Fairness in machine learning has been extensively studied in single-task settings, while fair multi-task learning (MTL), especially with heterogeneous tasks (classification, detection, regression) and partially missing labels, remains largely unexplored. Existing fairness methods are predominantly classification-oriented and fail to extend to continuous outputs, making a unified fairness objective difficult to formulate. Further, existing MTL optimization is structurally misaligned with fairness: constraining only the shared representation, allowing task heads to absorb bias and leading to uncontrolled task-specific disparities. Finally, most work treats fairness as a zero-sum trade-off with utility, enforcing symmetric constraints that achieve parity by degrading well-served groups. We introduce FairMT, a unified fairness-aware MTL framework that accommodates all three task types under incomplete supervision. At its core is an Asymmetric Heterogeneous Fairness Constraint Aggregation mechanism, which consolidates task-dependent asymmetric violations into a unified fairness constraint. Utility and fairness are jointly optimized via a primal--dual formulation, while a head-aware multi-objective optimization proxy provides a tractable descent geometry that explicitly accounts for head-induced anisotropy. Across three homogeneous and heterogeneous MTL benchmarks encompassing diverse modalities and supervision regimes, FairMT consistently achieves substantial fairness gains while maintaining superior task utility. Code will be released upon paper acceptance.

With the rapid advancement of intelligent education, Computerized Adaptive Testing (CAT) has attracted increasing attention by integrating educational psychology with deep learning technologies. Unlike traditional paper-and-pencil testing, CAT aims to efficiently and accurately assess examinee abilities by adaptively selecting the most suitable items during the assessment process. However, its real-time and sequential nature presents limitations in practical scenarios, particularly in large-scale assessments where interaction costs are high, or in sensitive domains such as psychological evaluations where minimizing noise and interference is essential. These challenges constrain the applicability of conventional CAT methods in time-sensitive or resourceconstrained environments. To this end, we first introduce a novel task called one-shot adaptive testing (OAT), which aims to select a fixed set of optimal items for each test-taker in a one-time selection. Meanwhile, we propose PEOAT, a Personalization-guided Evolutionary question assembly framework for One-shot Adaptive Testing from the perspective of combinatorial optimization. Specifically, we began by designing a personalization-aware initialization strategy that integrates differences between examinee ability and exercise difficulty, using multi-strategy sampling to construct a diverse and informative initial population. Building on this, we proposed a cognitive-enhanced evolutionary framework incorporating schema-preserving crossover and cognitively guided mutation to enable efficient exploration through informative signals. To maintain diversity without compromising fitness, we further introduced a diversity-aware environmental selection mechanism. The effectiveness of PEOAT is validated through extensive experiments on two datasets, complemented by case studies that uncovered valuable insights.

Model merging has emerged as a practical paradigm for integrating multiple independently trained models into a single model without joint retraining. Previous studies have demonstrated the effectiveness of combining parameters through strategies such as parameter decomposition, coefficient optimization, and subspace learning, significantly reducing the need for expensive joint training and achieving strong empirical performance across diverse tasks. However, these approaches predominantly treat merging as a problem of parameter space decomposition or fusion coefficient optimization, while overlooking the critical role of directional information in both parameter and feature spaces. In practice, naïve merging introduces inconsistencies in dominant parameter directions and disrupts structural coherence across models, which can degrade performance. Moreover, coefficient-based optimization methods implicitly assume compatible feature-space directions across models. However, Neural Collapse indicates that class features follow structured directional patterns, which may differ across independently trained models, making coefficient optimization alone insufficient. In this work, we emphasize the importance of \emph{directional alignment} and introduce a unified geometric framework, \emph{Merging with Directional Alignment} (\method{}), which aligns directional structures consistently in both the parameter and feature spaces. Our analysis shows that directional alignment improves structural coherence, and extensive experiments across benchmarks, model scales, and task configurations further validate the effectiveness of our approach.

We investigate the static portfolio selection problem of S-shaped and non-concave utility maximization under first-order and second-order stochastic dominance (SD) constraints. In many S-shaped utility optimization problems, one should require a liquidation boundary to guarantee the existence of a finite concave envelope function. A first-order SD (FSD) constraint can replace this requirement and provide an alternative for risk management. We explicitly solve the optimal solution under a general S-shaped utility function with a first-order stochastic dominance constraint. However, the second-order SD (SSD) constrained problem under non-concave utilities is difficult to solve analytically due to the invalidity of Sion's maxmin theorem. For this sake, we propose a numerical algorithm to obtain a plausible and sub-optimal solution for general non-concave utilities. The key idea is to detect the poor performance region with respect to the SSD constraints, characterize its structure and modify the distribution on that region to obtain (sub-)optimality. A key financial insight is that the decision maker should follow the SD constraint on the poor performance scenario while conducting the unconstrained optimal strategy otherwise. We provide numerical experiments to show that our algorithm effectively finds a sub-optimal solution in many cases. Finally, we develop an algorithm-guided piecewise-neural-network framework to learn the solution of the SSD problem, which demonstrates accelerated convergence compared to standard neural network approaches.

This study analyzes the impact of heterogeneity ("Variety") in Big Data by comparing classification strategies across structured (Epsilon) and unstructured (Rest-Mex, IMDB) domains. A dual methodology was implemented: evolutionary and Bayesian hyperparameter optimization (Genetic Algorithms, Optuna) in Python for numerical data, and distributed processing in Apache Spark for massive textual corpora. The results reveal a "complexity paradox": in high-dimensional spaces, optimized linear models (SVM, Logistic Regression) outperformed deep architectures and Gradient Boosting. Conversely, in text-based domains, the constraints of distributed fine-tuning led to overfitting in complex models, whereas robust feature engineering -- specifically Transformer-based embeddings (ROBERTa) and Bayesian Target Encoding -- enabled simpler models to generalize effectively. This work provides a unified framework for algorithm selection based on data nature and infrastructure constraints.

