Projects

Publications

2025

[J32] Scalable synthesis of formally verified neural value function for hamilton-jacobi reachability analysis
Yujie Yang, Hanjiang Hu, Tianhao Wei, Shengbo Eben Li and Changliu Liu
Journal of Artificial Intelligence Research, 2025
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Hamilton-Jacobi (HJ) reachability analysis provides a formal method for guaranteeing safety in constrained control problems. It synthesizes a value function to represent a long-term safe set called feasible region. Early synthesis methods based on state space discretization cannot scale to high-dimensional problems, while recent methods that use neural networks to approximate value functions result in unverifiable feasible regions. To achieve both scalability and verifiability, we propose a framework for synthesizing verified neural value functions for HJ reachability analysis. Our framework consists of three stages: pre-training, adversarial training, and verification-guided training. We design three techniques to address three challenges to improve scalability respectively: boundary-guided backtracking (BGB) to improve counterexample search efficiency, entering state regularization (ESR) to enlarge feasible region, and activation pattern alignment (APA) to accelerate neural network verification. We also provide a neural safety certificate synthesis and verification benchmark called Cersyve-9, which includes nine commonly used safe control tasks and supplements existing neural network verification benchmarks. Our framework successfully synthesizes verified neural value functions on all tasks, and our proposed three techniques exhibit superior scalability and efficiency compared with existing methods.
[J30] Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods
Xusheng Luo, Tianhao Wei, Simin Liu, Ziwei Wang, Luis Mattei-Mendez, Taylor Loper, Joshua Neighbor, Casidhe Hutchison and Changliu Liu
ACM Transactions on Cyber-Physical Systems, 2025
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This work addresses the certification of the local robustness of vision-based two-stage 6D object pose estimation. The two-stage method for object pose estimation achieves superior accuracy by first employing deep neural network-driven keypoint regression and then applying a Perspective-n-Point (PnP) technique. Despite advancements, the certification of these methods’ robustness remains scarce. This research aims to fill this gap with a focus on their local robustness on the system level–the capacity to maintain robust estimations amidst semantic input perturbations. The core idea is to transform the certification of local robustness into neural network verification for classification tasks. The challenge is to develop model, input, and output specifications that align with off-the-shelf verification tools. To facilitate verification, we modify the keypoint detection model by substituting nonlinear operations with those more amenable to the verification processes. Instead of injecting random noise into images, as is common, we employ a convex hull representation of images as input specifications to more accurately depict semantic perturbations. Furthermore, by conducting a sensitivity analysis, we propagate the robustness criteria from pose to keypoint accuracy, and then formulating an optimal error threshold allocation problem that allows for the setting of a maximally permissible keypoint deviation thresholds. Viewing each pixel as an individual class, these thresholds result in linear, classification-akin output specifications. Under certain conditions, we demonstrate that the main components of our certification framework are both sound and complete, and validate its effects through extensive evaluations on realistic perturbations. To our knowledge, this is the first study to certify the robustness of large-scale, keypoint-based pose estimation given images in real-world scenarios.

[C94] Learn With Imagination: Safe Set Guided State-wise Constrained Policy Optimization
Feihan Li, Yifan Sun, Weiye Zhao, Rui Chen, Tianhao Wei and Changliu Liu
Learning for Dynamics and Control Conference, 2025
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Deep reinforcement learning (RL) excels in various control tasks, yet the absence of safety guarantees hampers its real-world applicability. In particular, explorations during learning usually results in safety violations, while the RL agent learns from those mistakes. On the other hand, safe control techniques ensure persistent safety satisfaction but demand strong priors on system dynamics, which is usually hard to obtain in practice. To address these problems, we present Safe Set Guided State-wise Constrained Policy Optimization (S-3PO), a pioneering algorithm generating state-wise safe optimal policies with zero training violations, i.e., learning without mistakes. S-3PO first employs a safety-oriented monitor with black-box dynamics to ensure safe exploration. It then enforces an "imaginary" cost for the RL agent to converge to optimal behaviors within safety constraints. S-3PO outperforms existing methods in high-dimensional robotics tasks, managing state-wise constraints with zero training violation. This innovation marks a significant stride towards real-world safe RL deployment.
[C100] Modelverification. jl: a comprehensive toolbox for formally verifying deep neural networks
Tianhao Wei, Hanjiang Hu, Luca Marzari, Kai S Yun, Peizhi Niu, Xusheng Luo and Changliu Liu
Conference on Computer Aided Verification, 2025
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Deep Neural Networks (DNN) are crucial in approximating nonlinear functions across diverse applications, ranging from image classification to control. Verifying specific input-output properties can be a highly challenging task due to the lack of a single, self-contained framework that allows a complete range of verification types. To this end, we present \textttModelVerification.jl (MV), the first comprehensive, cutting-edge toolbox that contains a suite of state-of-the-art methods for verifying different types of DNNs and safety specifications. This versatile toolbox is designed to empower developers and machine learning practitioners with robust tools for verifying and ensuring the trustworthiness of their DNN models.

