The Metaverse promises immersive, real-time experiences; however, meeting its stringent latency and resource demands remains a major challenge. Conventional optimization techniques struggle to respond effectively under dynamic edge conditions and high user loads. In this study, we explore a slice-enabled in-network edge architecture that combines computing-in-the-network (COIN) with multi-access edge computing (MEC). In addition, we formulate the joint problem of wireless and computing resource management with optimal slice selection as a mixed-integer nonlinear program (MINLP). Because solving this model online is computationally intensive, we decompose it into three sub-problems (SP1) intra-slice allocation, (SP2) inter-slice allocation, and (SP3) offloading decision and train a distributed hierarchical DeepSets-based model (DeepSets-S) on optimal solutions obtained offline. In the proposed model, we design a slack-aware normalization mechanism for a shared encoder and task-specific decoders, ensuring permutation equivariance over variable-size wireless device (WD) sets. The learned system produces near-optimal allocations with low inference time and maintains permutation equivariance over variable-size device sets. Our experimental results show that DeepSets-S attains high tolerance-based accuracies on SP1/SP2 (Acc1 = 95.26% and 95.67%) and improves multiclass offloading accuracy on SP3 (Acc = 0.7486; binary local/offload Acc = 0.8824). Compared to exact solvers, the proposed approach reduces the execution time by 86.1%, while closely tracking the optimal system cost (within 6.1% in representative regimes). Compared with baseline models, DeepSets-S consistently achieves higher cost ratios and better utilization across COIN/MEC resources.

翻译：元宇宙承诺提供沉浸式实时体验，然而满足其严格的延迟与资源需求仍是一项重大挑战。传统优化技术在动态边缘条件与高用户负载下难以有效响应。本研究探索了一种支持切片的网内边缘架构，将网内计算（COIN）与多接入边缘计算（MEC）相结合。此外，我们将无线与计算资源管理及最优切片选择的联合问题建模为一个混合整数非线性规划（MINLP）。由于在线求解该模型计算量巨大，我们将其分解为三个子问题：（SP1）切片内分配、（SP2）切片间分配和（SP3）卸载决策，并基于离线获得的最优解训练一个分布式分层DeepSets模型（DeepSets-S）。在所提模型中，我们为共享编码器和任务特定解码器设计了一种松弛感知归一化机制，确保对可变规模无线设备（WD）集合的置换等变性。学习后的系统能以低推理时间生成接近最优的分配方案，并保持对可变规模设备集合的置换等变性。实验结果表明，DeepSets-S在SP1/SP2上实现了基于容限的高准确率（Acc1 = 95.26% 和 95.67%），并提升了SP3的多类卸载准确率（Acc = 0.7486；二元本地/卸载 Acc = 0.8824）。与精确求解器相比，所提方法将执行时间降低了86.1%，同时紧密跟踪最优系统成本（在典型场景中差距在6.1%以内）。与基线模型相比，DeepSets-S在COIN/MEC资源上持续实现了更高的成本比和更好的利用率。