The emergence of Turing patterns is often the collective result of multi-layered interactions and ubiquitous environmental fluctuations. While Turing instability has been extensively studied in single-layered and deterministic networks, the synergistic role of multiplex topology and multiplicative noise remains unexplored. This paper proposes a multiplex-networked stochastic activator-inhibitor system, where state-dependent multiplicative noise driven by mutually independent edge noise processes is incorporated into both intra-layer and inter-layer diffusion processes, with an intensity proportional to the density differences between neighboring nodes. By utilizing the stability theorem of stochastic differential equations, a sufficient condition for almost sure convergence to the uniform stationary state is derived. The results reveal that multiplicative noise affects pattern onset non-monotonically, while stronger noise promotes pattern formation and reduces the observed hysteresis width. In addition, inter-layer coupling can exert a complex, non-monotonic influence on Turing instability, and the critical thresholds may exhibit saturation at strong coupling under certain parameter settings. Finally, topological analysis reveals pronounced robustness of the forward threshold across the examined Pure-BA configurations, where pattern onset is governed predominantly by hub-localized critical modes. This behavior contrasts with the greater sensitivity to connectivity and inter-layer architecture observed in Pure-ER and Pure-WS networks. These findings provide new insights into the constructive role of noise and multiplex architecture in driving network self-organization.
We consider imitation learning (IL), which mimics a policy from finite expert trajectories. A prevalent framework of IL is adversarial imitation learning (AIL) that trains a discriminator to distinguish samples from the expert and the imitator. Although AIL achieves impressive performance on some artificial tasks, we observe that the learned discriminator may overfit to the limited expert data, especially when encountering tasks with high-dimensional state spaces. We find that the imbalance between expert demonstrations and generated samples during the training of the discriminator can affect its training margin, consequently resulting in overfitting of the discriminator. Building upon this, we propose expert policy support expansion (EXPOSE). Apart from the discriminator and the generator, EXPOSE additionally learns two random network distillations (RNDs), namely, an expert RND (e-RND) and a policy RND (p-RND). The p-RND incentivizes the imitator to explore the state-action space, while the e-RND filters out expert-level samples from the imitator and adds them to the expert dataset, explicitly expanding the support of the expert policy. Extensive empirical results on tasks from the DeepMind Control Suite and Meta-World benchmarks demonstrate that EXPOSE achieves an average improvement of 40
In this paper, we consider joint active user detection, channel estimation and data decoding for unsourced random access (URA) in cell-free massive multiple-input multiple-output (CF-mMIMO) systems with backhaul constraints, where the access points (APs) may receive concurrent transmissions from hundreds of low-power terminal devices. In such scenarios, the coarse quantization of baseband signals at APs introduces nonlinear distortion that severely degrades joint detection and decoding. To address this issue, we develop a Bayesian inference framework that models the quantized observations as a generalized linear model (GLM). By building upon this model, we extend the vector approximate message passing net (VAMP-Net) and MIMO low-density parity-check net (MIMO-LDPC-Net) into generalized VAMP-Net and generalized MIMO-LDPC-Net, enabling quantization-aware joint activity detection, channel estimation, and data decoding. Simulation results demonstrate that the proposed approach achieves at least an order of magnitude lower detection and decoding error rates than the existing linear-model-based algorithms, particularly under low-bit backhaul quantization, while maintaining moderate additional computational overhead compared with SLM-based unfolded receivers, making it suitable for large-scale CF-mMIMO systems.
