Intelligence
Mathematical Framework
The NexusAI platform employs multi-layer perceptron architectures with adaptive depth scaling. Each neural layer applies a non-linear transformation to the input data, enabling the system to learn hierarchical representations of complex patterns.
Forward Propagation
z[l] = W[l] · a[l-1] + b[l] → a[l] = σ(z[l])
Each layer computes a weighted sum of inputs and applies an activation function σ (ReLU, GELU, or Swish depending on layer depth).
Network Topology
Chain Rule
∂L/∂W[l] = ∂L/∂a[l] · ∂a[l]/∂z[l] · ∂z[l]/∂W[l]
Gradients flow backward through the network via the chain rule, computing partial derivatives with respect to each weight matrix.
Weight Update
W[l] ← W[l] - α · ∂L/∂W[l]
Weights are updated proportionally to the gradient, scaled by learning rate α. Adaptive methods (Adam, AdaGrad) modify this update rule dynamically.
Training Loss Convergence