arXiv subjects

Majid Zamani

Publications and source records attributed to Majid Zamani.

At least 19 recordsLinked to original sources

arXiv2026

Data-Driven Formal Methods for Complex Dynamical Systems: A Survey

Data-driven approaches with formal guarantees have recently emerged as a powerful means for the verification and controller synthesis of complex dynamical systems. Interest in these methods is rapidly growing, as system models are often unavailable in practice, and challenges such as nonlinear behavior, uncertainty, and the curse of dimensionality typically render accurate modeling infeasible. These difficulties motivate leveraging limited data collected from the system while still providing formal guarantees on its overall behavior. The community has therefore proposed a few hundred articles on the development of data-driven frameworks that enable the formal verification and synthesis of dynamical systems without explicit models, addressing complex specifications beyond stability. Despite this rapid growth, existing results remain scattered and lack a coherent organization, limiting a clear understanding of their principles, distinctions, and practical potential. This survey fills this gap by providing a comprehensive overview of these data-driven methods for both deterministic and stochastic dynamical systems. We structure the literature around three main methodological pillars in formal methods: (in)finite-abstraction-based techniques, functional certificate approaches, such as control barrier certificates, and compositional methods. For each of these approaches, we classify the resulting data-driven guarantees into three main categories: (i) statistical guarantees grounded in probably approximately correct and scenario-based frameworks, (ii) guarantees derived from Lipschitz continuity, and (iii) guarantees exploiting structural properties. While the literature on deterministic systems is considerably richer, we also devote particular attention to the stochastic counterpart, highlighting the inherent differences and challenges that arise compared to the deterministic case.

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arXiv2026

DBNN: Neural Spike Classification Using a Deep Binarized Neural Network

Implantable brain-computer interfaces require on-node spike sorting to reduce telemetry bandwidth and power while maintaining reliable neural decoding. This paper presents a hardware-oriented deep binarized neural network (DBNN) spike-sorting system with two binarized hidden layers with 256 neurons and a fixed-point output layer to enable multiplier-free inference dominated by sign-controlled accumulation and bit-wise logic. The proposed classifier operates on compact 16-sample spike waveforms to reduce the implementation cost (16-256-256-3) and achieves a median classification accuracy of 98.7% on both synthetic and in-vivo datasets. An FPGA prototype on a Cyclone V device operates at 50 MHz and requires 528 cycles per spike, corresponding to a 0.01 ms compute latency, while consuming 828 ALMs and 1023 registers with zero DSP blocks. For ASIC feasibility, the DBNN is implemented using FreePDK45-based flow; synthesis in Synopsys Design Compiler indicates an estimated silicon area of 0.014 mm2 and an operating power of 122 nW at 20 kHz under a 1.1 V supply. These results demonstrate that the proposed DBNN spike sorter offers a favorable trade-off between accuracy and implementation cost, supporting low-power, implantable neural interfaces. Overall, the proposed DBNN spike sorter achieves high accuracy (98.7%) with extremely low hardware cost (0.014 mm2, 122 nW at 20 kHz) and multiplier-free operation, making it suitable for low-power, implantable neural interfaces. This paper introduces the first DBNN designed for real-time neural spike sorting, striking an excellent balance between input data size and network complexity.

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arXiv2026

Trajectory-based Safety of Monotone Systems: Verification and Control Synthesis

This paper presents a novel data-driven framework for the robust safety verification and safe control synthesis of unknown monotone discrete-time systems. While existing data-driven safety analysis approaches are often either heuristic in nature or require large amounts of data to provide rigorous guarantees, we leverage the structural property of monotonicity to significantly reduce data requirements while still ensuring formal safety guarantees. Our approach is built upon a new class of certificates called dominance functions, constructed directly from collected system trajectories, which themselves need not be safe. By exploiting the monotone structure of the dynamics, we show that dominance functions are (i) dissipative, meaning that they decrease monotonically along system trajectories, and (ii) sufficiently \expressive to characterize safety certificates for monotone systems. Together, these properties establish dominance functions as principled building blocks for the systematic construction of formal safety certificates directly from trajectory data. For both robust safety verification and safe control synthesis, we develop an efficient sampling-based optimization framework that searches for safety certificates represented as linear combinations of dominance functions constructed from collected trajectories. We validate our data-driven framework on two monotone systems by successfully deriving safety certificates from a small number of trajectories.

