Extensive research has produced robust methods for unsupervised data visualization. Yet supervised visualization—where expert labels guide representations—remains underexplored, as most supervised approaches prioritize classification over visualization. Recently, RF-PHATE, a diffusion-based manifold learning method leveraging random forests and information geometry, marked significant progress in supervised visualization. However, its lack of an explicit mapping function limits scalability and its application to unseen data, posing challenges for large datasets and label-scarce scenarios. To overcome these limitations, we introduce Random Forest Autoencoders (RF-AE), a neural network-based framework for out-of-sample kernel extension that combines the flexibility of autoencoders with the supervised learning strengths of random forests and the geometry captured by RF-PHATE. RF-AE enables efficient out-of-sample supervised visualization and outperforms existing methods, including RF-PHATE's standard kernel extension, in both accuracy and interpretability. Additionally, RF-AE is modality-agnostic, demonstrates strong robustness to hyperparameters, supports both classification and regression, and natively accommodates missing feature values. Our code is available at https://github.com/JakeSRhodesLab/RF-AE.

Raman spectroscopy provides chemical and compositional information that can serve as a structural fingerprint for various materials. Therefore, simulations of Raman spectra, including both quantum perturbation analyses and ground-state calculations are of significant interest. However, highly accurate full quantum mechanical (QM) simulations of Raman spectra have previously been confined to small systems. For large systems such as biological materials, the computational cost of full QM simulations is extremely high, and their extension to such systems remains challenging. In the work described here, by employing robust new algorithms and advances in implementation for the many-core architectures, we are able to perform fast, accurate, and massively parallel full ab initio simulations of the Raman spectra of biological systems with excellent strong and weak scaling, thereby providing a starting point for applying QM approaches to structural studies of such systems.

Although the joint design of content caching and retrieving has the potential of relieving the backhaul pressure, either caching or retrieving would significantly influence the distribution of interference in caching-enabled small cell network (CSCN). The complicated interference, if not properly managed, would inversely deteriorate the network performance. In this work, we further investigate the tradeoff of content caching and retrieving in term of network spatial throughput (ST). Specifically, the analysis manifests that, compared to the condition of caching less content, ST is more likely to be reduced with increasing amount of retrieving content when more content is pre-cached by small cell base station (SBS). To maximize the ST, we formulate an optimization problem, which is solved by the joint design of content caching and retrieving. Moreover, a critical SBS density is derived from the optimization result, beyond which less content should be retrieving if more content is pre-cached by SBS. Therefore, the tradeoff between content caching and retrieving could be captured. More importantly, it is shown that a backhaul-free region exists, where the maximization of ST under joint optimization is identical to that under caching optimization. This indicates that the backhaul pressure can be significantly relieved through caching optimization in dense CSCN.