People can innately recognize human facial expressions in unnatural forms, such as when depicted on the unusual faces drawn in cartoons or when applied to an animal's features. However, current machine learning algorithms struggle with out-of-domain transfer in facial expression recognition (FER). We propose a biologically-inspired mechanism for such transfer learning, which is based on norm-referenced encoding, where patterns are encoded in terms of difference vectors relative to a domain-specific reference vector. By incorporating domain-specific reference frames, we demonstrate high data efficiency in transfer learning across multiple domains. Our proposed architecture provides an explanation for how the human brain might innately recognize facial expressions on varying head shapes (humans, monkeys, and cartoon avatars) without extensive training. Norm-referenced encoding also allows the intensity of the expression to be read out directly from neural unit activity, similar to face-selective neurons in the brain. Our model achieves a classification accuracy of 92.15\% on the FERG dataset with extreme data efficiency. We train our proposed mechanism with only 12 images, including a single image of each class (facial expression) and one image per domain (avatar). In comparison, the authors of the FERG dataset achieved a classification accuracy of 89.02\% with their FaceExpr model, which was trained on 43,000 images.