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arXiv2026

HyperCertificates: Verification of Discrete-time Dynamical Systems against HyperLTL Specifications

We introduce a functional inductive framework to verify discrete-time dynamical systems against hyperproperties specified as Hyperlinear temporal logic formulae via a notion of HyperCertificates. Unlike linear temporal logic (LTL) formulae which are concerned with individual traces of a system, hyperproperties are properties that are concerned with how the traces of a system relate to one another. HyperLTL is an extension of LTL for hyperproperties, and is useful to describe specifications such as opacity, privacy as well as notions of robustness. Our notion of HyperCertificates consists of a pair of functions, where the first models the lookahead, and the second relies on a combination of barrier and ranking functions. We use closure certificates, to act as a model for this lookahead and then rely on barrier and ranking function arguments modulo this lookahead to provide guarantees against HyperLTL formulae. We demonstrate how our approach is automatable via existing techniques such as sum-of-squares optimization (SOS) and satisfiability modulo theories (SMT) solvers. Finally, we demonstrate our approach on some case studies.

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arXiv2026

Hierarchical Control for Continuous-time Systems via General Approximate Alternating Simulation Relations

This paper introduces a general approximate alternating simulation relation (\emph{$\varepsilon$-gAAS relation}) for continuous-time systems, which relaxes existing simulation relations to tolerate larger mismatches between abstract and concrete models. The definition of gAAS for continuous-time systems is first proposed, and its properties are investigated. Then, a control refinement method is developed to enable hierarchical control for the gAAS relation. Finally, case studies demonstrate the effectiveness of the proposed approach, highlighting its advantages over existing methods.

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arXiv2026

Digital Guardians: The Past and The Future of Cyber-Physical Resilience

Resilience in cyber-physical systems (CPS) is the fundamental ability to maintain safety and critical functionality despite adverse "perturbations," which includes security attacks, environmental disruptions, and hardware or software failures. This survey provides a comprehensive review of CPS resilience, framing the field through five interconnected themes that are required in an integrated whole to achieve real-world resilience. The article first posits that resilience is a system-wide property emerging from interactions between hardware, software, and human users. Second, it addresses the challenges of learning-enabled CPS, which often operate in data-scarce environments characterized by imbalanced or noisy data, requiring innovative solutions like synthetic data generation and foundation model adaptation. Third, the survey examines proactive measures for resilience, which include distinctive aspects of verification, testing, and redundancy. Fourth, it explores recovery mechanisms, moving beyond traditional fault models to design "just good enough" recovery strategies that prioritize safety-critical functions during perturbations. Finally, it highlights the central role of the human, focusing on the different levels of human intervention, the necessity of trust calibration, and the requirement for explainable AI to support human-CPS teaming. These themes are illustrated through representative application domains, primarily Connected and Autonomous Transportation Systems (CATS) and Medical CPS (MCPS). By integrating the five interconnected themes, this survey provides a systematic roadmap for achieving the resilient CPS in increasingly complex and adversarial environments.

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arXiv2026

MetaSort: An Accelerated Approach for Non-uniform Compression and Few-shot Classification of Neural Spike Waveforms

Many previous works in spike sorting study spike classification and compression independently. In this paper, a novel algorithm is proposed called MetaSort to address these two problems. To deal with compression, a novel adaptive level crossing algorithm is proposed to approximate spike shapes with high fidelity. Meanwhile, the latent feature representation is used to handle the classification problem. Besides, to guarantee MetaSort is robust and discriminative, the geometric information of data is exploited simultaneously in the proposed framework by meta-transfer learning. Empirical experiments with in-vivo spike data demonstrate that MetaSort delivers promising performance, highlighting its potential and motivating continued development toward an ultra-low-power, on-chip implementation.

