In this paper, we propose Graph Retention Networks (GRNs) as a unified architecture for deep learning on dynamic graphs. The GRN extends the concept of retention into dynamic graph data as graph retention, equipping the model with three key computational paradigms: parallelizable training, low-cost $\mathcal{O}(1)$ inference, and long-term chunkwise training. This architecture achieves an optimal balance between efficiency, effectiveness, and scalability. Extensive experiments on benchmark datasets demonstrate its strong performance in both edge-level prediction and node-level classification tasks with significantly reduced training latency, lower GPU memory overhead, and improved inference throughput by up to 86.7x compared to SOTA baselines. The proposed GRN architecture achieves competitive performance across diverse dynamic graph benchmarks, demonstrating its adaptability to a wide range of tasks.

Hierarchical time series forecasting in retail requires forecasts that are both accurate and aggregation coherent across multiple levels. Most existing methods follow a two-stage pipeline that first generates base forecasts and then reconciles them, which limits the exploitation of hierarchical structure in learning. We propose an end-to-end graph-based neural reconciliation framework that jointly models hierarchy-aware dependencies, temporal dynamics, and coherent forecasting within a single differentiable architecture. The framework combines graph neural networks and gated recurrent units with an explicit bottom-up reconciliation module that guarantees exact aggregation consistency. We evaluate the framework on two retail datasets, Italian and Walmart, under both without-promotion and with-promotion settings. The strongest variants, TGLP-BUN (Temporal Graph Linear Projection with Bottom-Up Nonlinear reconciliation) and TALP-BUN (Temporal Attention Linear Projection with Bottom-Up Nonlinear reconciliation), achieve the strongest overall performance against strong statistical and end-to-end deep-learning baselines. The gains are concentrated at higher levels on the sparse Italian hierarchy and are more broadly distributed across the Walmart hierarchy, especially when promotional information is included. Node-wise error distributions and Diebold–Mariano tests further show that these improvements are systematic across series rather than driven by only a small subset of nodes.

The current parallel storage systems use thousands of inexpensive disks to meet the storage requirement of applications. Data redundancy and/or coding are used to enhance data availability, for instance, Row-diagonal parity (RDP) and EVENODD codes, which are widely used in RAID-6 storage systems, provide data availability with up to two disk failures . To reduce the probability of data unavailability, whenever a single disk fails, disk recovery will be carried out. We find that the conventional recovery schemes of RDP and EVENODD codes for a single failed disk only use one parity disk. However, there are two parity disks in the system, and both can be used for single disk failure recovery. In this article, we propose a hybrid recovery approach that uses both parities for single disk failure recovery, and we design efficient recovery schemes for RDP code (RDOR-RDP) and EVENODD code (RDOR-EVENODD). Our recovery scheme has the following attractive properties: (1) “ read optimality ” in the sense that our scheme issues the smallest number of disk reads to recover a single failed disk and it reduces approximately 1/4 of disk reads compared with conventional schemes; (2) “ load balancing property ” in that all surviving disks will be subjected to the same (or almost the same) amount of additional workload in rebuilding the failed disk. We carry out performance evaluation to quantify the merits of RDOR-RDP and RDOR-EVENODD on some widely used disks with DiskSim. The offline experimental results show that RDOR-RDP and RDOR-EVENODD outperform the conventional recovery schemes of RDP and EVENODD codes in terms of total recovery time and recovery workload on individual surviving disk. However, the improvements are less than the theoretical value (approximately 25%), as RDOR-RDP and RDOR-EVENODD change the disk access pattern from purely sequential to a more random one compared with their conventional schemes.

Modern storage systems use thousands of inexpensive disks to meet the storage requirement of applications. To enhance the data availability, some form of redundancy is used. For example, conventional RAID-5 systems provide data availability for single disk failure only, while recent advanced coding techniques such as row-diagonal parity (RDP) can provide data availability with up to two disk failures. To reduce the probability of data unavailability, whenever a single disk fails, disk recovery (or rebuild) will be carried out. We show that conventional recovery scheme of RDP code for a single disk failure is inefficient and suboptimal. In this paper, we propose an optimal and efficient disk recovery scheme, Row-Diagonal Optimal Recovery (RDOR), for single disk failure of RDP code that has the following properties: (1) it is read optimal in the sense that it issues the smallest number of disk reads to recover the failed disk; (2) it has the load balancing property that all surviving disks will be subjected to the same amount of additional workload in rebuilding the failed disk. We carefully explore the design state space and theoretically show the optimality of RDOR. We carry out performance evaluation to quantify the merits of RDOR on some widely used disks.