Complex Networks

Generating graph ensembles with precisely controlled structural properties is central to investigating how network structure shapes function. Canonical ensembles impose constraints only in expectation (soft constraints), letting individual realizations fluctuate around the target, whereas enforcing hard constraints with prescribed precision in every realization remains challenging beyond fixing the degree sequence. Here we show that a reinforcement learning framework can drive a graph through degree-preserving rewirings to satisfy a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. By replacing the entropically dominated Metropolis--Hastings random walk with directed transport, the learned policy reduces generation cost by at least an order of magnitude while retaining over 98% of configurational diversity. Trained on small graphs, the framework generalizes across sizes and topologies without retraining, enabling quantitative isolation of secondary observables such as the clustering coefficient. These results establish reinforcement learning as a practical paradigm for hard-constrained graph generation.

Stereo image super-resolution aims to generate high-resolution images by leveraging complementary information from binocular systems. Although previous studies have achieved impressive results, the potential of intra-view and cross-view information has not been fully exploited. To address this issue, we propose a novel multi-scale interaction network for stereo image super-resolution. Specifically, we design a Multi-scale Spatial-Channel Attention Module that utilizes multi-scale large separable kernel attention and simple channel attention to improve intra-view feature extraction. Additionally, we propose a Dual-View Epipolar Attention Module, utilizing an optimal transport algorithm to achieve more accurate matching along the epipolar line. Extensive experimental and ablation studies show that our method achieves competitive results that outperform most SOTA methods.

Diffusion inference remains costly for edge deployment, yet existing accelerators focus almost exclusively on score networks because standard drift is merely a trivial linear scaling. Kuramoto orientation diffusion replaces this trivial drift with locally coupled phase interactions, improving sampling efficiency but introducing a new hardware bottleneck: a center-dependent nonlinear 5 x 5 stencil evaluated at every reverse step. This kernel maps poorly to conventional CNN accelerators and matrix-oriented engines. We present SA-Kura, to our knowledge the first digital systolic-array accelerator dedicated to locally coupled Kuramoto drift. By reformulating pair-wise sinusoidal coupling into neighbor accumulation independent of the center phase followed by a single center-dependent multiply-subtract combination, SA-Kura eliminates in-PE transcendental units and enables regular systolic execution with register-level reuse. SA-Kura was implemented in synthesizable RTL, integrated into a lightweight RISC-V-based SoC, prototyped on FPGA, and evaluated through 45 nm CMOS synthesis and power analysis. For the drift kernel only, compared with software execution of the same kernel on the processor core in the same SoC platform, SA-Kura reduces latency and energy by 193x and 69.4x, respectively. Compared with a standalone Jetson Orin Nano CUDA implementation of the same kernel, it is 6.57x faster and achieves approximately 46.0x lower energy per pixel.

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for a new target task, especially when the sample size $m$ of the training data for the latter is low. In this work, we rigorously analyze the potential benefit of transfer learning in terms of sample efficiency. Specifically, taking an optimal transport viewpoint of transfer learning, we find that when the data dimension $d$ is higher than $3$, the sample complexity for transfer learning is $O(m^{-(α+1)/d})$, with $α$ indicating the smoothness of the data distribution, as opposed to the $O(m^{-p/d})$ sample complexity for direct learning with $p$ indicating the smoothness of the optimal target model. Our finding theoretically supports a better sample efficiency for transfer learning, when the target task is optimizing over a family of not-so-smooth models (i.e., highly complex networks with the possible use of non-smooth activation functions). Using image classification as an example, we numerically demonstrate the sample efficiency for transfer learning, that is, in the data hungry regime, the model performance can be significantly improved by transfer learning.

Traditional anomaly detection marks events when measured signals cross predefined thresholds. This captures the moment of transition but not the structural pressure that precedes it. We propose treating large behavioral populations as geometric energy landscapes whose deformation can be measured before and during major transitions. The central thesis is that structure precedes geometry: the structural organization of the population is the signal, and geometric metrics are instruments for measuring it. Applied to the Tor anonymity network across 67 consecutive daily observation windows, the dual-observer pipeline identifies a stable nine-dimensional load-bearing subspace invariant across the observation period and validates this structure by Monte Carlo simulation at 16.8 sigma above the noise floor. Primary detection gates achieve 0.0% false positive rate on 24 confirmed stable windows. Forensic analysis of the February 20, 2026 confirmed infrastructure event formally falsifies the relay-departure hypothesis, identifying connectivity degradation without topology change as a detectable network failure mode. The result is a candidate structural-monitoring framework for behavioral populations with sufficient telemetry.

The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.

Large language models are increasingly deployed as automated judges to evaluate the strength of arguments. As this role expands, their legitimacy depends on consistency, transparency, and the ability to separate argumentative structure from rhetorical appeal. However, we show that holistic judging - a common LLM-as-a-Judge practice where a model provides a global verdict on a debate - suffers from substantial inter-model disagreement. We argue that this instability arises from collapsing a debate's complex interaction structure into a single opaque score. To address this, we propose GRASP (Gradual Ranking with Attacks and Support Propagation), a deterministic framework that aggregates stable local interaction judgments into a global ranking via a convergent attack--defense propagation operator. We show that local interaction judgments are more reproducible than holistic rankings in LLM-as-a-Judge evaluations, allowing GRASP to produce more consistent global rankings. We further show that GRASP scores do not correlate with human "convincingness" labels, highlighting a vital sociotechnical distinction: GRASP does not measure persuasion, factuality, or rhetorical appeal, but structural sufficiency - a defense-aware notion of argument robustness over the explicit interaction graph. Overall, GRASP offers a transparent and auditable alternative to holistic LLM judging.

Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and structural anomalies that break standard metric properties. We show that such misspecification pushes the data-generating distribution outside the model class, causing Bayesian inference to become overconfident and poorly calibrated. To address this, we propose a generalized posterior framework for random geometric graphs. We introduce Link-Sequential R-SafeBayes, a method that exploits dyadic conditional independence to estimate prequential risk and adaptively tune posterior regularization. Experiments on synthetic and real-world networks demonstrate improved calibration, better link prediction performance, and a reliable criterion for selecting latent geometries across Euclidean, spherical, and hyperbolic spaces.

We introduce \textbf{Prism}, a framework for structural symmetry diagnosis in complex networks. Given a graph Laplacian $L$ and a duality operator $P$ (a symmetric involution), Prism computes the \emph{duality defect} $δ(L,P) = \|LP - PL\|_F / \|L\|_F$ -- a scalar measuring how far the network deviates from structural self-consistency. When $P$ encodes the network's true symmetry, $δ$ starts near zero and rises monotonically as structure degrades; an arbitrary $P$ gives noise. We prove that the optimal $L'$ satisfying $[L', P] = 0$ is given by a closed-form block-diagonal projection, and provide an unsupervised alternating optimization that learns $P$ from the graph's own Fiedler vector. Experiments on synthetic networks show the true-$P$ defect is $3.38\times$ more sensitive to structural degradation than an index-reversal baseline and more sensitive than modularity. On Zachary's Karate Club with edge noise, Prism achieves $94.5\%$ community detection accuracy at $5\%$ noise versus $76.6\%$ for the raw Laplacian baseline. Applied to live S&P~500 data (2026-05-17), Prism detects rising structural stress (defect $0.43 \to 0.73$ over 90 days) while surface correlations remain low -- a signal invisible to correlation-based methods. In a historical backtest spanning five major stress events (2011--2020), the duality defect exhibits a consistent pattern: it reaches elevated levels \emph{before} the correlation spike that accompanies each crisis, and sustains high readings during periods of structural fragility that conventional metrics classify as calm. The duality defect is a first-principles structural admissibility condition, requiring no training data and computable in milliseconds.

