py18.py

import numpy as np
import nnfs
from nnfs.datasets import spiral_data

nnfs.init()

# Dense layer
class Layer_Dense:

    # Layer initialization
    def __init__(self, n_inputs, n_neurons,
                 weight_regularizer_l1=0, weight_regularizer_l2=0,
                 bias_regularizer_l1=0, bias_regularizer_l2=0):
        # Initialize weights and biases
        self.weights = 0.01 * np.random.randn(n_inputs, n_neurons)
        self.biases = np.zeros((1, n_neurons))
        # Set regularization strength
        self.weight_regularizer_l1 = weight_regularizer_l1
        self.weight_regularizer_l2 = weight_regularizer_l2
        self.bias_regularizer_l1 = bias_regularizer_l1
        self.bias_regularizer_l2 = bias_regularizer_l2

    # Forward pass
    def forward(self, inputs, training):
        # Remember input values
        self.inputs = inputs
        # Calculate output values from inputs, weights and biases
        self.output = np.dot(inputs, self.weights) + self.biases

    # Backward pass
    def backward(self, dvalues):
        # Gradients on parameters
        self.dweights = np.dot(self.inputs.T, dvalues)
        self.dbiases = np.sum(dvalues, axis=0, keepdims=True)

        # Gradients on regularization
        # L1 on weights
        if self.weight_regularizer_l1 > 0:
            dL1 = np.ones_like(self.weights)
            dL1[self.weights < 0] = -1
            self.dweights += self.weight_regularizer_l1 * dL1
        # L2 on weights
        if self.weight_regularizer_l2 > 0:
            self.dweights += 2 * self.weight_regularizer_l2 * self.weights
        
        # L1 on biases
        if self.bias_regularizer_l1 > 0:
            dL1 = np.ones_like(self.biases)
            dL1[self.biases < 0] = -1
            self.dbiases += self.bias_regularizer_l1 * dL1
        # L2 on biases
        if self.bias_regularizer_l2 > 0:
            self.dbiases += 2 * self.bias_regularizer_l2 * self.biases

        # Gradient on values
        self.dinputs = np.dot(dvalues, self.weights.T)

# Dropout
class Layer_Dropout:

    # Init
    def __init__(self, rate):
        # Store rate, we invert it as for example for dropout
        # of 0.1 we need success rate of 0.9
        self.rate = 1 - rate
    
    # Forward pass
    def forward(self, inputs, training):
        # Save input values
        self.inputs = inputs
        
        # If not in training mode, return values
        if not training:
            self.output = inputs.copy()
            return
        
        # Generate and save scaled mask
        self.binary_mask = np.random.binomial(1, self.rate, size=inputs.shape) / self.rate
        # Apply mas to output values
        self.output = inputs * self.binary_mask
    
    # Backward pass
    def backward(self, dvalues):
        # Gradient on values
        self.dinputs = dvalues * self.binary_mask

# Input "layer"
class Layer_Input:

    # Forward pass
    def forward(self, inputs, training):
        self.output = inputs

# ReLU activation
class Activation_ReLU:

    # Forward pass
    def forward(self, inputs, training):

        # Remember input values
        self.inputs = inputs
        # Calculate output values from inputs
        self.output = np.maximum(0, inputs)

    # Backward pass
    def backward(self, dvalues):
        # Since we need to modify original variable,
        # let's make a copy of values first
        self.dinputs = dvalues.copy()

        # Zero gradient where input values were negative
        self.dinputs[self.inputs <= 0] = 0


# Common loss class
class Loss:

    # Set/remember trainable layers
    def remember_trainable_layers(self, trainable_layers):
        self.trainable_layers = trainable_layers
    
    # Calculates the data and regularization losses
    # given model output and ground truth values
    def calculate(self, output, y, *, include_regularization=False):

        # Calculate sample losses
        sample_losses = self.forward(output, y)

        # Calculate mean loss
        data_loss = np.mean(sample_losses)
        
        # If just data loss, return it
        if not include_regularization:
            return data_loss

        # Return the data and regularization losses
        return data_loss, self.regularization_loss()
    
    # Regularization loss calculation
    def regularization_loss(self):

        # 0 by default
        regularization_loss = 0

        # Calculate regularization loss
        # Iterate all trainable layers
        for layer in self.trainable_layers:
    
            # L1 regularization - weights
            # Calculate only when factor greater then 0
            if layer.weight_regularizer_l1 > 0:
                regularization_loss += layer.weight_regularizer_l1 * np.sum(np.abs(layer.weights))
            
