Corrected filter location grid

[AmarSaini]

This is a great implementation! One small note:

On line 151:

grid_i = torch.arange(start=0.0, end=N, device=self.device, requires_grad=True,).view(1, -1)

I believe you should set the arange to be from 1 -> N, rather than from 0 -> (N-1):

grid_i = torch.arange(start=1.0, end=N+1, device=self.device, requires_grad=True,).view(1, -1)

Doing this will ensure that the filter locations are around the center, gx and gy. Here's a figure from the paper for reference:

Currently the grid is shifted more towards the top-left by 1 filter.

Below are some diagrams showing the differences between the current grid and the correct grid:

The red dot is the center gx and gy. The green rectangle is the current grid layout/filter locations, and the red rectangle is the correct grid layout/filter locations, using the recommended code change mentioned above.

Example 1 (N=5): Notice how the filter grid contains gx and gy, but isn't centered around it!

Example 2 (N=2): Notice how the filter locations don't even contain gx and gy! One of DRAW's optimal configurations for MNIST was using a read_N of 2

Details about the above figure:

Image size: 25 x 25 gx = 10 gy = 12 N = 5 (for the first example) N = 2 (for the second example) (delta) stride = 3

To calculate the NxN filter locations: We can use Equations 19 and 20 from the paper.

In your code it's:

# Equation 19.
mu_x = gx + (grid_i - N / 2 - 0.5) * delta
# Equation 20.
mu_y = gy + (grid_i - N / 2 - 0.5) * delta

To draw the rectangle, we need the top-left and bottom-right filter locations. We can simple set the starting and ending grid_i values as so:

With the current arange, we would set grid_i = 0 and grid_i = N-1 With the proposed arange, we would set grid_i = 1 and grid_i = N