TensorState’s Documentation

Introduction

TensorState is a toolbox designed to analyze the way neural networks process information to calculate metrics about the network architecture.

Both Tensorflow and PyTorch are supported, but complex networks may prove problematic for some of the network functions (such as automatically building an efficiency model). Let us know if you run into problems.

Please send comments, suggestions, and feedback to nicholas.j.schaub@gmail.com.

Table of Contents

Installation

Introduction

TensorState uses accelerated Cython code to capture neural layer state information. This can create some issues when trying to install on architectures do not include prepackaged wheels. Please read the appropriate section carefully to make sure installation of the package is successful.

Most dependencies should be installed when using pip, however some may not be installed. Please contact me if there are any installation errors so I can fix it.

Windows and Python >= 3.6

Precompiled wheels exist for Windows 10 and versions of Python from 3.6 to 3.8. No special dependencies are required.

pip install TensorState

Linux

For Linux, there are manylinux wheels that should support most versions of Linux (pip install TensorState). In some cases it may try to compile from source (e.g. Alpine linux). When compiling, it is necessary to install numpy and Cython prior to installation.

pip install numpy==1.19.2 Cython==3.0a1

pip install TensorState

Mac OSX

There are currently no OSX wheels, so compilation from source is necessary following the instructions in the Linux section.

Troubleshooting

Currently, there is no fallback for working on platforms that do not have a C++ compiler or are working on platforms other than x86 architectures such as ARM. If there is interest, please contact me.

The TensorState package is a work in progress, but the following tutorials demonstrate the current useful functionality of the package.

List of Tutorials

A Simple Tensorflow Tutorial

Introduction

The core ideas behind this package were originally described in our paper, Assessing Intelligence in Artificial Neural Networks.

This package simplifies the capture of neural layers states, and provides some utility functions to assist in analyzing the state space of neural layers.

In this tutorial, we are going to build a classic convolutional neural network, LeNet-5. Then we are going to use TensorState to evaluate the network architecture, getting the efficiency of each layer and calculating the artificial intelligence quotient.

Build and Train LeNet-5

Get MNIST

To train this model, we need to get the MNIST data set. Fortunately, it comes packaged with Keras in Tensorflow. The original data was 8-bit and a single channel, so we need to add a channel axis and we are going to normalize the image to have pixel values ranging from 0-1.

import os

# Set the log level to hide some basic warning/info generated by Tensorflow
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'

# Fix for cudnn error on RTX gpus
os.environ['TF_FORCE_GPU_ALLOW_GROWTH'] = 'true'

import tensorflow.keras as keras

# Load the data
mnist = keras.datasets.mnist
(train_images,train_labels), (test_images,test_labels) = mnist.load_data()

# Normalize the data
train_images = train_images/255
test_images = test_images/255

# Add a channel axis
train_images = train_images[..., tf.newaxis]
test_images = test_images[..., tf.newaxis]

Create a LeNet-5 Model

The general structure of our LeNet-5 model will roughly follow the structure of the original network described by LeCun et al. However, we are going to make a few modifications to make it more modern relative to the original architecture, such as addition of l2 weight regularization, exponential linear units, and batch normalization. So, we start off by setting the Tensorflow random seed (to make the results reproducible) and set up the parameters of the convolutional layers.

import tensorflow as tf

# Set the random seed for reproducibility
tf.random.set_seed(0)

# Set the convolutional layer settings
reg = keras.regularizers.l2(0.0005)
kwargs = {'activation': 'elu',
          'kernel_initializer': 'he_normal',
          'kernel_regularizer': reg,
          'bias_regularizer': reg}

Next, we create the layers of the network. LeNet-5 has 2 convolutional layers and 2 fully connected layers. We will use max pooling layers after each convolutional layer, and we will add a batch normalization layer to all by the last fully connected layer.

