This text explores the connection between the gradient descent algorithm in machine learning and Newton’s laws of motion. It explains that gradient descent is used to update parameters in a neural network to minimize a loss function, drawing parallels to the concept of potential and conservative forces in Newtonian physics. The article emphasizes the unified mathematical framework underlying these seemingly disparate concepts.
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Exploring the shared language of gradient descent and Newton’s motion equations
Overview of a neural network training
In supervised neural network tasks, the goal is to minimize the difference between predicted and true values. This is achieved through a function called the loss function, denoted as L. Training the neural network involves updating the parameters to minimize the loss function, essentially optimizing via gradient descent.
Optimizing via gradient descent
Gradient descent is used to calculate new parameters by moving in the opposite direction of the gradient of the loss function, effectively minimizing the loss. This motion corresponds to the physical trajectory of a particle seeking to rest in the lowest possible potential around it, demonstrating the non-random nature of the algorithm.
Newton’s Second Law
Newton’s second law of motion has a mathematical formulation similar to the gradient descent equation. It describes how momentum of a body always points towards the direction where the potential decreases the fastest, with a step size given by Δt.
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