            # L2 regularization - weights
            if layer.weight_regularizer_l2 > 0:
                regularization_loss += layer.weight_regularizer_l2 * np.sum(layer.weights * layer.weights)
            
            # L1 regularization - biases
            # Calculate only when factor greater than 0
            if layer.bias_regularizer_l1 > 0:
                regularization_loss += layer.bias_regularizer_l1 * np.sum(np.abs(layer.biases))
            
            # L2 regularization - biases
            if layer.bias_regularizer_l2 > 0:
                regularization_loss += layer.bias_regularizer_l2 * np.sum(layer.biases * layer.biases)
            
        return regularization_loss

# Softmax activation
class Activation_Softmax:

    # Calculate predictions for outputs
    def predictions(self, outputs):
        return np.argmax(outputs, axis=1)
    
    # Forward pass
    def forward(self, inputs, training):\
        # Remember input values
        self.inputs = inputs
        # Get unnormalized probabilities
        exp_values = np.exp(inputs - np.max(inputs, axis=1, keepdims=True))
        # Normalizae them for each sample
        probabilities = exp_values / np.sum(exp_values, axis=1, keepdims=True)

        self.output = probabilities

    # Backward pass
    def backward(self, dvalues):
        # Create uninitialized array
        self.dinputs = np.empty_like(dvalues)
        # Enumerate outputs and gradients
        for index, (single_output, single_dvalues) in enumerate(zip(self.output, dvalues)):
            # Flatten output array
            single_output = single_output.reshape(-1, 1)
            # Calculate Jacobian matrix of the output
            jacobian_matrix = np.diagflat(single_output) - np.dot(single_output, single_output.T)
            # Calculate sample-wise gradient
            # and add it to the array of sample gradients
            self.dinputs[index] = np.dot(jacobian_matrix, single_dvalues)

# Cross-entropy loss
class Loss_CategoricalCrossentropy(Loss):
    # Forward pass
    def forward(self, y_pred, y_true):
        # Number of samples in a batch
        samples = len(y_pred)
        # Clip data to prevent division by 0
        # Clip both sides to not drag mean towards any value
        y_pred_clipped = np.clip(y_pred, 1e-7, 1 - 1e-7)

        # Probabilities for target values
        # only if categorical labels
        if len(y_true.shape) == 1:
            correct_confidences = y_pred_clipped[range(samples), y_true]
        # mask values - only for one-hot encoded labels
        elif len(y_true.shape) == 2:
            correct_confidences = np.sum(y_pred_clipped * y_true, axis=1)
        # Losses
        negative_log_likelihoods = -np.log(correct_confidences)

        return negative_log_likelihoods
    
    # Backward pass
    def backward(self, dvalues, y_true):
        # Number of samples
        samples = len(dvalues)
        # Number of labels in every sample
        # We'll use the first sample to count them
        labels = len(dvalues[0])
        # If labels are sparse, turn them into one-hot vector
        if len(y_true.shape) == 1:
            y_true = np.eye(labels)[y_true]
        # Calculate gradient
        self.dinputs = -y_true / dvalues
        # Normalize gradient
        self.dinputs = self.dinputs / samples

# Softmax classifier - combined Softmax activation
# and cross-entropy loss for faster backward step
class Activation_Softmax_Loss_CategoricalCrossentropy():

    # Backward pass
    def backward(self, y_pred, y_true):
        # Number of samples
        samples = len(y_pred)
        # If labels are one-hot encoded,
        # turn them into discrete values
        if len(y_true.shape) == 2:
            y_true = np.argmax(y_true, axis=1)
        # Copy so we can safely modify
        self.dinputs = y_pred.copy()
        # Calculate gradient
        self.dinputs[range(samples), y_true] -= 1
        # Normalize gradient
        self.dinputs = self.dinputs / samples

# Sigmoid activation
class Activation_Sigmoid:

    # Calculate predictions for outputs
    def predictions(self, outputs):
        return (outputs > 0.5) * 1
    
    # Forward pass
    def forward(self, inputs, training):
        # Save input and calculate/save output
        # of the sigmoid funtion
        self.inputs = inputs
        self.output = 1 / (1 + np.exp(-inputs))
    
    def backward(self, dvalues):
        # derivative - calculate from output of the sigmoid function
        self.dinputs = dvalues * (1 - self.output) * self.output

