Complex Networks

In this paper, we study the detection of an echo chamber in a social network, i.e., the identification of a set of nodes that agree on a topic, while disagreeing with the rest of nodes. We argue that this problem is different from other social network analysis problems such as community detection, and from other graph problems such as maximum graph cut and maximum clique. To the best of our knowledge, we are the first to formalize the objective function of echo chamber detection, by using the theory of Fourier transforms of set functions (Stobbe and Krause, 2012). We propose scalable semidefinite relaxation, solved via an interior point method and sparse linear algebra. Experimentally, our algorithm recovers the ground truth echo chamber better than competing methods on small synthetic experiments. Our algorithm produces echo chambers with better network properties than competing methods on large real-world datasets. To independently validate our proposed objective function, we show that our algorithm finds echo chambers with more agreements with suspended users than competing methods on a small real-world dataset.

In networked dynamical systems, the parameter of primary mechanistic interest is signed interaction structure. Recovering this structure from perturbation time-series data is a fundamental identification problem, compounded by three coupled obstacles: the combinatorial complexity of interaction architectures, ambiguity of causal attribution under limited interventions, and state-dependent dynamics that confound structural inference. Each obstacle is structural in origin and calls for a structural solution. We address these challenges by adopting a reductionist approach, introducing Fundamental Dynamical Units (FDUs): signed three-node interaction patterns as composable primitives that convert the interaction hypothesis space into a finite, constructive, and tractable representation. We show that local interaction structure determines the perturbation conditions required to disentangle direct from relayed influence, making intervention design a structural consequence of the FDU representation. We embed FDU-regularized structural inference within a physics-informed neural ordinary differential equation (ODE) whose governing-equation constraint transforms structural hypotheses into verifiable dynamical predictions, enabling joint recovery of interaction structure and perturbation-resolved trajectories. Validated on synthetic benchmarks with known ground truth, the framework supports structural commitment, expressed through FDU primitives, motif-prescribed intervention design, and physics-informed learning, as a principled basis for mechanistically interpretable inference in networked dynamical systems.

We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.

Graph Neural Networks (GNNs) are powerful models for handling attributed graphs in tasks such as classification, link prediction, and community detection, as they enable the aggregation of information from both structural and semantic sources. However, progress in community detection is hindered by the lack of high-quality datasets, since ground-truth community labels are often unavailable and most algorithms proposed in recent literature rely on the same benchmark datasets for model training and evaluation. To address this issue, attributed random graph generators are commonly employed to create synthetic graphs for assessing the strengths and limitations of GNN-based models. Nevertheless, most existing generators rely heavily on power-law degree distributions, despite recent evidence indicating that scale-free networks are rare, particularly in social network contexts. Moreover, state-of-the-art attributed graph generators provide limited flexibility, as they do not allow users to construct communities with varying densities, degree distributions, and sub-community structures. To overcome these limitations, we introduce the Synthetic Community-Aware Attributed Graph Generator (SynCo), a graph generation algorithm that allows users to control the node degree distribution and sub-community structure. We evaluate SynCo across three different tasks: graph mimicking, hyperparameter evaluation, and node clustering tuning. The results show that our model outperforms state-of-the-art approaches in synthetic graph generation and data augmentation, while preserving the original distributions of duplicated and augmented datasets, as confirmed by statistical tests well know in literature. We also demonstrate the ability of SynCo to generate nodes in large scale, up to 2.1 million nodes.

Large language models (LLMs) are rapidly emerging as a new paradigm for modeling social networks by representing users and their relationships and interactions through natural language. Unlike classical network models or deep learning approaches, LLMs can simulate context-aware social behavior and language-driven interactions, enabling more realistic modeling of network formation and dynamic social processes. However, existing studies are scattered across different research communities and lack a unified perspective. This survey presents the first comprehensive review of LLMs for social network modeling by organizing the literature into two broad categories: network generative models and dynamic process models. Network generative models are further classified into selection-based and interaction-based approaches, while dynamic process models are categorized into opinion dynamics, information diffusion, and rumor propagation, each with their underlying modeling mechanisms. LLMs enable rich textual social interactions and decision-making, but they also exhibit many limitations, including inherent social biases and prompt sensitivity. We outline these open research challenges and discuss future directions in LLM-based social network modeling.

Networks describe systems in biology and beyond, from protein interactions and social relationships to power grids and citation records. Reasoning about such systems requires understanding their structure: which elements are central, which connections bridge separate communities, and how it changes when elements are removed. Although large language models (LLMs) excel at natural language, they struggle with such questions when networks are given as edge lists, sentences or measurement tables, because their structural meaning must be inferred. Here we introduce BioGlyph, which compiles network topology into an interpretable and transferable language of structural roles. BioGlyph combines graph partitioning and structural measurements to identify roles such as hubs, community cores and cross-community connectors, and fixed rules to translate them into a universal vocabulary. The representation describes each element through its structural role, supporting evidence and semantic consequences, leaving both the network and the LLM unchanged. Across twenty networks spanning five domains, BioGlyph substantially improves open LLMs' ability to answer structural reasoning questions, outperforming edge-based, numerical and learned representations by up to 26 percentage points in system accuracy. Ablations show that the gain comes from explicitly encoding structural roles in semantically interpretable terms. The gain is more prominent in dense, community-structured networks and diminishes in sparse networks whose topology is more readily inferred from text. In a budding-yeast protein-interaction network, BioGlyph exposes biological organization: cross-community connectors are enriched for essential genes, whereas peripheral proteins are depleted. BioGlyph thus provides an interpretable representation for both language models and scientists to reason about network structure.

We use tools from nonlinear algebra to study the equilibria of small linear translational spring networks. Specifically we use the techniques of homotopy continuation, monodromy, and parameter homotopy (a.k.a. cheater homotopy) to solve all rigid linear translational spring networks up to $5$ nodes in both $2$ and $3$ dimensions. We describe a method of implementing parameter homotopy that arises naturally from the physical structure of the system. We give precise total degree bounds on the maximum number of solutions for general planar spring networks. We discuss further efficiency gains obtained from polyhedral homotopy methods. We compare the computation efficiency of these techniques against a baseline of Newton's method.

Traditional network models from network science, such as the Erdos-Renyi and configuration models, generate random networks that reproduce few selected topological properties observed in real-world networks. Deep graph generative models emerge as a data-driven approach, leveraging deep neural network architectures to learn complex structural distributions directly from real-world networks to generate more realistic synthetic networks. Because real social contact networks cannot be shared due to privacy risks, synthetic networks serve as an alternative for developing and evaluating epidemic mitigation strategies. In this work, we evaluate deep graph generative models as well as the configuration from a network science perspective by assessing both the topological similarity between generated and real-world networks and their utility in identifying effective node immunization strategies to sup- press epidemic/misinformation spreading. It is found that two deep graph generative models produce synthetic networks that closely resemble the structural properties of real-world networks, enabling them to identify effective immunization strategies.

