Fix finite-difference example in conv-layer to use horizontal neighbors

[Chessing234]

Closes #2669.

Bug

The paragraph introducing the [1, -1] edge-detection kernel in chapter_convolutional-neural-networks/conv-layer.md says the kernel

computes the difference between the values of horizontally adjacent pixels [and] is a discrete approximation of the first derivative in the horizontal direction

but the two formulas on that same line describe a vertical difference:

x_{i,j} - x_{(i+1),j}
-\partial_i f(i,j) = lim (f(i,j) - f(i+eps,j)) / eps

Root cause

With the book's (row i, column j) indexing, moving in j is horizontal; moving in i is vertical. The kernel K = [[1.0, -1.0]] is 1×2 and applied along the width axis, so at position (i, j) cross-correlation produces

1 * X[i, j] + (-1) * X[i, j+1]  =  X[i, j] - X[i, j+1]

i.e. a difference between horizontal neighbors, approximating the partial derivative along j. The prose is correct; the two symbolic expressions used the wrong axis.

Why the fix is correct

Three edits on that single line, all swapping the i-axis offsets for j-axis ones so the formulas match the surrounding prose and the actual behaviour of the 1×2 kernel:

• x_{i,j} - x_{(i+1),j} → x_{i,j} - x_{i,j+1}
• -\partial_i f(i,j) → -\partial_j f(i,j)
• f(i+\epsilon, j) → f(i, j+\epsilon)

No other changes; the Python block directly below (K = d2l.tensor([[1.0, -1.0]]) and the worked example on a 6×8 input) is unaffected and already illustrates the horizontal interpretation.

[smolix]

Hi @Chessing234 - I'm in the middle of refactoring d2l to move it to a more modern tooling (Quarto, latest versions of JAX, TF/Keras and PyTorch, better references, fix performance bugs, etc.). I'll have a first cut of this shortly. Reach out to me by e-mail and we can discuss more (no idea who you are, based off your GH info).