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Reversing Conway's game of life is famously hard to compute. However, it's possible to approximate the inverse using gradient descent if we formulate GoL as a continuous computation.

Here's how it works. We represent the board as a grid of continuous values in [0,1]. To compute the next step, we first take a convolution with a 3x3 kernel equivalent to the summation of the neighboring living cells. Then we map the result into [0, 1] range using a continuous function corresponding to the alive rule. In this article it uses a narrow Gaussian centered at n=3. Then we can compute the gradient descent to figure out an approximation of inverse step.