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Zhen Wu

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Published work

17 published item(s)

preprint2026arXiv

Causal Evidence for Attention Head Imbalance in Modality Conflict Hallucination

Modality-conflict hallucination occurs when multimodal large language models (MLLMs) prioritize erroneous textual premises over contradictory visual evidence. To understand why visual evidence fails to prevail during generation, we take a mechanistic perspective and examine which internal components drive or resist this failure. We perform head-level causal analysis using path patching across five open-source MLLMs and identify two groups of attention heads with opposing causal roles: hallucination-driving heads and hallucination-resisting heads. We find a consistent asymmetry: driving effects are more broadly distributed and carry greater aggregate weight, whereas resisting effects concentrate in a small number of high-importance heads. Ablation experiments further confirm that these groups exert opposing effects during generation: distributed driving influence and localized resistance together form an imbalanced routing structure that biases generation toward the erroneous premise. Motivated by this finding, we propose MACI (Modality-conflict-Aware Causal Intervention), a conditional intervention that suppresses causally identified hallucination-driving heads only when conflict is detected. Across five MLLMs, MACI achieves the largest hallucination reduction among compared inference-time baselines on the MMMC benchmark with a favorable hallucination-accuracy trade-off, and transfers zero-shot to the SCI-SemanticConflict test.

preprint2026arXiv

Locomotion Beyond Feet

Most locomotion methods for humanoid robots focus on leg-based gaits, yet natural bipeds frequently rely on hands, knees, and elbows to establish additional contacts for stability and support in complex environments. This paper introduces Locomotion Beyond Feet, a comprehensive system for whole-body humanoid locomotion across extremely challenging terrains, including low-clearance spaces under chairs, knee-high walls, knee-high platforms, and steep ascending and descending stairs. Our approach addresses two key challenges: contact-rich motion planning and generalization across diverse terrains. To this end, we combine physics-grounded keyframe animation with reinforcement learning. Keyframes encode human knowledge of motor skills, are embodiment-specific, and can be readily validated in simulation or on hardware, while reinforcement learning transforms these references into robust, physically accurate motions. We further employ a hierarchical framework consisting of terrain-specific motion-tracking policies, failure recovery mechanisms, and a vision-based skill planner. Real-world experiments demonstrate that Locomotion Beyond Feet achieves robust whole-body locomotion and generalizes across obstacle sizes, obstacle instances, and terrain sequences.

preprint2026arXiv

The spatiotemporal Born rule is quasiprobabilistic

Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint probabilities associated with measurements performed in sequence are defined in terms of the state-update rule. In this work, we show that one obtains a more unified perspective of space and time in quantum theory by embracing a quasiprobabilistic description of sequential measurements. More precisely, we show that there exists a unique \emph{pseudo}-density operator encoding canonical quasiprobabilities associated with sequential measurements in precisely the same manner that a density operator encodes joint probabilities associated with spacelike separated measurements, thus providing a natural extension of the Born rule into the temporal domain. As an application, we show how such a spatiotemporal Born rule combined in conjunction with a quantum Bayes' rule yields an operational notion of time-reversal symmetry for sequential measurements on an \emph{open} quantum system.

preprint2023arXiv

Linear-Quadratic Delayed Mean-Field Social Optimization

A linear quadratic (LQ) stochastic optimization problem with delay involving weakly-coupled large population is investigated in this paper. Different to classic mean field (MF) game, here agents cooperate with each other to minimize the so-called \emph{social} objective. With the aid of \emph{delayed person-by-person optimality} principle, one arrives at an auxiliary LQ delayed control problem by decentralized information. A decentralized strategy is obtained by feat of an MF type anticipated forward-backward stochastic differential delay equation (AFBSDDE) consistency condition. The discounting method with delay feature is employed to solve the consistency condition system. Finally, by some estimates of AFBSDDEs we derive the asymptotic social optimality.

preprint2022arXiv

Continuous-time mean-variance portfolio selection under non-Markovian regime-switching model with random horizon

In this paper, we consider a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion. We formulate this problem as a constrained stochastic linear-quadratic optimal control problem. The Markov chain is assumed to be independent of the Brownian motion. So the market is incomplete. We derive closed-form expressions for both the optimal portfolios and the efficient frontier. All the results are different from those in the problem with fixed time horizon.