2024

[J26] Improve Certified Training with Signal-to-Noise Ratio Loss to Decrease Neuron Variance and Increase Neuron Stability
Tianhao Wei, Ziwei Wang, Peizhi Niu, Abulikemu Abuduweili, Weiye Zhao, Casidhe Hutchison, Eric Sample and Changliu Liu
Transactions on Machine Learning Research, 2024
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Neural network robustness is a major concern in safety-critical applications. Certified robustness provides a reliable lower bound on worst-case robustness, and certified training methods have been developed to enhance it. However, certified training methods often suffer from over-regularization, leading to lower certified robustness. This work addresses this issue by introducing the concepts of neuron variance and neuron stability, examining their impact on over-regularization and model robustness. To tackle the problem, we extend the Signal-to-Noise Ratio (SNR) into the realm of model robustness, offering a novel perspective and developing SNR-inspired losses aimed at optimizing neuron variance and stability to mitigate over-regularization. Through both empirical and theoretical analysis, our SNR-based approach demonstrates superior performance over existing methods on the MNIST and CIFAR-10 datasets. In addition, our exploration of adversarial training uncovers a beneficial correlation between neuron variance and adversarial robustness, leading to an optimized balance between standard and robust accuracy that outperforms baseline methods.
[J24] State-wise Constrained Policy Optimization
Weiye Zhao, Rui Chen, Yifan Sun, Tianhao Wei and Changliu Liu
Transactions on Machine Learning Research, 2024
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[J23] Guard: A safe reinforcement learning benchmark
Weiye Zhao, Rui Chen, Yifan Sun, Ruixuan Liu, Tianhao Wei and Changliu Liu
Transactions on Machine Learning Research, 2024
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[C85] NN4SysBench: Characterizing Neural Network Verification for Computer Systems
Shuyi Lin, Haoyu He, Tianhao Wei, Kaidi Xu, Huan Zhang, Gagandeep Singh, Changliu Liu and Cheng Tan
The Thirty-eight Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2024
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[C83] Meta-Control: Automatic Model-based Control Synthesis for Heterogeneous Robot Skills
Tianhao Wei, Liqian Ma, Rui Chen, Weiye Zhao and Changliu Liu
Conference on Robot Learning, 2024
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The requirements for real-world manipulation tasks are diverse and often conflicting; some tasks require precise motion while others require force compliance; some tasks require avoidance of certain regions while others require convergence to certain states. Satisfying these varied requirements with a fixed state-action representation and control strategy is challenging, impeding the development of a universal robotic foundation model. In this work, we propose Meta-Control, the first LLM-enabled automatic control synthesis approach that creates customized state representations and control strategies tailored to specific tasks. Our core insight is that a meta-control system can be built to automate the thought process that human experts use to design control systems. Specifically, human experts heavily use a model-based, hierarchical (from abstract to concrete) thought model, then compose various dynamic models and controllers together to form a control system. Meta-Control mimics the thought model and harnesses LLM’s extensive control knowledge with Socrates’ "art of midwifery" to automate the thought process. Meta-Control stands out for its fully model-based nature, allowing rigorous analysis, generalizability, robustness, efficient parameter tuning, and reliable real-time execution.