# Build the layers
input_layer = keras.layers.Input(shape=(28,28,1), name='input')

# Unit 1
conv_1 = keras.layers.Conv2D(20, 5, name='conv_1',**kwargs)(input_layer)
norm_1 = keras.layers.BatchNormalization(epsilon=0.00001,momentum=0.9)(conv_1)
maxp_1 = keras.layers.MaxPool2D((2,2), name='maxp_1')(norm_1)

# Unit 2
conv_2 = keras.layers.Conv2D(50, 5, name='conv_2', **kwargs)(maxp_1)
norm_2 = keras.layers.BatchNormalization(epsilon=0.00001,momentum=0.9)(conv_2)
maxp_2 = keras.layers.MaxPool2D((2,2), name='maxp_2')(norm_2)

# Fully Connected
conv_3 = keras.layers.Conv2D(100, 4, name='conv_3', **kwargs)(maxp_2)
norm_3 = keras.layers.BatchNormalization(epsilon=0.00001,momentum=0.9)(conv_3)

# Prediction
flatten = keras.layers.Flatten(name='flatten')(norm_3)
pred = keras.layers.Dense(10,name='pred')(flatten)

# Create the Keras model
model = keras.Model(
                    inputs=input_layer,
                    outputs=pred
                   )

Train the LeNet-5 Model

Next we train the LeNet-5 model, and stopping as soon as the validation accuracy stops increasing.

# Compile for training
model.compile(
              optimizer=keras.optimizers.SGD(learning_rate=0.001,momentum=0.9,nesterov=True),
              loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True,name='loss'),
              metrics=['accuracy']
             )

# Stop the model once the validation accuracy stops going down
earlystop_callback = tf.keras.callbacks.EarlyStopping(
                            monitor='val_accuracy',
                            mode='max',
                            patience=5,
                            restore_best_weights=True
                        )

# Train the model
model.fit(
          train_images, train_labels, epochs=200,
          validation_data=(test_images, test_labels),
          batch_size=200,
          callbacks=[earlystop_callback],
          verbose=1
         )

Use TensorState to Evaluate LeNet-5

To calculate neural layer efficiency, we need to capture the various states each layer takes on as the network processes data. This functionality is built into the StateCapture class, which is a Tensorflow layer that can be inserted into the model to automate the capturing of information passing through the network. The StateCapture layer acts like a probe that can be placed anywhere in the network: it records the information without modifying it, and passes it on to subsequent layers.

While StateCapture layers can be placed manually, there is a convenience function that can take an existing neural network and return a new network with StateCapture layers inserted at the designated areas. For example, we can attach a StateCapture layer to all convolutional layers.

import TensorState as ts
efficiency_model = ts.build_efficiency_model(model,attach_to=['Conv2D'],method='after')

In the above code, we feed the trained LeNet-5 model into the function, designate we want to attach StateCapture layers to all 2D convolutional layers, and we want to capture the states after the layer. We could also capture the inputs going into and out of the layer by using method='both'. For more information on the build_efficiency_model method and additional settings, please see the TensorState reference.

Now that the efficiency_model has been created, the StateCapture layers will collect all states of the network as images are fed to the network. Thus, to generate all possible states the network contains for the test data, we only need to predict the classes for the test data. Then we can look at how many states were collected for each layer.

predictions = efficiency_model.predict(train_images,batch_size=200)

for layer in efficiency_model.efficiency_layers:
    print('Layer {} number of states: {}'.format(layer.name,layer.state_count))

Note how efficiency_model has the efficiency layers stored in the efficiency_layers attribute of the model. The output of the above code should look something like this:

Layer conv_1_states number of states: 5760000
Layer conv_2_states number of states: 640000
Layer conv_3_states number of states: 10000

Since there are 10,000 images in the training data set, it is expected that the fully connected layer (conv_3_states) has 10,000 states recorded, since exactly one state will be recorded per image. The other layers are convolutional, generating multiple states per image. The number of states can be checked by determining the number of locations the convolutional operator is applied per image then multiplying by 10,000. For example, in a 28x28 image with a 5x5 convolutional operation performed on it, the dimensions of the output would be 24x24. Thus, the number of states for all 10,000 images would be 24*24*10,000=5,760,000 states, which is the number of states observed by conv_1_states.

Note

The state_count is the raw number of states observed, and there are likely states that occur multiple times.

