arXiv subjects

Wenjun Mei

Publications and source records attributed to Wenjun Mei.

36 records · Page 2Linked to original sources

arXiv2024

ReconDreamer: Crafting World Models for Driving Scene Reconstruction via Online Restoration

Closed-loop simulation is crucial for end-to-end autonomous driving. Existing sensor simulation methods (e.g., NeRF and 3DGS) reconstruct driving scenes based on conditions that closely mirror training data distributions. However, these methods struggle with rendering novel trajectories, such as lane changes. Recent works have demonstrated that integrating world model knowledge alleviates these issues. Despite their efficiency, these approaches still encounter difficulties in the accurate representation of more complex maneuvers, with multi-lane shifts being a notable example. Therefore, we introduce ReconDreamer, which enhances driving scene reconstruction through incremental integration of world model knowledge. Specifically, DriveRestorer is proposed to mitigate artifacts via online restoration. This is complemented by a progressive data update strategy designed to ensure high-quality rendering for more complex maneuvers. To the best of our knowledge, ReconDreamer is the first method to effectively render in large maneuvers. Experimental results demonstrate that ReconDreamer outperforms Street Gaussians in the NTA-IoU, NTL-IoU, and FID, with relative improvements by 24.87%, 6.72%, and 29.97%. Furthermore, ReconDreamer surpasses DriveDreamer4D with PVG during large maneuver rendering, as verified by a relative improvement of 195.87% in the NTA-IoU metric and a comprehensive user study.

cs.CV↗

arXiv2024

Multidimensional Opinion Dynamics with Heterogeneous Bounded Confidences and Random Interactions

This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other's opinions with a specific probability. This revised model is motivated by the observation that the standard Hegselmann-Krause (HK) dynamics requires unrealistic all-to-all interactions at certain configurations. For this randomized BC opinion dynamics, regardless of initial opinions and positive confidence bounds, we show that the agents' states converge to fixed final opinions in finite time almost surely and that the convergence rate follows a negative exponential distribution in mean square. Furthermore, we establish sufficient conditions for the heterogeneous BC opinion dynamics with random interactions to achieve consensus in finite time.

math.OC↗

arXiv2024

DriveDreamer4D: World Models Are Effective Data Machines for 4D Driving Scene Representation

Closed-loop simulation is essential for advancing end-to-end autonomous driving systems. Contemporary sensor simulation methods, such as NeRF and 3DGS, rely predominantly on conditions closely aligned with training data distributions, which are largely confined to forward-driving scenarios. Consequently, these methods face limitations when rendering complex maneuvers (e.g., lane change, acceleration, deceleration). Recent advancements in autonomous-driving world models have demonstrated the potential to generate diverse driving videos. However, these approaches remain constrained to 2D video generation, inherently lacking the spatiotemporal coherence required to capture intricacies of dynamic driving environments. In this paper, we introduce DriveDreamer4D, which enhances 4D driving scene representation leveraging world model priors. Specifically, we utilize the world model as a data machine to synthesize novel trajectory videos, where structured conditions are explicitly leveraged to control the spatial-temporal consistency of traffic elements. Besides, the cousin data training strategy is proposed to facilitate merging real and synthetic data for optimizing 4DGS. To our knowledge, DriveDreamer4D is the first to utilize video generation models for improving 4D reconstruction in driving scenarios. Experimental results reveal that DriveDreamer4D significantly enhances generation quality under novel trajectory views, achieving a relative improvement in FID by 32.1%, 46.4%, and 16.3% compared to PVG, S3Gaussian, and Deformable-GS. Moreover, DriveDreamer4D markedly enhances the spatiotemporal coherence of driving agents, which is verified by a comprehensive user study and the relative increases of 22.6%, 43.5%, and 15.6% in the NTA-IoU metric.

cs.CV↗

arXiv2024

Convergence of the Heterogeneous Deffuant-Weisbuch Model: A Complete Proof and Some Extensions

The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over $20$ years, its convergence proof is open. Our previous paper \cite{GC-WS-WM-FB:20} solves the problem for the case of uniform weighting factors greater than or equal to $1/2$, but the general case remains unresolved. This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions.