Exploring unknown environments with multiple UAVs requires coordination under intermittent communication, making decentralized operation a baseline assumption. We propose, within a decentralized framework, a novel exploration graph extension strategy based on frontier connectivity to extend exploration plans and maintain area partitioning among agents stable and robust to disconnections and changes in spatial layout. The proposed extension method is applied to two state-of-the-art area partitioning methods and evaluated in simulation. Experiments show improved performance over existing graph extension approaches with higher exploration efficiency under low communication rate.

We study landscapes for complex-parameterized networks. Our approach is motivated with an information-theoretic manifold perspective of the parameter and via classical optimization guarantees although of complex geometric variety such as through Dolbeault asymptotics. The descent path admits a Kähler information metric under a cross-entropy via the Wirtinger Hessian on the log-likelihood potential. We restrict attention to a descent update rule with natural gradient descent via a differentiated loss scaled by the inverse metric, so the descent path remains in the holomorphic tangent bundle. We emphasize Calabi-Yau information manifolds which profane theoretical guarantees via an ill-curvature-conditioned landscape. Under a Calabi-Yau metric, specifically in a non-compact setting with a global potential so defined geometrically rather than invoking the topological requirements of the Calabi conjecture, a wedged nowhere-vanishing holomorphic form is the top exterior product of the Kähler form up to constants, yielding a constant determinant condition with respect to a background metric and ill-conditioned eigenvalues under nonuniform and almost low-rank assumptions. Moreover, it has been discovered that negative curvature subverts the loss landscape, specifically sectional curvature, so we expand on this and draw interconnections to negative-definite Ricci curvature. Our arguments primarily exist in a geometric analytic modality, although we establish roots in deep learning theory such as through asymptotics at initialization and connections through failure modes of neural network guarantees under vanishing and negative Ricci curvature.

To avoid missing important variables and their connections in networks, more and more variables are included in network analysis. Here we show that in a setting with many more parameters than observations (high-dimensional) it is possible to get a conservative (i.e., low false positive rate) estimate of the neighbourhood for each node (which connections are in the network). A neighbourhood is often estimated with a linear model, and this leads to two interesting cases: (i) If the true model is linear, then neighbourhood selection work reasonably well, and (ii) if the true model is nonlinear, then neighbourhood selection requires a penalty for the high dimensions. Here we show the impact of the ridge parameter on the mean squared error, and how this leads to low test variance and hence to neighbourhoods with large numbers of edges. We connect these insights with results from machine learning, where the so-called double descent (when more parameters are included than observations, the mean squared error goes down a second time) has put the traditional view on model selection upside down. Essentially, for adequate neighbourhood selection in models with a large number of parameters, the volume of the model space needs to be included in the penalty. Most neighbourhood selection methods (e.g., Lasso, AIC, BIC) lead to spurious edges (high false positive rate), but we prove that in the high-dimensional setting, minimum description length leads to correct neighbourhood selection or smaller (low false positive rates) in both cases when either the model is correctly or incorrectly assumed linear

In a multi-agent system, there are often stubborn followers of specific opinions or beliefs. Motivated by this observation, in this paper, we aim to understand how stubborn agents affect the distribution of opinions in a network where both stubborn and non-stubborn agents interact with each other. To do so, we assume that all agents have an opinion in the set $\{0,1\}$ and each non-stubborn agent updates its opinion according to the $2k$\textit{-choices rule}, where the agent samples $2k$ neighbours (including both stubborn and non-stubborn neighbours) uniformly at random and adopts the majority opinion among the sampled group of neighbours and itself. We assume that a proportion of agents, $γ_i$, are stubborn followers of opinion $i\in \{0,1\}$. It is natural to expect that the steady-state distribution of the opinions in the network will be dominated by the opinion with the larger proportion of stubborn followers. We show that while this is true, the time to reach steady-state depends heavily on the values of the parameters $γ_0$ and $γ_1$. When the individual values of these parameters, as well as their difference, are small, it can take an exponentially long time (in the network size) to reach the steady-state. In sharp contrast, when at least one of the parameters $γ_0$ and $γ_1$ is large, the network reaches the steady-state in a time that is only logarithmic in the network size. Hence, there exists a sharp phase transition in the network dynamics based on the proportions of stubborn agents. We also characterise the behaviour of the system when the parameters $γ_0$ and $γ_1$ lie on the boundary of the phase transition. In this boundary region, we show using Stein's method that the dynamics are driven by a diffusion process which takes polynomial time to mix.

Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian. We study a continuum of degree-normalized spectral embeddings that includes these commonly used choices as special cases. Under a random dot product graph model, we establish a row-wise central limit theorem for this family of embeddings. The result provides an explicit description of how degree normalization affects both population geometry and the local uncertainty of embedded nodes. We use the limiting distributions to compare different normalizations in two-community stochastic block models through a projected-Gaussian Bayes-error diagnostic. These comparisons show that no single normalization is uniformly preferred. Instead, the favored normalization depends on network density, community imbalance, and block-probability structure. Typically, stronger normalization is favored in lower-density or more imbalanced settings. These results provide a unified distributional understanding of when and why alternative normalizations may improve spectral clustering.

A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework

Tipping-point dynamics describe the critical conditions under which a committed minority drives a population to abandon an established convention in favor of a new one. We present a transparent agent-based model of this process, in which agents hold one of two behavioral states and a mobile committed minority attempts to overturn the incumbent convention. Our goal was to examine how localized mobility, bounded agent memory, and network topology jointly influence the tipping threshold. Using a custom agent-based simulation framework, we found that in many configurations, tipping becomes effectively inevitable: given sufficient time, the population always converges to the minority state. This observation motivated a complementary analysis focused on the pace of convergence rather than its feasibility. We introduce a unified predictive model that accurately estimates how structural and behavioral parameters determine the time required for complete adoption, showing that mobility is the dominant accelerator while memory and connectivity modulate convergence in systematic ways. Together, these results extend classical tipping-point research by linking structural and behavioral factors not only to the likelihood of convention change but also to the timescale on which it unfolds. While we frame the model in terms of convention-like binary behavioral adoption, the same mechanisms bear on norm change and other contagion-like social processes.

Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare. We benchmark 13 unsupervised hyperbolic graph embedders under a unified protocol for link prediction and topology reconstruction on synthetic and empirical networks. The protocol captures both missing-link recovery and the preservation of local and global network structure. Maximum-likelihood and representation-learning-based approaches, including hybrid variants, achieve the strongest overall performance, although no method dominates across all tasks and structural regimes. Performance is more strongly associated with embedding paradigm than with disciplinary origin. We identify the network regimes in which different paradigms succeed or fail and provide practical guidance for method selection in downstream applications.

