The gradient says which way is uphill; the minus sign provides the strategy.

The gradient descent formula describes an iterative method for finding the minimum of a function by repeatedly moving in the direction of steepest decrease. At each step, parameters are adjusted by subtracting the gradient multiplied by a learning rate, often written as θ = θ − η∇J(θ). The gradient points uphill, so moving against it sends the solution downhill across the mathematical landscape. A large learning rate can overshoot the minimum; a tiny one may crawl toward it slowly. Repeated updates reduce error until the parameters settle near an optimum. It is used primarily in machine learning, numerical optimization, and data science.