arXiv subjects

Fabio Pasqualetti

Publications and source records attributed to Fabio Pasqualetti.

At least 19 recordsLinked to original sources

arXiv2026

Computing with Coupled Oscillator Networks: Optimization, Memory, and Modern AI Primitives

We explore how synchronization in coupled oscillator networks may be employed to perform a variety of computing tasks. These systems are becoming more attractive as an alternative to conventional digital computers due to the increasing energy demands of the latter, particularly for large-scale problems in machine learning and artificial intelligence. The ubiquity of coupled oscillator networks means that oscillator-based computing can be thought of as a universal computing paradigm encompassing systems with a diversity of physical realizations, e.g. as analog circuits, neurological systems, spintronic systems. The bridge between the dynamics of coupled oscillator networks and computational primitives they implement is the Ising model, which originates in statistical physics, and when applied to oscillator networks, explains the emergence of globally complex and disordered synchronization patterns from local interactions in the network. We discuss the application of coupled oscillator networks to three fundamental computing operations. First, oscillator networks as specialized hardware solvers of NP-hard combinatorial optimization problems, with the solution encoded in the synchrony patterns. Second, oscillator networks as associative memory systems, enabling storage and retrieval of data represented through phases of oscillations. Finally, oscillator networks as a dynamical implementation of attention, with synchronization providing the mechanism for the alignment of keys to queries. The ability of oscillator networks to implement these computational primitives paves the way for novel realizations of intelligent systems through a variety of physical substrates.

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arXiv2026

Programmable Sequential Memory in Coupled Oscillator Networks

The Hopfield network established that static memories can be stored as energy minima of an energy-based model. Real intelligent agents, however, must navigate sequences of memories rather than isolatedcsnapshots. Biological cortex addresses this through a separation of timescales, where fast synaptic dynamics encode individual states while slow neuromodulatory processes govern transitions between them. Inspired by this organization, we propose a sequential memory architecture that is fully continuous and admits exponential storage capacity. The architecture is programmable, since the transition structure is carried by a mechanism that is decoupled from the stored patterns, driven by the input context, and free to be chosen, optimized, or learned from data. Specifically, we construct an autonomous three-timescale dynamical system with three coupled layers. A fast Kuramoto layer stores phase patterns as exponentially stable phase-locked configurations, an intermediate recognition layer sets the dwell times, and a slow attention layer routes the transitions. We analyze the stability, dwell time, and capacity of the system, and we validate the dynamics through numerical simulations of sequential memory retrieval.

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arXiv2026

Multi-Agent Flow Matching with Decoupled Generative Guidance

Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.

cs.LG↗

arXiv2026

Online Optimization with Unknown Time-Varying Parameters Using Noisy Gradient Measurements

We study online optimization problems in which the cost function depends on latent, time-varying parameters that are unmeasurable and governed by unknown dynamics. Specifically, we consider a strongly convex cost function whose linear term evolves according to unknown linear stochastic dynamics about an unknown nominal operating point, while the algorithm has access only to finite noisy gradient measurements. We propose a solution that uses control theoretic tools to reconstruct the latent parameters from gradient observations using a Gauss-Markov estimator, then identifies the parameter dynamics using a bias-reduced instrumental variable estimator, and finally forecasts the parameters to compute the minimizer. We provide a high probability, finite-horizon bound on the expected tracking error. We illustrate our algorithm on a series of numerical examples.

math.OC↗

arXiv2026

Attention by Synchronization in Coupled Oscillator Networks

We address transformer attention on energy-constrained physical substrates. Softmax attention requires exponentiation and global reduction, operations with high energy cost on von Neumann hardware and no natural physical analog. We show that Kuramoto synchronization dynamics (which arise in electrical, mechanical, superconducting, and charge-density-wave oscillator arrays, among other physical systems) implement a well-defined attention operation. The resulting mechanism, \emph{fixed-query oscillator attention}, replaces softmax's arithmetic with the equilibration of a gradient flow on the sphere: queries are learned anchors fixed on the sphere, and free oscillators evolve under Kuramoto--Lohe dynamics until they settle at positions encoding attention weights via cosine similarity. Because the computation is equilibration, no global exponential normalization is needed. The fixed point is provably unique and globally attractive from almost every initial condition, a guarantee that holds across every physical realization. Empirically, at the minimal hardware configuration (oscillator dimension $d_{\mathrm{osc}} = 2$), oscillator attention matches softmax on keyword spotting, and on subject-verb agreement it trains more reliably while reaching softmax's accuracy. Softmax retains an advantage on causal language modeling, but the gap decays as a power law in $d_{\mathrm{osc}}$. The main objective of this work is not to replace softmax in software but to provide a mathematically grounded blueprint for accurate attention on physical substrates.

