Neural-network techniques are often transferred across architecture families by analogy, but such transfer is valid only when the assumptions required by a technique are preserved. We introduce this idea as inheritance between model classes. Using a unified node-level framework with tensor-valued activations, we prove that generalized feedforward networks (GFFNs) form a strict subset of generalized convolutional networks (GCNNs), so GCNN properties transfer directly to GFFNs. The reverse direction is not automatic: standard CNN nodes use spatial kernels, while FFN nodes use one scalar weight per input contribution. We introduce model projection to recover a restricted reverse inheritance path. Projection freezes each convolutional input-channel sub-function and learns one scalar coefficient for each input-output channel contribution, giving projected CNN nodes the GFFN-style trainable structure of scalar-weighted input recombination. This inherited structure leads naturally to parameter-efficient transfer learning. Across multiple ImageNet-pretrained CNN backbones and downstream image-classification datasets, model projection is competitive with standard and PEFT baselines and provides an effective initialization for subsequent full fine-tuning.