Pulse-coupled oscillator models inspired by firefly synchronization are widely used to study decentralized time coordination in distributed systems. We analyze a discrete-time, discrete-phase firefly-inspired synchronization model and show that collective synchrony emerges only near a critical balance between the quorum threshold (fraction of pulsing neighbors required to trigger a phase update) and the pulse duration (how long agents remain detectable to others). Within this parameter region, the system exhibits bimodal performance: it either reaches near-perfect synchronization or becomes trapped in stable multi-cluster states, where symmetrically phase-offset subgroups mutually reinforce one another and prevent global synchrony. Our analysis shows that reducing connectivity or introducing noise suppresses these low-performance states by breaking such symmetric interactions, indicating that highly connected or noiseless systems are not necessarily optimal for collective synchronization.

Learning meaningful latent representations from nonlinear fMRI data remains a fundamental challenge in neuroimaging analysis. Traditional independent component analysis, widely used due to its ability to estimate interpretable functional brain networks, relies on a linear mixing assumption for latent sources, limiting its ability to capture the inherently nonlinear and complex organization of brain dynamics. More recently, deep representation learning methods have emerged as promising alternatives for modeling nonlinear latent structure. However, many of these approaches have been evaluated primarily on simulated datasets or natural image benchmarks, with comparatively limited validation on real-world neuroimaging data such as fMRI. In this work, we are motivated by the $β$-TCVAE (Total Correlation Variational Autoencoder), a refinement of the $β$-VAE framework for learning latent representations without introducing additional hyperparameters during training. We adapt and modify this model to fMRI data for nonlinear source disentanglement, aiming to separate mixed spatial and temporal brain signals into interpretable components. We show that the $β$-TCVAE framework can recover meaningful nonlinear spatial components with biological relevance, including well-established intrinsic connectivity networks such as the default mode network. Furthermore, we evaluate the learned representations using functional network connectivity, showing that the latent structure captures coherent and interpretable brain organization patterns. This study provides a pilot investigation that bridges nonlinear representation learning and fMRI analysis.

Training and evaluating false data injection attack (FDIA) detectors for power systems is constrained by data scarcity. Operational grid measurements are commercially sensitive, and hand-crafted attacks fail to capture complex distributional structures imposed by network physics. We present \textsc{GenAI-FDIA}, a framework benchmarking a pool of $P{=}20$ architectures for physics-compliant FDIA synthesis, spanning Wasserstein GANs, MMD-VAEs, normalising flows, diffusion models, and cross-family hybrids. These are evaluated across three IEEE testbeds (14-bus DC, 30-bus DC, and 14-bus AC) under a 60/20/20 chronological split using data-driven Bad Data Detection (BDD) threshold calibration. Our empirical results verify that these models generate high-fidelity attacks, with all architectures achieving evasion rates of $ε_{\text{BDD}} \ge 86.6\%$ on the 14-bus network; additionally, limiting an attacker's topological knowledge induces a measurable degradation in stealthiness ($p \le 0.0022$). Crucially, we identify a previously unreported failure mode: applying affine physics projections directly in normalised feature spaces critically displaces the attack vector, collapsing BDD evasion from ${\sim}55\%$ to $<\!2\%$ on the 30-bus testbed. We resolve this via a novel inference-time harmoniser, restoring full stealthiness ($ε_{\text{BDD}}{=}100\%$) across all physics-informed variants without retraining. Finally, we isolate a covariance-collapse phenomenon ($κ\approx {-}0.076$) within advanced hybrid architectures and rectify it through 50-epoch warm-up schedules ($κ\to 0.785$, $Δ\text{MMD}={-}3.1\%$). Ultimately, \textsc{GenAI-FDIA} delivers a robust recovery blueprint applicable to any physics-constrained generative model deployed for power-system security.

We present vega-mir, an open-source Python library that bundles nine information-theoretic and statistical metrics for the analysis of symbolic music corpora behind a small, tested, citable API, and demonstrates two of them at corpus scale in case studies not addressed by the upstream Cygnus paper. Of the nine metrics, three (Shannon entropy, Kullback-Leibler divergence, Zipfian fits) were deployed in the companion Cygnus arXiv preprint; two (network analysis on chord-transition graphs and spectral analysis of rubato curves) are deployed in full case studies here; the four remaining (multi-dimensional Gini, chi-squared stationarity, Higuchi fractal dimension, interval distribution) are validated against analytic anchors and exercised as sanity checks on a bundled 8-composer dataset. The two case studies yield two main observations. First, on the fourteen MAESTRO composers with N >= 10 pieces, the PageRank value of the gravity-centre node correlates with the marginal Kullback-Leibler distance at rho = 0.61 (Spearman, composer-level jackknife N = 14); the categorical gravity-centre identity takes five distinct values across the corpus but is not itself correlated with marginal KL (rho = 0.13, p = 0.21). Second, on the 247-piece Bach multi-master corpus (Schiff, Gould, Richter), Gould holds the highest periodicity ratio of the three performers, not the lowest, inverting the cliché that low scalar rubato reads as "metronomic": Gould's rubato is small in amplitude but structured in time, with a median dominant period of 66 beats against Schiff's 102 and Richter's 104.

Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend the conditional entropy of heat diffusion from static graphs to temporal networks and study its properties. We provide an upper bound and explain how discrepancies from it arise from the presence of asymmetric temporal paths. Moreover, we show that this quantity is monotone in time, yielding an information-theoretic analog of the second law of thermodynamics for inhomogeneous diffusion on temporal networks. We then introduce a local version of conditional entropy, designed to probe diffusion over finite temporal windows, and show that it provides an informative signal for change-point detection in continuous-time temporal networks. We evaluate the proposed methodology on synthetic benchmarks, including comparative experiments with existing nonparametric baselines in the snapshot setting, and then apply it to a real-world temporal contact network from a French primary school. Finally, we show how to use detected change points to perform community detection on targeted sub-intervals, improving the quality and interpretability of the clustering results.

Pixel-space diffusion models bypass the reconstruction bottleneck of Variational Autoencoders (VAEs) but face a fundamental "granularity dilemma": capturing global semantics favors large patch scales, while generating high-fidelity details demands fine-grained inputs. To address this issue, we propose HyperDiT, a unified framework establishing Hyper-Connected Cross-Scale Interactions to bridge the semantic and pixel manifold. Diverging from injecting semantics by AdaLN, HyperDiT utilizes Cross-Attention mechanisms, enabling fine-grained tokens to query multi-level semantic anchors globally. To resolve the spatial mismatch during multi-scale interactions, we introduce Scale-Aware Rotary Position Embedding (SA-RoPE) to ensure precise geometric alignment among tokens of varying patch sizes. Furthermore, we incorporate Registers to learn the dense semantics from a pretrained Visual Foundation Model (VFM), effectively reducing generation hallucination and artifacts. Extensive experiments demonstrate that HyperDiT achieves state-of-the-art (SoTA) FID of $\mathbf{1.56}$ on ImageNet $256\times256$ directly within the pixel space. By combining the fine-grained stream with semantic guidance, HyperDiT offers a superior paradigm for high-fidelity pixel generation.

