Understanding Neural Networks: Approximating Unknown Functions
Artificial Intelligence leverages neural networks to estimate an unknown function, denoted as f(x) = y. Instead of directly computing this function, AI models construct an approximation, represented as f(x;θ), where θ symbolizes the network’s trainable parameters. The goal is to fine-tune these parameters so that the model’s output closely aligns with the actual function.
To achieve this, a loss function is introduced, measuring the discrepancy between the model’s predicted output (y') and the true value (y). One of the most common approaches for minimizing this difference is the L2 loss function, which penalizes larger errors more heavily, encouraging the model to learn an accurate mapping.
By iteratively adjusting its parameters through optimization techniques such as gradient descent, the neural network gradually refines its predictions. This process ensures that the model continuously improves, making it a powerful tool for solving complex problems across various scientific and technological domains.
