Gradient theory is a mathematical framework used to describe how changes in a function's output can be predicted based on changes in its input, typically applied in optimization problems. It is foundational in fields like machine learning and physics, where it helps in finding minima or maxima of functions by iteratively adjusting parameters in the direction of the steepest descent or ascent.

Gradient Theory

Gradient theory

mathematical framework

changes in a function's output

changes in its input

Optimization problems involve finding the best solution from a set of feasible solutions, often under given constraints. They are fundamental in various fields such as operations research, economics, and computer science, where the goal is to maximize or minimize an objective function.

optimization problems

Machine learning is a subset of artificial intelligence that involves the use of algorithms and statistical models to enable computers to improve their performance on a task through experience. It leverages data to train models that can make predictions or decisions without being explicitly programmed for specific tasks.

machine learning

Physics is the fundamental science that seeks to understand the nature and behavior of matter and energy in the universe, covering phenomena from the smallest subatomic particles to the largest cosmic structures. It provides the foundational principles that underpin other sciences and technologies, offering insights into the laws governing the physical world and enabling advancements in various fields.

physics

finding minima

Finding maxima

iteratively adjusting parameters

Steepest descent is an iterative optimization algorithm used to find the local minimum of a differentiable function by moving in the direction of the negative gradient. It is simple to implement but can be slow to converge, especially in poorly conditioned problems, due to its reliance on the gradient's direction alone.

CUSTOMIZE YOUR LEARNING

CUSTOMIZE YOUR LEARNING

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