# Binary cross-entropy loss
class Loss_BinaryCrossentropy(Loss):

    # Forward pass
    def forward(self, y_pred, y_true):

        # Clip data to prevent division by 0
        # Clip both sides to not drag mean towards any value
        y_pred_clipped = np.clip(y_pred, 1e-7, 1 - 1e-7)

        # Calculate sample-wise loss
        sample_losses = -(y_true * np.log(y_pred_clipped) + (1 - y_true) * np.log(1 - y_pred_clipped))
        sample_losses = np.mean(sample_losses, axis=-1)
        # Return losses
        return sample_losses
    
    # Backward pass
    def backward(self, y_pred, y_true):

        # Number of samples
        samples = len(y_pred)
        # Number of outputs in every sample
        # We'll use the first sample to count them
        outputs = len(y_pred[0])

        # Clip data to prevent division by 0
        # Clip both sides to not drag mean towards any value
        clipped_y_pred = np.clip(y_pred, 1e-7, 1 - 1e-7)

        # Calculate gradient
        self.dinputs = -(y_true / clipped_y_pred - (1 - y_true) / (1 - clipped_y_pred)) / outputs

        # Normalize gradient
        self.dinputs = self.dinputs / samples

# SGD optimizer (Stochastic Gradient Descent)
class Optimizer_SGD:
    # Initialize optimizer - set settings,
    # learning rate of 1. is default for this optimizer
    def __init__(self, learning_rate=1, decay=0., momentum=0.):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.momentum = momentum
    
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay: # if decay rate is not 0
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):

        # If we use momentum
        if self.momentum:

            # If layer does not contain momentum arrays,
            # create them, filled with zeroes
            if not hasattr(layer, 'weight_momentums'):
                layer.weight_momentums = np.zeros_like(layer.weights)
                # If there is no momentum array for weights
                # the array doesn't exist for biases either
                layer.bias_momentums = np.zeros_like(layer.biases)
            
            # Build weight updates with momentum - take previous
            # updates multiplied by retain factor and update with
            # current gradients
            weight_updates = self.momentum * layer.weight_momentums - self.current_learning_rate * layer.dweights
            layer.weight_momentums = weight_updates

            # Build bias updates
            bias_updates = self.momentum * layer.bias_momentums - self.current_learning_rate * layer.dbiases
            layer.bias_momentums = bias_updates
        
        # Vanilla SGD updates (as before momentum update)
        else:
            weight_updates = -self.current_learning_rate * layer.dweights
            bias_updates = -self.current_learning_rate * layer.dbiases
        
        # Update weights and biases using either
        # vanilla or momentum updates
        layer.weights += weight_updates
        layer.biases += bias_updates

    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1

# AdaGrad optimizer (Adaptive Gradient)
class Optimizer_Adagrad:
    # Initialize optimizer - set settings,
    # learning rate of 1. is default for this optimizer
    def __init__(self, learning_rate=1., decay=0., epsilon=1e-7):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.epsilon = epsilon
    
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay: # if decay rate is not 0
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):

        # If layer does not contain cache arrays,
        # create them, filled with zeroes
        if not hasattr(layer, 'weight_cache'):
            layer.weight_cache = np.zeros_like(layer.weights)
            layer.bias_cache = np.zeros_like(layer.biases)
        
        # Update cache with squared current gradients
        layer.weight_cache += layer.dweights**2
        layer.bias_cache += layer.dbiases**2

        # Vanilla SGD parameter update + normalization
        # with square rooted cache
        layer.weights += -self.current_learning_rate * layer.dweights / (np.sqrt(layer.weight_cache) + self.epsilon)
        layer.biases += -self.current_learning_rate * layer.dbiases / (np.sqrt(layer.bias_cache) + self.epsilon)

    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1


# RMSprop optimizer
class Optimizer_RMSprop:

    # Initialize optimizer - set settings,
    def __init__(self, learning_rate=0.001, decay=0., epsilon=1e-7, rho=0.9):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.epsilon = epsilon
        self.rho = rho
    
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay: # if decay rate is not 0
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):