Network dismantling is fundamental to analyzing the robustness and vulnerability of complex systems, yet practical heuristics must balance effectiveness and computational efficiency, and are usually designed manually by researchers. Existing large language model based automatic heuristic design methods can generate and screen candidates, yet they have difficulty further transforming candidate quality or failure states during execution into structural-level guid- ance for subsequent generation. We propose AutoSND, a three stage tree search framework for complete network dismantling pro- grams. Stage I broadly explores from simple heuristics and archives execution evidence. Stage II compiles candidate records into struc- tural policies concerning local signals, neighborhood access, and state update ranges. Stage III continues tree search conditioned on these policies and obtains the final quality prioritized and speed prioritized candidates, AutoSND-Q/S. Experiments on 12 real world networks and 3 large real world networks show that AutoSND achieves better search performance and stability and discovers more competitive and structurally interpretable network disman- tling programs. The final candidates form an interpretable structure that uses residual degree as the backbone, adjusts node order with bounded local signals, and restricts the state update range. Code is available at https://github.com/MirrorNew/AutoSND.

Delivering sustained power to distributed equipment in unstructured field environments using pre-planned wired networks or battery-based solutions presents significant infrastructure and logistics challenges. This paper presents Dendritic Recursive Pivoting (DeRP), a decentralized framework for multi-target network formation in robot swarms based solely on local communication and bearing-based sensing toward sinks. We envision a system in which robots, acting as a conduit, self-assemble a power network from a common source, forming branches at locally selected pivot points that approximate the Steiner points of Steiner trees to efficiently route to multiple Sinks. This branching operation is performed recursively to enable scalable and adaptive network formation without global planning. The proposed method is evaluated in terms of the total network length and estimated power loss, and is quantitatively compared against global baselines such as the Minimum Spanning Tree and Steiner tree solutions (GeoSteiner), which require complete knowledge of Sink locations. Specifically, we found that the networks formed by DeRP asymptotically form approximately 125% of the global minimum length while reducing power losses to 65% relative to Euclidean Steiner trees. In addition, we empirically characterize scaling behavior by measuring simulation completion time as the number of Sinks and robots increases, and find that this scaling was sub-linear for up to 100 sinks. The proposed approach enables resilient, adaptive power delivery in environments where deployment of traditional infrastructure is challenging.

Social dynamics encode the process in which individual network and discourse interactions aggregate into collective influence, narrative dominance and coordinate behavior. This paper uses the the GhostField architecture, a hybrid LLM-Enabled Agent Based Network-Dynamic (LAND) model as a social simulation framework to build the AuraSight scenario. In the AuraSight scenario, 314,244 heterogeneous cyber social agents and human actors exchange 529,327 messages over 30 days surrounding a fictional international song-writing contest. We methodologically examine emergent social dynamics across four analytical layers: ego-network topology, semantic network evolution, coordination dynamics and influence dynamics. Our results show how generated social simulations do also produce social dynamics, and how the dynamics of coordination and influence emerge not from individual agents but from the recursive interaction between network topology and narrative exchange.

Many learning problems require representations that reconcile direct input, nearby structure, and broader context. In implicit neural layers, these influences are usually absorbed into a single fixed-point update, making it hard to identify what enters from the stimulus, what propagates locally, what comes from global context, and what is produced by solver dynamics. Here we introduce SILVA Networks, Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields. SILVA separates stimulus, local interaction, global interaction, damping, and readout inside one fixed-point architecture. The same template is instantiated for images, molecules, citation networks, and long-range graph benchmarks through domain-specific definitions of nodes, neighborhoods, and global summaries. Experiments and ablations show task-dependent roles for these terms: local interactions are load-bearing in the graph tasks, MNIST gains little from recurrence at the tested capacity, and the clearest global benefit appears in a long-range node-classification benchmark. SILVA therefore provides an implicit representation whose internal interaction dynamics can be trained, ablated, visualized, and diagnosed.

Human cortical organoids provide an experimentally accessible model of early neural circuit formation, yet whether their activity reflects structured information processing rather than spontaneous synchronization is unclear. We developed a graph-computational framework to quantify stimulus-evoked propagation. This includes stimulus-conditioned functional graphs, a graph-constrained dynamical (graph-neural-network) model used as a system-identification tool, a biological message-passing principle bounding integration depth by observable propagation depth, and a suite of graph-level metrics. We carried this program out in full on longitudinal HD-MEA recordings from three organoids. Once the true acquisition sampling rate and stimulus timing were recovered, the evoked response proved to be a fast, near-synchronous network burst with no measurable outward propagation (peak-latency vs. distance slope = 0). The propagation/integration-depth metrics (Deff ,reachability index, dmax) therefore do not apply, and per-day connectivity graphs were not reliably estimable at the available trial count, a negative result with methodological consequences for applying such metrics to organoid data. Reframing around synchrony, response-population size and shared variability revealed a control-validated phenomenon, i.e., repeated daily stimulation progressively depressed and spatially contracted the evoked response. That repeated stimulation reshapes organoid networks is established, but longitudinal designs in which every preparation is stimulated cannot separate this from developmental maturation. We break that confound with a developmentally-matched, stimulation-naive control, where at day 7, an organoid receiving its first-ever stimulation engaged 93% of the array, whereas organoids with five prior sessions engaged 10%.

We formulate a statistical physics framework to model a networked stochastic dynamical system exhibiting bistability, driven by additive noise and social conformity. We apply this model to understand and mitigate AI-induced delusional spiraling-a phenomenon where algorithmic sycophancy from Large Language Models continuously reinforces inaccurate beliefs within a socially interacting society. By partitioning the network into a majority of regular agents and a minority of "aware" nodes (Teachers) placed at topological hubs, we use a degree-weighted mean-field approximation to reduce high-dimensional coupled Langevin equations into a single macroscopic drift equation. We provide a closed-form analytical derivation for the deterministic critical tipping time through a saddle-node bifurcation. We validate this analytical boundary using finite-size scaling and demonstrate a universal data collapse across diverse network topologies. Finally, we optimize an intervention strategy under a strict budget constraint that balances the topological footprint against driving velocity. We prove mathematically that under certain conditions, a highly concentrated, rapid intervention targeting massive hubs strictly outperforms a distributed, slow approach to rescue the network.

Temporal graphs are increasingly used to model dynamic systems in diverse domains such as social networks, financial networks, and traffic networks. Predicting both what the next event will be and when it will occur in these systems is crucial for understanding and anticipating complex behaviors, but has not been studied much. To address this gap, we propose a unified mathematical framework capable of capturing varying degrees of complexity across temporal graphs. Our framework is flexible and expressive enough to accommodate a wide range of network structures and temporal dynamics. Building upon this analysis, we introduce our novel approach for jointly predicting the next event and its occurrence time. Empirical evaluations across multiple datasets demonstrate that our method consistently outperforms existing techniques, particularly in scenarios involving irregular event patterns and complex temporal dependencies. These findings highlight the potential of our framework as a robust foundation for future research in temporal event prediction.

