Mesh autoencoders rely heavily on fixed quadric sampling schemes, which preserve only topological information, often leading to poor-quality shape up-sampling and overfitting. This paper introduces Neural QSLIM, a novel framework for geometry-aware mesh up-sampling. By randomly generating bijective coarse-to-fine mesh counterparts, our method trains a neural network to learn complex mesh shapes. During decoding, our approach takes a coarse triangle mesh from the bottleneck and reconstructs finer geometry using QSLIM-guided topological updates, while predicting vertex positions with the trained neural network. This design improves the accuracy of vertex positions while maintaining the desired topological structure, rather than relying on simple point projection as in classical mesh autoencoders. We demonstrate that our method enables more effective non-linear mesh up-sampling, resulting in efficient and flexible representations across various mesh autoencoder models.