Now that the states of each layer have been captured, let’s analyze the state space using the efficiency metric originally described by Schaub et al. The efficiency metric calculates the entropy of the state space and divides by the number of neurons in the layer, giving an efficiency value in the range 0.00-1.00.

for layer in efficiency_model.efficiency_layers:
    layer_efficiency = layer.efficiency()
    print('Layer {} efficiency: {:.1f}%'.format(layer.name,100*layer_efficiency))

Next, we can calculate the artificial intelligence quotient (aIQ). Since things like neural network efficiency and aIQ are metrics calculated over the entire network, the StateCapture layer does not have built-in methods to calculate these values.

beta = 2 # fudge factor giving a slight bias toward accuracy over efficiency

print()
print('Network metrics...')
print('Beta: {}'.format(beta))

network_efficiency = ts.network_efficiency(efficiency_model)
print('Network efficiency: {:.1f}%'.format(100*network_efficiency))

accuracy = np.sum(np.argmax(predictions,axis=1)==train_labels)/train_labels.size
print('Network accuracy: {:.1f}%'.format(100*accuracy))

aIQ  = ts.aIQ(network_efficiency,accuracy,beta)
print('aIQ: {:.1f}%'.format(100*aIQ))

Complete Example

import os

# Set the log level to hide some basic warning/info generated by Tensorflow
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'

# Fix for cudnn error on RTX gpus
os.environ['TF_FORCE_GPU_ALLOW_GROWTH'] = 'true'

import tensorflow as tf
import tensorflow.keras as keras
import TensorState as ts
import numpy as np
import time

""" Load MNIST and transform it """
# Load the data
mnist = keras.datasets.mnist
(train_images,train_labels), (test_images,test_labels) = mnist.load_data()

# Normalize the data
train_images = train_images/255
test_images = test_images/255

# Add a channel axis
train_images = train_images[..., tf.newaxis]
test_images = test_images[..., tf.newaxis]

""" Create a LeNet-5 model """
# Set the random seed for reproducibility
tf.random.set_seed(0)

# Set the convolutional layer settings
reg = keras.regularizers.l2(0.0005)
kwargs = {'activation': 'elu',
        'kernel_initializer': 'he_normal',
        'kernel_regularizer': reg,
        'bias_regularizer': reg}

# Build the layers
input_layer = keras.layers.Input(shape=(28,28,1), name='input')

# Unit 1
conv_1 = keras.layers.Conv2D(20, 5, name='conv_1',**kwargs)(input_layer)
norm_1 = keras.layers.BatchNormalization(epsilon=0.00001,momentum=0.9)(conv_1)
maxp_1 = keras.layers.MaxPool2D((2,2), name='maxp_1')(norm_1)

# Unit 2
conv_2 = keras.layers.Conv2D(50, 5, name='conv_2', **kwargs)(maxp_1)
norm_2 = keras.layers.BatchNormalization(epsilon=0.00001,momentum=0.9)(conv_2)
maxp_2 = keras.layers.MaxPool2D((2,2), name='maxp_2')(norm_2)

# Fully Connected
conv_3 = keras.layers.Conv2D(100, 4, name='conv_3', **kwargs)(maxp_2)
norm_3 = keras.layers.BatchNormalization(epsilon=0.00001,momentum=0.9)(conv_3)

# Prediction
flatten = keras.layers.Flatten(name='flatten')(norm_3)
pred = keras.layers.Dense(10,name='pred')(flatten)

# Create the Keras model
model = keras.Model(
                    inputs=input_layer,
                    outputs=pred
                )

print(model.summary())

""" Train the model """
# Compile for training
model.compile(
            optimizer=keras.optimizers.SGD(learning_rate=0.001,momentum=0.9,nesterov=True),
            loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True,name='loss'),
            metrics=['accuracy']
            )

# Stop the model once the validation accuracy stops going down
earlystop_callback = tf.keras.callbacks.EarlyStopping(
                            monitor='val_accuracy',
                            mode='max',
                            patience=5,
                            restore_best_weights=True
                        )

