Systolic arrays are the dominant compute fabric for neural network inference. Prior work has addressed column-level fault detection efficiently with uniform test patterns, but row-level (PE-level) fault localization within a faulty column remains open without resorting to hardware redundancy. The fundamental obstacle is that uniform test inputs destroy per-row signatures: any test that activates every row equally cannot distinguish which row is the source of an observed deviation. In this paper, we propose a lightweight, purely algorithmic remedy based on coprime test vectors. By assigning pairwise coprime integers as test-input entries, a permanent weight-register fault produces a deviation whose divisibility signature uniquely identifies the faulty row. Under a general bounded error model, a single test pass localizes the faulty row with high probability. This error model covers a broader class of faults than what prior dataflow-aware testing work has primarily emphasized. When one round is insufficient, a second pass using a ratio computation achieves exact localization; for the special case of single-bit errors, odd coprime entries guarantee exact localization in one round. For INT16 arithmetic, a single test pass covers array sizes up to $256{\times}256$ with localization probability above $0.98$, at a test cost under $1\%$ of one inference GEMM tile.

翻译：脉动阵列是神经网络推理的主要计算架构。现有工作已利用统一测试模式高效实现了列级故障检测，但在不借助硬件冗余的前提下，故障列内行级（PE级）定位问题仍未解决。根本障碍在于统一测试输入会消除各行特征：任何均匀激活所有行的测试都无法区分观测偏差源自哪一行。本文提出一种基于互质测试向量的轻量级纯算法解决方案。通过为测试输入赋值两两互质的整数，永久性权重寄存器故障产生的偏差可通过其可整除性特征唯一识别故障行。在通用有界错误模型下，单次测试即可高概率定位故障行。该模型覆盖的故障类别比先前数据流感知测试方法主要关注的更为广泛。当单轮测试不足时，采用比值计算的第二轮测试可实现精确定位；对于单比特错误这一特例，奇互质条目可确保单轮精确定位。针对INT16算术，当阵列规模达$256{\times}256$时，单次测试定位概率超过$0.98$，测试成本低于一次推理GEMM块的$1\%$。