Polarization in online communities is often studied through either language or interaction structure, but the two views are rarely connected in a unified measurement pipeline. Prior work links them by building interaction graphs from human judgments of agreement and disagreement, leaving a gap between language as observed text and structure as an engineered representation of that text. We address this gap with a language-grounded signed-network pipeline that derives continuous signed edge weights from LLM stance scores and quantifies structural polarization using two complementary measures: a spectral Eigen-Sign score and a partition-based frustration score. After normalization, the two measures show substantial agreement while retaining important differences in their sensitivity to edge magnitude. Applying the framework to Reddit Brexit discussions, we analyze how window-level discourse signals, including toxicity, extreme scalar claims, and perplexity, relate to temporal variation in structural polarization. Edge-level and ablation analyses show that continuous, confidence-weighted signed edges reveal intensity-sensitive patterns that are muted under sign-only representations. We further report an exploratory one-step-ahead forecasting analysis suggesting that lagged language signals may contain information about future polarization beyond structural persistence. Together, the results demonstrate how discourse and signed-network structure can be connected in a single framework for measuring and interpreting polarization dynamics over time.

Existing AI systems for modeling human behavior operate at the level of individuals or detect events after they occur. As a result, they systematically fail to capture the collective dynamics that determine whether a group remains stable or transitions into escalation or breakdown. We propose a different foundation: a group of interacting humans constitutes a complex dynamical system in the precise mathematical sense, exhibiting emergence, nonlinearity, feedback loops, sensitivity near critical points, and phase transitions between qualitatively distinct regimes. The state of such a system is not located within any single participant; it is distributed across mutual influence loops and observable through the micro-dynamics of the body. We introduce BEHAVE (Behavioral Engine for Human Activity Vector Estimation), a formal framework that models collective dynamics as continuous behavioral fields defined over an interaction space derived from observable physical signals. Kinematic micro-signals (position, velocity, body orientation, gestural activity) are structured into a directed interaction graph and aggregated into a basis of behavioral fields capturing distinct, non-redundant axes of collective state. The framework rests on one theorem and two structural propositions characterizing the tension field, the field basis, and the criticality index. Perception and forecasting layers are implemented using neural models, enabling data-driven learning and approximation of system dynamics. BEHAVE is formulated as a computational system for learning, representing, and forecasting collective dynamics from data. A working pipeline is demonstrated on a 7-agent negotiation snapshot. The same fields, recalibrated, apply to crowd safety, crisis-team dynamics, education, and clinical contexts.

RSNet is an open-source R package that provides a resampling-based framework for robust and interpretable network inference, designed to address the limited-sample-size challenges common in high-dimensional data. It supports both the estimation of partial correlation networks modeled as Gaussian networks and conditional Gaussian Bayesian networks for mixed data types that combine continuous and discrete variables. The framework incorporates multiple resampling strategies, including bootstrap, subsampling, and cluster-based approaches, to accommodate both independent and correlated observations. To enhance interpretability, RSNet integrates graphlet-based topology analysis that captures higher-order connectivity and edge sign information, enabling single-node and subnetwork-level insights. Notably, RSNet is the first R package to efficiently construct signed graphlet degree vector matrices (GDVMs) in near-constant time for sparse networks, providing scalable analysis of higher-order network structure. Collectively, RSNet offers a versatile tool for statistically reliable and interpretable network inference in high-dimensional data.

Local interaction laws governing multi-agent systems can be difficult to recover from trajectory data, even when the dynamics are observed faithfully. In systems governed by a nonlinear sheaf Laplacian -- a generalization of the graph Laplacian accommodating heterogeneous state spaces and asymmetric communication channels -- the coordination law is encoded by edge potential functions whose gradients produce the inter-agent forces. Because trajectory observations record node-state evolution, they expose only the aggregate effect of the edge forces at each node: distinct interaction laws that agree at the node level are indistinguishable from trajectory data alone. We show that the fundamental obstruction to recovery is topological, measured by sheaf cohomology, and that unique recovery from an unconstrained function class is possible if and only if this cohomology vanishes. When the obstruction is nontrivial, we show that recovery within a finite-dimensional parameterized class is possible precisely when a data-dependent information matrix is positive definite. Experiments validate the theory and illustrate that accurate trajectory reproduction need not certify recovery of the underlying interaction law.

In this paper, the effects of graph gluing operations in networks of multi-agent systems and their impact on system performance are investigated. In many practical applications, multiple multi-agent subsystems must be interconnected through communication links to accomplish complex tasks, resulting in a larger communication network. Such interconnections modify the underlying graph topology and consequently affect the consensus behavior and convergence rate of the network. In particular, this paper examines both bridge gluing and interface gluing and analyzes how the number and structure of communication links between subsystems influence the Fiedler eigenvalue of the resulting graph. Since the Fiedler eigenvalue is directly related to the convergence rate of consensus dynamics, the proposed analysis establishes a clear relationship between interconnection strategies, algebraic connectivity, and system performance. The results provide theoretical insight into how different gluing mechanisms alter the spectral properties of the graph Laplacian and, in turn, the convergence characteristics of the networked multi-agent system. Simulation studies are presented to illustrate the theoretical findings and to validate the effectiveness of the proposed framework.

Mode connectivity has been widely studied, yet the role of the optimizer remains underexplored. We revisit it through optimizer-induced implicit regularization, asking how connectivity behaves when restricted to solutions constrained by a given optimizer. For two-layer ReLU networks, we show that solutions from a single optimizer -- AdamW, Muon, or others in the Lion-$\mathcal{K}$ family -- form a connected set at sufficiently large width, a result not implied by prior work. We then characterize how optimizer-induced regions interact: at large width two different regions can be disjoint or overlap depending on regularization, while in our small-width example AdamW and Muon converge to disconnected zero-loss components separated by a provable loss barrier. Empirically, in GPT-2 pretraining, we observe same-optimizer paths preserve each model's spectrum while cross-optimizer paths traverse a smooth transition. Our results reveal optimizer-dependent structure beyond classical mode connectivity literature.

Link prediction (inferring missing or future connections between nodes in a graph) is a fundamental problem in network science with widespread applications in, e.g., biological systems, recommender systems, finance and cybersecurity. The ability to accurately predict links has significant real-world applications, such as detecting fraudulent financial transactions or identifying drug-target interactions in biomedicine. Despite a rich literature, link prediction is still challenging, especially for graphs enriched with information on edges (direction) and nodes (attributes). In fact, research on link prediction, especially the one based on Graph Deep Learning (GDL), has mostly focused on undirected graphs, without fully leveraging node attributes. Here, we fill this gap by proposing Gravity-GraphSAGE (GG-SAGE), a modified version of GraphSAGE, a GDL model for node embeddings, composed of a gravity-inspired decoder. This implementation is the first example in the literature of a GraphSAGE backbone adopted for directed link prediction. Using the benchmark datasets Cora, Citeseer, PubMed and 16 real-world graphs from the online Netzschleuder repository, we show that our proposed model outperforms state-of-the-art GDL link prediction techniques. Using further experimental evidence, we relate the quality of the output of our model with various characteristics of the graph, suggesting that our framework scales well when applied to data of increasing complexity.