cs.LG↗

arXiv2026

On the Degree of Safety: Beyond Safe or Unsafe with Control Barrier Functions

A valid control barrier function (CBF) certifies if its represented safe set can be rendered forward invariant, and the sign of its value indicates whether a state is safe or not, but it does not quantify a degree of safety beyond the binary indication. In this paper, we show that among valid CBFs representing the same safe set, interior values and gradients can be changed arbitrarily, so neither quantity determines a degree of safety that is independent of how the set is represented. We also show that whether a candidate CBF-based inequality constraint is feasible does not by itself quantify a degree of safety. In particular, infeasibility can occur either because the safe set is not controlled invariant or because the candidate CBF representation fails. This motivates our distinction between intrinsic and representational infeasibility. Finally, we introduce the invariance authority demand (IAD), a representation-independent degree of safety that quantifies the control authority required for controlled invariance and can be used to guide set or actuator repair.

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arXiv2026

Provably Safe Generative Sampling with Constricting Barrier Functions

Flow-based generative models, such as diffusion models and flow matching models, have achieved remarkable success in learning complex data distributions. However, a critical gap remains for their deployment in safety-critical domains: the lack of formal guarantees that generated samples will satisfy hard constraints. We propose a safety filtering framework that acts as an online shield for any pre-trained generative model. Our key insight is to cooperate with the generative process rather than override it. We define a constricting safety tube that is relaxed at the initial noise distribution and progressively tightens to the target safe set at the final data distribution, mirroring the coarse-to-fine structure of the generative process itself. By characterizing this tube via Control Barrier Functions (CBFs), we synthesize a feedback control input through a convex Quadratic Program (QP) at each sampling step. As the tube is loosest when noise is high and intervention is cheapest in terms of control energy, most constraint enforcement occurs when it least disrupts the model's learned structure. We prove that this mechanism guarantees safe sampling in discrete-time. The minimum-norm control synthesized at each step minimizes the per-step contribution to the KL divergence between the safe and original distributions. Across all experiments, we observe 100% constraint satisfaction. Our framework applies to any pre-trained flow-based sampling scheme requiring no retraining or architectural modifications. We validate the approach across constrained image generation, physically-consistent trajectory sampling, and safe robotic manipulation policies, achieving 100% constraint satisfaction while preserving semantic fidelity.

cs.LG↗

arXiv2026

Quantifying the cost of network computations to unpack structure-function relationships in the brain

The brain supports computations through coordinated patterns of activity on an underlying network. These networks---from microscale navigational circuits in insects to macroscale brain areas in humans---are organized in structured ways that are thought to support their function. We seek a unifying quantitative framework to understand how network structure shapes the computations a network can readily support. To do so, we frame computation as a goal-directed transition of activity and quantify its cost on a given network using control theory. We then define the distribution of costs across all possible transitions as a $\textit{computational affordance landscape}$ that encodes which computations a network structure readily supports. We apply this framework to a circuit model for how insects maintain a sense of direction and show that updating orientation is the least costly computation, with predicted inputs consistent with known circuitry. In the human brain, we find that the affordance landscape varies systematically with the functional role of each network. Sensory networks display more heterogeneous landscapes (reflecting their role in specialized information processing), whereas association networks display more homogeneous landscapes (reflecting their role in generalized information processing). In recurrent neural networks trained on cognitive tasks, we show that learning progressively increases landscape heterogeneity, reshaping the distribution of affordable computations. Generally, we establish a quantitative framework for studying relationships between structure and computation in neural circuits, with future applications extending to other biological and physical networks.

