Neural Network
A model of layered, weighted connections between simple units that together approximate complex functions.
Definition
A neural network is composed of units (neurons) arranged in layers. Each unit computes a weighted sum of its inputs, adds a bias, and applies a nonlinear activation function. Stacking layers lets the network represent complex mappings from input to output.
In practice a network is a computational graph of differentiable operations, and modern frameworks automatically compute gradients through that graph. This makes it easy to compose novel architectures from standard layers, which is why experimentation in deep learning is fast compared with methods requiring hand-derived gradients.
The universal approximation property guarantees that a network can represent a wide class of functions, but it says nothing about whether training will find that representation from finite data, or how large the network must be. In practice, architecture choices that match a problem's structure, convolution for images, attention for sequences, matter far more than raw capacity, because they bias learning toward solutions that generalize.
Training adjusts the weights and biases to minimize a loss using gradient descent, with gradients computed by backpropagation.
Structure
- Input layer: receives the raw features.
- Hidden layers: learn intermediate representations.
- Output layer: produces predictions.
- Weights: the learned parameters connecting units.
Why it matters
A network with a nonlinear activation and enough units is a universal approximator: in principle it can represent any continuous function to arbitrary accuracy. In practice, architecture, data, and optimization determine what it actually learns.
Fusion connection
Compact networks serve as differentiable surrogates inside Kronos design loops, mapping machine parameters to predicted plasma performance so optimizers can search efficiently.