Differentiable approximation for counting negative values in array

Question

Differentiable approximation for counting negative values in array

iRestMyCaseYourHonor

2022年4月12日 19:01

I have an array of time of arrivals and I want to convert it to count data using pytorch in a differentiable way.

Example arrival times:

arrival_times = [2.1, 2.9, 5.1]

and let's say the total range is 6 seconds. What I want to have is:

counts = [0, 0, 2, 2, 2, 3]

For this task, a non-differentiable way works perfect:

x = [1, 2, 3, 4,5,6]
counts = torch.sum(torch.Tensor(arrival_times)[:, None]  torch.Tensor(x), dim=0)

It turns out the operation here is not differentiable. I need a differentiable approximation of this operation.

What I could think of is to subtract the x from arrival_times with broadcasting which leads the following array.

[
[1.1, 0.1, -0.9, -1.9, -2.9, -3.9]
[1.9, 0.9, -0.1, -1.1, -2.1, -3.1]
[4.1, 3.1, 2.1, 1.1, 0.1, -0.9]
]

And then somehow count the number of negative (and also zero preferably) elements vertically which will give us the counts [0, 0, 2, 2, 2, 3].

Is there a way to do this or completely new idea for such approximation?

Topic gradient pytorch

Category Data Science

iRestMyCaseYourHonor · Accepted Answer · 2021年11月9日 09:56

I tried a hacky way to do this. Still open for suggestions.

        diffs = arrival_times[..., None] - torch.Tensor(x)
        zeros = torch.zeros_like(diffs)
        minimums = torch.minimum(diffs, zeros)
        eps, r_eps = 0.001, 1000
        epsilons = torch.ones_like(diffs) * -eps
        maximums = torch.maximum(minimums, epsilons) * -r_eps
        counts = torch.sum(maximums, dim=1)

The hackiness comes from multiplying by eps. In this way, any arrival time that is between 0 - 0.001 away from its closest second will be polluting the count. It's still differentiable but did not give good results in training for my case.

Differentiable approximation for counting negative values in array

About