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Lecture 2
Associative Memory
- imagine you hear a song in a busy coffee shop (noisy input source), and after a while your memory converges onto a specific piece of information (the whole memory)
- this is an example of auto-associative memory
- remembering a face from a name is heteroassociative memory
Towards an algorithm for recall
- dx/dt = -x
- this is a differential equation, or a dynamical system
- proposed by Newton and Leibniz to describe laws of nature
- we want to describe functions that abide by this equation
- such functions describe phenomena in nature abiding by the law that the differential equation expresses
- we want to do this with more than intuition
- we want to actually calculate the functions
Recall algorithm
- dx is (x_later − x_earlier) and dt is a number we choose (usually very small)
- (x_later − x_earlier)/dt = -x_earlier
- choosing x_earlier on the right is Euler's explicit method; x_later on the right is Euler's implicit method (more frequently used in video games)
- x_later = -x_earlier*dt + x_earlier
- x_later iteratively adjusts based on x_earlier