Superposition Interference

Problem

Measure interference in a feature dictionary. Given a (num_features, num_neurons) weight matrix W, compute the Gram matrix G = W W^T and return [max_abs_off_diagonal, mean_abs_off_diagonal] over the off-diagonal entries.

The signature is superposition_interference(W).

Hint

Features stored at an angle to each other interfere; orthogonal features do not.

Test cases

case 1

in: [[[1,0],[0,1]]]

expected: [0,0]

case 2

in: [[[1,1],[1,0]]]

expected: [1,1]

case 3

in: [[[1,0,0],[0.5,0.5,0],[0,0,1]]]

expected: [0.5,0.1666666667]

case 4

in: [[[1,2],[3,4],[5,6]]]

expected: [39,22.3333333333]

Starter codePython

def superposition_interference(W):
    # Your code here
    pass

4 test cases · run your code against them in the editor