arXiv subjects

Zongli Lin

Publications and source records attributed to Zongli Lin.

18 recordsLinked to original sources

arXiv2026

A Constrained Kuramoto Gradient-Flow System Can Perform High-Accuracy Finite-Time Inference

A central question in physical inference is whether strongly constrained dynamical systems can realize accurate input--output maps through their own finite-time evolution. We study this question in Kuramoto phase networks, whose deterministic dynamics form an input-conditioned gradient flow and whose predictions are read directly from output oscillators. As a constructive training approach, we develop a two-stage teacher--student procedure. A neural teacher is first converted into an explicit phase trajectory whose terminal oscillator activations reproduce the teacher outputs, and the Kuramoto parameters are trained by matching the student vector field along this prescribed path. Because accurate teacher-forced path matching does not ensure accurate autonomous inference, we then differentiate through the autonomous finite-time rollout and directly align its terminal output with the neural target. The resulting oscillator system, with $74$ oscillators, reaches mean test accuracies of $96.711\%$ on MNIST and $86.399\%$ on Fashion-MNIST. This capability persists across neural-teacher architectures, matched system sizes, thermal perturbations, and integration-grid refinement. Together, these results provide a constructive demonstration that a strongly constrained, small-sized Kuramoto gradient-flow system can be trained for high-accuracy finite-time inference through a direct oscillator readout.

physics.app-ph↗

arXiv2026

Chirality of a $Z_q$ Model as Directional Phase Shifts in Oscillator Networks

Chirality in a discrete $Z_q$ spin interaction distinguishes clockwise from counterclockwise phase differences, but its manifestation in continuous nonlinear dynamics is unclear. We show that any pairwise $Z_q$ Hamiltonian admits a unique equilibrium-preserving embedding into a continuous phase-energy landscape that matches the discrete energy on the $q$-state phase grid, where every grid point is stationary. This embedding reveals that a $Z_q$ kernel is nonchiral if and only if the sine components of the relaxation vanish. Chirality of the discrete $Z_q$ model is therefore exactly the odd part of the continuous phase interaction. In the induced nonlinear phase dynamics, this odd part becomes an orientation-dependent phase shift in the multi-harmonic coupling, and chiral reversal flips this shift while preserving the coupling magnitudes. In self-sustaining oscillator networks, the shift is further realized as a direction-dependent delay. Transistor-level ring-oscillator simulations validate the predicted phase locking and reversal of directed phase bias. These results show that algebraic handedness in a discrete spin Hamiltonian can be represented as tunable time-domain asymmetry in continuous nonlinear dynamics.

nlin.CD↗

arXiv2026

Delayed Coupling Restores Ising Phase Dynamics in Physical Oscillator Networks

Oscillator-based Ising machines, in which the phases of coupled self-sustaining oscillators evolve toward decreasing an Ising Hamiltonian, are commonly interpreted as physical realizations of the Ising model. This interpretation, however, requires the phase dynamics generated by the physical oscillator network to match a prescribed Ising dynamics. Here we show that this correspondence is generally not guaranteed. For arbitrary self-sustaining oscillators under weak coupling, we derive the physical phase interaction from the harmonic overlap between the injected waveform and the perturbation projection vector (also referred to as impulse sensitivity function). We find that uncompensated harmonic phase mismatches between these two quantities generate even components in the physical coupling function, causing a network with the correct coupling topology to implement a non-Ising dynamics. We further show that delayed coupling provides a universal phase-compensation mechanism. For a fixed delay, we derive a condition on the delay under which the even components is minimized in the sense of L2-norm, and oscillator examples confirm that the predicted delay substantially suppresses the even components and brings the realized coupling function closer to the prescribed odd interaction. We then show that a periodically modulated delay can, under suitable moment conditions, eliminate the even components in the phase dynamics. These results establish a general design principle for implementing prescribed energy-based dynamics in physical oscillator networks.

physics.app-ph↗

arXiv2026

A Momentum-based Stochastic Algorithm for Linearly Constrained Nonconvex Optimization

