Backpropagation and Gradients
Backpropagation and
Gradients
Agenda
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Motivation
Backprop Tips & Tricks
Matrix calculus primer
Example: 2-layer Neural Network
Motivation
Recall: Optimization objective is minimize loss
Goal: how should we tweak the parameters to decrease
the loss slightly?
Plotted on WolframAlpha
Approach #1: Random search
Intuition: the way we tweak parameters is the
direction we step in our optimization
What if we randomly choose a direction?
Approach #2: Numerical gradient
Intuition: gradient describes rate of change of a
function with respect to a variable surrounding an
infinitesimally small region
Finite Differences:
Challenge: how do we compute the gradient
independent of each input?
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