# Train the model
model.fit(
        train_images, train_labels, epochs=200,
        validation_data=(test_images, test_labels),
        batch_size=200,
        callbacks=[earlystop_callback],
        verbose=1
        )

""" Evaluate model efficiency """
# Attach StateCapture layers to the model
efficiency_model = ts.build_efficiency_model(model,attach_to=['Conv2D'],method='after')

# Collect the states for each layer
print()
print('Running model predictions to capture states...')
start = time.time()
predictions = efficiency_model.predict(test_images,batch_size=200)
print('Finished in {:.3f}s!'.format(time.time() - start))

# Count the number of states in each layer
print()
print('Getting the number of states in each layer...')
for layer in efficiency_model.efficiency_layers:
    print('Layer {} number of states: {}'.format(layer.name,layer.state_count))

# Calculate each layers efficiency
print()
print('Evaluating efficiency of each layer...')
for layer in efficiency_model.efficiency_layers:
    start = time.time()
    print('Layer {} efficiency: {:.1f}% ({:.3f}s)'.format(layer.name,100*layer.efficiency(),time.time() - start))

# Calculate the aIQ
beta = 2 # fudge factor giving a slight bias toward accuracy over efficiency

print()
print('Network metrics...')
print('Beta: {}'.format(beta))

network_efficiency = ts.network_efficiency(efficiency_model)
print('Network efficiency: {:.1f}%'.format(100*network_efficiency))

accuracy = np.sum(np.argmax(predictions,axis=1)==test_labels)/test_labels.size
print('Network accuracy: {:.1f}%'.format(100*accuracy))

aIQ  = ts.aIQ(network_efficiency,accuracy,beta)
print('aIQ: {:.1f}%'.format(100*aIQ))

A Simple PyTorch Tutorial

Introduction

The core ideas behind this package were originally described in our paper, Assessing Intelligence in Artificial Neural Networks.

This package simplifies the capture of neural layers states, and provides some utility functions to assist in analyzing the state space of neural layers.

In this tutorial, we are going to build a classic convolutional neural network, LeNet-5. Then we are going to use TensorState to evaluate the network architecture, getting the efficiency of each layer and calculating the artificial intelligence quotient.

Build and Train LeNet-5

Get MNIST

To train this model, we need to get the MNIST data set. The data comes already rescaled to floats ranging between 0-1, so no rescaling is required.

from pathlib import Path
import requests, pickle, gzip
import torch
from torch.utils.data import TensorDataset, DataLoader

# Set up the directories
DATA_PATH = Path("data")
PATH = DATA_PATH/"mnist"
PATH.mkdir(parents=True, exist_ok=True)

# Download the data if it doesn't exist
URL = "http://deeplearning.net/data/mnist/"
FILENAME = "mnist.pkl.gz"
if not (PATH / FILENAME).exists():
        content = requests.get(URL + FILENAME).content
        (PATH / FILENAME).open("wb").write(content)

# Load the data
with gzip.open((PATH / FILENAME).as_posix(), "rb") as f:
    ((x_train, y_train), (x_valid, y_valid), _) = pickle.load(f, encoding="latin-1")

    x_train, y_train, x_valid, y_valid = map(
            torch.tensor, (x_train, y_train, x_valid, y_valid)
        )

    train_ds = TensorDataset(x_train,y_train)
    train_dl = DataLoader(train_ds,batch_size=200,shuffle=True)
    valid_ds = TensorDataset(x_valid,y_valid)
    valid_dl = DataLoader(valid_ds,batch_size=200)

Create a LeNet-5 Model

The general structure of our LeNet-5 model will roughly follow the structure of the original network described by LeCun et al. However, we are going to make a few modifications to make it more modern relative to the original architecture, such as addition of l2 weight regularization, exponential linear units, and batch normalization. So, we start off by setting the Tensorflow random seed (to make the results reproducible). Then we build the LeNet-5 class to define out network.