We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions. To this end, we train deep belief networks (DBNs) with different configurations, where the first layer can use Gaussian visible units with more than two states (i.e., non-binary units). We then allow the DBN to "dream" samples conditioned on visible units that we keep fixed, and we measure the deviation of this dreamed system from the real one. We also corroborate, using a discrete thermometer based on a convolutional network, that the reconstructions remain in a critical state. Across several training sessions with different architectures, we show that, despite the complexity of the problem, the DBN can recover samples that remain critical even under input noise, with a gradual degradation of physical observables relative to the original sample.

Investigating how affective states such as confusion and frustration persist and transition during co-situated collaborative problem solving (CPS) is important for understanding the dynamics of epistemic emotions. However, the accurate identification of affective states remain challenging as there is no gold-standard truth in this space. Here, we analyze affective states collected through retrospective cued-recall during an in-person CPS task. Using ordered network analysis (ONA), we examine (1) the overall ordered structure of affective states and how this structure differs across self-caught and probe-caught reporting methods, and (2) what aspects of this ordered structure are emphasized differently in slower and faster groups. We find that ONA reveals differences in persistence and transition patterns that are not apparent from descriptive summaries alone. In particular, we observe a stable epistemic core linking curiosity, optimism, and confusion, with different reporting methods emphasizing different connections among states. An analysis between faster and slower groups show that roles of confusion and disengagement also shift significantly during collaboration, particularly in their relationship to conflict. We interpret our findings in the context of collaboration and discuss their implications in developing AI systems that support CPS.

Photonic reservoir computing has attracted increasing attention as a fast and low-cost approach for time-series prediction. Photonic reservoir computing utilizes the high speed, broad bandwidth, and spatial parallelism of light. However, the effect of the internal connection structure (network topology) on the computing performance has not been investigated for large-scale photonic reservoirs. In this study, we experimentally and numerically demonstrate photonic reservoir computing using a spatial light modulator to systematically evaluate the relationship between the network topology and the performance of reservoir computing. We introduce complex network structures such as small-world and scale-free network topologies of the internal nodes in the reservoir. We perform the memory capacity measurement and the one-step-ahead prediction task of the chaotic time series to compare the performance. We found that the small-world network exhibits the maximum memory capacity and the best prediction performance. Our numerical calculations reveal that the performance of the time-series prediction can be optimized by changing the rewiring probability of the network and the leak rate of the reservoir. We also implement photonic human brain network as a reservoir, which is designed by the connectomes of human brain activities. We found that the network topology strongly affects the performance of reservoir computing, and the small-world network structure outperforms the other configurations.

A formal model enables verifying reachability, localizing an outage, or anticipating the blast radius of a change. Yet, virtually no production network has one, since writing a model by hand demands rare expertise and is hard to keep current as the network changes frequently. At its core, network modeling is a typographical exercise: it translates network artifacts (e.g., configurations, topology, and routing state) into rules in formal logic. Translation of this kind is what large language models (LLMs) nowadays do well. Unlike free-form AI reasoning, such translation can be formally verified. Once modeling is no longer the bottleneck, trusting AI to reason over large, complex networks no longer makes sense. Our position therefore cuts against the prevailing race to put autonomous AI agents in charge end-to-end. We instead confine AI to translation and rely on a solver for reliable long-horizon reasoning, building a reusable formal model of general network behavior that can then be specialized to specific tasks, e.g., root-cause analysis (RCA). We build TypoNet that constructs and validates a symbolic model of an emulated production-scale WAN from the network's own artifacts. Our preliminary evaluation shows TypoNet helps in two ways. On its own, TypoNet answers operational questions (e.g., reachability verification and change-impact analysis) faster, more cheaply, and more reliably than an LLM. As a tool for an AI agent, TypoNet boosts fault localization at lower cost. The result makes the case for AI that builds verifiable network models and relies on a solver for reliable long-horizon reasoning.

Invariants, the relations expected to hold among measured signals of a network, underpin applications from verification to traffic generation, telemetry imputation, and input validation, yet writing them by hand demands rare expertise in both formal logic and networking. Automatic miners can help but fall short on two fronts: they still require the hardest input (the grammar of admissible invariants) and they learn only exact, hard'' rules, struggling with real-world approximation caused by inherent noise in data. LLMs are tools that can provide semantic reasoning over data, but are non-deterministic and opaque in their learning. Our key idea is to partition the invariant search problem into an AI-driven grammar discovery'' problem, followed by a statistics-driven ``search'' problem within the learned grammar. Taken together, this allows non-deterministic, hallucination-prone AI to help produce auditable invariants with formal guarantees. We design and implement such a system, Autogram, and evaluate it on both public and production telemetry data, recovering expert-derived invariants with high coverage and low false positives. We close with discussion on open problems on the path toward fully open-ended discovery.

The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies. Frequently used architectural paradigms depend on scale-free or small-world networks, assuming optimal communication efficiency. Our study mathematically dismantles that assumption for semantic data. By mapping multi-agent communication uncertainty trajectories onto a 768-dimensional Bio_ClinicalBERT embedding space via an analytical isotropic variance proxy using Barab'asi--Albert (BA) and Watts--Strogatz (WS) networks, we prove that structural bottlenecks compromise diagnostic safety. Our phase transition matrices illustrate that localized dense cliques confine hallucinated data, preventing global consensus and forcing the system toward a permanent entropy saturation threshold of $H_{\infty} \approx 5.947$. As a result, we measure a severe terminal cosine similarity degradation of 53.29%, completely overwriting the original ground-truth. Moreover, the terminal semantic drift reveals a catastrophic variance amplification of 51.81% ($ρ= 1.5181$) in highly clustered architectures, proving total system unpredictability when compared to Erdős--R'enyi configurations ($ρ= 1.0766$). Instead of reducing errors, hub-centric systems autonomously compound localized hallucinations. By introducing dynamic spectral monitoring operating at an $\mathcal{O}(N^3)$ time complexity and imposing a strict lower bound on algebraic connectivity ($λ_{2_{min}}$) via the continuous eigen-decomposition of the graph Laplacian, we present a mathematically rigorous technique to ensure global state diffusion. Securing the reliability of autonomous medical diagnostics necessitates treating topological stability as a non-negotiable quantitative imperative.

Controllable video generation remains challenging due to the difficulty of specifying precise multi-object interactions using text prompts or motion-control inputs that primarily constrain pixel movement. In practice, trajectory-based control often requires users to draw accurate tracks for multiple objects, which scales poorly with scene complexity and becomes ambiguous under occlusion or overlap. To enable flexible yet precise multi-subject control, we introduce $\textbf{GraphVid}$, a graph-conditioned image-to-video generation model that enables interactive control through structured interaction graphs. We further curate $\textbf{GraphVid-Bench}$, a large-scale interaction-centric video dataset with structured relational annotations to enable training of interaction-aware video generation models. Despite using substantially less training data and fewer trainable parameters than prior motion-control methods, GraphVid delivers strong controllability and video quality. Compared with Motion-I2V, GraphVid reduces FID by up to 39.9% and FVD by 37.6%, while improving PSNR (9.87=>15.98) and SSIM (0.38=>0.61). Our results highlight the potential of structured semantic interfaces as a powerful paradigm for controllable video generation.

