Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches, which lack generalizability--- for each new model, the algorithm has to be executed from the beginning. Therefore, for an unseen architecture, one cannot use the subset chosen for a different model. In this work, we propose $\texttt{SubSelNet}$, a non-adaptive subset selection framework, which tackles these problems. Here, we first introduce an attention-based neural gadget that leverages the graph structure of architectures and acts as a surrogate to trained deep neural networks for quick model prediction. Then, we use these predictions to build subset samplers. This naturally provides us two variants of $\texttt{SubSelNet}$. The first variant is transductive (called Transductive-$\texttt{SubSelNet}$), which computes the subset separately for each model by solving a small optimization problem. Such an optimization is still super fast, thanks to the replacement of explicit model training by the model approximator. The second variant is inductive (called Inductive-$\texttt{SubSelNet}$), which computes the subset using a trained subset selector, without any optimization. Our experiments show that our model outperforms several methods across several real datasets.