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arXiv2026

Vector Certificates for $\omega$-regular Specifications

The recently introduced notions of ranking functions and closure certificates utilize well-foundedness arguments to facilitate the verification of dynamical systems against $\omega$-regular properties. A ranking function and a closure certificate are real-valued functions defined over states and state pairs of a dynamical system whose zero superlevel sets are inductive state invariant and inductive transition invariant, respectively. The search for such certificates can be automated by fixing a specific template class, such as a polynomial of a fixed degree, and then using optimization techniques such as sum-of-squares (SOS) programming to find it. Unfortunately, such certificates may not be found for a fixed template. In such a case, one must change the template; for example, increase the degree of the polynomial. In this paper, we consider a notion of multiple functions in the form of vector certificates. Taking inspiration from the literature on vector barrier certificates as generalizations of standard barrier certificates for safety verification, we propose vector co-B\"uchi ranking functions and vector closure certificates as nontrivial generalizations of ranking functions and closure certificates, respectively. Both notions consist of a set of functions that jointly overapproximate an inductive invariant by considering each function to be a linear combination of the others. The advantage of such certificates is that they allow us to prove properties even when a single function for a fixed template cannot be found using standard approaches. We present an SOS programming approach to search for these functions and demonstrate the effectiveness of our proposed method in verifying $\omega$-regular specifications in several case studies.

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arXiv2026

Interpolation-Inspired Closure Certificates

Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of transition invariants, to verify dynamical systems against $\omega$-regular properties including safety. A closure certificate, defined over state pairs of a dynamical system, is a real-valued function whose zero superlevel set characterizes an inductive transition invariant of the system. The search for such a certificate can be effectively automated by assuming it to be within a specific template class, e.g. a polynomial of a fixed degree, and then using optimization techniques such as sum-of-squares (SOS) programming to find it. Unfortunately, one may not be able to find such a certificate for a fixed template. In such a case, one must change the template, e.g. increase the degree of the polynomial. In this paper, we consider a notion of multiple closure certificates dubbed interpolation-inspired closure certificates. An interpolation-inspired closure certificate consists of a set of functions which jointly over-approximate a transition invariant by first considering one-step transitions, then two, and so on until a transition invariant is obtained. The advantage of interpolation-inspired closure certificates is that they allow us to prove properties even when a single function for a fixed template cannot be found using standard approaches. We present SOS programming and a scenario program to find these sets of functions and demonstrate the effectiveness of our proposed method to verify persistence and general $\omega$-regular specifications in some case studies.

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arXiv2025

Robustness Certificates for Neural Networks Against Data Poisoning and Evasion Attacks

The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing defenses lack formal guarantees or rely on restrictive assumptions about the model class, attack type, extent of poisoning, or point-wise certification, limiting their practical reliability. This paper introduces a principled formal robustness certification framework that models gradient-based training as a discrete-time dynamical system (dt-DS) and formulates poisoning robustness as a formal safety verification problem. By adapting the concept of barrier certificates (BCs) from control theory, we introduce sufficient conditions to certify a robust radius ensuring that the terminal model remains safe under worst-case ${\ell}_p$-norm-based poisoning. To make this practical, we parameterize BCs as neural networks trained on finite sets of poisoned trajectories. We further derive probably approximately correct (PAC) bounds by solving a scenario convex program (SCP), which yields a confidence lower bound on the certified robustness radius generalizing beyond the training set. Importantly, our framework also extends to certification against test-time attacks, making it the first unified framework to provide formal guarantees in both training and test-time attack settings. Experiments on MNIST, SVHN, CIFAR-10, and CIFAR-100 show that our approach certifies non-trivial perturbation budgets while being model-agnostic and requiring no prior knowledge of the attack or contamination level.

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arXiv2025

Monotone Neural Barrier Certificates

This report presents a neurosymbolic framework for safety verification and control synthesis in high-dimensional monotone dynamical systems without relying on explicit models or conservative Lipschitz bounds. The approach combines the expressiveness of neural networks with the rigor of symbolic reasoning via barrier certificates, functional analogs of inductive invariants that formally guarantee safety. Prior data-driven methods often treat dynamics as black-box models, relying on dense state-space discretization or Lipschitz overapproximations, leading to exponential sample complexity. In contrast, monotonicity--a pervasive structural property in many real-world systems--provides a symbolic scaffold that simplifies both learning and verification. Exploiting order preservation reduces verification to localized boundary checks, transforming a high-dimensional problem into a tractable, low-dimensional one. Barrier certificates are synthesized using monotone neural network architectures with embedded monotonicity constraints--trained via gradient-based optimization guided by barrier conditions. This enables scalable, formally sound verification directly from simulation data, bridging black-box learning and formal guarantees within a unified neurosymbolic framework.

