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Nowadays, the extensive exploitation of Deep Neural Networks (DNNs) in safety-critical applications raises new reliability concerns. In practice, methods for fault injection by emulation in hardware are efficient and widely used to study the resilience of DNN architectures for mitigating reliability issues already at the early design stages. However, the state-of-the-art methods for fault injection by emulation incur a spectrum of time-, design-and control-complexity problems. To overcome these issues, a novel resiliency assessment method called APPRAISER is proposed that applies functional approximation for a non-conventional purpose and employs approximate computing errors for its interest. By adopting this concept in the resiliency assessment domain, APPRAISER provides thousands of times speed-up in the assessment process, while keeping high accuracy of the analysis. In this paper, APPRAISER is validated by comparing it with state-of-the-art approaches for fault injection by emulation in FPGA. By this, the feasibility of the idea is demonstrated, and a new perspective in resiliency evaluation for DNNs is opened.