To overcome the performance limitations in modern computing, such as the power wall, emerging computing paradigms are gaining increasing importance. Approximate computing offers a promising solution by substantially enhancing energy efficiency and reducing latency, albeit with a trade-off in accuracy. Another emerging method is memristor-based In-Memory Computing (IMC) which has the potential to overcome the Von Neumann bottleneck. In this work, we combine these two approaches and propose two Serial APProximate IMPLY-based full adders (SAPPI). When embedded in a Ripple Carry Adder (RCA), our designs reduce the number of steps by 39%-41% and the energy consumption by 39%-42% compared to the exact algorithm. We evaluated our approach at the circuit level and compared it with State-of-the-Art (SoA) approximations where our adders improved the speed by up to 10% and the energy efficiency by up to 13%. We applied our designs in three common image processing applications where we achieved acceptable image quality with up to half of the RCA approximated. We performed a case study to demonstrate the applicability of our approximations in Machine Learning (ML) underscoring the potential gains in more complex scenarios. The proposed approach demonstrates energy savings of up to 296 mJ (21%) and a reduction of 1.3 billion (20%) computational steps when applied to Convolutional Neural Networks (CNNs) trained on the MNIST dataset while maintaining accuracy.

翻译：为克服现代计算中的性能限制（如功耗墙），新兴计算范式正日益重要。近似计算通过显著提升能效并降低延迟提供了一种有前景的解决方案，尽管需要以精度为代价。另一种新兴方法是基于忆阻器的内存计算（IMC），它有望克服冯·诺依曼瓶颈。本研究融合这两种方法，提出了两种基于IMPLY的串行近似全加器（SAPPI）。当嵌入行波进位加法器（RCA）时，相较于精确算法，我们的设计将运算步骤减少39%-41%，能耗降低39%-42%。我们在电路层面评估了该方法，并与现有先进（SoA）近似方案进行对比，结果显示我们的加法器在速度上提升最高达10%，能效提升最高达13%。我们将设计应用于三种常见图像处理任务，在最高半数RCA单元近似化的情况下仍获得可接受的图像质量。通过案例研究展示了该近似方法在机器学习（ML）中的适用性，揭示了其在复杂场景中的潜在增益。当应用于MNIST数据集训练的卷积神经网络（CNN）时，所提方法在保持精度的同时实现了最高296 mJ（21%）的能耗节约与13亿次（20%）计算步骤的减少。