q-bio.NC↗

arXiv2026

QUIET: Quantifying Underutilized Influential Edges for Targeted Synchronization

Network control theory can be used to model intrinsic and extrinsic strategies to steer neural dynamics. Standard approaches are node-centric, structural, and focused on achieving desired instantaneous states. Here, we develop an edge-centric approach which incorporates both structure and function to achieve extended patterns of neural dynamics characterized by desired synchronization states. Our method, Quantifying Underutilized Influential Edges for Targeted Synchronization (QUIET), is an edge-centric framework that integrates structural controllability of individual white matter connections and mutual information between pairwise functional timeseries to identify energy-efficient synchronization pathways. QUIET identifies quiet highways, edges that are structurally influential but functionally underutilized, to optimize regional synchronization. We validated QUIET across 75 synthetic configurations, where QUIET-ranked edge sets significantly outperformed random selection in 93% of cases (p<0.01). The framework, tested on Human Connectome Project participants, revealed that the control energy required for synchronization of the salience network correlates with fluid intelligence. QUIET, applied to healthy adults undergoing dexmedetomidine-induced unresponsiveness, showed that the frontoparietal and default-mode networks exhibited the largest control energy required for synchronization in both awake and sedated states. QUIET is released as a stand-alone software to be used to study theoretically-defined synchronization pathways, which in turn could inform testable hypotheses in perturbative studies.

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arXiv2026

Constricting Tubes for Prescribed-Time Safe Control

We propose a constricting Control Barrier Function (CBF) framework for prescribed-time control of control-affine systems with input constraints. Given a system starting outside a target safe set, we construct a time-varying safety tube that shrinks from a relaxed set containing the initial condition to the target set at a user-specified deadline. Any controller rendering this tube forward invariant guarantees prescribed-time recovery by construction. The constriction schedule is bounded and tunable by design, in contrast to prescribed-time methods where control effort diverges near the deadline. Feasibilityå under input constraints reduces to a single verifiable condition on the constriction rate, yielding a closed-form minimum recovery time as a function of control authority and initial violation. The framework imposes a single affine constraint per timestep regardless of state dimension, scaling to settings where grid-based reachability methods are intractable. We validate on an 18-dimensional multi-agent system, demonstrating scalability and prescribed-time recovery with bounded control effort.

math.OC↗

arXiv2026

Oscillator-Based Associative Memory with Exponential Capacity: Theory, Algorithms, and Hardware Implementation

Associative memory systems enable content-addressable storage and retrieval of patterns, a capability central to biological neural computation and artificial intelligence. Classical implementations such as Hopfield networks face fundamental limitations in memory capacity, scaling at most linearly with network size. We present an associative memory architecture based on Kuramoto oscillator networks with honeycomb topology in which memories are encoded as stable phase-locked configurations. The honeycomb network consists of multiple cycles that share nodes in a chain-like arrangement, creating a one-dimensional lattice of chained+loops. We prove that this architecture achieves exponential memory capacity: a network of $N$ oscillators can store $(2\lceil n_c/4 \rceil - 1)^m$ distinct patterns, where $m$ honeycomb cycles each contain $n_c$ oscillators. Moreover, we fully characterize all stable configurations and prove that each memory's basin of attraction maintains a guaranteed minimum size independent of network scale. Simulations using charge-density-wave (CDW) oscillators validate predicted phase-locking behavior, demonstrating practical realizability in neuromorphic hardware.

cs.NE↗

arXiv2026

Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems

In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for drift-free and linear time-invariant (LTI) dynamics. The central idea is to first excite the system with white noise so that a forward diffusion process explores the reachable regions of state space, and then to design a deterministic feedback law that acts as a denoising mechanism driving the system back toward a desired target distribution supported on the target set. This denoising phase provides a feedback controller that steers the control system to the target set. In this framework, control synthesis reduces to constructing a deterministic reverse process that reproduces the desired evolution of state densities. We derive existence conditions ensuring such deterministic realizations of time-reversals for controllable drift-free and LTI systems, and show that the resulting feedback laws provide a tractable alternative to nonlinear control by viewing density control as a relaxation of controlling a system to target sets. Numerical studies on a unicycle model with obstacles, a five-dimensional driftless system, and a four-dimensional LTI system demonstrate reliable diffusion-inspired density control.

math.OC↗

arXiv2026

Geometric SSM: LTI State Space Models for Selective Tasks

A key claim in recent work on Selective State Space Models is that selectivity, the ability to focus on relevant information while filtering irrelevant inputs, requires breaking the Linear Time-Invariant (LTI) property through time-varying dynamics. We challenge this claim by demonstrating that LTI systems can achieve selectivity when designed using principles from geometric control. We introduce the Geometric SSM, in which different input patterns excite distinct invariant subspaces of the dynamics. Unlike Mamba's memoryless selection mechanism, our approach employs a dynamic residual generator that maintains temporal memory, enabling recognition of multi-token patterns without time-varying system matrices. The Geometric SSM achieves near-perfect performance on a novel extended induction head task where Mamba fails, while preserving efficient FFT-based training. Our results demonstrate that geometric control theory can inform the design of novel selective sequence models that combine theoretical rigor with practical efficiency.