preprint2022arXiv

Exploiting Unlabeled Data for Target-Oriented Opinion Words Extraction

Target-oriented Opinion Words Extraction (TOWE) is a fine-grained sentiment analysis task that aims to extract the corresponding opinion words of a given opinion target from the sentence. Recently, deep learning approaches have made remarkable progress on this task. Nevertheless, the TOWE task still suffers from the scarcity of training data due to the expensive data annotation process. Limited labeled data increase the risk of distribution shift between test data and training data. In this paper, we propose exploiting massive unlabeled data to reduce the risk by increasing the exposure of the model to varying distribution shifts. Specifically, we propose a novel Multi-Grained Consistency Regularization (MGCR) method to make use of unlabeled data and design two filters specifically for TOWE to filter noisy data at different granularity. Extensive experimental results on four TOWE benchmark datasets indicate the superiority of MGCR compared with current state-of-the-art methods. The in-depth analysis also demonstrates the effectiveness of the different-granularity filters. Our codes are available at https://github.com/TOWESSL/TOWESSL.

preprint2022arXiv

Linear-Quadratic Large-Population Problem with Partial Information: Hamiltonian Approach and Riccati Approach

This paper studies a class of partial information linear-quadratic mean-field game problems. A general stochastic large-population system is considered, where the diffusion term of the dynamic of each agent can depend on the state and control. We study both the control constrained case and unconstrained case. In control constrained case, by using Hamiltonian approach and convex analysis, the explicit decentralized strategies can be obtained through projection operator. The corresponding Hamiltonian type consistency condition system is derived, which turns out to be a nonlinear mean-field forward-backward stochastic differential equation with projection operator. The well-posedness of such kind of equations is proved by using discounting method. Moreover, the corresponding $\varepsilon$-Nash equilibrium property is verified. In control unconstrained case, the decentralized strategies can be further represented explicitly as the feedback of filtered state through Riccati approach. The existence and uniqueness of a solution to a new Riccati type consistency condition system is also discussed. As an application, a general inter-bank borrowing and lending problem is studied to illustrate that the effect of partial information cannot be ignored.

preprint2022arXiv

Linear-Quadratic Mean Field Games of Controls with Non-Monotone Data

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the interaction is via the joint law of both the state and control. By the stochastic maximum principle, we first analyze the limiting behavior of the representative player and obtain his/her optimal control in a feedback form with the given distributional flow of the population and its control. The mean field equilibrium is determined by the Nash certainty equivalence (NCE) system. Thanks to the common noise, we do not require any monotonicity conditions for the solvability of the NCE system. We also study the master equation arising from LQ mean field games of controls, which is a finite-dimensional second-order parabolic equation. It can be shown that the master equation admits a unique classical solution over an arbitrary time horizon without any monotonicity conditions. Beyond that, we can solve the $N$-player games directly by further assuming the non-degeneracy of the idiosyncratic noises. As byproducts, we prove the quantitative convergence results from the $N$-player game to the mean field game and the propagation of chaos property for the related optimal trajectories.

preprint2022arXiv

Two Equivalent Families of Linear Fully Coupled Forward Backward Stochastic Differential Equations

In this paper, we investigate two families of fully coupled linear Forward-Backward Stochastic Differential Equations (FBSDE). Within these families, one could get the same well-posedness of FBSDEs with totally different structures. The first family of FBSDEs are proved to be equivalent with respect to the Unified Approach. Thus one could get the well-posedness of the whole family if one member exists a unique solution. Another equivalent family of FBSDEs are investigated by introducing a linear transformation method. By reason of the fully coupling structure between the forward and backward equations, it leads to a highly interdependence in solutions. We are able to lower the coupling of FBSDEs, by virtue of the idea of transformation, without losing the well-posedness. Moreover, owing to the non-degeneracy of the transformation matrix, the solution to original FBSDE is totally determined by solutions of FBSDE after transformation. In addition, an example of optimal Linear Quadratic (LQ) problem is presented to illustrate.

preprint2020arXiv

Dynamic Programming Principle for Backward Doubly Stochastic Recursive Optimal Control Problem and Sobolev Weak Solution of The Stochastic Hamilton-Bellman Equation

