**Adversarial Training for Robust Autonomous Systems**

Adversarial Training for Robust Autonomous Systems

# Example using PyTorch
import torch
import torch.nn as nn
import torch.optim as optim

# Define a model
model = nn.Sequential(
    nn.Linear(784, 128),  # input layer (28x28 images) -> hidden layer
    nn.ReLU(),
    nn.Linear(128, 10)   # hidden layer -> output layer (10 classes)
)

# Define a robust loss function with adversarial training
def robust_loss(model, inputs, labels, epsilon=0.1):
    # Generate adversarial examples using projected gradient descent
    inputs_adv = inputs + epsilon * torch.sign(torch gradients(model(inputs), labels).sign())
    return model(inputs_adv).softmax() - labels

In this code snippet, we implement a simple adversarial training mechanism for a neural network model. The robust_loss function uses projected gradient descent to generate adversarial examples that are slightly modified versions of the original input data. This forces the model to learn a more robust representation that can handle small perturbations in the input space, making it more resistant to attacks and noise. This is a crucial aspect of developing reliable and safe autonomous systems.

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