Face Recognition (FR) systems in surveillance settings often encounter Low Resolution (LR) faces, those whose face region falls below the standard 112 $\times$ 112 input size. While labelled High Resolution (HR) training data is abundant, labelled native-LR data, and above all paired native LR/HR data, is scarce. One workaround is to synthesize LR data from the available HR faces, but how much synthesis effort is repaid in recognition accuracy remains unclear. We present a study of simple synthetic generation strategies for a compact, edge device-oriented face recognition system, spanning interpolation-based degradation, knowledge distillation, a Prepended Domain Transformer (PDT), Real ESRGAN-style degradation, and a learned Super Resolution (SR) front-end with an identity-aware loss. We evaluate these strategies on synthetic cross-resolution face benchmarks (LFW, CFP-FP, AgeDB-30) and on TinyFace, a real-world native LR dataset, and expose a synthetic-real gap: the degradation setting that is optimal on synthetic benchmarks is not the one that is optimal on real LR. We find that more synthesis effort does not help monotonically: the learned SR front-end does not surpass a direct feed of the aligned LR image into a strong backbone, while simple interpolation augmentation of a compact backbone is the only synthesis that improves over its own baseline. We conclude that generative methods for LR face recognition must be validated on real LR and against a direct-feed baseline, and release our pipeline at https://idiap.ch/paper/synth-lrfr

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