This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based augmented Lagrangian method that employs a Polyak-type gradient estimator and requires only one stochastic gradient evaluation per iteration. Under the standard stochastic oracle model and the smoothness condition of the expected objective, we establish a convergence guarantee in terms of the first-order KKT residual of the original constrained problem. In particular, the proposed method computes an $\epsilon$-stationary solution in expectation within $O(\epsilon^{-4})$ stochastic gradient evaluations. Numerical experiments further show that the proposed method achieves competitive iteration complexity and improved wall-clock efficiency compared with representative recursive-momentum baselines.

math.OC↗

arXiv2026

Dynamic Average Consensus with Privacy Guarantees and Its Application to Battery Energy Storage Systems

A privacy-preserving dynamic average consensus (DAC) algorithm is proposed that achieves consensus while preventing external eavesdroppers from inferring the reference signals and their derivatives. During the initialization phase, each agent generates a set of sinusoidal signals with randomly selected frequencies and exchanges them with its neighboring agents to construct a masking signal. Each agent masks its reference signals using this composite masking signal before executing the DAC update rule. It is shown that the developed scheme preserves the convergence properties of the conventional DAC framework while preventing information leakage to external eavesdroppers. Furthermore, the developed algorithm is applied to state-of-charge (SoC) balancing in a networked battery energy storage system to demonstrate its practical applicability. Simulation results validate the theoretical findings.

eess.SY↗

arXiv2026

Privacy-Preserving Dynamic Average Consensus by Masking Reference Signals

In multi-agent systems, dynamic average consensus (DAC) is a decentralized estimation strategy in which a set of agents tracks the average of time-varying reference signals. Because DAC requires exchanging state information with neighbors, attackers may gain access to these states and infer private information. In this paper, we develop a privacy-preserving method that protects each agent's reference signal from external eavesdroppers and honest-but-curious agents while achieving the same convergence accuracy and convergence rate as conventional DAC. Our approach masks the reference signals by having each agent draw a random real number for each neighbor, exchanges that number over an encrypted channel at the initialization, and computes a masking value to form a masked reference. Then the agents run the conventional DAC algorithm using the masked references. Convergence and privacy analyses show that the proposed algorithm matches the convergence properties of conventional DAC while preserving the privacy of the reference signals. Numerical simulations validate the effectiveness of the proposed privacy-preserving DAC algorithm.

eess.SY↗

arXiv2025

An Accelerated Distributed Optimization with Equality and Inequality Coupling Constraints

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus optimization problem over a connected network. To efficiently solve this dual problem and hence the primal problem, we design an accelerated linearized algorithm that, at each round, a look-ahead linearization of the separable objective is combined with a quadratic penalty on the Laplacian constraint, a proximal step, and an aggregation of iterations. On the theory side, we prove non-ergodic rates for both the primal optimality error and the feasibility error. On the other hand, numerical experiments show a faster decrease of optimality error and feasibility residual than augmented-Lagrangian tracking and distributed subgradient baselines under the same communication budget.

math.OC↗

arXiv2025

Non-Ergodic Convergence Algorithms for Distributed Consensus and Coupling-Constrained Optimization

We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without smoothness or strong convexity, we establish non-ergodic sublinear rates of order O(1/\sqrt{k}) for both the objective optimality and the consensus violation. Leveraging duality, we then show that the economic dispatch problem admits a dual consensus formulation, and that applying the same algorithm to the dual economic dispatch yields non-ergodic O(1/\sqrt{k}) decay for the error of the summation of the cost over the network and the equality-constraint residual under convexity and Slater's condition. Numerical results on the IEEE 118-bus system demonstrate faster reduction of both objective error and feasibility error relative to the state-of-the-art baselines, while the dual variables reach network-wide consensus.

math.OC↗

arXiv2025

A Distributed Gradient-based Algorithm for Optimization Problems with Coupled Equality Constraints

This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each iteration. Such approaches become computationally burdensome or intractable when local cost functions are complex. To address this challenge, we propose a novel distributed gradient-based algorithm that avoids solving a local optimization problem at each iteration by leveraging first-order approximations and projection onto local feasible sets. The algorithm operates in a fully distributed manner, requiring only local communication without exchanging gradients or primal variables. We rigorously establish sublinear convergence for general convex cost functions and linear convergence under strong convexity and smoothness conditions. Numerical simulation on the IEEE 118-bus system demonstrates the superior computational efficiency and scalability of the proposed method compared to several state-of-the-art distributed optimization algorithms.