Molecular optimization in drug discovery aims to discover molecules with improved target properties, but practical lead optimization often requires more than high predicted scores. A useful candidate should also be actionable: it should be reachable from known molecules through valid local structural transformations, so that it can be interpreted as a plausible revision within an evolving chemical series. Existing de novo and single-molecule optimization methods do not explicitly model such reachability, especially when both the target molecules and the intermediate molecules connecting them to known compounds are unknown. In this work, we formulate actionable molecular optimization as sequential expansion of a molecule-transfer graph, where nodes are molecules and edges encode valid local transformations. We propose MolWorld, a molecule world model-guided framework that treats the current molecule-transfer graph as an evolving search state. At each iteration, MolWorld selects local anchor contexts, generates candidate molecules conditioned on these contexts, evaluates their properties, and uses a learned world model to update the evolving molecule world by retaining admissible candidates and inserting them into the molecule-transfer graph. The expanded molecule world then guides subsequent optimization. Experiments on property optimization and docking-based tasks show that MolWorld discovers high-property molecules while maintaining substantially stronger structural connectivity, supporting actionable and sequential molecular design.

Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring these networks from event-based observations, which arise naturally in finance, seismology, and neuroscience. While there is substantial algorithmic work addressing this important problem, theoretical results are scarce. In this paper we ask the following fundamental question: what is the minimum time that one must observe the dynamics in order to exactly recover the underlying network, as a function of the number $d$ of interacting entities? For a class of stationary Hawkes processes with sparse, weak interactions, we prove that an observation time of order $\log d$ is sufficient and necessary. For the upper bound we construct a two-stage estimator that uses clipped and binned event data for screening, followed by a least-squares refinement, and apply concentration bounds derived from the Poisson cluster representation. For the lower bound we combine Fano's inequality with Jacod's Girsanov formula for point processes on a suitable subclass of networks.

Understanding how molecular alterations propagate across biological systems to drive disease remains a central challenge. Although high-throughput profiling enables comprehensive characterization of tumor states, most models neglect structured biological relationships or lack interpretability across scales. Here we present PPI-Net, a hierarchical graph neural network that integrates protein-protein interaction (PPI) networks with pathway-level representations to model disease from molecular interactions to functional processes. Patient-specific molecular profiles are embedded within a shared interaction network from STRING and propagated through a multi-layer Reactome hierarchy using graph attention, enabling aggregation of gene-level signals into higher-order biological programs. Across RNA-seq data from ten cancer types from The Cancer Genome Atlas, PPI-Net achieves robust predictive performance, with balanced accuracy exceeding 90% in multiple cohorts. Comparative analysis on RNA-Seq data from breast cancer demonstrated that PPI-Net's integration of the Reactome hierarchy improved balanced accuracy by 6.7% relative to a PPI-only model, while hierarchical multi-level supervision improved balanced accuracy by 12.3% relative to using only a single top-level prediction head. Applying a multi-omics approach using RNA-seq and methylation data improves model interpretation, recovering canonical oncogenic modules, including TP53-AKT signaling and stress response pathways, while revealing convergence onto coherent programs such as ion signaling and cellular responses to stimuli. These results demonstrate that integrating interaction networks with pathway hierarchies enables accurate prediction while providing mechanistic insight into cancer biology.

Neural network verification is an active and rapidly maturing research area, with a growing ecosystem of solvers and tools. The VNN-LIB standard was introduced to support interoperability in this ecosystem, but Version1.0 has several serious short-comings as a formal foundation: it lacks a precise syntax, semantics, and type system, offers limited expressivity, and relies on externally defined ONNX models whose semantics are informal and constantly evolving. The latter distinguishes VNN-LIB from established standards such as SMT-LIB, where queries are self-contained and have fixed semantics. In this paper we address these challenges by developing the theoretical foundations of VNN-LIB2.0. Our key contribution is the introduction of the notion of a \emph{network theory}, which abstractly characterises the minimal semantic interface required from a neural network model format. This abstraction enables VNN-LIB to be defined independently of any specific ONNX version while remaining compatible with evolving model representations. Building on this foundation, we present a formal syntax for a more expressive query language, a type system for it over the numeric domains provided by the network theory, and finally a formal semantics. To ensure internal consistency, the standard is mechanised in the Agda theorem prover. VNN-LIB~2.0 therefore provides robust and rigorous foundations for trustworthy neural network verification.

Graph pooling is commonly applied in graph classification, yet its empirical gains over standard WL-1 expressive GNNs are often marginal or inconsistent. We study this gap by analysing the interaction between node features and graph topology and their effect on pooling objectives. Our analysis reveals that pooling operators require node features that are well-aligned with the graph's topology -- a condition often overlooked and not guaranteed in empirical networks. We formalise fundamental requirements for node features to enable effective pooling, and introduce a quantitative measure of feature quality. Our empirical evaluation shows that, when these requirements are satisfied, pooling can be beneficial and improve performance on appropriate datasets.

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

Surgical team performance arises from complex interactions between technical execution and non-technical skills, including communication and coordination dynamics. However, current surgical AI systems predominantly model visual workflow signals, lacking structured representations of intraoperative team interactions over time. We propose a real-time actionable approach for modeling surgical team dynamics using time-expanded interaction graphs, where team members are modeled as time-indexed nodes and communication exchanges define directed edges. This spatio-temporal expansion enables dynamic interaction modeling, while allowing efficient inference with a static graph neural network. The model predicts procedural efficiency as the deviation from the expected duration and supports real-time deployment. Beyond prediction, we perform a counterfactual analysis to identify minimal changes in communication structure and interpretable behavioral variables associated with improved predicted outcomes. Experiments on recorded surgical procedures show that structured modeling of team interactions improves early identification of prolonged interventions and provides coherent, actionable explanations. This work advances surgical AI toward real-time, team-aware, and actionable decision support in the operating room.

Analyzing human vasculature and vessel-like, tubular structures, such as airways, is crucial for disease diagnosis and treatment. Current methods often rely on small sub-regions or simplified tree-like structures, rendering analysis of entire organ-level networks at clinical resolution computationally challenging. To this end, we propose VAEsselSparse, an efficient encoder-decoder model to obtain a meaningful yet compact representation of the entire organ-level vascular network at sub-millimeter resolution. VAEsselSparse leverages the inherent sparsity of 3D vascular structures via sparse convolutions and attention mechanisms, achieving substantial spatial compression rates of 8 x 8 x 8. We demonstrate superior reconstruction performance compared to dense counterparts and previous methods. Importantly, the resulting latent space retains clinically relevant discriminative features readily usable for classification tasks, such as aneurysm/stenosis or subvariants of the circle of Willis. Moreover, the compact latent space of VAEsselSparse serves as an effective representation for learning vessel-specific priors through generative models, enabling the synthesis of realistic vasculature.

