Neural Network with Nonlinear Exponential Activation Function

[majorado]

Here's the code for a neural network using the nonlinear exponential function (y = e^(mx + b)) as an activation function in Python with TensorFlow and Keras:

import tensorflow as tf
from tensorflow.keras import layers
# Define the non-linear exponential activation function (custom layer)
class ExponentialActivation(layers.Layer):
  def __init__(self, **kwargs):
    super(ExponentialActivation, self).__init__(**kwargs)

  def call(self, inputs):
    return tf.exp(tf.matmul(inputs, self.kernel) + self.bias)

  def get_config(self):
    config = super(ExponentialActivation, self).get_config()
    config.update({'units': int(self.kernel.shape[1])})
    return config

# Define the neural network
def create_model(input_dim, hidden_dim, output_dim):
  # Input layer
  inputs = layers.Input(shape=(input_dim,))

  # Hidden layer with exponential activation
  hidden = layers.Dense(hidden_dim, activation=ExponentialActivation())(inputs)

  # Output layer
  outputs = layers.Dense(output_dim)(hidden)

  # Create the model
  model = tf.keras.Model(inputs=inputs, outputs=outputs)
  return model

# Example usage
model = create_model(10, 5, 1)  # 10 input features, 5 hidden neurons, 1 output neuron

# Compile the model (define loss function and optimizer)
model.compile(loss='mse', optimizer='adam')

# Train the model (replace with your training data)
model.fit(x_train, y_train, epochs=10)

# Make predictions (replace with your test data)
predictions = model.predict(x_test)

Explanation:

• Custom Activation Layer: We define a custom layer ExponentialActivation that inherits from layers.Layer. This layer performs the non-linear exponential function using matrix multiplication (tf.matmul) for weights (self.kernel) and bias (self.bias), followed by the exponential function (tf.exp).
• Model Creation: The create_model function defines the network architecture. It takes input dimension, hidden layer dimension, and output dimension as arguments.
• Hidden Layer: The hidden layer uses the custom ExponentialActivation function.
• Output Layer: The output layer has a single neuron.
• Model Compilation: The model is compiled with a mean squared error (mse) loss function and the Adam optimizer.
• Training and Prediction: Train the model with your training data (x_train, y_train) and then use it to make predictions on your test data (x_test). Important Notes:
• This is a simple example. Real-world applications might require more complex architectures and hyperparameter tuning.
• The exponential function can be numerically unstable for large values. Consider alternative non-linear activations like leaky ReLU for better training behavior. Python data model: special methods