Appendix for "Episodic Multi-T ask Learning with Heterogeneous Neural Processes" In this section, we list frequently asked questions from researchers who help proofread this manuscript. As shown in Table 1, we use "Heterogeneous tasks" to distinguish the different branches of multi-task Meanwhile, "Episodic training" is used to describe the data-feeding strategy. Thus, "Heterogeneous tasks" is not available here (-). In episodic multi-task learning, we restrict the scope of the problem to the case where tasks in the same episode are related and share the same target space. This also implies that tasks with the same target space are related.

Step 2. The deduction in Step 1 can be iterated repeatedly due to the symmetry of

Kullback-Leibler (KL) divergence is one of the most important measures to calculate the difference between probability distributions. In this paper, we theoretically study several properties of KL divergence between multivariate Gaussian distributions.

Detecting unobserved confounders is crucial for reliable causal inference in observational studies. Existing methods require either linearity assumptions or multiple heterogeneous environments, limiting applicability to nonlinear single-environment settings. To bridge this gap, we propose Kernel Regression Confounder Detection (KRCD), a novel method for detecting unobserved confounding in nonlinear observational data under single-environment conditions. KRCD leverages reproducing kernel Hilbert spaces to model complex dependencies. By comparing standard and higherorder kernel regressions, we derive a test statistic whose significant deviation from zero indicates unobserved confounding. Theoretically, we prove two key results: First, in infinite samples, regression coefficients coincide if and only if no unobserved confounders exist. Second, finite-sample differences converge to zero-mean Gaussian distributions with tractable variance. Extensive experiments on synthetic benchmarks and the Twins dataset demonstrate that KRCD not only outperforms existing baselines but also achieves superior computational efficiency.

Zero-Touch Networks (ZTNs) represent a transformative paradigm toward fully automated and intelligent network management, providing the scalability and adaptability required for the complexity of sixth-generation (6G) networks. However, the distributed architecture, high openness, and deep heterogeneity of 6G networks expand the attack surface and pose unprecedented security challenges. To address this, security automation aims to enable intelligent security management across dynamic and complex environments, serving as a key capability for securing 6G ZTNs. Despite its promise, implementing security automation in 6G ZTNs presents two primary challenges: 1) automating the lifecycle from security strategy generation to validation and update under real-world, parallel, and adversarial conditions, and 2) adapting security strategies to evolving threats and dynamic environments. This motivates us to propose SecLoop and SA-GRPO. SecLoop constitutes the first fully automated framework that integrates large language models (LLMs) across the entire lifecycle of security strategy generation, orchestration, response, and feedback, enabling intelligent and adaptive defenses in dynamic network environments, thus tackling the first challenge. Furthermore, we propose SA-GRPO, a novel security-aware group relative policy optimization algorithm that iteratively refines security strategies by contrasting group feedback collected from parallel SecLoop executions, thereby addressing the second challenge. Extensive real-world experiments on five benchmarks, including 11 MITRE ATT&CK processes and over 20 types of attacks, demonstrate the superiority of the proposed SecLoop and SA-GRPO. We will release our platform to the community, facilitating the advancement of security automation towards next generation communications.

Collaborative pursuit-evasion in cluttered environments presents significant challenges due to sparse rewards and constrained Fields of View (FOV). Standard Multi-Agent Reinforcement Learning (MARL) often suffers from inefficient exploration and fails to scale to large scenarios. We propose PGF-MAPPO (Path-Guided Frontier MAPPO), a hierarchical framework bridging topological planning with reactive control. To resolve local minima and sparse rewards, we integrate an A*-based potential field for dense reward shaping. Furthermore, we introduce Directional Frontier Allocation, combining Farthest Point Sampling (FPS) with geometric angle suppression to enforce spatial dispersion and accelerate coverage. The architecture employs a parameter-shared decentralized critic, maintaining O(1) model complexity suitable for robotic swarms. Experiments demonstrate that PGF-MAPPO achieves superior capture efficiency against faster evaders. Policies trained on 10x10 maps exhibit robust zero-shot generalization to unseen 20x20 environments, significantly outperforming rule-based and learning-based baselines.