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[C81] Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation
Hanjiang Hu, Yujie Yang, Tianhao Wei and Changliu Liu
Conference on Robot Learning, 2024
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Control barrier functions (CBFs) are important in safety-critical systems and robot control applications. Neural networks have been used to parameterize and synthesize CBFs with bounded control input for complex systems. However, it is still challenging to verify pre-trained neural networks CBFs (neural CBFs) in an efficient symbolic manner. To this end, we propose a new efficient verification framework for ReLU-based neural CBFs through symbolic derivative bound propagation by combining the linearly bounded nonlinear dynamic system and the gradient bounds of neural CBFs. Specifically, with Heaviside step function form for derivatives of activation functions, we show that the symbolic bounds can be propagated through the inner product of neural CBF Jacobian and nonlinear system dynamics. Through extensive experiments on different robot dynamics, our results outperform the interval arithmetic-based baselines in verified rate and verification time along the CBF boundary, validating the effectiveness and efficiency of the proposed method with different model complexity. The code can be found at https://github.com/intelligent-control-lab/verify-neural-CBF.
[C77] Absolute Policy Optimization: Enhancing Lower Probability Bound of Performance with High Confidence
Weiye Zhao, Feihan Li, Yifan Sun, Rui Chen, Tianhao Wei and Changliu Liu
International Conference on Machine Learning, 2024
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[C66] Multimodal Safe Control for Human-Robot Interaction
Ravi Pandya, Tianhao Wei and Changliu Liu
American Control Conference, 2024
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[T3] Safeguarding and Empowering General Purpose Robots through Abstraction and Constraint Certification
Tianhao Wei
PhD Thesis, 2024
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Robots are increasingly deployed across various domains, from industrial automation to domestic assistance. Ensuring that robots operate safely and intelligently is crucial to preventing potential risks such as injury, loss of life, and economic costs. This thesis addresses key challenges in deploying robots in complex real-world environments, including providing formal safety guarantees in uncertain conditions, scaling safety guarantees to realistic high-dimensional systems, allowing the robot to behave intelligently while remaining explainable and trustworthy, and ensuring the robustness of neural network components. This thesis introduces a suite of tools to tackle these challenges. The first tool, Meta-Control, synthesizes heterogeneous robot skills with a hiearchical control approach, which could decompose system-level safety requirements into module-level constraints. These constraints are categorized into control and neural network constraints. For control constraints, the toolset introduces Abstract Safe Control for hierarchical safety guarantees, Robust Safe Control for handling model uncertainty through a control-limits aware robust framework, Neural Network Dynamic Models (NNDM) Safe Control for integrating data-driven models with safety guarantees, and Benchmark of Interactive Safety for benchmarking and unifying different safe control algorithms. For neural network constraints, the toolset introduces ModelVerification.jl toolbox for verifying neural network safety specifications, online verification for online assurance under domain shifts and network update, and the Signal-to-Noise Ratio (SNR) loss method to enhance stability and robustness of neural networks. These tools enable the provision of formal safety guarantees with partially known or unknown dynamic models in uncertain, interactive environments, achieving state-of-the-art control safety and neural network safety. This allows robot arms to perform various tasks efficiently and safely, advancing the development of reliable and trustworthy general-purpose robots.

[U] Absolute State-wise Constrained Policy Optimization: High-Probability State-wise Constraints Satisfaction
Weiye Zhao, Feihan Li, Yifan Sun, Yujie Wang, Rui Chen, Tianhao Wei and Changliu Liu
arXiv:2410.01212, 2024
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Enforcing state-wise safety constraints is critical for the application of reinforcement learning (RL) in real-world problems, such as autonomous driving and robot manipulation. However, existing safe RL methods only enforce state-wise constraints in expectation or enforce hard state-wise constraints with strong assumptions. The former does not exclude the probability of safety violations, while the latter is impractical. Our insight is that although it is intractable to guarantee hard state-wise constraints in a model-free setting, we can enforce state-wise safety with high probability while excluding strong assumptions. To accomplish the goal, we propose Absolute State-wise Constrained Policy Optimization (ASCPO), a novel general-purpose policy search algorithm that guarantees high-probability state-wise constraint satisfaction for stochastic systems. We demonstrate the effectiveness of our approach by training neural network policies for extensive robot locomotion tasks, where the agent must adhere to various state-wise safety constraints. Our results show that ASCPO significantly outperforms existing methods in handling state-wise constraints across challenging continuous control tasks, highlighting its potential for real-world applications.

2023

[C63] Zero-shot Transferable and Persistently Feasible Safe Control for High Dimensional Systems by Consistent Abstraction
Tianhao Wei, Shucheng Kang, Ruixuan Liu and Changliu Liu
IEEE Conference on Decision and Control, 2023
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[C61] Building Verified Neural Networks for Computer Systems with Ouroboros
Tianhao Wei, Zhihao Jia, Changliu Liu and Cheng Tan
Sixth Conference on Machine Learning and Systems, 2023
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[C60] State-wise safe reinforcement learning: A survey
Weiye Zhao, Tairan He, Rui Chen, Tianhao Wei and Changliu Liu
International Joint Conferences on Artificial Intelligence, 2023
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[C56] Safety index synthesis via sum-of-squares programming
Weiye Zhao, Tairan He, Tianhao Wei, Simin Liu and Changliu Liu
American Control Conference, 2023
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[U] Robust Safe Control with Multi-Modal Uncertainty
Tianhao Wei, Liqian Ma, Ravi Pandya and Changliu Liu
arXiv:2309.16830, 2023
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2022

