Gradient flow refers to the path taken by a point in a space as it moves in the direction of the steepest descent of a function, often used in optimization problems to find local minima. It is fundamental in machine learning algorithms where it guides the adjustment of parameters to minimize loss functions effectively.

Gradient Flow

Gradient flow

path taken by a point

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.

steepest descent

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

Local minima are points in a function where the function value is lower than at any nearby points, making them crucial in optimization problems. They can pose challenges in finding the global minimum, especially in complex, multi-dimensional spaces where algorithms might get 'stuck' at these points instead of finding the true lowest point.

local minima

Machine learning algorithms are computational methods that enable systems to learn from data and improve their performance over time without being explicitly programmed. These algorithms are the backbone of artificial intelligence applications, driving advancements in fields such as natural language processing, computer vision, and predictive analytics.

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