math.OC↗

arXiv2024

Convergence Analysis of Weighted-Median Opinion Dynamics with Prejudice

The Friedkin-Johnsen (FJ) model introduces prejudice into the opinion evolution and has been successfully validated in many practical scenarios; however, due to its weighted average mechanism, only one prejudiced agent can always guide all unprejudiced agents synchronizing to its prejudice under the connected influence network, which may not be in line with some social realities. To fundamentally address the limitation of the weighted average mechanism, a weighted-median opinion dynamics has been recently proposed; however, its theoretical analysis is challenging due to its nonlinear nature. This paper studies the weighted-median opinion dynamics with prejudice, and obtains the convergence and convergence rate when all agents have prejudice, and a necessary and sufficient condition for asymptotic consensus when a portion of agents have prejudice. These results are the first time to analyze the discrete-time and synchronous opinion dynamics with the weighted median mechanism, and address the phenomenon of the FJ model that connectivity leads to consensus when a few agents with the same prejudice join in an unprejudiced group.

eess.SY↗

arXiv2023

Evolutionary Games on Networks: Phase Transition, Quasi-equilibrium, and Mathematical Principles

The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be actually stable, but correspond to quasi-equilibriums instead. We find that various classic game models, like the evolutionary snowdrift game, evolutionary prisoner's dilemma, and spatial public goods game on square lattices and scale-free networks, exhibit the phase transition in convergence time to the equilibrium state. Moreover, mathematical principles are provided to explain the phase transition of convergence time and quasi-equilibrium of cooperation ratio. The findings explain why and when cooperation and defection have a long-term coexistence.

q-bio.PE↗

arXiv2022

Rethinking the Micro-Foundation of Opinion Dynamics: Rich Consequences of the Weighted-Median Mechanism

To identify the main mechanisms underlying complex opinion formation processes in social systems, researchers have long been exploring simple mechanistic mathematical models. Most existing opinion dynamics models are built on a common micro-foundation, i.e., the weighted-averaging opinion update. However, we argue that this universally-adopted mechanism features a non-negligible unrealistic feature, which brings unnecessary difficulties in seeking a proper balance between model complexity and predictive power. In this paper, we propose the weighted-median mechanism as a new micro-foundation of opinion dynamics, which, with minimal assumptions, fundamentally resolves the inherent unrealistic feature of the weighted-averaging mechanism. Derived from the cognitive dissonance theory in psychology, the weighted-median mechanism is supported by online experiment data and broadens the applicability of opinion dynamics models to multiple-choice issues with ordered discrete options. Moreover, the weighted-median mechanism, despite being the simplest in form, captures various non-trivial real-world features of opinion evolution, while some widely-studied averaging-based models fail to.

cs.SI↗

arXiv2022

Convergence, Consensus and Dissensus in the Weighted-Median Opinion Dynamics

Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated via experimental data. Numerical studies also indicate that this new mechanism recreates some non-trivial real-world features of opinion evolution. In this paper, we conduct a thorough theoretical analysis of the weighted-median opinion dynamics. We fully characterize the set of all equilibria, and we establish the almost-sure finite-time convergence for any initial condition. Moreover, we prove a necessary and sufficient graph-theoretic condition for the almost-sure convergence to consensus, as well as a sufficient graph-theoretic condition for almost-sure persistent dissensus. It turns out that the weighted-median opinion dynamics, despite its simplicity in form, exhibit rich dynamical behavior that depends on some delicate network structures. To complement our sufficient conditions for almost-sure dissensus, we further prove that, given the influence network, determining whether the system almost surely achieves persistent dissensus is NP-hard, which reflects the complexity the network topology contributes to opinion evolution.

eess.SY↗

arXiv2020

Structural Balance and Interpersonal Appraisals Dynamics: Beyond All-to-All and Two-Faction Networks

