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Reliability should be identified as the most important challenge in future nano-scale very large scale integration (VLSI) implementation technologies for the development of complex integrated systems. Normally, fault tolerance (FT) in a conventional system is achieved by increasing its redundancy, which also implies higher implementation costs and lower performance that sometimes makes it even infeasible. In contrast to custom approaches, a new class of applications is categorized in this paper, which is inherently capable of absorbing some degrees of vulnerability and providing FT based on their natural properties. Neural networks are good indicators of imprecision-tolerant applications. We have also proposed a new class of FT techniques called relaxed fault-tolerant (RFT) techniques which are developed for VLSI implementation of imprecision-tolerant applications. The main advantage of RFT techniques with respect to traditional FT solutions is that they exploit inherent FT of different applications to reduce their implementation costs while improving their performance. To show the applicability as well as the efficiency of the RFT method, the experimental results for implementation of a face-recognition computationally intensive neural network and its corresponding RFT realization are presented in this paper. The results demonstrate promising higher performance of artificial neural network VLSI solutions for complex applications in faulty nano-scale implementation environments.