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Resistive Random-Access Memory (RRAM) is well-suited to accelerate neural network (NN) workloads as RRAM-based Processing-in-Memory (PIM) architectures natively support highly-parallel multiply-accumulate (MAC) operations that form the backbone of most NN workloads. Unfortunately, NN workloads such as transformers require support for non-MAC operations (e.g., softmax) that RRAM cannot provide natively. Consequently, state-of-the-art works either integrate additional digital logic circuits to support the non-MAC operations or offload the non-MAC operations to CPU/GPU, resulting in significant performance and energy efficiency overheads due to data movement. In this work, we propose NEON, a novel compiler optimization to enable the end-to-end execution of the NN workload in RRAM. The key idea of NEON is to transform each non-MAC operation into a lightweight yet highly-accurate neural network. Utilizing neural networks to approximate the non-MAC operations provides two advantages: 1) We can exploit the key strength of RRAM, i.e., highly-parallel MAC operation, to flexibly and efficiently execute non-MAC operations in memory. 2) We can simplify RRAM's microarchitecture by eliminating the additional digital logic circuits while reducing the data movement overheads. Acceleration of the non-MAC operations in memory enables NEON to achieve a 2.28x speedup compared to an idealized digital logic-based RRAM. We analyze the trade-offs associated with the transformation and demonstrate feasible use cases for NEON across different substrates.