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The second-order training methods can converge much faster than first-order optimizers in DNN training. This is because the second-order training utilizes the inversion of the second-order information (SOI) matrix to find a more accurate descent direction and step size. However, the huge SOI matrices bring significant computational and memory overheads in the traditional architectures like GPU and CPU. On the other side, the ReRAM-based process-in-memory (PIM) technology is suitable for the second-order training because of the following three reasons: First, PIM's computation happens in memory, which reduces data movement overheads; Second, ReRAM crossbars can compute SOI's inversion in $O\left(1\right)$ time; Third, if architected properly, ReRAM crossbars can perform matrix inversion and vector-matrix multiplications which are important to the second-order training algorithms. Nevertheless, current ReRAM-based PIM techniques still face a key challenge for accelerating the second-order training. The existing ReRAM-based matrix inversion circuitry can only support 8-bit accuracy matrix inversion and the computational precision is not sufficient for the second-order training that needs at least 16-bit accurate matrix inversion. In this work, we propose a method to achieve high-precision matrix inversion based on a proven 8-bit matrix inversion (INV) circuitry and vector-matrix multiplication (VMM) circuitry. We design \archname{}, a ReRAM-based PIM accelerator architecture for the second-order training. Moreover, we propose a software mapping scheme for \archname{} to further optimize the performance by fusing VMM and INV crossbar. Experiment shows that \archname{} can achieve an average of 115.8$\times$/11.4$\times$ speedup and 41.9$\times$/12.8$\times$energy saving compared to a GPU counterpart and PipeLayer on large-scale DNNs.