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arXiv2025

Physics-Informed Reward Machines

Reward machines (RMs) provide a structured way to specify non-Markovian rewards in reinforcement learning (RL), thereby improving both expressiveness and programmability. Viewed more broadly, they separate what is known about the environment, captured by the reward mechanism, from what remains unknown and must be discovered through sampling. This separation supports techniques such as counterfactual experience generation and reward shaping, which reduce sample complexity and speed up learning. We introduce physics-informed reward machines (pRMs), a symbolic machine designed to express complex learning objectives and reward structures for RL agents, thereby enabling more programmable, expressive, and efficient learning. We present RL algorithms capable of exploiting pRMs via counterfactual experiences and reward shaping. Our experimental results show that these techniques accelerate reward acquisition during the training phases of RL. We demonstrate the expressiveness and effectiveness of pRMs through experiments in both finite and continuous physical environments, illustrating that incorporating pRMs significantly improves learning efficiency across several control tasks.

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arXiv2025

Control Closure Certificates

This paper introduces the notion of control closure certificates to synthesize controllers for discrete-time control systems against $\omega$-regular specifications. Typical functional approaches to synthesize controllers against $\omega$-regular specifications rely on combining inductive invariants (for example, via barrier certificates) with proofs of well-foundedness (for example, via ranking functions). Transition invariants, provide an alternative where instead of standard well-foundedness arguments one may instead search for disjunctive well-foundedness arguments that together ensure a well-foundedness argument. Closure certificates, functional analogs of transition invariants, provide an effective, automated approach to verify discrete-time dynamical systems against linear temporal logic and $\omega$-regular specifications. We build on this notion to synthesize controllers to ensure the satisfaction of $\omega$-regular specifications. To do so, we first illustrate how one may construct control closure certificates to visit a region infinitely often (or only finitely often) via disjunctive well-founded arguments. We then combine these arguments to provide an argument for parity specifications. Thus, finding an appropriate control closure certificate over the product of the system and a parity automaton specifying a desired $\omega$-regular specification ensures that there exists a controller $\kappa$ to enforce the $\omega$-regular specification. We propose a sum-of-squares optimization approach to synthesize such certificates and demonstrate their efficacy in designing controllers over some case studies.

cs.LO↗

arXiv2025

$k$-Inductive and Interpolation-Inspired Barrier Certificates for Stochastic Dynamical Systems

In this paper, we introduce two new types of barrier certificates that are based on multiple functions rather than a single one. A conventional barrier certificate for a stochastic dynamical system is a nonnegative real-valued function whose expected value does not increase as the system evolves. This requirement guarantees that the barrier certificate forms a nonnegative supermartingale and can be used to derive a lower bound on the probability that the system remains safe. A key advantage of such certificates is that they can be automatically searched for using tools such as optimization programs instantiated with a fixed template. When this search is unsuccessful, the common practice is to modify the template and attempt the synthesis again. Drawing inspiration from logical interpolation, we first propose an alternative framework that uses a collection of functions to jointly serve as a barrier certificate. We refer to this construct as an interpolation-inspired barrier certificate. Nonetheless, we observe that these certificates still require one function in the collection to satisfy a supermartingale condition. Motivated by recent work in the literature, we next combine k-induction with interpolation-inspired certificates to relax this supermartingale constraint. We develop a general and more flexible notion of barrier certificates, which we call k-inductive interpolation-inspired barrier certificates. This formulation encompasses multiple ways of integrating interpolation-inspired barrier certificates with k-induction. We highlight two specific instantiations among these possible combinations. For polynomial systems, we employ sum-of-squares (SOS) programming to synthesize the corresponding set of functions. Finally, through our case studies, we show that the proposed methods enable the use of simpler templates and yield tighter lower bounds on the safety probability.

math.OC↗

arXiv2025

A Real-time and Hardware Efficient Artfecat-free Spike Sorting Using Deep Spike Detection