Many complex systems such as brain networks, financial markets, and gene-regulatory circuits are described not by a fixed graph but by one that changes over time. A standard way to summarise such structure at each instant is the sparse precision (inverse-covariance) matrix, and the time-varying graphical lasso (TVGL) turns a multivariate signal into a smooth chain of these matrices. We introduce TVGL-CFM, a single model that learns the distribution of such chains and can both generate new, realistic time-varying network trajectories for a given class and forecast how an observed trajectory will continue. Each precision matrix lives on a curved space of positive-definite matrices, but a log-Euclidean chart flattens an entire trajectory into an ordinary vector space, so a simple conditional flow-matching model can be trained and sampled there while every decoded matrix is guaranteed to be a valid precision matrix. For forecasting we start the flow not from noise but from a rough extrapolation of the recent history, so the model only has to learn a small correction. Across EEG motor-imagery, chaotic systems, and gene-expression data, TVGL-CFM generates trajectories that keep the class-discriminative structure of real data, and it forecasts future connectivity more accurately than raw-signal baselines. Generating the structured precision trajectory directly is therefore more faithful than generating raw signals and estimating connectivity afterwards.

The Internet taught us that the value of a network depends on \emph{how} its nodes connect: broadcast stars scale as $V\!\propto\!N$ (Sarnoff), fully-connected meshes as $N^2$ (Metcalfe), and group-forming networks as $2^{N}$ (Reed). We ask the analogous question for networks of AI agents. We model the net value of connection as a function of coordination-group size, derive from it the properties an optimal collaboration protocol must have, and introduce ANet Patu-1 -- a self-organizing consensus protocol in which the network continuously re-forms its own coalitions, adaptively riding the upper envelope of all three regimes at $O(1)$ parallel consensus rounds. To measure value without opinion-grading, we score an emergent protocol by formally specifying it and deriving its complexity, the way distributed algorithms are analyzed. Two results follow. (i)~Emergence -- a crowd of the \emph{cheapest} model, when heterogeneous, starts weak but its collective value compounds with $N$ and \emph{overtakes} a crowd of a far \emph{stronger} model that is homogeneous: a crossover that marks a scaling law for collaboration rather than for scale. (ii)~Reflexivity -- a heterogeneous network, given only its own problem and no design hints, converges on ANet Patu-1 itself, reconstructing the high-dimensional law that governs its own connective value.

Generative AI chatbots promise to transform English as a Foreign Language (EFL) writing by providing immediate, personalised feedback. However, their pedagogical value depends on how learners engage with them - a process often treated as a "black box." This study uses Transition Network Analysis to model the temporal dynamics of Japanese EFL learners using "Penny," an LLM-powered writing chatbot. Analysis of over 4,500 writing sessions and 21,000 chatbot interactions reveals two dominant behavioural loops: a "Revision Loop," where feedback leads directly to successful error correction, and a "Chat Loop," where learners engage in sustained dialogue with the chatbot following feedback. Crucially, EFL proficiency significantly shapes interaction: high-proficiency learners engage more in open dialogue and negotiation with the chatbot, while low-proficiency learners rely more heavily on repetitive corrective feedback cycles. The findings demonstrate that AI-scaffolded writing is a non-linear, dialogic process and highlight the need for differentiated chatbot design to move beyond simple error correction and foster deeper cognitive engagement for all learners.

Network alignment identifies node correspondences across different networks and is a fundamental primitive in many data science applications, including social network analysis, fraud detection, and knowledge graph integration. However, state-of-the-art network alignment methods often achieve high accuracy by repeatedly constructing and updating dense matrices, sacrificing scalability in the process. To address this scalability limitation without compromising alignment accuracy, we present FastAlign, a scalable, sparsity-aware framework for optimal transport-based network alignment. Rather than introducing a new alignment model, FastAlign preserves the original OT formulation and reinterprets its computation as a set of recurring mixed sparse-dense operations. FastAlign combines sparsity-aware graph computation with domain-specific kernel fusion, including a custom SpMM kernel. Our results show that FastAlign achieves alignment quality comparable to state-of-the-art OT-based methods while substantially reducing end-to-end runtime up to 3.89x-9.45x on CPU and 2.24x-32.54x on GPU.

We present an interpretable network-based framework for representing idiomatic and figurative meaning across eight typologically diverse languages, totaling 160 conventional expressions, the large majority of which are idiomatic. Each expression is annotated with binary conceptual features (containment, concealment, emotional, social, etc.) derived from cognitive-linguistic theory, and pairwise Jaccard similarities define a weighted graph. Community detection reveals that idioms cluster by conceptual schema rather than by language, producing a structure consistent with cognitive-linguistic predictions. The conceptual network captures unique semantic information not present in distributional embeddings, can be scaled via automatic annotation with LLMs, improves downstream idiom detection, and remains robust when enriched with corpus frequencies. Cross-lingual transfer experiments show that conceptual proximity alone can identify acceptable translation equivalents across five language families, with substantial gains over embedding-based baselines. Ablation studies demonstrate that all three feature dimensions -- schemas, roles, and valence -- contribute non-redundantly to both the network's organizational properties and its performance on idiom detection, and that specific graph-derived signals (community membership, neighbor similarity) are particularly informative. The framework offers an interpretable, cross-linguistically stable representation of idiomatic meaning, combining theoretical grounding with practical utility.

Graph Neural Networks (GNNs) provide a learning-based framework for approximating graph quantities that are expensive to compute exactly. This paper investigates GNNs for scalable approximation of betweenness and closeness centrality, formulated as a node-ranking problem. Exact centrality values are used as supervision, and ranking quality is evaluated using Kendall's tau rank correlation. We study whether message-passing GNNs can learn transferable structural representations across different graph topologies rather than only fitting the distribution used during training. On unseen Erdos renyi graphs, the proposed models achieve tau = 0.851 for betweenness and tau = 0.894 for closeness. A large-scale betweenness model trained on graphs with N = 5,000 nodes achieves tau = 0.938, demonstrating scalability. Mixed-distribution training on Erdos renyi, Barabasi-Albert, and Gaussian Random Partition graphs improves betweenness transfer across graph families. In contrast, closeness centrality remains more sensitive to community-structured graphs and shows reduced transfer to real-world topologies. Finally, GNN inference achieves up to a 97.7x speedup over exact computation. These results show that mixed-distribution training can improve structural transfer in GNN-based centrality approximation, while identifying closeness centrality's sensitivity to topology as an open challenge.