math.OC↗

arXiv2025

Privacy-Preserving Distributed Control for a Networked Battery Energy Storage System

The increasing deployment of distributed Battery Energy Storage Systems (BESSs) in modern power grids necessitates effective coordination strategies to ensure state-of-charge (SoC) balancing and accurate power delivery. While distributed control frameworks offer scalability and resilience, they also raise significant privacy concerns due to the need for inter-agent information exchange. This paper presents a novel privacy-preserving distributed control algorithm for SoC balancing in a networked BESS. The proposed framework includes distributed power allocation law that is designed based on two privacy-preserving distributed estimators, one for the average unit state and the other for the average desired power. The average unit state estimator is designed via the state decomposition method without disclosing sensitive internal states. The proposed power allocation law based on these estimators ensures asymptotic SoC balancing and global power delivery while safeguarding agent privacy from external eavesdroppers. The effectiveness and privacy-preserving properties of the proposed control strategy are demonstrated through simulation results.

eess.SY↗

arXiv2025

From Ising to Potts: Physics-inspired Potts machines of coupled oscillators for low-energy sampling and combinatorial optimization

The $q$-state Potts model is a fundamental model in statistical physics that generalizes the Ising model and plays a key role in the study of phase transitions, critical phenomena, complex systems, and combinatorial optimization. Sampling low-energy configurations of the $q$-state Potts model is essential to these studies, but it remains challenging. While physics-inspired dynamical sampling has been extensively explored for the Ising case ($q=2$) in the form of Ising machines, its generalization to general $q$-state Potts models remains largely unexplored. To fill this gap, we propose a class of physics-inspired dynamical samplers that directly target general $q$-state Potts models, which we refer to as the oscillator Potts machine (OPM). We show, through theoretical analysis and numerical experiments, that the OPM exhibits a systematic low-energy bias with respect to the underlying Potts energy landscape. Furthermore, we demonstrate, via phase perturbation analysis, that the OPM, as overdamped Langevin dynamics, can be realized with a network of self-sustaining oscillators, demonstrating that the OPM is naturally realizable in hardware using standard technology such as CMOS. We design a small-scale ring-oscillator circuit that implements a three-state OPM and validate its operation through transistor-level simulation. Leveraging the low-energy bias of the OPM for Potts models, we then apply it to large-scale max-$K$-cut problems by mapping these instances to $q$-state Potts Hamiltonians and compare its performance against established algorithms. Our results position the OPM as a promising, physically grounded dynamical system framework for multi-state sampling and combinatorial optimization.

cond-mat.stat-mech↗

arXiv2025

Training oscillator Ising machines to assign the dynamic stability of their equilibrium points

We propose a neural network model, which, with appropriate assignment of the stability of its equilibrium points (EPs), achieves Hopfield-like associative memory. The oscillator Ising machine (OIM) is an ideal candidates for such a model, as all its $0/\pi$ binary EPs are structurally stable with their dynamic stability tunable by the coupling weights. Traditional Hopfield-based models store the desired patterns by designing the coupling weights between neurons. The design of coupling weights should simultaneously take into account both the existence and the dynamic stability of the EPs for the storage of the desired patterns. For OIMs, since all $0/\pi$ binary EPs are structurally stable, the design of the coupling weights needs only to focus on assigning appropriate stability for the $0/\pi$ binary EPs according to the desired patterns. In this paper, we establish a connection between the stability and the Hamiltonian energy of EPs for OIMs, and, based on this connection, provide a Hamiltonian-Regularized Eigenvalue Contrastive Method (HRECM) to train the coupling weights of OIMs for assigning appropriate stability to their EPs. Finally, numerical experiments are performed to validate the effectiveness of the proposed method.

cs.NE↗

arXiv2023

A Note on Analyzing the Stability of Oscillator Ising Machines

The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While prior work on the stability of the so-called Oscillator Ising Machines (OIMs) has used the linearization method, in this letter, we present a complementary method to analyze stability using the second order derivative test of the energy / cost function. We establish the equivalence between the two methods, thus augmenting the tool kit for the design and implementation of OIMs.