Flow matching (FM) has shown promising results in data-driven planning. However, it inherently lacks formal guarantees for ensuring state and action constraints, whose satisfaction is a fundamental and crucial requirement for the safety and admissibility of planned trajectories on various systems. Moreover, existing FM planners do not ensure the dynamical consistency, which potentially renders trajectories inexecutable. We address these shortcomings by proposing SAD-Flower, a novel framework for generating Safe, Admissible, and Dynamically consistent trajectories. Our approach relies on an augmentation of the flow with a virtual control input. Thereby, principled guidance can be derived using techniques from nonlinear control theory, providing formal guarantees for state constraints, action constraints, and dynamic consistency. Crucially, SAD-Flower operates without retraining, enabling test-time satisfaction of unseen constraints. Through extensive experiments across several tasks, we demonstrate that SAD-Flower outperforms various generative-model-based baselines in ensuring constraint satisfaction.

Reinforcement Learning (RL) has emerged as a powerful framework for sequential decision-making in dynamic environments, particularly when system parameters are unknown. This paper investigates RL-based control for entropy-regularized linear-quadratic (LQ) control problems with multiplicative noise over an infinite time horizon. First, we adapt the regularized policy gradient (RPG) algorithm to stochastic optimal control settings, proving that despite the non-convexity of the problem, RPG converges globally under conditions of gradient domination and almost-smoothness. Second, based on zero-order optimization approach, we introduce a novel model free RL algorithm: Sample-based regularized policy gradient (SB-RPG). SB-RPG operates without knowledge of system parameters yet still retains strong theoretical guarantees of global convergence. Our model leverages entropy regularization to address the exploration versus exploitation trade-off inherent in RL. Numerical simulations validate the theoretical results and demonstrate the efficiency of SB-RPG in unknown-parameters environments.

In the realm of distributed artificial intelligence (AI) and privacy-focused medical applications, this paper proposes a multi-view clustering framework that links quantum field theory with federated healthcare analytics. The method uses heat kernel coefficients from spectral analysis to convert Euclidean distances into geometry-aware similarity measures that capture the structure of diverse medical data. The framework is presented through the heat kernel distance (HKD) transformation, which has convergence guarantees. Two algorithms have been developed: The first, Heat Kernel-Enhanced Multi-View Fuzzy Clustering (HK-MVFC), is used for central analysis. The second, Federated Heat Kernel Multi-View Fuzzy Clustering (FedHK-MVFC), is used for secure, privacy-preserving learning across hospitals. FedHK-MVFC uses differential privacy and secure aggregation to enable HIPAA-compliant collaboration. Tests on synthetic cardiovascular patient datasets demonstrate increased clustering accuracy, reduced communication, and retained efficiency compared to centralized methods. After being validated on 10,000 synthetic patient records across two hospitals, the methods proved useful for collaborative phenotyping involving electrocardiogram (ECG) data, cardiac imaging data, and behavioral data. The proposed methods' theoretical contributions include update rules with proven convergence, adaptive view weighting, and privacy-preserving protocols. These contributions establish a new standard for geometry-aware federated learning in healthcare, translating advanced mathematics into practical solutions for analyzing sensitive medical data while ensuring rigor and clinical relevance.

Diffusion models excel in high-fidelity image generation but face scalability limits due to transformers' quadratic attention complexity. Plug-and-play token reduction methods like ToMeSD and ToFu reduce FLOPs by merging redundant tokens in generated images but rely on GPU-inefficient operations (e.g., sorting, scattered writes), introducing overheads that negate theoretical speedups when paired with optimized attention implementations (e.g., FlashAttention). To bridge this gap, we propose Token Merge with Attention (ToMA), an off-the-shelf method that redesigns token reduction for GPU-aligned efficiency, with three key contributions: 1) a reformulation of token merge as a submodular optimization problem to select diverse tokens; 2) merge/unmerge as an attention-like linear transformation via GPU-friendly matrix operations; and 3) exploiting latent locality and sequential redundancy (pattern reuse) to minimize overhead. ToMA reduces SDXL/Flux generation latency by 24%/23%, respectively (with DINO $Δ< 0.07$), outperforming prior methods. This work bridges the gap between theoretical and practical efficiency for transformers in diffusion. Code available at https://github.com/WenboLuu/ToMA.

Behavior Regularized Policy Optimization (BRPO) leverages asymmetric (divergence) regularization to mitigate the distribution shift in offline Reinforcement Learning. This paper is the first to study the open question of symmetric regularization. We show that symmetric regularization does not permit an analytic optimal policy $π^*$, posing a challenge to practical utility of symmetric BRPO. We approximate $π^*$ by the Taylor series of Pearson-Vajda $χ^n$ divergences and show that an analytic policy expression exists only when the series is capped at $n=5$. To compute the solution in a numerically stable manner, we propose to Taylor expand the conditional symmetry term of the symmetric divergence loss, leading to a novel algorithm: Symmetric $f$-Actor Critic (S$f$-AC). S$f$-AC achieves consistently strong results across various D4RL MuJoCo tasks. Additionally, S$f$-AC avoids per-environment failures observed in IQL, SQL, XQL and AWAC, opening up possibilities for more diverse and effective regularization choices for offline RL.