Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models

Structural causal models provide a unified semantics for interventions and counterfactuals, but most identifiability results rely on restrictive assumptions like global monotonicity, which are often violated in embodied interaction, where the same exogenous perturbation can induce opposite responses under different contact contexts. We ask what structure still suffices once global monotonicity is dropped. We introduce non-monotone triangular structural causal models (NM-TM-SCM), which retain triangular recursion but replace global monotonicity with mechanism-wise invertibility and context-independent inverse transport. We prove that these conditions are equivalent to exogenous isomorphism and imply complete counterfactual identifiability, and we give a counterexample showing that local invertibility alone is insufficient. We instantiate the theory in CausalInverter, with triangular invertible layers, orientation gates, and transport-stability regularization. On synthetic non-monotonic mechanisms, the structural bias yields systematic counterfactual gains as non-monotonicity increases. On MuJoCo Door, our model achieves perfect event-level counterfactual recovery, lowers continuous angle error relative to a Transformer baseline, and delivers substantially more stable recovery than Transformer and conditional-flow predictors. On MuJoCo Push, where non-monotonicity is weaker, the same low-data predictors remain competitive or better, consistent with a bias-variance boundary. These results identify a broader identifiable regime between globally monotone triangular models and unconstrained black-box world models.

QoS-Aware Integrated Sensing, Communication, and Control with Movable Antenna

Integrated sensing, communication, and control (ISCC) has emerged as a key enabler for low-altitude wireless networks with enhanced adaptability through resource allocation co-design and intelligent environment awareness. However, dynamic interference and channel attenuation constrain the potential of the ISCC system. To address this challenge, we propose a novel movable antenna-empowered ISCC system. An achievable data rate maximization problem is formulated while guaranteeing the sensing and control quality-of-service (QoS) by optimizing the positions of the antennas and the beamforming strategy for communication, sensing, and control co-design. An efficient alternating optimization (AO)-based algorithm is proposed to solve the highly coupled non-convex problem. Numerical results demonstrate that the proposed AO-based algorithm achieves substantial gains in the achievable data rate and the control QoS compared with benchmark schemes.