We study networked binary classification on a directed acyclic graph (DAG) where each agent observes only a subset of the feature columns of a shared dataset. Agents act sequentially along the DAG: each receives prediction columns from its parents (if any), augments its local features with these columns, fits a logistic predictor by minimizing binary cross-entropy (BCE), and forwards its prediction column to its outgoing neighbors. We ask whether this sequential distributed training procedure achieves information aggregation, meaning that some agent attains small excess loss compared to the best logistic predictor trained with access to all feature columns. This question was studied for linear regression under squared loss by Kearns, Roth, and Ryu (SODA 2026). Extending their guarantees to classification is nontrivial because their analysis relies on quadratic structure that does not directly transfer to BCE with a logistic link. We analyze the resulting sequential logit-passing protocol and prove: (i) an excess loss upper bound of $O(M/\sqrt{D})$ on depth-$D$ paths under the condition that every $M$ contiguous subsequence of $M$ agents collectively observe all features, and (ii) a close lower bound showing instances with excess loss of at least $Ω(k/D)$ where $k$ is the dimension of the feature space. Together, these results identify network depth as a fundamental bottleneck for information aggregation in networked logistic regression.

Mixture-of-experts (MoE) architectures have turned LLM serving into a cluster-scale workload in which communication consumes a considerable portion of LLM serving runtime. This has prompted industry to invest heavily in expensive high-bandwidth scale-up networks. We question whether such costly infrastructure is strictly necessary. We present the first systematic cross-layer analysis of network cost-effectiveness for MoE LLM serving, comparing four representative XPU (e.g., GPU/TPU) topologies (scale-up, scale-out, 3D torus, and 3D full-mesh). We find that lower-cost switchless topologies are more cost-effective than the scale-up topology across all serving scenarios explored, improving cost-effectiveness by 20.6-56.2%. In particular, the 3D full-mesh topology is Pareto-optimal in terms of the performance-cost tradeoff. We also find that current scale-up link bandwidths are over-provisioned: reducing the link bandwidth improves throughput per cost by up to 27%. A forward-looking analysis of upcoming GPU generations indicates that the cost-performance advantage of switchless networks will likely persist.

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result, numerous hyperbolic graph representation learning methods have been proposed in recent years. However, their practical adoption and systematic comparison remain challenging, as implementations are fragmented and shared tools for reproducible and fair evaluation are lacking. In this work, we introduce a unified open-source framework for hyperbolic graph representation learning that integrates several widely used embedding methods under a common optimization interface. The novel framework enables consistent training, visualization, and evaluation of hyperbolic embeddings, and interfaces seamlessly with standard network analysis tools. Leveraging this unified setup, we conduct an experimental study of hyperbolic embedding methods on real-world networks, focusing on two canonical downstream tasks: link prediction and node classification. Beyond predictive accuracy, the study offers practical insights into the strengths and limitations of existing approaches, thereby facilitating informed method selection and fostering reproducible research in hyperbolic graph representation learning.

Classical continuous-space neural networks fundamentally struggle to lock into exact mathematical symmetries, such as modular arithmetic and non-commutative algebra. To approximate these discrete logical rules, they often rely on massive parameter scaling, resulting in stochastic instability even after delayed generalization phenomena known as grokking. Here, we introduce the Universal Quantum Transformer (UQT), a fundamentally novel, quantum-native computing architecture that uses the physical properties of multi-qubit systems as a universal inductive bias for exact mathematical and algebraic reasoning. Rather than translating classical neural mechanisms, our framework relies entirely on parameterized geometric phase embedding and $SU(2)$ wave-interference. We demonstrate that the quantum attention circuit, operating on a highly compact 5-qubit substrate, perfectly learns two highly distinct formal classes: cyclic modular arithmetic ($\mathbb{Z}_{11}$) and non-Abelian algebra (the $S_4$ permutation group). While classical attention-based networks exhibit stochastic instability at convergence, the UQT achieves mathematically exact, deterministic generalization. We refer to this phenomenon as crystallization: a step beyond the well-known phenomenon of grokking. Crucially, this framework yields massive computational and memory advantages by theoretically bypassing the quadratic bottleneck of classical self-attention, and by logarithmically compressing the required representation dimension to eliminate the massive over-parameterization inherent to classical networks. Finally, we deploy this architecture on noisy intermediate-scale quantum (NISQ) hardware, proving its viability on current IBM Quantum computers. These results establish parameterized quantum topology as a universally superior physical substrate for exact artificial intelligence.

Prior work on node classification has shown that Graph Neural Networks (GNNs) can learn representations that transfer across graphs, when underlying graph properties are shared. For a fixed graph, one would then expect GNNs trained for link prediction to learn a representation consistent with that learnt for node classification. We show this intuition does not hold in the general case. Instead, we find popular link prediction models can learn a trivial mini-batch dependent heuristic, enabled by batch-normalisation layers, to solve the edge classification task. When correcting for this, we observe increased alignment of the network representation with node-class relevant features, suggesting the network has learnt a graph representation that better aligns with the underlying graph's properties. Our findings suggest that standard link prediction training may be leading us to overestimate link predictors' ability to learn a generalised representation of a graph that is consistent across tasks.

As Generative AI (GenAI) becomes integral to education, fostering GenAI literacy is critical. However, current assessments largely rely on self-reported scales, lacking insights into how literacy manifests in actual learning processes. This study leverages Learning Analytics (LA) to bridge this gap. We collected interaction logs from 162 university students engaged in a GenAI-assisted abstract writing task. Using Epistemic Network Analysis (ENA), we modeled and compared the questioning strategies of students with varying GenAI literacy levels. Preliminary results reveal distinct interaction signatures: high-literacy students engage in iterative refinement and strategic questioning, while low-literacy students rely on direct generation commands. This work contributes to the workshop by demonstrating how process data can characterize GenAI literacy, paving the way for data-driven literacy assessment and real-time interventions.

In multi-agent reinforcement learning (MARL), the integration of a communication mechanism, allowing agents to better learn to coordinate their actions and converge on their objectives by sharing information. Based on an interaction graph, a subclass of methods employs graph neural networks (GNNs) to learn the communication, enabling agents to improve their internal representations by enriching them with information exchanged. With growing research, we note a lack of explicit structure and framework to distinguish and classify MARL approaches with communication based on GNNs. Thus, this paper surveys recent works in this field. We propose a generalized GNN-based communication process with the goal of making the underlying concepts behind the methods more obvious and accessible.

Accurate modeling of human mobility is critical for tackling urban planning and public health challenges. In undeveloped regions, the absence of comprehensive travel surveys necessitates reconstructing mobility networks from publicly available data. Here we develop neuroGravity, a physics-informed deep learning model that reliably reconstructs mobility flows from limited observations and transfers to unobserved cities. Using only urban facility and population distributions, we find that neuroGravity's regional representations strongly correlate with socioeconomic and livability status, offering scalable proxies for costly surveys. Furthermore, we uncover that spatial income segregation plays a key role in model transferability: mobility networks are most reliably reconstructed when target cities share similar segregation levels with the source. We design an index to quantify this segregation and accurately predict transferability. Finally, we generate mobility flow proxies for over 1,200 cities worldwide, highlighting neuroGravity's potential to mitigate critical data shortages in resource-limited, underdeveloped areas.

This paper aims to synthesize current knowledge on generative AI in IT project management using the PRISMA methodology to provide researchers with a comprehensive perspective on techniques, applications, adoption trends, limitations, and integration across project management tools and process groups. The analysis reveals a clear dominance of OpenAI's GPT in the included studies but relying primarily on prompt engineering, suggesting that research in this area remains at an exploratory stage. Finally, it identifies and discusses three promising research directions for AI-enabled project management, including process group-specific AI agents, project role-based AI agents, and hybrid collaborative networks that enable human-guided orchestration.

