/ˈɡreɪ.di.ənt dɪˈsɛnt/
noun … “finding the lowest point by taking small, informed steps.”
Gradient Descent is an optimization algorithm widely used in machine learning, deep learning, and numerical analysis to minimize a loss function by iteratively adjusting parameters in the direction of steepest descent. The loss function measures the discrepancy between predicted outputs and actual targets, and the gradient indicates how much each parameter contributes to that error. By following the negative gradient, the algorithm gradually moves toward parameter values that reduce error, ideally converging to a minimum.
At a mathematical level, Gradient Descent relies on calculus. For a function f(θ), the gradient ∇f(θ) is a vector of partial derivatives with respect to each parameter θᵢ. The update rule is θ = θ - η ∇f(θ), where η is the learning rate that controls step size. Choosing an appropriate learning rate is critical: too small leads to slow convergence, too large can overshoot minima or cause divergence. Variants such as stochastic gradient descent (SGD) and mini-batch gradient descent balance convergence speed and stability by using subsets of data per update.
Gradient Descent is integral to training Neural Networks, where millions of weights are adjusted to reduce prediction error. It also underpins classical statistical models like Linear Regression and Logistic Regression, where closed-form solutions exist but iterative optimization remains flexible for larger datasets or complex extensions. Beyond machine learning, it is used in numerical solutions of partial differential equations, convex optimization, and physics simulations.
Practical implementations of Gradient Descent often incorporate enhancements to improve performance and avoid pitfalls. Momentum accumulates a fraction of past updates to accelerate convergence and overcome shallow regions. Adaptive methods such as AdaGrad, RMSProp, and Adam adjust learning rates per parameter based on historical gradients. Regularization techniques are applied to prevent overfitting by penalizing extreme parameter values, ensuring the model generalizes beyond training data.
Example conceptual workflow of gradient descent:
initialize parameters randomly
compute predictions based on current parameters
calculate loss between predictions and targets
compute gradient of loss w.r.t. each parameter
update parameters in the negative gradient direction
repeat until loss stabilizes or maximum iterations reachedThe intuition behind Gradient Descent is like descending a foggy mountain: you cannot see the lowest valley from above, but by feeling the slope beneath your feet and stepping downhill repeatedly, you gradually reach the bottom. Each small adjustment builds upon previous ones, turning a complex landscape of errors into a tractable path toward optimal solutions.