LeNet-5 has 2 convolutional layers and 2 fully connected layers. We will use max pooling layers after each convolutional layer, and we will add a batch normalization layer to all by the last fully connected layer.

import torch.nn as nn

# Set the random seed for reproducibility
torch.manual_seed(0)

# Build the layers
class LeNet5(nn.Module):

    def __init__(self):
        super().__init__()

        # Unit 1
        self.conv_1 = nn.Conv2d(1, 20, kernel_size=5, stride=1)
        torch.nn.init.kaiming_normal_(self.conv_1.weight)
        torch.nn.init.zeros_(self.conv_1.bias)
        self.elu_1 = nn.ELU()
        self.norm_1 = nn.BatchNorm2d(20,eps=0.00001,momentum=0.9)
        self.maxp_1 = nn.MaxPool2d(2,stride=2)

        # Unit 2
        self.conv_2 = nn.Conv2d(20, 50, kernel_size=5, stride=1)
        torch.nn.init.kaiming_normal_(self.conv_2.weight)
        torch.nn.init.zeros_(self.conv_2.bias)
        self.elu_2 = nn.ELU()
        self.norm_2 = nn.BatchNorm2d(50,eps=0.00001,momentum=0.9)
        self.maxp_2= nn.MaxPool2d(2,stride=2)

        # Fully Connected
        self.conv_3 = nn.Conv2d(50, 100, kernel_size=4, stride=1)
        torch.nn.init.kaiming_normal_(self.conv_3.weight)
        torch.nn.init.zeros_(self.conv_3.bias)
        self.elu_3 = nn.ELU()
        self.norm_3 = nn.BatchNorm2d(100,eps=0.00001,momentum=0.9)

        # Prediction
        self.flatten = nn.Flatten()
        self.pred = nn.Linear(100,10)
        torch.nn.init.kaiming_normal_(self.pred.weight)
        torch.nn.init.zeros_(self.pred.bias)

    def forward(self,data):
        x = data.view(-1, 1, 28, 28)
        x = self.conv_1(x)
        x = self.maxp_1(self.norm_1(self.elu_1(x)))
        x = self.conv_2(x)
        x = self.maxp_2(self.norm_2(self.elu_2(x)))
        x = self.conv_3(x)
        x = self.norm_3(self.elu_3(x))
        x = self.pred(self.flatten(x))
        return x.view(-1, x.size(1))

# Set the device to run the model on (gpu if available, cpu otherwise)
dev = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")

# Create the Keras model
model = LeNet5().to(dev)

Train the LeNet-5 Model

First, set up the parameters used for training. This will be set up to run with early stopping, similar to how Tensorflow has an early stopping callback. The patience parameter determines how many epochs to let past after the highest accuracy value is observed.

import torch.optim as optim

num_epochs = 200
loss_func = nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(),lr=0.001,momentum=0.9,
                    weight_decay=0.0005,nesterov=True)
last_valid_accuracy = 0
val_count = 0
patience = 5

Next, create the function to process training and evaluation for all samples.

def epoch_func(x,y,train=False):
    predictions = model(x)
    num = len(x)
    accuracy = (torch.argmax(predictions,axis=1)==y).float().sum()/num
    loss = loss_func(predictions,y)

    if train:
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()

    return loss,accuracy,num

Finally, run the training and evaluation loop.

import time

for epoch in range(num_epochs):
    start = time.time()
    model.train()
    losses, accuracies, nums = zip(
        *[epoch_func(xb.to(dev), yb.to(dev), True) for xb, yb in train_dl]
    )
    train_loss = np.sum(np.multiply(losses,nums))/np.sum(nums)
    train_accuracy = np.sum(np.multiply(accuracies,nums))/np.sum(nums)

    model.eval()
    with torch.no_grad():
        losses, accuracies, nums = zip(
            *[epoch_func(xb.to(dev), yb.to(dev), False) for xb, yb in valid_dl]
        )
    valid_loss = np.sum(np.multiply(losses,nums))/np.sum(nums)
    valid_accuracy = np.sum(np.multiply(accuracies,nums))/np.sum(nums)

    print('Epoch {}/{} ({:.2f}s): TrainLoss={:.4f}, TrainAccuracy={:.2f}%, ValidLoss={:.4f}, ValidAccuracy={:.2f}%'.format(
        str(epoch+1).zfill(3),num_epochs,time.time()-start,
        train_loss,100*train_accuracy,valid_loss,100*valid_accuracy
    ))

