## 2 Related Works
### Applicability of LSTM with (Edge) FL and IIoT Applications  
The architecture of the IIoT-FL framework is provided to illustrate the collaborative procedures involved in model training and inference between local IIoT nodes and theparameter server (see Figure 1). In the primary framework, (edge) FL policy can be jointly optimized by multi-agent deep Q-networks in terms of resource allocation and computation offloading [32]. However, QoS-specific prediction can be separately studied and integrated for improving the congestion-aware control platform. LSTM-based prediction can be deployed to detect the congestion rates of local model updates and optimize the aggregation scheduling. In the initial phase, the global model is initialized with primary parameters and hyperparameters, and it is subsequently distributed to the local nodes. To participate in the FL execution, an IIoT node needs to have auxiliary memory and intrinsic storage for tasks such as (1) loading data from local storage, (2) computing the local model, (3) saving the model to local auxiliary memory storage, (4) loading the saved model for testing, and (5) storing the final model output [15; 33]. Loss optimization occurs at each local IIoT node. The optimal local models are then uploaded to the parameter server for the aggregation process. The congestion-aware scheduling (using the LSTM-based approach) assists the policy settings to avoid model drops. Through this procedure, the integration of FL brings forth several key advantages for deploying distributed AI models in IIoT services, including personalized data protection, service differentiation, efficient low-latency communications, and optimization of AI model learning [34; 35; 36; 37]. In the context of controlling FL networking states, an LSTM-based controller can be used to model and manage the dynamic flows of model updates and connections, due to its capability of learning and predicting patterns, adapting to changing conditions, and making decisions based on the history of states and aggregation procedures. In Figure 1, there are key components in LSTM for FL, including: input data \(\left(X_{M_{n(i)}}\right)\), input gate (\(i_{t}\)), forget gate (\(f_{t}\)), output gate (\(o_{t}\)), cell state (\(\widetilde{C}_{t}\)), new cell state (\(C_{t}\)), hidden state (\(h_{t}\)), and congestion  
Figure 1: Architecture of IIoT-FL framework with LSTM-based congestion-aware aggregation. rate prediction \(Y_{M_{n(t)}}\). \(M_{n(t)}\) represents the set of local loss-minimized model parameters from participant \(n\) at \(t\)-index round communications. With LSTM-based settings, the FL controller can be significantly improved with proactive hidden state information to predict the scheduling load congestion. In [38], a privacy-preserving scheme was proposed to enhance the security of local model updating procedures within FL model aggregation. The proposed scheme served to mitigate the impact of malicious participants and strengthen the flexibility of participant selection. Furthermore, considering the expanding scale of IIoT equipment, ref. [39] proposed the management of data by converging deep reinforcement learning with FL to handle the training of extensive datasets. By converting raw data into model parameters, FL optimizes offloading decisions for IIoT tasks and directs them towards optimal edge aggregators equipped with sufficient serving resources. Consecutively, the utilization of fronthaul communication resources is minimized. From an edge perspective, an MEC-assisted FL framework was coupled with a digital twin to tackle computation offloading and resource allocation problems [40]. MEC was employed to mitigate the resource limitations of local participants and helped the core network congestion. The proposed framework greatly optimized the key performance indicators in system costs and FL training efficiencies. Furthermore, QoS-centric resource allocation in FL policy was also studied over edge IIoT networks for minimizing delay, energy consumption, and cost expenditure [41].