Microbial density is clinically important for tumor assessment and treatment decision-making, and recent advances in deep learning suggest that it can be non-invasively inferred from multimodal MRI. In this work, MRI-based Microbial Density Stratification (MRI-MDS) is first investigated as a patient-level representation learning task, and Center Heatmap-driven Macro-micro modeling Network (CHM-Net) is introduced for this task. CHM-Net first establishes the link between imaging phenotypes and microbial states through center heatmap-guided small-lesion response localization. Building upon this, it constructs patient-level macro-micro evidence from localized heatmap responses for microbial density prediction. Experiments on the novel GBNPC 2026 dataset constructed for MRI-MDS demonstrate the effectiveness of CHM-Net, achieving superior performance over representative baselines with a 12.06% absolute ACC gain over the strongest competing result. Additionally, auxiliary validation on two 3D medical image datasets further verifies its robustness across volumetric medical image classification scenarios. The project is available at https://anonymous.4open.science/r/CHM-Net-942E/.

Cyber-physical power systems are vulnerable to cascading failures caused by tight interdependencies between power and communication infrastructures. Evaluating these failures over large N-k contingency sets with a high-fidelity simulator is computationally prohibitive for resilience planning. Using the previously published Modified Implicative Interdependency Model (MIIM) as the ground-truth cascade simulator, this paper develops a machine-learning surrogate that predicts contingency severity from leakage-free structural features and derives a component-criticality ranking for prioritized hardening analysis. On the IEEE 118-bus system, the Gradient Boosting surrogate achieves Spearman correlations of 0.849 for per-contingency severity prediction and 0.853 for per-component criticality ranking, while remaining stable across three independently sampled datasets. MIIM-derived component criticality itself reproduces only to a Spearman of approximately 0.85 under the present sampling pipeline, and the surrogate operates at this empirical ceiling to within sampling variation. Topological centrality measures on the full interdependent network provide meaningful baselines (Spearman 0.60-0.69), and feature ablation shows that the surrogate's advantage is driven primarily by inter-layer dependency information. These results support a two-stage workflow in which the surrogate rapidly ranks candidate components and MIIM is reserved for selective verification.

While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally. This graph encodes the data manifold in its original high-dimensional space, before the distortion that UMAP's 2D projection introduces. We demonstrate the untapped potential of this internal representation, showing how standard graph algorithms applied to this graph enhance data sensemaking: (1) PageRank identifies representative data points, (2) k-core decomposition reveals dense core regions versus sparse periphery, and (3) clustering coefficient detects tight-knit neighborhoods with highly-similar data points. Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, we show that these graph-based analyses are not only practical but also competitive with or complementary to purpose-built methods (e.g., k-medoids for exemplar selection, HDBSCAN for density-based clustering).

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

Dependency parsing consists of finding a tree representation for a sequence. Unsupervised dependency parsing aims to develop parsing methods without a gold standard during model training. In human languages, an unsupervised parser can be evaluated because some gold standard is usually available or can be created. For other species, a gold standard is unknown. Thus one may conclude that it is impossible to determine the accuracy of an unsupervised parser and, consequently, dependency parsing is unfeasible in other species. However, here we apply recent advances in network science to demonstrate that the proportion of correct edges retrieved by a parser must be high for the sequences of vocalizations or gestures that non-human primates produce due to the fast decay of the sequence length distribution. In contrast, human language sequences lack that property. Therefore, evaluation without a gold standard is feasible in non-human primates but a hard problem in humans.

Deep learning models have emerged in machine learning and related fields, demonstrating astonishing performance in various visual tasks. Despite their great success, however, these models are unable to fully encode intrinsic visual structures, and often ignore the spatial, topological, and semantic information contained within an image. Graph neural networks offer a good framework to face this aspect, but their effective use for visual tasks has been only partly explored and mainly starting from a limited perspective. This work aims to address this gap by conducting a systematic comparison of current graph construction techniques within the context of a fixed three-layer GCN architecture. Through an empirical study, it demonstrates in particular how the network structure affects performance and provides an important methodological contribution regarding the computational stages preceding graph utilization, which will be strongly influenced by the structure itself.

Is word acquisition in children uneven with respect to semantic and lexical categories? To answer this question, we model early language learning as a search on a graph-based mental lexicon, driven by two interacting processes: spreading activation and an enforced exploration (rather than exploitation) of lexical categories. We evaluate model performance on four languages (German, English, Dutch, and Rioplatense Spanish), using CDIs as ground-truth data for lexical categories, normative ages derived from the Wordbank repository, and state-of-the-art resources for reconstructing graphs of word similarities. We find that spreading activation outperforms a shortest path baseline in simulating normative word acquisition. At the category level, we highlight complex transitions between CDIs. By studying their sequences in terms of burstiness and average persistence time within the same CDI, we find that spreading activation better captures the exploration dynamics observed empirically. Overall, our findings suggest that vocabulary development can be understood through the non-trivial interplay between activation dynamics and some degree of constraints regulating the visiting of lexical categories in complex networks.

i-EXAM is a planning-powered tool that helps system administrators to create security profiles of complex networks and perform what-if analyses to identify network hardening strategies. It leverages planning compilation that provides soundness and completeness guarantees to identify attack paths, evaluate security metrics, generate diverse hardening strategies, and explain these strategies in natural language using Large Language Models.

Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size. We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree. Together, they provide a principled alternative to classical junction-tree constructions. The proposed framework represents the joint distribution by lower-dimensional sub-models that can be learned and stored separately. This decomposition reduces computational cost and naturally enables parallel computation. Based on a minimal d-decomposition tree, we further develop two parallel algorithms for parameter estimation and probabilistic inference. Experiments show that the proposed method substantially improves computational efficiency over junction-tree methods while maintaining inference accuracy, especially for low-dimensional queries.

Large language model (LLM) agents are increasingly deployed in interacting populations, raising the question of what such populations come to believe collectively. Whether a population aggregates genuine knowledge or collapses into a false consensus directly affects how much such systems can be trusted. Classical social-network models assume that the network itself determines how beliefs combine. This assumption breaks down for LLM agents, whose limited attention takes in only part of what they are exposed to, so these models overstate how much information a population actually pools and cannot tell genuine consensus from herding. We introduce SNLA, a framework that models how much each agent actually influences others, rather than merely how the network connects them. This influence depends on each agent's position in the network and on how sharply attention focuses. Theoretically, we show on a tractable proxy that narrow attention causes herding, where the effective sample size stays bounded regardless of population size, while wide attention recovers wisdom-of-crowds behavior only when the exposure graph is undirected and degree-regular. Empirically, a controlled testbed validates these predictions directly, and the herding-wisdom transition reproduces on operator-controlled variants of three multi-agent LLM benchmarks.