math.OC↗

arXiv2023

Stability of Oscillator Ising Machines: Not All Solutions Are Created Equal

Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the global minima of the Lyapunov function (commonly referred to as the energy function) describing the coupled oscillator system and the ground state of the Ising Hamiltonian. However, the properties of the oscillator Ising machine (OIM) from a nonlinear control viewpoint, such as the stability of the OIM solutions remains unexplored. Therefore, in this work, using nonlinear control-theoretic analysis, we (i) Identify the conditions required to ensure the functionality of the coupled oscillators as an Ising machine; (ii) Show that all globally optimal phase configurations may not always be stable, resulting in some configurations being more favored over others, and thus, creating a biased OIM; (c) Elucidate the impact of the stability of locally optimal phase configurations on the quality of the solution computed by the system. Our work, fostered through the unique convergence between nonlinear control theory and analog systems for computing, provides a new toolbox for the design and implementation of dynamical system-based computing platforms.

math.DS↗

arXiv2022

Formulating Oscillator-Inspired Dynamical Systems to Solve Boolean Satisfiability

Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many of which are still challenging to solve using conventional digital solvers. In this work, we formulate two oscillator-inspired dynamical systems to solve quintessential computationally intractable problems in Boolean satisfiability (SAT). The system dynamics are engineered such that they facilitate solutions to two different flavors of the SAT problem. We formulate the first dynamical system to compute the solution to the 3-SAT problem, while for the second system, we show that its dynamics map to the solution of the Max-NAE-3-SAT problem. Our work advances understanding of how this physics-inspired approach can be used to address challenging problems in computing.

math.DS↗

arXiv2022

Computational Models based on Synchronized Oscillators for Solving Combinatorial Optimization Problems

The equivalence between the natural minimization of energy in a dynamical system and the minimization of an objective function characterizing a combinatorial optimization problem offers a promising approach to designing dynamical system-inspired computational models and solvers for such problems. For instance, the ground state energy of coupled electronic oscillators, under second harmonic injection, can be directly mapped to the optimal solution of the Maximum Cut problem. However, prior work has focused on a limited set of such problems. Therefore, in this work, we formulate computing models based on synchronized oscillator dynamics for a broad spectrum of combinatorial optimization problems ranging from the Max-K-Cut (the general version of the Maximum Cut problem) to the Traveling Salesman Problem. We show that synchronized oscillator dynamics can be engineered to solve these different combinatorial optimization problems by appropriately designing the coupling function and the external injection to the oscillators. Our work marks a step forward towards expanding the functionalities of oscillator-based analog accelerators and furthers the scope of dynamical system solvers for combinatorial optimization problems.

math.OC↗

arXiv2018

SITUP: Scale Invariant Tracking using Average Peak-to-Correlation Energy

Robust and accurate scale estimation of a target object is a challenging task in visual object tracking. Most existing tracking methods cannot accommodate large scale variation in complex image sequences and thus result in inferior performance. In this paper, we propose to incorporate a novel criterion called the average peak-to-correlation energy into the multiresolution translation filter framework to obtain robust and accurate scale estimation. The resulting system is named SITUP: Scale Invariant Tracking using Average Peak-to-Correlation Energy. SITUP effectively tackles the problem of fixed template size in standard discriminative correlation filter based trackers. Extensive empirical evaluation on the publicly available tracking benchmark datasets demonstrates that the proposed scale searching framework meets the demands of scale variation challenges effectively while providing superior performance over other scale adaptive variants of standard discriminative correlation filter based trackers. Also, SITUP obtains favorable performance compared to state-of-the-art trackers for various scenarios while operating in real-time on a single CPU.

eess.IV↗

arXiv2018

OSLO: Automatic Cell Counting and Segmentation for Oligodendrocyte Progenitor Cells

Reliable cell counting and segmentation of oligodendrocyte progenitor cells (OPCs) are critical image analysis steps that could potentially unlock mysteries regarding OPC function during pathology. We propose a saliency-based method to detect OPCs and use a marker-controlled watershed algorithm to segment the OPCs. This method first implements frequency-tuned saliency detection on separate channels to obtain regions of cell candidates. Final detection results and internal markers can be computed by combining information from separate saliency maps. An optimal saliency level for OPCs (OSLO) is highlighted in this work. Here, watershed segmentation is performed efficiently with effective internal markers. Experiments show that our method outperforms existing methods in terms of accuracy.

eess.IV↗