NNUE Weight Symmetry

[Klamath233]

Unlike Chess, CC has a symmetrical initial board. Therefore, I'm expecting the initial weights to be symmetrical as well. However, this is not the case:

 NNUE derived piece values:
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|   r   |   n   |   b   |   a   |   k   |   a   |   b   |   n   |   r   |
| -6.70 | -2.83 | -0.93 | -0.85 |       | -0.89 | -1.12 | -2.77 | -6.48 |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|       |       |       |       |       |       |       |       |       |
|       |       |       |       |       |       |       |       |       |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|       |   c   |       |       |       |       |       |   c   |       |
|       | -3.99 |       |       |       |       |       | -3.84 |       |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|   p   |       |   p   |       |   p   |       |   p   |       |   p   |
| +0.18 |       | -0.19 |       | -1.03 |       | -0.32 |       | -0.02 |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|       |       |       |       |       |       |       |       |       |
|       |       |       |       |       |       |       |       |       |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|       |       |       |       |       |       |       |       |       |
|       |       |       |       |       |       |       |       |       |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|   P   |       |   P   |       |   P   |       |   P   |       |   P   |
| -0.15 |       | +0.20 |       | +0.69 |       | +0.31 |       | +0.05 |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|       |   C   |       |       |       |       |       |   C   |       |
|       | +3.74 |       |       |       |       |       | +3.67 |       |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|       |       |       |       |       |       |       |       |       |
|       |       |       |       |       |       |       |       |       |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
|   R   |   N   |   B   |   A   |   K   |   A   |   B   |   N   |   R   |
| +7.01 | +2.69 | +1.00 | +0.86 |       | +0.93 | +1.17 | +2.74 | +6.81 |
+-------+-------+-------+-------+-------+-------+-------+-------+-------+

Why is this the case? I'm assuming this comes from the asymmetry of the training data. I'm wondering if one can leverage the symmetry of the CC board to optimize training. I'm very new to engine design so let me know if this is not significant practically and why.

[PikaCat-OuO]

For Pikafish, the asymmetry only happens when the king is on the middle file due to technical reasons. When the king is not on the middle file, it's symmetry. We are using a half mirroring model for NNUE, king on file f will be mirrored to file d.
For two mirrored pieces in a symmetry position, the asymmetry comes from the training data, which is not likely to fix.

[Klamath233]

Thanks. That makes total sense.