This paper introduces SupplyNetPy, an open-source, well-documented Python library for modeling and discrete-event simulation of supply chain networks with arbitrary multi-echelon structures. It supports multiple replenishment policies, perishable inventory, node disruptions, and stochastic demand and lead times. All components are extensible via inheritance. Users describe a supply chain as a graph with node and link attributes, while the library handles simulation, providing logs and extensive node and network level performance reports. This paper presents the motivation, design, key features, and architecture of SupplyNetPy, along with detailed validation results (against analytical benchmarks, a commercial tool, and a published case study). A key motivation behind SupplyNetPy's development is programmatic generation and simulation of complex models, enabling design-space exploration, what-if analysis, training data generation, and supply chain digital twins.

Decentralised federated learning, based on peer-to-peer communication, is increasingly proposed for on-device training of machine learning models, promising a privacy-preserving, communication-efficient training process with no risk of single-point failure. However, the role of structural and temporal inhomogeneities in such fully decentralised settings remains poorly understood. Here, we investigate their effects when model parameters are locally averaged during aggregation. We show that the decentralised federated learning process is governed, both in the early phase and the late, stationary limit, by the same dynamics as a lazy random-walk diffusion process on temporal networks. Based on this mapping, we demonstrate that the typical experimental scenario used in decentralised federated learning leads to unrealistically rapid convergence because of ignoring the temporal and structural inhomogeneities inherent in the communication network. We analyse real-world temporal networks and find that inhomogeneities most often dramatically slow down diffusion, hence the convergence process.

Accurate trajectory prediction in autonomous driving hinges on modeling dynamic and context-dependent interactions among traffic agents. However, most existing approaches are purely data-driven and lack structural priors, which limits their generalization under distribution shifts. In this work, interaction modeling is revisited through the structure and dynamics of traffic networks, and SWIFT (Small-World Interaction Framework for Trajectory prediction) is proposed as a unified framework that integrates small-world networks with traffic flow theory. SWIFT introduces structural inductive biases via a Small-World Interaction Network that captures both local and global dependencies, and a Flow Regime Encoder that adapts the interaction structure to scene-level traffic states. Interaction reasoning is further enhanced through a multi-relational graph module that explicitly encodes direct and higher-order agent relationships. Extensive experiments on three real-world datasets, nuScenes, MoCAD, and NGSIM, show that SWIFT consistently outperforms strong baselines in prediction accuracy across diverse traffic regimes. Beyond accuracy, SWIFT exhibits improved generalization to unseen locations and regimes, robustness under noisy observations, and strong performance with limited training data, supporting the effectiveness of its structure-aware design.

Hierarchical Navigable Small World (HNSW) graphs serve as the industry standard due to their logarithmic complexity and strong empirical performance. However, HNSW relies on greedy graph traversal, a heuristic that provides no theoretical guarantees of correctness. In this paper, we propose a novel "Certify-then-Rectify" framework that bridges the gap between the speed of heuristic search and the rigor of exact retrieval. Rather than discarding HNSW, our approach first employs a distribution-free statistical certifier to dynamically evaluate the quality of a standard HNSW search with minimal overhead. If certification indicates that the retrieved neighbors are of low quality, the framework safely escalates to a rigorous exact recovery algorithm. To make this exact recovery computationally feasible, we reinterpret the HNSW graph as a geometric spanner and utilize Extreme Value Theory to stochastically estimate its maximum empirical stretch factor. This allows us to mathematically bound the maximum distance of true nearest neighbors. Extensive evaluations on benchmark datasets demonstrate that our tiered framework delivers the average-case speed of HNSW while ensuring the worst-case correctness of exact search and outperforming other applicable approaches.

Characterizing the scenario underlying an epidemic from its disease cascade is an important task in simulation analytics. We propose boundary degree, the count of an infected node's contacts in the underlying contact network that were not infected, as a per-node cascade feature for this task. Through systematic ablation on realistic social contact networks of Tennessee and Virginia, we show that boundary degree alone improves scenario identification accuracy by 19%. Edge features, whose importance was observed empirically by prior work, consistently improve accuracy across all settings; we provide theoretical grounding for this observation. These effects are complementary. We prove that certain epidemic scenarios are indistinguishable without boundary or edge information. Prior feature engineering approaches included aggregate boundary statistics, but these were not among the top-ranked feature groups; the per-node representation we propose reveals their importance clearly. Our results suggest that contact tracing applications should track contacts with non-infected individuals, not only transmissions.

A growing number of techniques leverage the spatial structures that underlie many real-world datasets. Despite these advances, the complementary task of estimating spatial structures and understanding their role within these techniques has often been overlooked. In neurophysiological data analysis specifically, numerous methods exist to estimate brain connectivity, but most are not explicitly model-based, dynamic, multivariate, or directed. To address these limitations, we previously introduced noise-driven heat modelling on graphs for neurophysiological connectivity estimation. In this study, we extend this framework by relaxing earlier noise assumptions and adding regularisation to improve robustness. We also develop a simulation procedure to characterise and evaluate our technique in a controlled setting. Finally, we demonstrate that the technique is able to capture meaningful spatial structure across two experiments, each using two real-world datasets. The explicit model formulation of our connectivity estimator has the potential to improve the interpretability of graph-based techniques across a wide range of applications. The code implementing our method is available at https://github.com/sgoerttler/Heat_Connectivity.

Every existing vector database and agent memory framework treats memory as passive storage that agents query explicitly. No system propagates knowledge between agents through the memory layer itself. We introduce HyphaeDB, an agent-native memory infrastructure that reinterprets the Hierarchical Navigable Small World (HNSW) graph topology the data structure at the core of every modern vector database not as a search optimization, but as a communication fabric for multi-agent AI systems. In HyphaeDB, agents are nodes in the vector space with persistent positions, knowledge propagates via a gossip protocol through the graph's neighbor structure with energy-based attenuation, and emergent behaviors contradiction detection, pattern crystallization, and consensus formation arise from the combination of topology, propagation dynamics, and local interaction rules. We present the architecture built on three primitives (knowledge nodes, topology edges, and memory diffs), a multi-layer abstraction hierarchy with promotion via emergent consensus, and theoretical analysis grounding the system in small-world network theory, epidemic broadcast protocols, and swarm intelligence. We provide a reference implementation on PostgreSQL with pgvector and describe a concrete deployment in Swarm-Driven Development, a multi-agent software engineering methodology. HyphaeDB represents, to our knowledge, the first system to combine navigable small world topology with gossip-based knowledge propagation for multi-agent coordination.