Identifying critical nodes in complex networks is a fundamental task in graph mining. Yet, methods addressing an all-or-nothing coverage mechanics in a bipartite dependency network, a graph with two types of nodes where edges represent dependency relationships across the two groups only, remain largely unexplored. We formalize the CriticalSet problem: given an arbitrary bipartite graph modeling dependencies of items on contributors, identify the set of k contributors whose removal isolates the largest number of items. We prove that this problem is NP-hard and requires maximizing a supermodular set function, for which standard forward greedy algorithms provide no approximation guarantees. Consequently, we model CriticalSet as a coalitional game, deriving a closed-form centrality, ShapleyCov, based on the Shapley value. This measure can be interpreted as the expected number of items isolated by a contributor's departure. Leveraging these insights, we propose MinCov, a linear-time iterative peeling algorithm that explicitly accounts for connection redundancy, prioritizing contributors who uniquely support many items. Extensive experiments on synthetic and large-scale real datasets, including a Wikipedia graph with over 250 million edges, reveal that MinCov and ShapleyCov significantly outperform traditional baselines. Notably, MinCov achieves near-optimal performance, within 0.02 AUC of a Stochastic Hill Climbing metaheuristic, while remaining several orders of magnitude faster.

The Composed Image Retrieval (CIR) task provides a flexible retrieval paradigm via a reference image and modification text, but it heavily relies on expensive and error-prone triplet annotations. This paper systematically investigates the Noisy Triplet Correspondence (NTC) problem introduced by annotations. We find that NTC noise, particularly hard noise'' (i.e., the reference and target images are highly similar but the modification text is incorrect), poses a unique challenge to existing Noise Correspondence Learning (NCL) methods because it breaks the traditional small loss hypothesis''. We identify and elucidate three key, yet overlooked, challenges in the NTC task, namely (C1) Modality Suppression, (C2) Negative Anchor Deficiency, and (C3) Unlearning Backlash. To address these challenges, we propose a Cone-based robuSt noisE-unlearning comPositional network (ConeSep). Specifically, we first propose Geometric Fidelity Quantization, theoretically establishing and practically estimating a noise boundary to precisely locate noisy correspondence. Next, we introduce Negative Boundary Learning, which learns a ``diagonal negative combination'' for each query as its explicit semantic opposite-anchor in the embedding space. Finally, we design Boundary-based Targeted Unlearning, which models the noisy correction process as an optimal transport problem, elegantly avoiding Unlearning Backlash. Extensive experiments on benchmark datasets (FashionIQ and CIRR) demonstrate that ConeSep significantly outperforms current state-of-the-art methods, which fully demonstrates the effectiveness and robustness of our method.

Federated learning (FL) is a key paradigm for distributed model learning across decentralized data sources. Communication in each FL round typically consists of two phases: (i) distributing the global model from a server to clients, and (ii) collecting updated local models from clients to the server for aggregation. This paper focuses on a type of FL where communication between a client and the server is relay-based over dynamic networks, making routing optimization essential. A typical scenario is in-orbit FL, where satellites act as clients and communicate with a server (which can be a satellite, ground station, or aerial platform) via multi-hop inter-satellite links. This paper presents a comprehensive tractability analysis of routing optimization for in-orbit FL under different settings. For global model distribution, these include the number of models, the objective function, and routing schemes (unicast versus multicast, and splittable versus unsplittable flow). For local model collection, the settings consider the number of models, client selection, and flow splittability. For each case, we rigorously prove whether the global optimum is obtainable in polynomial time or the problem is NP-hard. Together, our analysis draws clear boundaries between tractable and intractable regimes for a broad spectrum of routing problems for in-orbit FL. For tractable cases, the derived efficient algorithms are directly applicable in practice. For intractable cases, we provide fundamental insights into their inherent complexity. These contributions fill a critical yet unexplored research gap, laying a foundation for principled routing design, evaluation, and deployment in satellite-based FL or similar distributed learning systems.

Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used in ecology research. Such networks are often sparse and inherently imperfect in their detection. Existing models mainly focus on interaction recovery, while the induced similarity graphs are much less studied. Moreover, sparsity is often not controlled, and scale is unbalanced, leading to oversparse or poorly rescaled estimates with degrading structural recovery. To address these issues, we propose a framework for structured sparse nonnegative low-rank factorization with detection probability estimation. We impose nonconvex $\ell_{1/2}$ regularization on the latent similarity and connectivity structures to promote sparsity within-group similarity and cross-group connectivity with better relative scale. The resulting optimization problem is nonconvex and nonsmooth. To solve it, we develop an ADMM-based algorithm with adaptive penalization and scale-aware initialization and establish its asymptotic feasibility and KKT stationarity of cluster points under mild regularity conditions. Experiments on synthetic and real-world ecological datasets demonstrate improved recovery of latent factors and similarity/connectivity structure relative to existing baselines.

Influence maximization (IM) is a fundamental problem in complex network analysis, with a wide range of real-world applications. To date, existing approaches to influential node identification in IM have predominantly relied on standard graphs, failing to capture higher-order intrinsic interactions embedded in many real-world systems. Hypergraphs can be employed to better capture higher-order interactions. However, using hypergraphs may lead to an excessively large search space and increased complexity in modeling cascading dynamics, making it challenging to accurately identify influential nodes. Therefore, in this study, we propose a new hypergraph-modeled IM method, based on the Discrete Particle Swarm Optimization algorithm and the threshold model. In the proposed method, a particle (i.e., a candidate solution) represents the selection information of seed nodes, and the fitness function is designed to accurately and efficiently evaluate the influence of seed nodes via a two-layer local influence approximation. We also propose a degree-based initialization strategy to improve the quality of initial solutions and develop rules for updating particles' velocity and position, incorporated with a local search to drive particles toward better solutions. Experimental results demonstrate that the proposed method outperforms baseline methods on both synthetic and real-world hypergraphs. In addition, ablation studies validate the effectiveness of both the local search and the initialization strategies.

Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs and thus struggle to capture temporal dependencies. Snapshot-based techniques partially address this issue but often encounter data sparsity and class imbalance, particularly in networks with transient interactions such as telecommunication call detail records (CDRs). Temporal Graph Networks (TGNs) model dynamic graphs by updating node embeddings over time; however, their predictive accuracy under sparse conditions remains limited. In this study, we improve the TGN framework by extracting enclosing subgraphs around candidate links, enabling the model to jointly learn structural and temporal information. Experiments on a sparse CDR, email, message dataset show that our approach increases average precision by at least 2% over standard TGNs, demonstrating the advantages of integrating local topology for robust link prediction in dynamic networks.

Grounded Laplacians provide the spectral link between external information and network convergence. This paper establishes positive-stability results for grounded Laplacians in directed signed matrix-weighted networks, where directionality, antagonism, and singular edge weight matrices coexist. First, under in-degree dominance and positive-negative reachability, we derive explicit local thresholds for the grounding gains. Second, a scaled, kernel-based certificate replaces the unscaled degree condition with a signed matrix-weighted Dirichlet decomposition and a joint-kernel test for the scaled symmetric part. The computable margin $γ_p$ lower-bounds the minimum real part of the spectrum and certifies exponential contraction in the $P$-norm. Under absolute generalized balance, the kernel-intersection test is given; the balanced and definite-edge unbalanced undirected cases follow. As an application, non-trivial consensus (NTC) on signed matrix-weighted networks is studied. Informed agents, external signals and coupling terms are designed to steer all agents to any prescribed nonzero state without requiring structural balance. Switching topology case retains non-trivial consensus result under certain conditions. Realizing NTC on signed matrix-weighted networks demonstrates that groups with both cooperative and antagonistic multi-dimensional interactions can achieve consensus, which was previously deemed exclusive to fully cooperative groups.

