Learning goal: changing a seed can change the result at fixed architecture and hyperparameters. That variation can be measured and informs reporting. Initialization gain separately affects signal and gradient scales, including attenuation or amplification. Both gain and depth matter; a gradient ratio alone cannot diagnose absolute gradient magnitudes.

Dashed gray: truth; thin: twelve trained 1→16→16→1 tanh networks with Adam.

Log first/last-hidden-layer gradient-norm ratio versus depth; horizontal 1 means equal endpoint magnitudes.

Observe: changing gain can make the twelve fitted curves spread differently, changing the distribution of final losses. The lower plot summarizes gradient ratios across nine seeds: gain 0.5 and 1 give comparatively flat ratios over depths 2 to 32 here. This does not imply unchanged absolute gradients. In contrast, the gain-2 ratio rises from about 0.39 to 2.8 in this experiment. These measurements motivate checking both depth and initialization scale. Unscaled residual branches also change signal accumulation and gradients. Scaling or normalization may help, but neither is universally required nor guaranteed by this ratio alone.