This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs). Different from existing efforts, we focus on hidden representations analysis rather than pure downstream task performance and analyze NFMs through a three-part evaluation: Embedding Geometry Analysis to assess representation space utilization, Metric Alignment Assessment to measure correspondence with domain-expert features, and Causal Sensitivity Testing to evaluate robustness to protocol perturbations. Using five diverse network datasets spanning controlled and real-world environments, we evaluate four stateof-the-art NFMs, revealing that they all exhibit significant anisotropy, inconsistent feature sensitivity patterns, an inability to separate the high-level context, payload dependency, and other properties. Our work identifies numerous limitations across all models and demonstrates that addressing them can significantly improve model performance (up to 0.35 increase in F1 scores without architectural changes).

Detecting structural change in dynamic network data has wide-ranging applications. Existing approaches typically divide the data into time bins, extract network features within each bin, and then compare these features over time. This introduces an inherent tradeoff between temporal resolution and statistical stability of the extracted features. Despite this tradeoff, reminiscent of time-frequency tradeoffs in signal processing, most methods rely on a fixed temporal resolution. Choosing an appropriate resolution parameter is typically difficult, and can be especially problematic in domains like cybersecurity, where anomalous behavior may emerge at multiple time scales.

We study the evolution of hidden-weight spectra in wide neural networks trained by (stochastic) gradient descent. We develop a two-level dynamical mean-field theory (DMFT) that jointly tracks bulk and outlier spectral dynamics for spiked ensembles whose spike directions remain statistically dependent on the random bulk. We apply this framework to two settings: (1) infinite-width nonlinear networks in mean-field/$μ$P scaling and (2) deep linear networks in the proportional high-dimensional limit, where width, input dimension, and sample size diverge with fixed ratios. Our theory predicts how outliers evolve with training time, width, output scale, and initialization variance. In deep linear networks, $μ$P yields width-consistent outlier dynamics and hyperparameter transfer, including width-stable growth of the leading NTK mode toward the edge of stability (EoS). In contrast, NTK parameterization exhibits strongly width-dependent outlier dynamics, despite converging to a stable large-width limit. We show that this bulk+outlier picture is descriptive of simple tasks with small output channels, but that tasks involving large numbers of outputs (ImageNet classification or GPT language modeling) are better described by a restructuring of the spectral bulk. We develop a toy model with extensive output channels that recapitulates this phenomenon and show that edge of the spectrum still converges for sufficiently wide networks.

We examine an adaptive learning framework for nonatomic congestion games where the players' cost functions may be subject to exogenous fluctuations (e.g., due to disturbances in the network, variations in the traffic going through a link, etc.).

In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well as path-wise within the space of second-order stochastic (random) processes \( L^2(Ω, \mathcal{F},\mathbb{P}) \). Additionally, we provide quantitative error estimates using the modulus of continuity of the processes. These results highlight the effectiveness of SINNOs for approximating stochastic processes with potential applications in COVID-19 case prediction.

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph topology identification and statistical inference methods for multidimensional relational data. Approaches for undirected links connecting graph nodes are outlined, going all the way from correlation metrics to covariance selection, and revealing ties with smooth signal priors. To account for directional (possibly causal) relations among nodal variables and address the limitations of linear time-invariant models in handling dynamic as well as nonlinear dependencies, a principled framework is surveyed to capture these complexities through judiciously selected kernels from a prescribed dictionary. Generalizations are also described via structural equations and vector autoregressions that can exploit attributes such as low rank, sparsity, acyclicity, and smoothness to model dynamic processes over possibly time-evolving topologies. It is argued that this approach supports both batch and online learning algorithms with convergence rate guarantees, is amenable to tensor (that is, multi-way array) formulations as well as decompositions that are well-suited for multidimensional network data, and can seamlessly leverage high-order statistical information.

Abstract--The rise of 5G/6G network technologies promises to enable applications like autonomous vehicles and virtual reality, resulting in a significant increase in connected devices and necessarily complicating network management. Even worse, these applications often have strict, yet heterogeneous, performance requirements across metrics like latency and reliability. Much recent work has thus focused on developing the ability to predict network performance. However, traditional methods for network modeling, like discrete event simulators and emulation, often fail to balance accuracy and scalability. Network Digital Twins (NDTs), augmented by machine learning, present a viable solution by creating virtual replicas of physical networks for real-time simulation and analysis. State-of-the-art models, however, fall short of full-fledged NDTs, as they often focus only on a single performance metric or simulated network data. We introduce M3Net, a Multi-Metric Mixture-of-experts (MoE) NDT that uses a graph neural network architecture to estimate multiple performance metrics from an expanded set of network state data in a range of scenarios. We show that M3Net significantly enhances the accuracy of flow delay predictions by reducing the MAPE (Mean Absolute Percentage Error) from 20.06% to 17.39%, while also achieving 66.47% and 78.7% accuracy on jitter and packets dropped for each flow. Emerging 5G and 6G mobile network architectures aim to support new applications like autonomous vehicles and mixed reality [1], [2], both of which require significantly expanded network capabilities. These and other new applications envisioned as part of the 5G and 6G network ecosystem will lead to massive numbers of connected devices with heterogeneous performance expectations, which increases the complexity and cost of managing communication networks [2]. For example, interactive applications like augmented reality generally require response latencies under 200ms [3], while safety-critical applications like autonomous vehicles might require highly reliable delivery of high-priority packets [4].

The proliferation of autonomous Unmanned Aerial Vehicles (UAVs) in Beyond Visual Line of Sight (BVLOS) applications is critically dependent on resilient, high-bandwidth, and low-latency communication links. Existing solutions face critical limitations: TCP's head-of-line blocking stalls time-sensitive data, UDP lacks reliability and congestion control, and cellular networks designed for terrestrial users degrade severely for aerial platforms. This paper introduces AQUILA, a cross-layer communication architecture built on QUIC to address these challenges. AQUILA contributes three key innovations: (1) a unified transport layer using QUIC's reliable streams for MAVLink Command and Control (C2) and unreliable datagrams for video, eliminating head-of-line blocking under unified congestion control; (2) a priority scheduling mechanism that structurally ensures C2 latency remains bounded and independent of video traffic intensity; (3) a UAV-adapted congestion control algorithm extending SCReAM with altitude-adaptive delay targeting and telemetry headroom reservation. AQUILA further implements 0-RTT connection resumption to minimize handover blackouts with application-layer replay protection, deployed over an IP-native architecture enabling global operation. Experimental validation demonstrates that AQUILA significantly outperforms TCP- and UDP-based approaches in C2 latency, video quality, and link resilience under realistic conditions, providing a robust foundation for autonomous BVLOS missions.