Time series data are essential for a wide range of applications, yet access to high-quality datasets is often constrained by privacy concerns, acquisition costs, and labelling challenges. Synthetic time series generation has emerged as a promising approach to address these limitations. In this work, we investigate the use of complex network mappings for synthetic time series generation, focusing on the Quantile Graph (QG) representation and its inverse. While the inverse QG mapping has been previously proposed, its potential as a general-purpose data generator has not been systematically evaluated. We address this gap through a comprehensive empirical study assessing both the fidelity and utility of synthetic time series generated by the Inverse Quantile Graph (InvQG) framework. The evaluation combines statistical feature analysis, network-based topological characteristics, and performance in downstream clustering and classification tasks, using simulated and real-world datasets. The results show that InvQG effectively preserves marginal distributions and short-term temporal dependencies across a wide range of models, while exhibiting predictable limitations in capturing long-range or higher-order dynamics.

Reaching consensus on massive discussion networks is critical for reducing noise and achieving optimal collective outcomes. However, the natural tendency of humans to preserve their initial ideas constrains the emergence of global solutions. To address this, Collective Intelligence (CI) platforms facilitate the discovery of globally superior solutions. We introduce a dynamical system based on the standard $O(N)$ model to drive the aggregation of semantically similar ideas. The system consists of users represented as nodes in a $d=2$ lattice with nearest-neighbor interactions, where their ideas are represented by semantic vectors computed with a pretrained embedding model. We analyze the system's equilibrium states as a function of the coupling parameter $β$. Our results show that $β> 0$ drives the system toward a ferromagnetic-like phase (global consensus), while $β< 0$ induces an antiferromagnetic-like state (maximum dissent), where users maximize semantic distance from their neighbors. This framework offers a controllable method for managing the tradeoff between cohesion and diversity in CI platforms.

Jet identification plays a central role in analyzing data from high-energy collider experiments. While deep learning has improved jet classification, it often lacks interpretability. We introduce the Kinematic Interaction Graph Network (KIGNet), a graph neural network that integrates kinematic variables into jet classification by constructing four graph representations per jet, each weighted by a distinct variable: angular separation ($Δ$), relative transverse momentum ($k_T$), momentum fraction ($z$), and invariant mass squared ($m^2$). Three of these ($Δ$, $k_T$, $z$) are motivated by the Lund jet plane, grounded in perturbative QCD factorization; the fourth ($m^2$) adds complementary mass-scale sensitivity for heavy-flavor identification. Using Gradient-weighted Class Activation Mapping (Grad-CAM), we determine which variables dominate classification. Angular separation and relative transverse momentum account for about 76% of the total Grad-CAM attribution (40.72% and 35.67%), with momentum fraction and invariant mass contributing the remaining 24%. This hierarchy is consistent with the soft-collinear structure of QCD radiation in the training data, showing that the network learns physically interpretable representations rather than spurious correlations. On the JetClass dataset, KIGNet achieves a macro-accuracy of 95.07%, macro-AUC of 96.61%, and macro-AUPR of 81.52%, relative improvements of 2.45%, 3.40%, and 19.11% over the state-of-the-art baseline. On the Aspen Open Jets dataset of real CMS collision data, KIGNet produces substantially more structured latent representations than the baseline, reducing the Davies-Bouldin Index by 52.15% ($0.8395 \rightarrow 0.4017$) and increasing the Dunn Index by 42.33% ($0.0189 \rightarrow 0.0269$), confirming that physics-informed kinematic encoding generalizes beyond idealized simulation to experimental detector conditions.

Whether artificial neural networks organize information comparably to the human brain remains unclear. Prior brain--AI alignment studies are constrained by specific inputs and tasks, limiting cross-modal comparison. Here we introduce a brain--model topological alignment space, mapping Transformer attention topology onto human intrinsic connectivity networks (ICNs) to enable task-free, modality-agnostic comparison. Analyzing 151 Transformer-based models with 62,480 attention head graphs, we observe a continuous arc-shaped distribution reflecting varying alignment. Models optimized for global semantics aligned with higher-order ICNs, while local-detail models aligned with sensory ICNs. Non-intuitive findings include reduced alignment in DINOv2 compared to its predecessors and a counterintuitive scaling inversion in distilled DeiT models, while fine-tuning and instruction tuning had limited effect. Alignment scores showed no significant correlation with ImageNet accuracy (r = 0.266, p = 0.156). This work offers a quantitative framework for comparing the organizational principles of artificial and biological systems.

This paper establishes analytical stability boundaries for robot-mediated human-human (dyadic) interaction systems, subject to haptic communication under network-induced time delays. Bypassing conservative approximations, we employ a frequency-domain zero-crossing methodology to extract explicit stability limits based on the robotic hardware dynamics and coupling stiffness. To demonstrate the scalability of this mathematical framework, we extend the analysis from an elastic coupling to a highly complex, asymmetric virtual proxy topology. The theoretical analysis reveals how interaction stiffness non-linearly constrains the system's stability margin, heightening its vulnerability to delay. Furthermore, we validate these theoretical boundaries through experimental trials, highlighting the correlation between analytical stability margins and empirical motor performance. The proposed framework provides rigorous design guidelines for stable remote dyadic systems and suggests the prerequisites for effective delay-compensation strategies.

Medium Access Control (MAC) protocols, essential for wireless networks, are typically manually configured. While deep reinforcement learning (DRL)-based protocols enhance task-specified network performance, they suffer from poor generalizability and resilience, demanding costly retraining to adapt to dynamic environments. To overcome this limitation, we introduce a game-theoretic LLM-empowered multi-agent DRL (MARL) framework, in which the uplink transmission between a base station and a varying number of user equipments is modeled as a dynamic multi-follower Stackelberg game (MFSG), capturing the network's natural hierarchical structure. Within this game, LLM-driven agents, coordinated through proximal policy optimization (PPO), synthesize adaptive, semantic MAC protocols in response to network dynamics. Protocol action grammar (PAG) is employed to ensure the reliability and efficiency of this process. Under this system, we further analyze the existence and convergence behavior in terms of a Stackelberg equilibrium by studying the learning dynamics of LLM-empowered unified policies in response to changing followers. Simulations corroborate that our framework achieves a 77.6% greater throughput and a 65.2% fairness improvement over conventional baselines. Besides, our framework generalizes excellently to a fluctuating number of users without requiring retraining or architectural changes.

Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their explanatory capacity to descriptive observations. Inspired by the successful integration of geometric insights in network science, we propose leveraging discrete geometry to examine the dynamic reconfigurations in neural interactions during social exchanges. Unlike conventional synchrony approaches, our method interprets inter-brain connectivity changes through the evolving geometric structures of neural networks. This geometric framework is realized through a pipeline that identifies critical transitions in network connectivity using entropy metrics derived from curvature distributions. By doing so, we significantly enhance the capacity of hyperscanning methodologies to uncover underlying neural mechanisms in interactive social behavior.