[J15] Persistently feasible robust safe control by safety index synthesis and convex semi-infinite programming
Tianhao Wei, Shucheng Kang, Weiye Zhao and Changliu Liu
IEEE Control Systems Letters, 2022
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[C45] A Composable Framework for Policy Design, Learning, and Transfer Toward Safe and Efficient Industrial Insertion
Rui Chen, Chenxi Wang, Tianhao Wei and Changliu Liu
IEEE/RSJ International Conference on Intelligent Robots and Systems, 2022
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Delicate industrial insertion tasks (e.g., PC board assembly) remain challenging for industrial robots. The challenges include low error tolerance, delicacy of the components, and large task variations with respect to the components to be inserted. To deliver a feasible robotic solution for these insertion tasks, we also need to account for hardware limits of existing robotic systems and minimize the integration effort. This paper proposes a composable framework for efficient integration of a safe insertion policy on existing robotic platforms to accomplish these insertion tasks. The policy has an interpretable modularized design and can be learned efficiently on hardware and transferred to new tasks easily. In particular, the policy includes a safe insertion agent as a baseline policy for insertion, an optimal configurable Cartesian tracker as an interface to robot hardware, a probabilistic inference module to handle component variety and insertion errors, and a safe learning module to optimize the parameters in the aforementioned modules to achieve the best performance on designated hardware. The experiment results on a UR10 robot show that the proposed framework achieves safety (for the delicacy of components), accuracy (for low tolerance), robustness (against perception error and component defection), adaptability and transferability (for task variations), as well as task efficiency during execution plus data and time efficiency during learning.

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[C40] Safe Control with Neural Network Dynamic Models
Tianhao Wei and Changliu Liu
Learning for Dynamics and Control Conference, 2022
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Safety is critical in autonomous robotic systems. A safe control law should ensure forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, how to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to synthesize safe control for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as a barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence to a subset of the user-defined safe set. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. The optimality gap is less than 10−8, and the safety constraint violation is 0.

2021

[W] Online Verification of Deep Neural Networks under Domain or Weight Shift
Tianhao Wei and Changliu Liu
RSS R4P Workshop, 2021
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Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before deployment, which are limited to relatively simple specifications and fixed networks. These methods are not ready to be applied to real-world problems with complex and/or dynamically changing specifications and networks. To effectively handle such problems, verification needs to be performed online when these changes take place. However, it is still challenging to run existing verification algorithms online. Our key insight is that we can leverage the temporal dependencies of these changes to accelerate the verification process. This paper establishes a novel framework for scalable online verification to solve real-world verification problems with dynamically changing specifications and/or networks. We propose three types of acceleration algorithms: Branch Management to reduce repetitive computation, Perturbation Tolerance to tolerate changes, and Incremental Computation to reuse previous results. Experiment results show that our algorithms achieve up to 100× acceleration, and thus show a promising way to extend neural network verification to real-world applications.

2019

[C23] Safe Control Algorithms Using Energy Functions: A Unified Framework, Benchmark, and New Directions
Tianhao Wei and Changliu Liu
IEEE Conference on Decision and Control, 2019
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Safe autonomy is important in many application domains, especially for applications involving interactions with humans. Existing safe control algorithms are similar to each other in the sense that: they all provide control input to maintain a low value of an energy function that measures safety. In different methods, the energy function is called a potential function, a safety index, or a barrier function. The connections and relative advantages among these methods remain unclear. This paper introduces a unified framework to derive safe control laws using energy functions. We demonstrate how to integrate existing controllers based on potential field method, , barrier function method, and sliding mode algorithm into this unified framework. In addition to theoretical comparison, this paper also introduces a benchmark which implements and compares existing methods on a variety of problems with different system dynamics and interaction modes. Based on the comparison results, a new method, called the sublevel safe set algorithm, is derived under the unified framework by optimizing the hyperparameters. The proposed algorithm achieves the best performance in terms of safety and efficiency on all benchmark problems.
[C21] Agen: Adaptable generative prediction networks for autonomous driving
Wenwen Si, Tianhao Wei and Changliu Liu
IEEE Intelligent Vehicles Symposium, 2019
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In highly interactive driving scenarios, accurate prediction of other road participants is critical for safe and efficient navigation of autonomous cars. Prediction is challenging due to the difficulty in modeling various driving behavior, or learning such a model. The model should be interactive and reflect individual differences. Imitation learning methods, such as parameter sharing generative adversarial imitation learning (PS-GAIL), are able to learn interactive models. However, the learned models average out individual differences. When used to predict trajectories of individual vehicles, these models are biased. This paper introduces an adaptable generative prediction framework (AGen), which performs online adaptation of the offline learned models to recover individual differences for better prediction. In particular, we combine the recursive least square parameter adaptation algorithm (RLS-PAA) with the offline learned model from PS-GAIL. RLS-PAA has analytical solutions and is able to adapt the model for every single vehicle efficiently online. The proposed method is able to reduce the root mean squared prediction error in a 2.5s time window by 60%, compared with PS-GAIL.