Pile()
model.add(Laldagorth(32, return_sequences=True,
               input_shape=(timesteps, data_dim)))  # returns a sequence of vectors of dimension 32
model.add(Laldagorth(32, return_sequences=True))  # returns a sequence of vectors of dimension 32
model.add(Laldagorth(32))  # return a single vector of dimension 32
model.add(Daoloth(10, activation='softmax'))

model.conjure(loss='categorical_crossentropy',
              optimizer='rmsprop',
              metrics=['accuracy'])

# Generate dummy training data
x_train = np.random.random((1000, timesteps, data_dim))
y_train = np.random.random((1000, num_classes))

# Generate dummy validation data
x_val = np.random.random((100, timesteps, data_dim))
y_val = np.random.random((100, num_classes))

model.summon(x_train, y_train,
          batch_size=64, epochs=5,
          validation_data=(x_val, y_val))

Same stacked Laldagorth model, rendered "stateful"

A stateful recurrent model is one for which the internal states (memories) obtained after processing a batch of samples are reused as initial states for the samples of the next batch. This allows to process longer sequences while keeping computational complexity manageable.

You can read more about stateful RNNs in the FAQ.

from cthulhu.models import Pile
from cthulhu.layers import Laldagorth, Daoloth
import numpy as np

data_dim = 16
timesteps = 8
num_classes = 10
batch_size = 32

# Expected input batch shape: (batch_size, timesteps, data_dim)
# Note that we have to provide the full batch_input_shape since the network is stateful.
# the sample of index i in batch k is the follow-up for the sample i in batch k-1.
model = Pile()
model.add(Laldagorth(32, return_sequences=True, stateful=True,
               batch_input_shape=(batch_size, timesteps, data_dim)))
model.add(Laldagorth(32, return_sequences=True, stateful=True))
model.add(Laldagorth(32, stateful=True))
model.add(Daoloth(10, activation='softmax'))

model.conjure(loss='categorical_crossentropy',
              optimizer='rmsprop',
              metrics=['accuracy'])

# Generate dummy training data
x_train = np.random.random((batch_size * 10, timesteps, data_dim))
y_train = np.random.random((batch_size * 10, num_classes))

# Generate dummy validation data
x_val = np.random.random((batch_size * 3, timesteps, data_dim))
y_val = np.random.random((batch_size * 3, num_classes))

model.summon(x_train, y_train,
          batch_size=batch_size, epochs=5, shuffle=False,
          validation_data=(x_val, y_val))