    # Early stopping criteria
    if valid_accuracy > last_valid_accuracy:
        val_count = 0
        last_valid_accuracy = valid_accuracy
    else:
        val_count += 1

    if val_count >= patience:
        break

Use TensorState to Evaluate LeNet-5

To calculate neural layer efficiency, we need to capture the various states each layer takes on as the network processes data. This functionality is built into the StateCaptureHook class, which is a hook that can be called before or after the designated layers to automate the capturing of information passing through the network. The StateCaptureHook acts like a probe that can be placed anywhere in the network: it records the information without modifying it, and passes it on to subsequent layers.

While StateCaptureHook’s can be placed manually, there is a convenience function that automatically adds hooks at the designated layers. For example, we can attach a StateCaptureHook to all convolutional layers.

import TensorState as ts
efficiency_model = ts.build_efficiency_model(model,attach_to=['Conv2d'],method='after')

In the above code, we feed the trained LeNet-5 model into the function, designate we want to attach StateCaptureHook’s to all 2D convolutional layers, and we want to capture the states after the layer. We could also capture the inputs going into and out of the layer by using method='both'. For more information on the build_efficiency_model method and additional settings, please see the TensorState reference.

Now that the efficiency_model has been created, the StateCaptureHooks will collect all states of the network as images are fed to the network. Thus, to generate all possible states the network contains for the test data, we only need to evaluate the test data. Then we can look at how many states were collected for each layer.

model.eval()
with torch.no_grad():
    losses, accuracies, nums = zip(
        *[epoch_func(xb.to(dev), yb.to(dev), False) for xb, yb in valid_dl]
    )

for layer in efficiency_model.efficiency_layers:
    print('Layer {} number of states: {}'.format(layer.name,layer.state_count))

Note how efficiency_model has the efficiency layers stored in the efficiency_layers attribute of the model. The output of the above code should look something like this:

Layer conv_1_post_states number of states: 5760000
Layer conv_2_post_states number of states: 640000
Layer conv_3_post_states number of states: 10000

Since there are 10,000 images in the training data set, it is expected that the fully connected layer (conv_3_post_states) has 10,000 states recorded, since exactly one state will be recorded per image. The other layers are convolutional, generating multiple states per image. The number of states can be checked by determining the number of locations the convolutional operator is applied per image then multiplying by 10,000. For example, in a 28x28 image with a 5x5 convolutional operation performed on it, the dimensions of the output would be 24x24. Thus, the number of states for all 10,000 images would be 24*24*10,000=5,760,000 states, which is the number of states observed by conv_1_post_states.

Note

The state_count is the raw number of states observed, and there are likely states that occur multiple times.

Now that the states of each layer have been captured, let’s analyze the state space using the efficiency metric originally described by Schaub et al. The efficiency metric calculates the entropy of the state space and divides by the number of neurons in the layer, giving an efficiency value in the range 0.00-1.00.

for layer in efficiency_model.efficiency_layers:
    layer_efficiency = layer.efficiency()
    print('Layer {} efficiency: {:.1f}%'.format(layer.name,100*layer_efficiency))

Next, we can calculate the artificial intelligence quotient (aIQ). Since things like neural network efficiency and aIQ are metrics calculated over the entire network, the StateCaptureHook’s do not have built-in methods to calculate these values.

beta = 2 # fudge factor giving a slight bias toward accuracy over efficiency

print()
print('Network metrics...')
print('Beta: {}'.format(beta))

network_efficiency = ts.network_efficiency(efficiency_model)
print('Network efficiency: {:.1f}%'.format(100*network_efficiency))

accuracy = np.sum(np.multiply(accuracies,nums))/np.sum(nums)
print('Network accuracy: {:.1f}%'.format(100*accuracy))

aIQ  = ts.aIQ(network_efficiency,accuracy.cpu().item(),beta)
print('aIQ: {:.1f}%'.format(100*aIQ))