In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for this kind of optimal control problem and show that the value function is the unique Sobolev weak solution for the corresponding stochastic Hamilton-Jacobi-Bellman equation.

preprint2020arXiv

Latent Opinions Transfer Network for Target-Oriented Opinion Words Extraction

Target-oriented opinion words extraction (TOWE) is a new subtask of ABSA, which aims to extract the corresponding opinion words for a given opinion target in a sentence. Recently, neural network methods have been applied to this task and achieve promising results. However, the difficulty of annotation causes the datasets of TOWE to be insufficient, which heavily limits the performance of neural models. By contrast, abundant review sentiment classification data are easily available at online review sites. These reviews contain substantial latent opinions information and semantic patterns. In this paper, we propose a novel model to transfer these opinions knowledge from resource-rich review sentiment classification datasets to low-resource task TOWE. To address the challenges in the transfer process, we design an effective transformation method to obtain latent opinions, then integrate them into TOWE. Extensive experimental results show that our model achieves better performance compared to other state-of-the-art methods and significantly outperforms the base model without transferring opinions knowledge. Further analysis validates the effectiveness of our model.

preprint2016arXiv

Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in General Case

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum principle and the dynamic programming principle for such control problem without the assumption that the value is smooth enough, the set inclusions among the sub- and super-jets of the value function and the first-order and second-order adjoint processes as well as the generalized Hamiltonian function are established. Moreover, by comparing these results with the classical ones in Yong and Zhou [{\em Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999}], it is natural to obtain the first- and second-order adjoint equations of Hu [{\em Direct method on stochastic maximum principle for optimization with recursive utilities, arXiv:1507.03567v1 [math.OC], 13 Jul. 2015}].

preprint2016arXiv

Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in Local Case

This paper deals with a nonsmooth version of the connection between the maximum principle and dynamic programming principle, for the stochastic recursive control problem when the control domain is convex. By employing the notions of sub- and super-jets, the set inclusions are derived among the value function and the adjoint processes. The general case for non-convex control domain is open.

preprint2015arXiv

On well-posedness of forward-backward SDEs-A unified approach

In this paper, we study the well-posedness of the Forward-Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental longstanding problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (uniformly Lipschitz in its spatial variable). We show that the regulariy of such decoupling field is closely related to the bounded solution to an associated characteristic BSDE, a backward stochastic Riccati-type equation with superlinear growth in both components $Y$ and $Z$. We establish various sufficient conditions for the well-posedness of an ODE that dominates the characteristic BSDE, which leads to the existence of the desired regular decoupling random field, whence the solvability of the original FBSDE. A synthetic analysis of the solvability is given, as a "User's Guide," for a large class of FBSDEs that are not covered by the existing methods. Some of them have important implications in applications.

preprint2014arXiv

Mean Field Linear-Quadratic-Gaussian (LQG) Games: Major and Minor Players

This paper is concerned with a backward-forward stochastic differential equation (BFSDE) system, in which a large number of negligible agents are coupled in their dynamics via state average. Here some BSDE is introduced as the dynamics of major player, while dynamics of minor players are described by SDEs. Some auxiliary mean-field SDEs (MFSDEs) and a $3\times2$ mixed forward-backward stochastic differential equation (FBSDE) system are considered and analyzed instead of involving the fixed-point analysis as in other mean-field games. We also derive the decentralized strategies which are shown to satisfy the $ε$-Nash equilibrium property.

preprint2010arXiv

Backward Stochastic Differential Equations with Markov Chains and The Application: Homogenization of PDEs System

Stemmed from the derivation of the optimal control to a stochastic linear-quadratic control problem with Markov jumps, we study one kind of backward stochastic differential equations (BSDEs) that the generator f is affected by a Markovian switching. Then, the case that the Markov chain is involved in a large state space is considered. Following the classical approach, a hierarchical approach is adopted to reduce the complexity and a singularly perturbed Markov chain is involved. We will study the asymptotic property of BSDE with the singularly perturbed Markov chain. At last, as an application of our theoretical result, we show the homogenization of one system of partial differential equations (PDEs) with a singularly perturbed Markov chain.