Spike sorting is a valuable tool in understanding brain regions. It assigns detected spike waveforms to their origins, helping to research the mechanism of the human brain and the development of implantable brain-machine interfaces (iBMIs). The presence of noise and artefacts will adversely affect the efficacy of spike sorting. This paper proposes a framework for low-cost and real-time implementation of deep spike detection, which consists of two one-dimensional (1-D) convolutional neural network (CNN) model for channel selection and artefact removal. The framework utilizes simulation and hardware layers, and it applies several low-power techniques to optimise the implementation cost of a 1-D CNN model. A compact CNN model with 210 bytes memory size is achieved using structured pruning, network projection and quantization in the simulation layer. The hardware layer also accommodates various techniques including a customized multiply-accumulate (MAC) engine, novel fused layers in the convolution pipeline and proposing flexible resource allocation for a power-efficient and low-delay design. The optimized 1-D CNN significantly decreases both computational complexity and model size, with only a minimal reduction in accuracy. Classification of 1-D CNN on the Cyclone V 5CSEMA5F31C6 FPGA evaluation platform is accomplished in just 16.8 microseconds at a frequency of 2.5 MHz. The FPGA prototype achieves an accuracy rate of 97.14% on a standard dataset and operates with a power consumption of 2.67mW from a supply voltage of 1.1 volts. An accuracy of 95.05% is achieved with a power of 5.6mW when deep spike detection is implemented using two optimized 1-D CNNs on an FPGA board.

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arXiv2025

Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes

Ensuring safety in cyber-physical systems (CPSs) is a critical challenge, especially when system models are difficult to obtain or cannot be fully trusted due to uncertainty, modeling errors, or environmental disturbances. Traditional model-based approaches rely on precise system dynamics, which may not be available in real-world scenarios. To address this, we propose a data-driven safety verification framework that leverages matrix zonotopes and barrier certificates to verify system safety directly from noisy data. Instead of trusting a single unreliable model, we construct a set of models that capture all possible system dynamics that align with the observed data, ensuring that the true system model is always contained within this set. This model set is compactly represented using matrix zonotopes, enabling efficient computation and propagation of uncertainty. By integrating this representation into a barrier certificate framework, we establish rigorous safety guarantees without requiring an explicit system model. Numerical experiments demonstrate the effectiveness of our approach in verifying safety for dynamical systems with unknown models, showcasing its potential for real-world CPS applications.

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arXiv2025

On the Completeness and Ordering of Path-Complete Barrier Functions

This paper is concerned with path-complete barrier functions which offer a graph-based methodology for verifying safety properties in switched systems. The path-complete framework leverages algebraic (barrier functions) as well as combinatorial (graph) components to characterize a set of safety conditions for switched systems, thus offering high flexibility (two degrees of freedom) in searching for suitable safety certificates. In this paper, we do not propose any new safety criteria. Instead, we further investigate the role that the combinatorial component plays in the safety verification problem. First, we prove that path-completeness, which is a property on a graph that describes the switching sequences, is necessary to obtain a set of valid safety conditions. As a result, the path-complete framework is able to provide a complete characterization of safety conditions for switched systems. Furthermore, we provide a systematic methodology for comparing two path-complete graphs and the conservatism associated with the resulting safety conditions. Specifically, we prove that under some conditions, such as when there exists a simulation relation between two path-complete graphs, it is possible to conclude that one graph is always able to provide less conservative safety conditions than another, independent of the algebraic properties of the switched system and the template of the barrier function under consideration. Such a result paves the way for a systematic use of the path-complete framework with barrier functions, as one can then consistently choose the appropriate graph that provides less conservative safety conditions.

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arXiv2025

A Meta-Fusion Architecture for Few-Shot Classification of Spike Waveforms in High-Bandwidth Brain-Machine Interfacing

There is a need for fast adaptation in spike sorting algorithms to implement brain-machine interface (BMIs) in different applications. Learning and adapting the functionality of the sorting process in real-time can significantly improve the performance. However, deep neural networks (DNNs) depend on large amounts of data for training models and their performance sustainability decreases when data is limited. Inspired by meta-learning, this paper proposes a few-shot spike sorting (FS-SS) framework with variable network model size that requires minimal learning training and supervision. The framework is not only compatible with few-shot adaptations, but also it uses attention mechanism and dilated convolutional neural networks. This allows scaling the network parameters to learn the important features of spike signals and to quickly generalize the learning ability to new spike waveforms in recording channels after few observations. The FS-SS was evaluated by using freely accessible datasets, also compared with the other state-of-the-art algorithms. The average classification accuracy of the proposed method is 99.28%, which shows extreme robustness to background noise and similarity of the spike waveforms. When the number of training samples is reduced by 90%, the parameter scale is reduced by 68.2%, while the accuracy only decreased by 0.55%. The paper also visualizes the model's attention distribution under spike sorting tasks of different difficulty levels. The attention distribution results show that the proposed model has clear interpretability and high robustness.

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