Learning goal: distinguish three separate roles. Repeated downsampling can expand receptive-field coverage rapidly, but the particular pooling operation can discard detail that upsampling alone cannot uniquely recover. Skips offer another information route. Residual connections change deep signal and gradient paths; normalization changes feature scales and gradient geometry.

One-dimensional encoder–decoder toy: original low-frequency signal plus peaks, down-and-up reconstruction, then a skip-assisted reconstruction.

Switch between receptive field versus depth, frequency retention, and training error across connection types.

High-frequency error without skip = — With skip = — Low-frequency error without skip = — Layers to target coverage, flat stack = — Downsample every two layers = — Layer-32 initial RMS, plain / residual / residual+LN = —

Observe: increase downsampling from 0 to 3; the reconstruction loses peaks while broad low-frequency structure changes less. In frequency view, after two levels, many short-period components are strongly attenuated in this measurement. This is not a universal feature-size cutoff. The skip route retains information: at two levels, displayed high-frequency error changes from 0.0797 to 0.0090. That information bypasses the bottleneck. For target receptive field 128, the flat stack needs 32 layers layers, while this downsampled construction needs 9 layers. In the depth view, beyond 16 layers, the plain model stalls near its no-learning baseline in this experiment. Other connections change the outcome, but thresholds depend on architecture and training. Downsampling, residual paths, and normalization address different design questions.