Complex adaptive systems often develop organized structures without centralized control. Yet the local mechanisms by which functional organization emerges and persists remain incompletely understood. Here we propose Surviving by Serving (SBS) as a general principle of self-organization: components persist as long as their outputs are utilized by other components, whereas prolonged non-utilization promotes adaptation and exploration. To investigate this idea, we introduce a minimal multi-agent model in which agents transform shared resources and receive only local feedback when their outputs are subsequently utilized elsewhere in the system. Despite the absence of global objectives, the system spontaneously self-organizes into functional interaction networks. We observe the emergence of stable transformation chains, core-periphery organization, and the generation of novel states that enable previously inaccessible target conditions to be reached. Remarkably, self-sustaining interaction networks can arise even without external selection pressures, creating a pre-adaptive search phase from which later functional solutions emerge. These findings suggest that functional utilization may provide a simple, substrate-independent mechanism for the emergence and stabilization of organized structure in complex adaptive systems.

Collective behavior arises when locally interacting units produce coordinated global organization, from synchronization in dynamical systems to task-relevant information flow on graphs. The central challenge is not only to explain how collective behavior emerges, but to design local interaction rules that can produce desired global organization and generalize across graphs, dynamics and tasks.To address this challenge, we introduce the Swarm-Inspired Emergent Synchronizer (SIES), a graph-dynamical framework that learns generalizable local-interaction laws for controllable collective organization. Each node is an agent-like dynamical unit with a state and task cue, and signed source-target-conditioned attention acts as an adaptive coupling term inside an explicit evolution model. Therefore, SIES combines an explicit dynamical engine with local agent intelligence, similar to biological swarms. For synchronization control, SIES learns a generalizable coupling operator that produces prescribed synchronization patterns for CDSs across untrained network scales, target phase relations, and intrinsic node dynamics without retraining. The learned operator also reaches gait-related modes faster than three oscillator baselines and generalizes synchronization-driven locomotion to simulated multi-legged robots of different scales and a physical hexapod after leg disablement. For graph representation learning, SIES applies the same signed interaction principle to message passing and achieves the highest performance among the compared methods on heterophilous node-classification benchmarks. Together, these results position SIES as a generalizable and learnable graph-dynamical interaction framework with promise for synchronization control, adaptive robot coordination, and heterophilous graph representation learning.

This paper develops a noncooperative model of directed network formation in which agents create links to access valuable information while sharing the costs generated along the paths through which information is obtained. Each agent is endowed with a positive amount of information and chooses, simultaneously, which other agents to contact. A directed link initiated by one agent allows her to access the information of the contacted agent and of the latter's reachable network, but each link in the resulting information path entails a unit cost. Payoffs therefore depend on the total value of accessible information net of the accumulated connection costs required to obtain it. The paper characterizes the relationship between strategy profiles and directed graphs, defines accessibility, paths, components, and minimal connectedness, and studies the Nash architectures induced by individual best responses. The central result is that strict Nash equilibria must take the form of circular directed networks. Moreover, circular networks are exactly the Nash networks that use the minimum number of links while allowing every agent to access all available information. Although noncircular weak Nash networks may exist, they are structurally redundant and do not satisfy the same minimality property. The model also shows that strict Nash networks are both Pareto optimal and efficient in terms of aggregate welfare. Finally, the paper compares this framework with Bala and Goyal's model, emphasizing that shared path costs and heterogeneous information values generate different equilibrium implications. The analysis supports the equivalence between strict stability and minimal connectivity in directed information networks.

Graph Neural Networks are great for link prediction in various network-like structures; however, the question of their speed/quality tradeoff has been barely studied. While in practice the time it takes to do inference matters little for small benchmarks, the latency does limit applicability in large-scale domains. In this work, we explore early-exiting strategies that can be applied to Graph Neural Networks to solve the problem of link-prediction faster. We use no auxiliary losses to enforce early exiting, allowing it to emerge as an implicit property of the architecture. We show that our method enables early exiting in several setups, moving the Pareto frontier on the HeaRT benchmark for GCN and SAS-GNN backbones. Our findings show that inference speed of GNNs on many link-prediction problems can be improved, while losing little, or even winning in terms of prediction quality. The code is available in our repository: https://github.com/knyazer/link_prediction.

Collective artificial intelligence, where multiple agents work on shared tasks, holds potential to solve expansive problems in fields from medicine to collective governance. But while prescriptive engineering solutions abound, we lack descriptive scientific understanding of artificial collectives, and therefore principles for how to design resource efficient multi-agent systems. Through systematic experiments with optimizing agents, we characterize how agent interpretive abilities, rationality bounds, and task qualities interact to shape collective performance. Agents range from specialists, with narrow interpretive abilities, to generalists, with broad ones. Collectives of specialists correspond to sparse, centralized networks, while collectives of generalists correspond to dense, decentralized ones. We show that interpretive network properties have small performance effects on average (0.07 standard deviations of performance). However, for specific task qualities, these effects are 4.5 times larger (0.33 sd) and can reach much higher for certain task qualities (1.84 sd). This leads collectives of generalists to perform better on tasks that involve generating, choosing, and coordinating, while collectives of specialists with a few generalist mediators perform better on tasks that involve negotiating. Rationality bounds then moderate these relationships. At loose bounds, specialists outperform generalists through more effective sampling of high-dimensional decision spaces. At tight bounds, generalists outperform specialists through better gradient estimation. A fundamental trade-off between performance and convergence speed emerges at moderate bounds. These findings suggest that multi-agent design could benefit from matching interpretive networks to both task demands and agents' computational limits, with implications for the efficiency and energy costs of multi-agent systems.

Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. To close this gap, we introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate each data point's target value. The data model is analytically tractable with known critical exponents that fix its properties without requiring hyperparameter tuning. We leverage a mapping between percolation clusters, random trees, and additive coalescence to propose an almost linear-time algorithm to jointly sample a random tree and its hierarchical latent decomposition, enabling data generation at arbitrary scale. Using probing experiments, we find that the model's ground-truth latent variables can be linearly decoded from neural network activations. Together, sparsity, self-similarity, power-law statistics, and analytical tractability make critical percolation a principled testbed for interpretability research.

Compositionality is believed to be the foundation for generalization, enabling models to reuse meaningful primitives in novel combinations. Yet, models trained with standard gradient-based optimization rarely, and often only weakly, exhibit compositional internal structure, and it remains unclear how or why such compositionality forms. In this work, we show that compositionality emerges in a narrow connectivity-depth sweet spot. Along the connectivity axis, compositionality only appears in some specifically sparse networks, heavily depends on which connections remain rather than on weights' sparsity alone. Along the depth axis, compositionality emerges within a narrow, target-dependent regime, peaking at specific depths, while both shallower and deeper networks fail. When either the depth or connectivity condition is violated, gradient descent silently converges to fractured solutions rather than compositional ones. To discover and exploit this emergence, we introduce (i) similarity-based pruning (SP) to recover compositional connectivity and (ii) a heuristic depth predictor to estimate where compositionality is most likely to appear. Finally, we support these empirical findings with a theoretical framework based on compositional sparsity, volume-ratio arguments, and feature-interference bounds, explaining why compositional solutions are reachable only in a narrow depth-connectivity regime.