        # If layer does not contain cache arrays,
        # create them, filled with zeroes
        if not hasattr(layer, 'weight_cache'):
            layer.weight_cache = np.zeros_like(layer.weights)
            layer.bias_cache = np.zeros_like(layer.biases)
        
        # Update cache with squared current gradients
        layer.weight_cache = self.rho * layer.weight_cache + (1 - self.rho) * layer.dweights**2
        layer.bias_cache = self.rho * layer.bias_cache + (1 - self.rho) * layer.dbiases**2

        # Vanilla SGD parameter update + normalization
        # with square rooted cache
        layer.weights += -self.current_learning_rate * layer.dweights / (np.sqrt(layer.weight_cache) + self.epsilon)
        layer.biases += -self.current_learning_rate * layer.dbiases / (np.sqrt(layer.bias_cache) + self.epsilon)

    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1

# RMSprop optimizer
class Optimizer_Adam:

    # Initialize optimizer - set settings,
    def __init__(self, learning_rate=0.001, decay=0., epsilon=1e-7, beta_1=0.9, beta_2=0.999):
        self.learning_rate = learning_rate
        self.current_learning_rate = learning_rate
        self.decay = decay
        self.iterations = 0
        self.epsilon = epsilon
        self.beta_1 = beta_1
        self.beta_2 = beta_2
    
    # Call once before any parameter updates
    def pre_update_params(self):
        if self.decay: # if decay rate is not 0
            self.current_learning_rate = self.learning_rate * (1. / (1. + self.decay * self.iterations))
    
    # Update parameters
    def update_params(self, layer):

        # If layer does not contain cache arrays,
        # create them, filled with zeroes
        if not hasattr(layer, 'weight_cache'):
            layer.weight_momentums = np.zeros_like(layer.weights)
            layer.weight_cache = np.zeros_like(layer.weights)
            layer.bias_momentums = np.zeros_like(layer.biases)
            layer.bias_cache = np.zeros_like(layer.biases)
        
        # Update momentum with current gradients
        layer.weight_momentums = self.beta_1 * layer.weight_momentums + (1 - self.beta_1) * layer.dweights
        layer.bias_momentums = self.beta_1 * layer.bias_momentums + (1 - self.beta_1) * layer.dbiases
        # Get corrected momentum
        # self.iteration is 0 at first pass
        # and we need to start with 1 here
        weight_momentums_corrected = layer.weight_momentums / (1 - self.beta_1 ** (self.iterations + 1))
        bias_momentums_corrected = layer.bias_momentums / (1 - self.beta_1 ** (self.iterations + 1))

        # Update cache with squared current gradients
        layer.weight_cache = self.beta_2 * layer.weight_cache + (1 - self.beta_2) * layer.dweights**2
        layer.bias_cache = self.beta_2 * layer.bias_cache + (1 - self.beta_2) * layer.dbiases**2
        # Get corrected cache
        weight_cache_corrected = layer.weight_cache / (1 - self.beta_2 ** (self.iterations + 1))
        bias_cache_corrected = layer.bias_cache / (1 - self.beta_2 ** (self.iterations + 1))

        # Vanilla SGD parameter update + normalization
        # with square rooted cache
        layer.weights += -self.current_learning_rate * weight_momentums_corrected / (np.sqrt(weight_cache_corrected) + self.epsilon)
        layer.biases += -self.current_learning_rate * bias_momentums_corrected / (np.sqrt(bias_cache_corrected) + self.epsilon)

    # Call once after any parameter updates
    def post_update_params(self):
        self.iterations += 1

# Linear activation
class Activation_Linear:

    # Calculate predictions for outputs
    def predictions(self, outputs):
        return outputs
    
    # Forward pass
    def forward(self, inputs, training):
        # Just remember values
        self.inputs = inputs
        self.output = inputs

    # Backward pass
    def backward(self, dvalues):
        # derivative is 1 -> 1 * dvalues = dvalues -> See the chain rule
        self.dinputs = dvalues.copy()

# Mean Squared Error Loss
class Loss_MeanSquaredError(Loss): # L2 loss

    # Forward pass
    def forward(self, y_pred, y_true):

        # Calculate loss
        sample_losses = np.mean((y_true - y_pred)**2, axis=-1)

        # Return losses
        return sample_losses
    
    # Backward pass
    def backward(self, y_pred, y_true):

        # Number of samples
        samples = len(y_pred)
        # Number of outputs in every sample
        # We'll use the first sample to count them
        outputs = len(y_pred[0])