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arXiv2025

Habit learning is associated with efficiently controlled network dynamics in naive macaque monkeys

Primates utilize distributed neural circuits to learn habits in uncertain environments, but the underlying mechanisms remain poorly understood. We propose a formal theory of network energetics explaining how brain states influence sequential behavior. We test our theory on multi-unit recordings from the caudate nucleus and cortical regions of macaques performing a motor habit task. The theory predicts the energy required to transition between brain states represented by trial-specific firing rates across channels, assuming activity spreads through effective connections. We hypothesized that habit formation would correlate with lower control energy. Consistent with this, we observed smaller energy requirements for transitions between similar saccade patterns and those of intermediate complexity, and sessions exploiting fewer patterns. Simulations ruled out confounds from neurons' directional tuning. Finally, virtual lesioning demonstrated robustness of observed relationships between control energy and behavior. This work paves the way for examining how behavior arises from changing activity in distributed circuitry.

q-bio.NC↗

arXiv2025

Dynamics-aware Diffusion Models for Planning and Control

This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical application. We propose a novel framework that integrates system dynamics directly into the diffusion model's denoising process through a sequential prediction and projection mechanism. This mechanism, aligned with the diffusion model's noising schedule, ensures generated trajectories are both consistent with expert demonstrations and adhere to underlying physical constraints. Notably, our approach can generate maximum likelihood trajectories and accurately recover trajectories generated by linear feedback controllers, even when explicit dynamics knowledge is unavailable. We validate the effectiveness of our method through experiments on standard control tasks and a complex non-convex optimal control problem involving waypoint tracking and collision avoidance, demonstrating its potential for efficient trajectory generation in practical applications. Our code repository is available at www.github.com/darshangm/dynamics-aware-diffusion.

cs.RO↗

arXiv2025

Vibrational Stabilization of Complex Network Systems

Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on stabilization assume that network systems states can be measured online so that feedback control strategies can be used. However, in many real-world scenarios, systems states, e.g., neuronal activity in the brain, are often difficult to measure. In this paper, we take this situation into account and study the stabilization problem of linear network systems with an open-loop control strategy (vibrational control). We derive a graph-theoretic sufficient condition for structural vibrational stabilizability, under which network systems can always be stabilized. We further provide an approach to select the locations in the network for control placement and design corresponding vibrational inputs to stabilize systems that satisfy this condition. Finally, we provide some numerical results that demonstrate the validity of our theoretical findings.

math.OC↗

arXiv2025

Vibrational Control of Complex Networks

The stability of complex networks, from power grids to biological systems, is crucial for their proper functioning. It is thus important to control such systems to maintain or restore their stability. Traditional approaches rely on real-time state measurements for feedback control, but this can be challenging in many real-world systems, such as the brain, due to their complex and dynamic nature. This paper utilizes vibrational control -- an open-loop strategy -- to regulate network stability. Unlike conventional methods targeting network nodes, our approach focuses on manipulating network edges through vibrational inputs. We establish sufficient graph-theoretic conditions for vibration-induced functional modifications of network edges and stabilization of network systems as a whole. Additionally, we provide methods for designing effective vibrational control inputs and validate our theoretical findings through numerical simulations.

math.OC↗

arXiv2025

Vibrational Stabilization of Cluster Synchronization in Oscillator Networks

Cluster synchronization is of great importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as neurological disorders in the brain. Therefore, it is crucial to restore normal system functions by stabilizing the appropriate cluster synchronization patterns. Most existing studies focus on designing controllers based on state measurements to achieve system stabilization. However, in many real-world scenarios, measuring system states in real time, such as neuronal activity in the brain, poses significant challenges, rendering the stabilization of such systems difficult. To overcome this challenge, in this paper, we employ an open-loop control strategy, vibrational control, which does not require any state measurements. We establish some sufficient conditions under which vibrational inputs stabilize cluster synchronization. Further, we provide a tractable approach to design vibrational control. Finally, numerical experiments are conducted to demonstrate our theoretical findings.

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