Causal Diffusion Models for Counterfactual Outcome Distributions in Longitudinal Data

Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate uncertainty quantification in existing methods. We introduce the Causal Diffusion Model (CDM), the first denoising diffusion probabilistic approach explicitly designed to generate full probabilistic distributions of counterfactual outcomes under sequential interventions. CDM employs a novel residual denoising architecture with relational self-attention, capturing intricate temporal dependencies and multimodal outcome trajectories without requiring explicit adjustments (e.g., inverse-probability weighting or adversarial balancing) for confounding. In rigorous evaluation on a pharmacokinetic-pharmacodynamic tumor-growth simulator widely adopted in prior work, CDM consistently outperforms state-of-the-art longitudinal causal inference methods, achieving a 15-30% relative improvement in distributional accuracy (1-Wasserstein distance) while maintaining competitive or superior point-estimate accuracy (RMSE) under high-confounding regimes. By unifying uncertainty quantification and robust counterfactual prediction in complex, sequentially confounded settings, without tailored deconfounding, CDM offers a flexible, high-impact tool for decision support in medicine, policy evaluation, and other longitudinal domains.

The Condition-Number Principle for Prototype Clustering

We develop a geometric framework that links objective accuracy to structural recovery in prototype-based clustering. The analysis is algorithm-agnostic and applies to a broad class of admissible loss functions. We define a clustering condition number that compares within-cluster scale to the minimum loss increase required to move a point across a cluster boundary. When this quantity is small, any solution with a small suboptimality gap must also have a small misclassification error relative to a benchmark partition. The framework also clarifies a fundamental trade-off between robustness and sensitivity to cluster imbalance, leading to sharp phase transitions for exact recovery under different objectives. The guarantees are deterministic and non-asymptotic, and they separate the role of algorithmic accuracy from the intrinsic geometric difficulty of the instance. We further show that errors concentrate near cluster boundaries and that sufficiently deep cluster cores are recovered exactly under strengthened local margins. Together, these results provide a geometric principle for interpreting low objective values as reliable evidence of meaningful clustering structure.

AI-Native 6G Physical Layer with Cross-Module Optimization and Cooperative Control Agents

In this article, a framework of AI-native cross-module optimized physical layer with cooperative control agents is proposed, which involves optimization across global AI/ML modules of the physical layer with innovative design of multiple enhancement mechanisms and control strategies. Specifically, it achieves simultaneous optimization across global modules of uplink AI/ML-based joint source-channel coding with modulation, and downlink AI/ML-based modulation with precoding and corresponding data detection, reducing traditional inter-module information barriers to facilitate end-to-end optimization toward global objectives. Moreover, multiple enhancement mechanisms are also proposed, including i) an AI/ML-based cross-layer modulation approach with theoretical analysis for downlink transmission that breaks the isolation of inter-layer features to expand the solution space for determining improved constellation, ii) a utility-oriented precoder construction method that shifts the role of the AI/ML-based CSI feedback decoder from recovering the original CSI to directly generating precoding matrices aiming to improve end-to-end performance, and iii) incorporating modulation into AI/ML-based CSI feedback to bypass bit-level bottlenecks that introduce quantization errors, non-differentiable gradients, and limitations in constellation solution spaces. Furthermore, AI/ML based control agents for optimized transmission schemes are proposed that leverage AI/ML to perform model switching according to channel state, thereby enabling integrated control for global throughput optimization. Finally, simulation results demonstrate the superiority of the proposed solutions in terms of BLER and throughput. These extensive simulations employ more practical assumptions that are aligned with the requirements of the 3GPP, which hopefully provides valuable insights for future standardization discussions.