        # Gradient on values
        self.dinputs = -2 * (y_true - y_pred) / outputs
        # Normalize gradients
        self.dinputs = self.dinputs / samples

# Mean Absolute Error Loss
class Loss_MeanAbsoluteError(Loss): # L1 Loss

    # Forward pass
    def forward(self, y_pred, y_true):

        # Calculate loss
        sample_losses = np.mean(np.abs(y_true - y_pred), axis=-1)

        # Return losses
        return sample_losses
    
    # Backward pass
    def backward(self, y_pred, y_true):

        # Number of samples
        samples = len(y_pred)
        # Number of outputs in every sample
        # We'll use the first sample to count them
        outputs = len(y_pred[0])

        # Calculate gradient
        self.dinputs = -np.sign(y_true - y_pred) / outputs
        # Normalize gradient
        self.dinputs = self.dinputs / samples

# Model class
class Model:

    def __init__(self):
        # Create a list of network objects
        self.layers = []
        # Softmax classifier's output object
        self.softmax_classifier_output  = None
    
    # Add objects to the model
    def add(self, layer):
        self.layers.append(layer)

    # Set loss and optimizer
    def set(self, *, loss, optimizer, accuracy):
        self.loss = loss
        self.optimizer = optimizer
        self.accuracy = accuracy
    
    # Finalize the model
    def finalize(self):

        # Create and set the input layer
        self.input_layer = Layer_Input()

        # Count all the objects
        layer_count = len(self.layers)
        
        # Initialize a list containing trainable layers:
        self.trainable_layers = []

        # Iterate the objects
        for i in range(layer_count):

            # If it's the first layer,
            # the previous layer object is the input layer
            if i == 0:
                self.layers[i].prev = self.input_layer
                self.layers[i].next = self.layers[i+1]
            
            # All layers except for the first and the last
            elif i < layer_count - 1:
                self.layers[i].prev = self.layers[i-1]
                self.layers[i].next = self.layers[i+1]
            
            # The last layer - the next object is the loss
            # Also, let's save aside the reference to the last object
            # whose output is the model's output
            else:
                self.layers[i].prev = self.layers[i-1]
                self.layers[i].next = self.loss
                self.output_layer_activation = self.layers[i]
                
            # If layer contains an attribute called "weights",
            # it's a trainable layer.
            # Add it to the list of trainable layers.
            # We don't need to check for biases,
            # checking for weights is enough
            if hasattr(self.layers[i], 'weights'):
                self.trainable_layers.append(self.layers[i])
            
        # Update loss object with trainable layers
        self.loss.remember_trainable_layers(self.trainable_layers)
        
        # If output activation is Softmax and
        # loss function is Categorical Cross-Entropy
        # create an object of combined activation
        # and loss function containing
        # faster gradient calculation
        if isinstance(self.layers[-1], Activation_Softmax) and \
            isinstance(self.loss, Loss_CategoricalCrossentropy):
            # Create an object of combined activation and loss function
            self.softmax_classifier_output = Activation_Softmax_Loss_CategoricalCrossentropy()

    # Train the model
    def train(self, X, y, *, epochs=1, print_every=1, validation_data=None):

        # Initialize accuracy object
        self.accuracy.init(y)
        
        # Main training loop
        for epoch in range(1, epochs+1):

            # Perform the forward pass
            output = self.forward(X, training=True)
            
            # Calculate loss
            data_loss, regularization_loss = self.loss.calculate(output, y, include_regularization=True)
            loss = data_loss + regularization_loss
            
            # Get predictions and calculate accuracy
            predictions = self.output_layer_activation.predictions(output)
            accuracy = self.accuracy.calculate(predictions, y)
            
            # Perform backword pass
            self.backward(output, y)
            
            # Optimize (update parameters)
            self.optimizer.pre_update_params()
            for layer in self.trainable_layers:
                self.optimizer.update_params(layer)
            self.optimizer.post_update_params()
            
            # Print a summary
            if not epoch % print_every:
                print(f'epoch: {epoch}, ' +
                      f'acc: {accuracy:.3f}, ' +
                      f'loss: {loss:.3f} (' +
                      f'data_loss: {data_loss:.3f}, ' +
                      f'reg_loss: {regularization_loss:.3f}), ' +
                      f'lr: {self.optimizer.current_learning_rate}')
                
