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Cross-survey generalization is a critical challenge in stellar spectral analysis, particularly in cases such as transferring from low- to moderate-resolution surveys. We investigate this problem using pre-trained models, focusing on simple neural networks such as multilayer perceptrons (MLPs), with a case study transferring from LAMOST low-resolution spectra (LRS) to DESI medium-resolution spectra (MRS). Specifically, we pre-train MLPs on either LRS or their embeddings and fine-tune them for application to DESI stellar spectra. We compare MLPs trained directly on spectra with those trained on embeddings derived from transformer-based models (self-supervised foundation models pre-trained for multiple downstream tasks). We also evaluate different fine-tuning strategies, including residual-head adapters, LoRA, and full fine-tuning. We find that MLPs pre-trained on LAMOST LRS achieve strong performance, even without fine-tuning, and that modest fine-tuning with DESI spectra further improves the results. For iron abundance, embeddings from a transformer-based model yield advantages in the metal-rich ([Fe/H] > -1.0) regime, but underperform in the metal-poor regime compared to MLPs trained directly on LRS. We also show that the optimal fine-tuning strategy depends on the specific stellar parameter under consideration. These results highlight that simple pre-trained MLPs can provide competitive cross-survey generalization, while the role of spectral foundation models for cross-survey stellar parameter estimation requires further exploration.