Final answer:
Momentum in physics is the product of mass and velocity and is pivotal for analyzing collisions and conservation in classical and modern physics. In Gradient Descent, momentum is an enhancement that accelerates convergence by adding consistency to the direction of optimization. It also allows for changing system mass in scenarios like rocket motion.
Step-by-step explanation:
Understanding Momentum in Physics
The concept of momentum is paramount in physics, reflecting the quantity of motion that an object possesses. It is a vector that combines both mass and velocity, indicating the direction and magnitude of motion. Momentum, which is crucial for analyzing collisions and conservation laws, is expressed in the formula p = mv, where p represents momentum, m is mass, and v is velocity. The conservation of momentum is foundational in classical and modern physics, especially in the realm of subatomic particle collision analysis.
In the context of Gradient Descent, momentum refers to a technique that accelerates the convergence of the algorithm by moving it in a consistent direction, avoiding oscillations and local minima traps. This is achieved by adding a fraction of the previous update vector to the current update, effectively pushing the optimization process in a persistent direction. This enhancement to Gradient Descent is analogous to the physical momentum, as it helps the procedure maintain its course in the optimization landscape.
Expressing force in terms of changing momentum also allows for the consideration of changing mass, such as in the motion of rockets, where both mass and velocity can vary.