Complete Example

import requests, pickle, gzip, time

from pathlib import Path
import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import TensorDataset, DataLoader
import numpy as np

import TensorState as ts

# Set the device to run the model on (gpu if available, cpu otherwise)
dev = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")

""" Load MNIST and transform it """
# Set up the directories
DATA_PATH = Path("data")
PATH = DATA_PATH/"mnist"
PATH.mkdir(parents=True, exist_ok=True)

# Download the data if it doesn't exist
URL = "http://deeplearning.net/data/mnist/"
FILENAME = "mnist.pkl.gz"
if not (PATH / FILENAME).exists():
        content = requests.get(URL + FILENAME).content
        (PATH / FILENAME).open("wb").write(content)

# Load the data
with gzip.open((PATH / FILENAME).as_posix(), "rb") as f:
    ((x_train, y_train), (x_valid, y_valid), _) = pickle.load(f, encoding="latin-1")

    x_train, y_train, x_valid, y_valid = map(
            torch.tensor, (x_train, y_train, x_valid, y_valid)
        )

    train_ds = TensorDataset(x_train,y_train)
    train_dl = DataLoader(train_ds,batch_size=200,shuffle=True)
    valid_ds = TensorDataset(x_valid,y_valid)
    valid_dl = DataLoader(valid_ds,batch_size=200)

""" Create a LeNet-5 model """
# Set the random seed for reproducibility
torch.manual_seed(0)

# Build the layers
class LeNet5(nn.Module):

    def __init__(self):
        super().__init__()

        # Unit 1
        self.conv_1 = nn.Conv2d(1, 20, kernel_size=5, stride=1)
        torch.nn.init.kaiming_normal_(self.conv_1.weight)
        torch.nn.init.zeros_(self.conv_1.bias)
        self.elu_1 = nn.ELU()
        self.norm_1 = nn.BatchNorm2d(20,eps=0.00001,momentum=0.9)
        self.maxp_1 = nn.MaxPool2d(2,stride=2)

        # Unit 2
        self.conv_2 = nn.Conv2d(20, 50, kernel_size=5, stride=1)
        torch.nn.init.kaiming_normal_(self.conv_2.weight)
        torch.nn.init.zeros_(self.conv_2.bias)
        self.elu_2 = nn.ELU()
        self.norm_2 = nn.BatchNorm2d(50,eps=0.00001,momentum=0.9)
        self.maxp_2= nn.MaxPool2d(2,stride=2)

        # Fully Connected
        self.conv_3 = nn.Conv2d(50, 100, kernel_size=4, stride=1)
        torch.nn.init.kaiming_normal_(self.conv_3.weight)
        torch.nn.init.zeros_(self.conv_3.bias)
        self.elu_3 = nn.ELU()
        self.norm_3 = nn.BatchNorm2d(100,eps=0.00001,momentum=0.9)

        # Prediction
        self.flatten = nn.Flatten()
        self.pred = nn.Linear(100,10)
        torch.nn.init.kaiming_normal_(self.pred.weight)
        torch.nn.init.zeros_(self.pred.bias)

    def forward(self,data):
        x = data.view(-1, 1, 28, 28)
        x = self.conv_1(x)
        x = self.maxp_1(self.norm_1(self.elu_1(x)))
        x = self.conv_2(x)
        x = self.maxp_2(self.norm_2(self.elu_2(x)))
        x = self.conv_3(x)
        x = self.norm_3(self.elu_3(x))
        x = self.pred(self.flatten(x))
        return x.view(-1, x.size(1))

# Create the Keras model
model = LeNet5().to(dev)

""" Train the model """
num_epochs = 200
loss_func = nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(),lr=0.001,momentum=0.9,
                    weight_decay=0.0005,nesterov=True)
last_valid_accuracy = 0
val_count = 0
patience = 5

def epoch_func(x,y,train=False):
    predictions = model(x)
    num = len(x)
    accuracy = (torch.argmax(predictions,axis=1)==y).float().sum()/num
    loss = loss_func(predictions,y)

    if train:
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()

