Gradient Descent Direction via Negative Gradient Vector Computation
The core principle dictates that in unconstrained optimization within Euclidean space, the direction of steepest descent for a differentiable scalar function is defined by the negative gradient vector at a given point. This mechanism relies on the formal application of partial derivatives and the chain rule to construct an ascent-descent path orthogonal to level sets of the objective function. It represents a fundamental first-order iterative method within numerical optimization theory, serving as the foundational update rule for minimizing differentiable loss landscapes in continuous domains.
Gradient Descent Direction via Negative Gradient Vector Computation
Walks through gradient descent on a loss function: computing the gradient, stepping opposite to it with a learning rate, convergence criteria, and the stochastic variant for large datasets.