We present a novel interdisciplinary framework that bridges synchronization theory and multi-agent AI systems by adapting the Kuramoto model to describe the collective dynamics of heterogeneous AI agents engaged in complex task execution. By representing AI agents as coupled oscillators with both phase and amplitude dynamics, our model captures essential aspects of agent specialization, influence, and communication within networked systems. We introduce an order parameter to quantify the degree of coordination and synchronization, providing insights into how coupling strength, agent diversity, and network topology impact emergent collective behavior. Furthermore, we formalize a detailed correspondence between Chain-of-Thought prompting in AI reasoning and synchronization phenomena, unifying human-like iterative problem solving with emergent group intelligence. Through extensive simulations on all-to-all and deterministic scale-free networks, we demonstrate that increased coupling promotes robust synchronization despite heterogeneous agent capabilities, reflecting realistic collaborative AI scenarios. Our physics-informed approach establishes a rigorous mathematical foundation for designing, analyzing, and optimizing scalable, adaptive, and interpretable multi-agent AI systems. This work opens pathways for principled orchestration of agentic AI and lays the groundwork for future incorporation of learning dynamics and adaptive network architectures to further enhance system resilience and efficiency.

A new machine learning scheme, termed versatile reservoir computing, is proposed for sustaining the dynamics of heterogeneous complex networks. We show that a single, small-scale reservoir computer trained on time series from a subset of elements is able to replicate the dynamics of any element in a large-scale complex network, though the elements are of different intrinsic parameters and connectivities. Furthermore, by substituting failed elements with the trained machine, we demonstrate that the collective dynamics of the network can be preserved accurately over a finite time horizon. The capability and effectiveness of the proposed scheme are validated on three representative network models: a homogeneous complex network of non-identical phase oscillators, a heterogeneous complex network of non-identical phase oscillators, and a heterogeneous complex network of non-identical chaotic oscillators.

In this paper, we derive variational inference upper-bounds on the log-partition function of pairwise Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the use of ''hierarchies,'' similar to sum-of-squares (SoS) hierarchies is proposed, and we present a greedy algorithm to select among these relaxations. We carry extensive numerical experiments and compare with state-of-the-art methods for this inference problem.

Multi-agent reinforcement learning (MARL) studies crucial principles that are applicable to a variety of fields, including wireless networking and autonomous driving. We propose a photonic-based decision-making algorithm to address one of the most fundamental problems in MARL, called the competitive multi-armed bandit (CMAB) problem. Our numerical simulations demonstrate that chaotic oscillations and cluster synchronization of optically coupled lasers, along with our proposed decentralized coupling adjustment, efficiently balance exploration and exploitation while facilitating cooperative decision-making without explicitly sharing information among agents. Our study demonstrates how decentralized reinforcement learning can be achieved by exploiting complex physical processes controlled by simple algorithms.

Synaptic plasticity underlies learning and is thus central for development, memory, and recovery from injury. However, it is often difficult to detect changes in synaptic strength in vivo, since intracellular recordings are experimentally challenging. Here we present two methods aimed at inferring changes in the coupling between pairs of neurons from extracellularly recorded spike trains. First, using a generalized bilinear model with Poisson output we estimate time-varying coupling assuming that all changes are spike-timing-dependent. This approach allows model-based estimation of STDP modification functions from pairs of spike trains. Then, using recursive point-process adaptive filtering methods we estimate more general variation in coupling strength over time. Using simulations of neurons undergoing spike-timing dependent modification, we show that the true modification function can be recovered. Using multi-electrode data from motor cortex we then illustrate the use of this technique on in vivo data.

Photonic accelerators [1] have been gaining attention in recent years, and a variety of implementations and applications have now been explored [2-9]. These advancements can be attributed to a growing awareness of the saturating speed of performance improvements in conventional computational systems [10], despite the soaring demands for information processing in an extensive range of applications, especially in machine learning. Reinforcement learning [11] is a subfield of machine learning that involves optimizing computer outputs or actions to maximize the reward function. Its applications are now essential to our daily lives, ranging from self-driving vehicles [12] and targeted advertising [13] to wireless networking [14], and there is now a strong demand for computational acceleration. Specifically, what we focus on here is decision-making.

Unraveling the emergence of collective learning in systems of coupled artificial neural networks points to broader implications for machine learning, neuroscience, and society. Here we introduce a minimal model that condenses several recent decentralized algorithms by considering a competition between two terms: the local learning dynamics in the parameters of each neural network unit, and a diffusive coupling among units that tends to homogenize the parameters of the ensemble. We derive an effective theory for linear networks to show that the coarse-grained behavior of our system is equivalent to a deformed Ginzburg-Landau model with quenched disorder. This framework predicts depth-dependent disorder-order-disorder phase transitions in the parameters' solutions that reveal a depth-delayed onset of a collective learning phase and a low-rank microscopic learning path. We validate the theory in coupled ensembles of realistic neural networks trained on the MNIST dataset under privacy constraints. Interestingly, experiments confirm that individual networks -- trained on private data -- can fully generalize to unseen data classes when the collective learning phase emerges. Our work establishes the physics of collective learning and contributes to the mechanistic interpretability of deep learning in decentralized settings.

In this paper, we study two well known methods of Ising structure learning, namely the pseudolikelihood approach and the interaction screening approach, in the context of tensor recovery in $k$-spin Ising models. We show that both these approaches, with proper regularization, retrieve the underlying hypernetwork structure using a sample size logarithmic in the number of network nodes, and exponential in the maximum interaction strength and maximum node-degree. We also track down the exact dependence of the rate of tensor recovery on the interaction order $k$, that is allowed to grow with the number of samples and nodes, for both the approaches. Finally, we provide a comparative discussion of the performance of the two approaches based on simulation studies, which also demonstrate the exponential dependence of the tensor recovery rate on the maximum coupling strength.

Correlation matrices contain a wide variety of spatio-temp oral information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the entire underly ing system. This information can help to predict the underlying network structure, e.g., inferring neuronal connections from spiking data, deducing causal dependencies between genes from expression d ata, and discovering long spatial range influences in climate variations. Traditional methods of pr edicting correlation matrices utilize time series data of all the nodes of the underlying networks. Here, we use a supervised machine learning technique to predict the correlation matrix of entire syste ms from finite time series information of a few randomly selected nodes. The accuracy of the predict ion validates that only a limited time series of a subset of the entire system is enough to make g ood correlation matrix predictions. Furthermore, using an unsupervised learning algorithm, we furnish insights into the success of the predictions from our model. Finally, we employ the machine l earning model developed here to real-world data sets.

The white-matter (micro-)structural architecture of the brain promotes synchrony among neuronal populations, giving rise to richly patterned functional connections. A fundamental problem for systems neuroscience is determining the best way to relate structural and functional networks quantified by diffusion tensor imaging and resting-state functional MRI. As one of the state-of-the-art approaches for network analysis, graph convolutional networks (GCN) have been separately used to analyze functional and structural networks, but have not been applied to explore inter-network relationships. In this work, we propose to couple the two networks of an individual by adding inter-network edges between corresponding brain regions, so that the joint structure-function graph can be directly analyzed by a single GCN. The weights of inter-network edges are learnable, reflecting non-uniform structure-function coupling strength across the brain. We apply our Joint-GCN to predict age and sex of 662 participants from the public dataset of the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA) based on their functional and micro-structural white-matter networks. Our results support that the proposed Joint-GCN outperforms existing multi-modal graph learning approaches for analyzing structural and functional networks.