Gradient Descent

Computer Science

How It Works

Gradient descent is a first-order iterative optimization algorithm employed to minimize differentiable objective loss functions across computational parameter manifolds. At each iteration, model weights shift in the direction of steepest local descent—proportional to the negative gradient vector of the loss surface evaluated at the current state. The learning rate hyperparameter η governs step magnitude, balancing convergence velocity against numerical oscillation near minima.

Governing Equation
θ_{t+1} = θ_t - η ∇ J(θ_t) , ∇ J(θ) = [ (∂ J) / (∂ θ_1), …, (∂ J) / (∂ θ_n) ]^T