Title: From GPUs to RRAMs: Distributed In-Memory Primal-Dual Hybrid Gradient Method for Solving Large-Scale Linear Optimization Problem Show Chinese title

Title: 从GPU到RRAM：用于解决大规模线性优化问题的分布式内存内原始对偶混合梯度方法

Abstract: The exponential growth of computational workloads is surpassing the capabilities of conventional architectures, which are constrained by fundamental limits. In-memory computing (IMC) with RRAM provides a promising alternative by providing analog computations with significant gains in latency and energy use. However, existing algorithms developed for conventional architectures do not translate to IMC, particularly for constrained optimization problems where frequent matrix reprogramming remains cost-prohibitive for IMC applications. Here we present a distributed in-memory primal-dual hybrid gradient (PDHG) method, specifically co-designed for arrays of RRAM devices. Our approach minimizes costly write cycles, incorporates robustness against device non-idealities, and leverages a symmetric block-matrix formulation to unify operations across distributed crossbars. We integrate a physics-based simulation framework called MELISO+ to evaluate performance under realistic device conditions. Benchmarking against GPU-accelerated solvers on large-scale linear programs demonstrates that our RRAM-based solver achieves comparable accuracy with up to three orders of magnitude reductions in energy consumption and latency. These results demonstrate the first PDHG-based LP solver implemented on RRAMs, showcasing the transformative potential of algorithm-hardware co-design for solving large-scale optimization through distributed in-memory computing. Show Chinese abstract

Abstract: 计算工作负载的指数增长正在超越传统架构的能力，这些架构受到基本限制的约束。 基于RRAM的存内计算（IMC）通过提供模拟计算，显著提高了延迟和能耗的效率，提供了有希望的替代方案。 然而，为传统架构开发的现有算法并不适用于IMC，特别是对于约束优化问题，频繁的矩阵重新编程对IMC应用来说成本过高。 在这里，我们提出了一种分布式存内原始对偶混合梯度（PDHG）方法，专门针对RRAM器件阵列进行协同设计。 我们的方法减少了昂贵的写入周期，增强了对器件非理想性的鲁棒性，并利用对称块矩阵公式在分布式交叉条中统一操作。 我们集成了一种基于物理的仿真框架MELISO+，以在现实设备条件下评估性能。 与大规模线性规划的GPU加速求解器进行基准测试表明，我们的RRAM求解器在能耗和延迟方面实现了高达三个数量级的减少，同时保持了相当的准确性。 这些结果展示了第一个基于PDHG的在线性规划求解器在RRAM上的实现，展示了算法-硬件协同设计在通过分布式存内计算解决大规模优化问题方面的变革潜力。