Structural balance theory describes stable configurations of topologies of signed interpersonal appraisal networks. Existing models explaining the convergence of appraisal networks to structural balance either diverge in finite time, or could get stuck in jammed states, or converge to only complete graphs. In this paper, we study the open problem how steady non-all-to-all structural balance emerges via local dynamics of interpersonal appraisals. We first compare two well-justified definitions of structural balance for general non-all-to-all graphs, i.e., the triad-wise structural balance and the two-faction structural balance, and thoroughly study their relations. Secondly, based on three widely adopted sociological mechanisms: the symmetry mechanism, the influence mechanism, and the homophily mechanism, we propose two simple models of gossip-like appraisal dynamics, the symmetry-influence-homophily (SIH) dynamics and the symmetry-influence-opinion-homophily (SIOH) dynamics. In these models, the appraisal network starting from any initial condition almost surely achieves non-all-to-all triad-wise and two-faction structural balance in finite time respectively. Moreover, the SIOH dynamics capture the co-evolution of interpersonal appraisals and individuals' opinions. Regarding the theoretical contributions, we show that the equilibrium set of the SIH (SIOH resp.) dynamics corresponds to the set of all the possible triad-wise (two-faction resp.) structural balance configurations of the appraisal networks. Moreover, we prove that, for any initial condition, the appraisal networks in the SIH (SIOH resp.) dynamics almost surely achieve triad-wise (two-faction resp.) structural balance in finite time. Numerical studies of the SIH dynamics also imply some insightful take-home messages on whether multilateral relations reduce or exacerbate conflicts.

cs.SI↗

arXiv2020

Assign and Appraise: Achieving Optimal Performance in Collaborative Teams

Tackling complex team problems requires understanding each team member's skills in order to devise a task assignment maximizing the team performance. This paper proposes a novel quantitative model describing the decentralized process by which individuals in a team learn who has what abilities, while concurrently assigning tasks to each of the team members. In the model, the appraisal network represents team member's evaluations of one another and each team member chooses their own workload. The appraisals and workload assignment change simultaneously: each member builds their own local appraisal of neighboring members based on the performance exhibited on previous tasks, while the workload is redistributed based on the current appraisal estimates. We show that the appraisal states can be reduced to a lower dimension due to the presence of conserved quantities associated to the cycles of the appraisal network. Building on this, we provide rigorous results characterizing the ability, or inability, of the team to learn each other's skill and thus converge to an allocation maximizing the team performance. We complement our analysis with extensive numerical experiments.

cs.SI↗

arXiv2020

Interplay Between Homophily-Based Appraisal Dynamics and Influence-Based Opinion Dynamics: Modeling and Analysis

In social systems, the evolution of interpersonal appraisals and individual opinions are not independent processes but intertwine with each other. Despite extensive studies on both opinion dynamics and appraisal dynamics separately, no previous work has ever combined these two processes together. In this paper, we propose a novel and intuitive model on the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics. We assume that individuals' opinions are updated via the influence network constructed from their interpersonal appraisals, which are in turn updated based on the individual opinions via the homophily mechanism. By theoretical analysis, we characterize the set of equilibria and some transient behavior of our model. Moreover, we establish the equivalence among the convergence of the appraisal network to social balance, the modulus consensus of individual opinions, and the non-vanishing appraisals. Monte Carlo validations further show that the non-vanishing appraisals condition holds for generic initial conditions. Compared with previous works that explain the emergence of social balance via person-to-person homophily mechanism, our model provides an alternative explanation in terms of the person-to-entity homophily mechanism. In addition, our model also describes how individuals' opinions on multiple irrelevant issues become correlated and converge to modulus consensus over time-varying influence networks.

eess.SY↗

arXiv2020

LaSalle Invariance Principle for Discrete-time Dynamical Systems: A Concise and Self-contained Tutorial

LaSalle invariance principle was originally proposed in the 1950's and has become a fundamental mathematical tool in the area of dynamical systems and control. In both theoretical research and engineering practice, discrete-time dynamical systems have been at least as extensively studied as continuous-time systems. For example, model predictive control is typically studied in discrete-time via Lyapunov methods. However, there is a peculiar absence in the standard literature of standard treatments of Lyapunov functions and LaSalle invariance principle for discrete-time nonlinear systems. Most of the textbooks on nonlinear dynamical systems focus only on continuous-time systems. In Chapter 1 of the book by LaSalle [11], the author establishes the LaSalle invariance principle for difference equation systems. However, all the useful lemmas in [11] are given in the form of exercises with no proof provided. In this document, we provide the proofs of all the lemmas proposed in [11] that are needed to derive the main theorem on the LaSalle invariance principle for discrete-time dynamical systems. We organize all the materials in a self-contained manner. We first introduce some basic concepts and definitions in Section 1, such as dynamical systems, invariant sets, and limit sets. In Section 2 we present and prove some useful lemmas on the properties of invariant sets and limit sets. Finally, we establish the original LaSalle invariance principle for discrete-time dynamical systems and a simple extension in Section~3. In Section 4, we provide some references on extensions of LaSalle invariance principles for further reading. This document is intended for educational and tutorial purposes and contains lemmas that might be useful as a reference for researchers.