        # If there is validation data
        if validation_data is not None:
            
            # For better readability
            X_val, y_val = validation_data
            
            # Perform the forward pass
            output = self.forward(X_val, training=False)
            
            # Calculate the loss
            loss = self.loss.calculate(output, y_val)
            
            # Get predictions and calculate accuracy
            predictions = self.output_layer_activation.predictions(output)
            accuracy = self.accuracy.calculate(predictions, y_val)
            
            # Print a summary
            print(f'validation, ' +
                  f'acc: {accuracy:.3f}, ' +
                  f'loss: {loss:.3f}')
            
    # Performs forward pass
    def forward(self, X, training):

        # Call forward method on the input layer
        # This will set the output property that
        # the first layer in "prev" object is expecting
        self.input_layer.forward(X, training)

        # Call forward method of every object in a chain
        # Pass output of the previous object as a parameter
        for layer in self.layers:
            layer.forward(layer.prev.output, training)
        
        # "layer" is now the last object from the list,
        # return its output
        return layer.output
    
    # Performs backward pass
    def backward(self, output, y):
        
        # If softmax classifier
        if self.softmax_classifier_output is not None:
            # First call backward method
            # on the combined activation/loss
            # This will set dinputs property
            self.softmax_classifier_output.backward(output, y)
            
            # Since we will not call backward method of the last layer
            # which is Softmax activation, as we used combined
            # activation/loss object, let's set dinputs in this object
            self.layers[-1].dinputs = self.softmax_classifier_output.dinputs
            
            # Call backward method going through
            # all the objects but last
            # in reversed order passing dinputs as a parameter
            for layer in reversed(self.layers[:-1]):
                layer.backward(layer.next.dinputs)
            
            return
        
        # First call backward method on the loss
        # This will set dinputs property that the last
        # layer will try to access shortly
        self.loss.backward(output, y)
        
        # Call backward method going through all the objects
        # in reversed order pasing dinputs as a parameter
        for layer in reversed(self.layers):
            layer.backward(layer.next.dinputs)

# Common accuracy class
class Accuracy:
    
    # Calculates an accuracy
    # given predictions and ground truth values
    def calculate(self, predictions, y):
        
        # Get comparison results
        comparisons = self.compare(predictions, y)
        
        # Calculate an accuracy
        accuracy = np.mean(comparisons)
        
        # Return accuracy
        return accuracy

# Accuracy calculation for regression model
class Accuracy_Regression(Accuracy):
    
    def __init__(self):
        # Create precision property
        self.precision = None
    
    # Calculates precision value
    # based on passed in ground truth
    def init(self, y, reinit=False):
        if self.precision is None or reinit:
            self.precision = np.std(y) / 250
    
    # Compares predictions to the ground truth values
    def compare(self, predictions, y):
        return np.absolute(predictions - y) < self.precision

# Accuracy calculation for classification model
class Accuracy_Categorical(Accuracy):
    
    def __init__(self, *, binary=False):
        # Binary mode?
        self.binary = binary
    
    # No initialization is needed
    def init(self, y):
        pass
    
    # Compares predictions to the ground truth values
    def compare(self, predictions, y):
        if not self.binary and len(y.shape) == 2:
            y = np.argmax(y, axis=1)
        return predictions == y

# Create, train and test dataset
X, y = spiral_data(samples=1000, classes=3)
X_test, y_test = spiral_data(samples=100, classes=3)

# Instantiate the model
model = Model()

# Add layers
model.add(Layer_Dense(2, 512, weight_regularizer_l2=5e-4, bias_regularizer_l2=5e-4))
model.add(Activation_ReLU())
model.add(Layer_Dropout(0.1))
model.add(Layer_Dense(512,3))
model.add(Activation_Softmax())

# Set loss, optimizer and accuracy objects
model.set(
    loss=Loss_CategoricalCrossentropy(),
    optimizer=Optimizer_Adam(learning_rate=0.05, decay=5e-5),
    accuracy=Accuracy_Categorical()
)

# Finalize the model
model.finalize()

# Train the model
model.train(X, y, validation_data=(X_test, y_test), epochs=10000, print_every=100)