A fundamental challenge in microbial ecology is determining whether bacteria compete or cooperate in different environmental conditions. With recent advances in genome-scale metabolic models, we are now capable of simulating interactions between thousands of pairs of bacteria in thousands of different environmental settings at a scale infeasible experimentally. These approaches can generate tremendous amounts of data that can be exploited by state-of-the-art machine learning algorithms to uncover the mechanisms driving interactions. Here, we present Friend or Foe, a compendium of 64 tabular environmental datasets, consisting of more than 26M shared environments for more than 10K pairs of bacteria sampled from two of the largest collections of metabolic models. The Friend or Foe datasets are curated for a wide range of machine learning tasks -- supervised, unsupervised, and generative -- to address specific questions underlying bacterial interactions. We benchmarked a selection of the most recent models for each of these tasks and our results indicate that machine learning can be successful in this application to microbial ecology. Going beyond, analyses of the Friend or Foe compendium can shed light on the predictability of bacterial interactions and highlight novel research directions into how bacteria infer and navigate their relationships.

How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus, which is when the colors of all agents align. Agents attempt to do this locally through steps in which an agent changes their color to the color of the majority of their neighbors. In real life, agents may not know exactly how many of their neighbors are red or blue, which introduces uncertainty into this process. Modeling uncertainty as perturbations of relative magnitude $1+\varepsilon$ to these color neighbor counts, we show that even small values of $\varepsilon$ greatly hinder the ability to achieve consensus in a social network. We prove theoretically tight upper and lower bounds on the price of uncertainty, a metric defined in previous work by Balcan et al. to quantify the effect of uncertainty in network games.

We study neural architectures in which each hidden layer is defined by the stationary state of a dissipative Schrödinger-type dynamics on a learned latent graph. On stable branches, the local stationary problem defines a differentiable implicit graph layer. To learn the graph itself, we optimize over the stratified moduli space of weighted graphs and equip each stratum with a non-degenerate Kähler-Hessian metric that keeps natural-gradient descent and face crossing well posed. We then show that a multilayer stationary network is equivalent to an exact global stationary problem on a supra-graph, and that it admits a penalized global relaxation whose stationary states converge to the exact one as the penalty parameter tends to infinity. Reverse-mode differentiation is recovered as the adjoint of the exact global system, and the penalized adjoint converges to it in the same limit. Finally, under finite-dimensional strong-monotonicity and admissible-lift assumptions, the corresponding represented hypothesis classes coincide among resolvent feed-forward networks, graph-stationary networks, supra-graph stationary systems, and sheaf-based architectures with unitary connection. The resulting structural identifications yield complexity bounds controlled by sparse graph or supra-graph geometry rather than dense ambient connectivity.

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph structure of neural networks and their predictive performance, they often limit themselves to a narrow range of model networks, particularly lacking mesoscale structures such as communities. Our work advances this area by conducting a more comprehensive investigation, incorporating realistic network structures characterized by heterogeneous degree distributions and community structures, which are typical characteristics of many real networks. These community structures offer a nuanced perspective on network architecture. Our analysis employs model networks such as random and scale-free networks, alongside a comparison with a biological neural network and its subsets for more detailed analysis. We examine the impact of these structural attributes on the performance of image classification tasks. Our findings reveal that structural properties do affect performance to some extent. Specifically, within moderate-depth architectures, networks featuring coherent, densely interconnected communities demonstrate enhanced learning capabilities. Crucially, we find that this advantage is strictly depth-dependent: extending the architecture to eight layers reverses the effect entirely. This comparison with the biological neural network emphasizes the relevance of our findings to real-world structures, suggesting an intriguing connection worth further exploration. This study contributes meaningfully to network science and machine learning, providing insights that could inspire the design of more biologically informed neural networks.

Time series segmentation assigns a label to each part of a sequence. We formulate dense univariate segmentation as node classification on a graph whose nodes are the original time points. A local window provides node features without setting output granularity. We evaluate the approach on a TSSB-derived inductive benchmark built from disjoint UCR training and test instances. Under one fixed Graph Attention Network (GAT), visibility-based transformations achieve the highest mean ranks among eleven graph constructions. WDPVG, directed NVG, and weighted NVG form a statistically indistinguishable top group after Holm correction. On the 59-dataset Time Series Segmentation Benchmark, WDPVG+GAT reaches a weighted F1 of $0.916$, below seq2point at $0.951$ and statistically indistinguishable from same-feature MLP, random-forest, and 1-NN controls, because at this downsampled resolution each segment is short and the fixed $81$-sample window already spans most of it. At native resolution, where each segment is longer than that window, WDPVG+GAT is less sensitive to feature-window width and remains above the same-feature MLP at every tested window. The graph's advantage over these point-wise classifiers comes from context beyond the local window, which the visibility graph's long-range edges can supply, rather than from better features within it. In a separate resolution sweep, it is statistically tied with a window-searched seq2point while using about $70\times$ fewer parameters and $46\times$ less measured peak memory, although seq2point moves ahead after downsampling. This identifies a practical operating regime for finely sampled series when model size and repeated window tuning matter.

Traffic Engineering (TE) in large-scale networks like cloud Wide Area Networks (WANs) and Low Earth Orbit (LEO) satellite constellations is a critical challenge. Although learning-based approaches have been proposed to address the scalability of traditional TE algorithms, their practical application is often hindered by a lack of generalization, high training overhead, and a failure to respect link capacities. This paper proposes TELGEN, a novel TE algorithm that learns to solve TE problems efficiently in large-scale network scenarios, while achieving superior generalizability across diverse network conditions. TELGEN is based on the novel idea of transforming the problem of "predicting the optimal TE solution" into "predicting the optimal TE algorithm", which enables TELGEN to learn and efficiently approximate the end-to-end solving process of classical optimal TE algorithms. The learned algorithm is agnostic to the exact underlying network topology or traffic patterns, and is able to very efficiently solve TE problems given arbitrary inputs and generalize well to unseen topologies and demands. We train and evaluate TELGEN with random and real-world topologies, with networks of up to 5000 nodes and 3.6x10^6 links in testing. TELGEN shows less than 3% optimality gap while ensuring feasibility in all testing scenarios, even when the test network has 2-20x more nodes than the largest training network. It also saves up to 84% TE solving time than traditional interior-point method, and reduces up to 79.6% training time per epoch than the state-of-the-art learning-based algorithm.

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding network interdependencies is crucial to anticipate cascading failures and plan for disruptions. However, data on the topology of individual networks are often publicly unavailable due to privacy and security concerns. Additionally, interdependent links are often only revealed in the aftermath of a disruption as a result of cascading failures. We propose a scalable nonparametric Bayesian approach to reconstruct the topology of interdependent infrastructure networks from observations of cascading failures. Metropolis-Hastings algorithm coupled with the infrastructure-dependent proposal are employed to increase the efficiency of sampling possible graphs. Results of reconstructing a synthetic system of interdependent infrastructure networks demonstrate that the proposed approach outperforms existing methods in both accuracy and computational time. We further apply this approach to reconstruct the topology of one synthetic and two real-world systems of interdependent infrastructure networks, including gas-power-water networks in Shelby County, TN, USA, and an interdependent system of power-water networks in Italy, to demonstrate the general applicability of the approach.