    return loss,accuracy,num

for epoch in range(num_epochs):
    start = time.time()
    model.train()
    losses, accuracies, nums = zip(
        *[epoch_func(xb.to(dev), yb.to(dev), True) for xb, yb in train_dl]
    )
    train_loss = np.sum(np.multiply(losses,nums))/np.sum(nums)
    train_accuracy = np.sum(np.multiply(accuracies,nums))/np.sum(nums)

    model.eval()
    with torch.no_grad():
        losses, accuracies, nums = zip(
            *[epoch_func(xb.to(dev), yb.to(dev), False) for xb, yb in valid_dl]
        )
    valid_loss = np.sum(np.multiply(losses,nums))/np.sum(nums)
    valid_accuracy = np.sum(np.multiply(accuracies,nums))/np.sum(nums)

    print('Epoch {}/{} ({:.2f}s): TrainLoss={:.4f}, TrainAccuracy={:.2f}%, ValidLoss={:.4f}, ValidAccuracy={:.2f}%'.format(
        str(epoch+1).zfill(3),num_epochs,time.time()-start,
        train_loss,100*train_accuracy,valid_loss,100*valid_accuracy
    ))

    # Early stopping criteria
    if valid_accuracy > last_valid_accuracy:
        val_count = 0
        last_valid_accuracy = valid_accuracy
    else:
        val_count += 1

    if val_count >= patience:
        break

""" Evaluate model efficiency """
# Attach StateCapture layers to the model
efficiency_model = ts.build_efficiency_model(model,attach_to=['Conv2d'],method='after')

# Collect the states for each layer
print()
print('Running model predictions to capture states...')
start = time.time()
model.eval()
with torch.no_grad():
    losses, accuracies, nums = zip(
        *[epoch_func(xb.to(dev), yb.to(dev), False) for xb, yb in valid_dl]
    )
print('Finished in {:.3f}s!'.format(time.time() - start))

# Count the number of states in each layer
print()
print('Getting the number of states in each layer...')
for layer in efficiency_model.efficiency_layers:
    print('Layer {} number of states: {}'.format(layer.name,layer.state_count))

# Calculate each layers efficiency
print()
print('Evaluating efficiency of each layer...')
for layer in efficiency_model.efficiency_layers:
    start = time.time()
    print('Layer {} efficiency: {:.1f}% ({:.3f}s)'.format(layer.name,100*layer.efficiency(),time.time() - start))

# Calculate the aIQ
beta = 2 # fudge factor giving a slight bias toward accuracy over efficiency

print()
print('Network metrics...')
print('Beta: {}'.format(beta))

network_efficiency = ts.network_efficiency(efficiency_model)
print('Network efficiency: {:.1f}%'.format(100*network_efficiency))

accuracy = np.sum(np.multiply(accuracies,nums))/np.sum(nums)
print('Network accuracy: {:.1f}%'.format(100*accuracy))

aIQ  = ts.aIQ(network_efficiency,accuracy.cpu().item(),beta)
print('aIQ: {:.1f}%'.format(100*aIQ))

Reference

What is state space?

An Abstract Explanation

Traditionally, the fundamental unit of computation in the human nervous system has been the neuron. Some of the early thought in how the brain processes information suggested that particular neurons encode particular information, which may be called features in the data science community. Thus, if we have ~86 billion neurons, then we can roughly learn 86 billion features. However, as human intelligence progressed it was quickly discovered that even simple tasks often recruit multiple, seemingly unrelated areas of the brain. This led to the idea that the meaning of an individual neuron may not matter as much as how neurons fire as a collective, suggesting the number of neurons are an exponent rather than a coefficient to a human’s capacity to learn new tasks.

Recent research into artificial neural networks and how they function approach the subject in the antiquated approach to understanding human neurons, where each neuron encodes a particular feature or function. The idea of state space diverges and challenges this conception of neurons, and attempts to show how neurons in artificial neural networks operate in parallel rather than discrete units in the same way that the human brain operates. In this conception of a neuron layer, the features are encoded in the state of firing neurons rather than individual neurons. Thus, in the current conception of neural networks, a layer with 16 neurons would encode 16 features, but in the state space up to 2^16 features can be encoded (assuming neurons are either firing or not firing).