Large Language Models (LLMs) have achieved remarkable performance on single-turn tasks, yet their effectiveness deteriorates in multi-turn conversations. We define this phenomenon as cumulative contextual decay - a progressive degradation of contextual integrity caused by attention pollution, dilution, and drift. To address this challenge, we propose Rhea (Role-aware Heuristic Episodic Attention), a novel framework that decouples conversation history into two functionally independent memory modules: (1) an Instructional Memory (IM) that persistently stores high-fidelity global constraints via a structural priority mechanism, and (2) an Episodic Memory (EM) that dynamically manages user-model interactions via asymmetric noise control and heuristic context retrieval. During inference, Rhea constructs a high signal-to-noise context by applying its priority attention: selectively integrating relevant episodic information while always prioritizing global instructions. To validate this approach, experiments on multiple multi-turn conversation benchmarks - including MT-Eval and Long-MT-Bench+ - show that Rhea mitigates performance decay and improves overall accuracy by 1.04 points on a 10-point scale (a 16% relative gain over strong baselines). Moreover, Rhea maintains near-perfect instruction fidelity (IAR > 8.1) across long-horizon interactions. These results demonstrate that Rhea provides a principled and effective framework for building more precise, instruction-consistent conversational LLMs.

Adjusting the outdated knowledge of large language models (LLMs) after deployment remains a major challenge. This difficulty has spurred the development of knowledge editing, which seeks to accurately and efficiently modify a model's internal (parametric) knowledge without retraining it from scratch. However, existing methods suffer from two limitations. First, they depend on structured triplets that are misaligned with the free-text nature of LLM pretraining and fail to capture the nuanced relationships among facts. Second, they typically support one-time knowledge updates, with relatively limited research on the problem of sequential or lifelong editing. To address these gaps, we propose a new task, Lifelong Free-text Knowledge Editing (LF-Edit), which enables models to incorporate updates expressed in natural language and supports continual editing over time. Despite its promise, LF-Edit faces the dual challenge of integrating new knowledge while mitigating the forgetting of prior information. To foster research on this new task, we construct a large-scale benchmark, Multi-Rank Lifelong Free-text Editing Benchmark (MRLF-Bench), containing 16,835 free-text edit requests. We further design a cognitively inspired multi-rank evaluation framework encompassing four levels: memorization, understanding, constrained comprehension, and reasoning. To tackle the challenges inherent in LF-Edit, we introduce a novel approach named EvoEdit that enhances knowledge injection through Latent Perturbation Augmentation and preserves prior information via Knowledge-driven Parameter Fusion. Experimental results demonstrate that EvoEdit substantially outperforms existing knowledge editing methods on the proposed LF-Edit task.

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

World models have gained significant attention as a promising approach for autonomous driving. By emulating human-like perception and decision-making processes, these models can predict and adapt to dynamic environments. Existing methods typically map high-dimensional observations into compact latent spaces and learn optimal policies within these latent representations. However, prior work usually jointly learns ego-vehicle dynamics and environmental transition dynamics from the image input, leading to inefficiencies and a lack of robustness to variations in vehicle dynamics. To address these issues, we propose the Vehicle Dynamics embedded Dreamer (VDD) method, which decouples the modeling of ego-vehicle dynamics from environmental transition dynamics. This separation allows the world model to generalize effectively across vehicles with diverse parameters. Additionally, we introduce two strategies to further enhance the robustness of the learned policy: Policy Adjustment during Deployment (PAD) and Policy Augmentation during Training (PAT). Comprehensive experiments in simulated environments demonstrate that the proposed model significantly improves both driving performance and robustness to variations in vehicle dynamics, outperforming existing approaches.