Latent Gaussian Reconstruction Loss

Problem

Compute the Gaussian negative log-likelihood of latent dynamics predictions.

For a batch of latent vectors, add log(2 * pi) + log_var + (target - mu)^2 / exp(log_var) over every dimension, then return 0.5 times the sum divided by the batch size. An empty batch returns 0.0.

Hint

The log-variance head lets the model trade off uncertainty against reconstruction error.

Test cases

case 1

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

expected: 0.9189385332046727

case 2

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

expected: 1.4189385332046727

case 3

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

expected: 2.8378770664093453

case 4

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

expected: 2.3378770664093453

case 5

in: [[],[],[]]

expected: 0

Starter codePython

import math
def latent_gaussian_reconstruction_loss(mu, log_var, target):
    # Your code here
    pass

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