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Deep convolutional neural network (CNN) training via iterative optimization has had incredible success in finding optimal parameters. However, modern CNN architectures often contain millions of parameters. Thus, any given model for a single architecture resides in a massive parameter space. Models with similar loss could have drastically different characteristics such as adversarial robustness, generalizability, and quantization robustness. For deep learning on the edge, quantization robustness is often crucial. Finding a model that is quantization-robust can sometimes require significant efforts. Recent works using Graph Hypernetworks (GHN) have shown remarkable performance predicting high-performant parameters of varying CNN architectures. Inspired by these successes, we wonder if the graph representations of GHN-2 can be leveraged to predict quantization-robust parameters as well, which we call GHN-Q. We conduct the first-ever study exploring the use of graph hypernetworks for predicting parameters of unseen quantized CNN architectures. We focus on a reduced CNN search space and find that GHN-Q can in fact predict quantization-robust parameters for various 8-bit quantized CNNs. Decent quantized accuracies are observed even with 4-bit quantization despite GHN-Q not being trained on it. Quantized finetuning of GHN-Q at lower bitwidths may bring further improvements and is currently being explored.