Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work, we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the manifold assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in $\mathbb{R}^N$. Our work complements a large body of work on manifold learning, where the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distances.

In ML for network security, traditional workflows rely on high-quality labeled data and manual feature engineering, but limited datasets and human expertise hinder feature selection, leading to models struggling to capture crucial relationships and generalize effectively. Inspired by recent advancements in ML application domains like GPT-4 and Vision Transformers, we have developed netFound, a foundational model for network security. This model undergoes pre-training using self-supervised algorithms applied to readily available unlabeled network packet traces. netFound's design incorporates hierarchical and multi-modal attributes of network traffic, effectively capturing hidden networking contexts, including application logic, communication protocols, and network conditions. With this pre-trained foundation in place, we can fine-tune netFound for a wide array of downstream tasks, even when dealing with low-quality, limited, and noisy labeled data. Our experiments demonstrate netFound's superiority over existing state-of-the-art ML-based solutions across three distinct network downstream tasks: traffic classification, network intrusion detection, and APT detection. Furthermore, we emphasize netFound's robustness against noisy and missing labels, as well as its ability to generalize across temporal variations and diverse network environments. Finally, through a series of ablation studies, we provide comprehensive insights into how our design choices enable netFound to more effectively capture hidden networking contexts, further solidifying its performance and utility in network security applications.