math.DS↗

arXiv2020

Convergence Properties of the Heterogeneous Deffuant-Weisbuch Model

The Deffuant-Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence properties, easy to observe numerically, are only conjectures. This paper solves the convergence problem for the heterogeneous DW model with the weighting factor not less than $1/2$. We establish that, for any positive confidence bounds and initial values, the opinion of each agent will converge to a limit value almost surely, and the convergence rate is exponential in mean square. Moreover, we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents. Finally, we provide some sufficient conditions for the heterogeneous DW model to reach consensus.

eess.SY↗

arXiv2019

Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms

Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network \textcolor{blue}{converges to} social balance from an initially unbalanced configuration. These two models are based on two different socio-psychological mechanisms respectively: the homophily mechanism and the influence mechanism. Our main theoretical contribution is a comprehensive analysis for both models in three steps. First, we establish the well-posedness and bounded evolution of the interpersonal appraisals. Second, we fully characterize the set of equilibrium points; for both models, each equilibrium network is composed by an arbitrary number of complete subgraphs satisfying structural balance. Third, we establish the equivalence among three distinct properties: non-vanishing appraisals, convergence to all-to-all appraisal networks, and finite-time achievement of social balance. In addition to theoretical analysis, Monte Carlo validations illustrates how the non-vanishing appraisal condition holds for generic initial conditions in both models. Moreover, numerical comparison between the two models indicate that the homophily-based model might be a more universal explanation for the formation of social balance. Finally, adopting the homophily-based model, we present numerical results on the mediation and globalization of local conflicts, the competition for allies, and the asymptotic formation of a single versus two factions.

cs.SI↗

arXiv2018

Linear Stochastic Approximation Algorithms and Group Consensus over Random Signed Networks: A Technical Report with All Proofs

This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multi-agent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multi-dimensional linear SA algorithms and characterize the behavior of the multi-dimensional Friedkin-Johnsen model over random interaction networks.

math.OC↗

arXiv2017

On the Dynamics of Deterministic Epidemic Propagation over Networks

In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI), susceptible-infected-susceptible (SIS), and susceptible-infected-recovered (SIR) settings. In each setting, we provide a comprehensive nonlinear analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions. For the network SI setting, specific contributions include establishing its equilibria, stability, and positivity properties. For the network SIS setting, we review a well-known deterministic model, provide novel results on the computation and characterization of the endemic state (when the system is above the epidemic threshold), and present alternative proofs for some of its properties. Finally, for the network SIR setting, we propose novel results for transient behavior, threshold conditions, stability properties, and asymptotic convergence. These results are analogous to those well-known for the scalar case. In addition, we provide a novel iterative algorithm to compute the asymptotic state of the network SIR system.

cs.SI↗

arXiv2016

Dynamic Models of Appraisal Networks Explaining Collective Learning

This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

cs.SI↗

arXiv2016

Competitive Propagation: Models, Asymptotic Behavior and Multi-stage Games

In this paper we propose a class of propagation models for multiple competing products over a social network. We consider two propagation mechanisms: social conversion and self conversion, corresponding, respectively, to endogenous and exogenous factors. A novel concept, the product-conversion graph, is proposed to characterize the interplay among competing products. According to the chronological order of social and self conversions, we develop two Markov-chain models and, based on the independence approximation, we approximate them with two respective difference equations systems. Theoretical analysis on these two approximation models reveals the dependency of the systems' asymptotic behavior on the structures of both the product-conversion graph and the social network, as well as the initial condition. In addition to the theoretical work, accuracy of the independence approximation and the asymptotic behavior of the Markov-chain model are investigated via numerical analysis, for the case where social conversion occurs before self conversion. Finally, we propose a class of multi-player and multi-stage competitive propagation games and discuss the seeding-quality trade-off, as well as the allocation of seeding resources among the individuals. We investigate the unique Nash equilibrium at each stage and analyze the system's behavior when every player is adopting the policy at the Nash equilibrium.

cs.SI↗