Anomaly detection in multivariate time series is a critical task across a range of real-world domains, such as industrial automation and the internet of things. These environments are generally monitored by various types of sensors that produce complex, high-dimensional time-series data with intricate cross-sensor dependencies. While existing methods often utilize sequence modeling or graph neural networks to capture global sensor relationships, they typically treat all sensors uniformly—potentially overlooking the benefit of grouping sensors with similar temporal patterns. To this end, we propose a novel framework called Multi-task Learning Anomaly Detection (MLAD), which leverages clustering techniques to group sensors based on their temporal characteristics, and employs a multi-task learning paradigm to jointly capture both shared patterns across all sensors and specialized patterns within each cluster. MLAD consists of four key modules: (1) sensor clustering based on sensors’ time series, (2) representation learning with a cluster-constrained graph neural network, (3) multi-task forecasting with shared and cluster-specific learning layers, and (4) anomaly scoring. Extensive experiments on three public datasets demonstrate that MLAD achieves superior detection performance over state-of-the-art baselines. Ablation studies further validate the effectiveness of the modules of our MLAD. This study highlights the value of incorporating sensor heterogeneity into model design, which contributes to more accurate and robust anomaly detection in sensor-based monitoring systems.

World models aim to construct internal rep-1 resentations of the environment that support 2 predicting how the world evolves and enable 3 agents to plan actions through "imagination." 4 With rapid progress across game simulation, 5 autonomous driving, and robotics, the field 6 remains fragmented: different communities 7 adopt varying representations, interaction ab-8 stractions, and transition methods, leading to 9 distinct bottlenecks in physical consistency, 10 interaction reliability, and long-horizon sta-11 bility. In this survey, we adopt a minimal tran-12 sition formalism, s t+1 ∼ p θ (• | s t , a t), as a 13 unifying analytical lens and organize modern 14 world models around three irreducible design 15 dimensions: state representation (s t), action 16 representation (a t), and transition modeling 17 (p θ). Under this taxonomy, we examine (i) 18 2D video representations versus emerging 19 3D/4D state spaces and the trade-offs in scale, 20 metric structure, and latent physical factors; 21 (ii) semantic actions versus executable ac-22 tions and the tension between expressive spec-23 ification and reliable control; and (iii) im-24 plicit transition methods learned from data 25 versus explicit transition methods driven by 26 human-specified physical priors. Building 27 on these bottleneck-driven comparisons, we 28 further synthesize three research directions 29 motivated by current limitations: Active In-30 tervention Loop, Physical Laws Internaliza-31 tion, and Progressive Structural Integration. 32 Overall, this survey provides a consistent an-33 alytical vocabulary and an organized frame-34 work that explains how design choices affect 35 the capabilities and limitations of contempo-36 rary world models, and outlines promising 37 improvements for advancing Interactive Cog-38 nitive World Models. 39 verifiability, and robustness under distribution shift. 93 Building on this structured analysis, we further syn-94 thesize the bottlenecks revealed across the three dimen-95 sions and discuss promising research directions that are 96 strongly suggested by current limitations, including Ac-97 tive Intervention Loop, Physical Laws Internalization, 98 and Progressive Structural Integration. Overall, the 99 contribution of this survey is not to prescribe a single 100 implementation route, but to provide a consistent ana-101 lytical vocabulary and a bottleneck-driven organization 102 of the field that clarifies how different technical choices 103 shape the capabilities and limits of modern world mod-104 els, and outlines promising directions for advancing 105 toward Interactive Cognitive World Models. 106 2 Related Work & Motivation 107 The rapid progress of world models has prompted sev-108 eral recent surveys, each offering valuable summaries 109 from different viewpoints. Broad reviews [Zhu et al., 110 2024; Ding et al., 2025] cover general-purpose world 111 models and organize the literature by model families, 112 training pipelines, or downstream domains such as 113 video generation, driving, and agent learning. In paral-114 lel, more specialized surveys focus on particular desider-115 ata or modalities, including physical consistency in 116 video generation [Lin et al., 2025] and native 3D/4D 117 representations such as occupancy grids and LiDAR-118 based state spaces [Kong et al., 2025]. Together, these 119 works provide useful entry points and taxonomies for a 120 fast-growing area. Despite these contributions, a persis-121 tent challenge remains: existing surveys often rely on 122 domain-or architecture-centered groupings, making it 123 difficult to compare models across communities using 124 a consistent set of analytical variables, or to connect di-125 vergent failure modes to the underlying design choices 126 that produce them. 127 This survey addresses this gap by adopting the min-128 imal transition formalism in Eq. (1) as a unifying per-129 spective. Rather than introducing another domain-130 driven taxonomy, we organize the literature around 131 three irreducible design dimensions-state represen-132 tation (s t), action representation (a t), and transition 133 modeling (p θ)-and use this lens to analyze how differ-134 ent technical routes lead to distinct limitations. Build-135 ing on these bottleneck-driven comparisons, we further 136 synthesize a set of non-exhaustive research directions 137 that are strongly suggested by current evidence, aiming 138 to clarify what it would take for world models to sup-139 port stable representations, intentional interaction, and 140 reliable long-horizon dynamics in open-world settings. 141 3 State representation 142 The world state (s t) in the transition formalism (Eq. 1) 143

World models represent environments and predict how their states evolve under interventions. Their use in generative simulation and interactive environments, autonomous driving, and robotics and embodied control is growing, yet application validation remains fragmented across model families. Using the relation $s_{t+1}\sim p_{\theta }(\cdot \mid s_t,a_t)$, this review organizes the field around state representation, action representation, and transition modeling. We compare visual and geometric states with object-centric or belief/latent organization; semantic, hierarchical, latent, and executable actions; and autoregressive, diffusion-based, predictive latent, explicit-simulation, and learned–physics hybrid transitions. Across the three applications, we connect these choices to identity drift, non-executable plans, unsafe multimodal forecasts, long-horizon instability, and sim-to-real degradation. We then link each failure to six diagnostic dimensions: perceptual fidelity, physical validity, action consistency, rollout stability, calibration, and decision utility. The synthesis provides a cross-application engineering matrix and motivates Active Intervention Loops, Physical Laws Internalization, and Progressive Structural Integration. It identifies the State–Action–Transition commitments that shape application suitability and separates visual plausibility from evidence of interactive or deployment readiness.