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In lossy data compression, the probability that the minimum distortion is larger or smaller than the permissible level for sufficiently large message lengths, when the code rate R is larger or smaller than the rate-distortion function are termed the error exponents. The error exponents can be evaluated from a rigorous assessment. An alternative approach to evaluation using the replica method (RM) developed in statistical mechanics is presented in this paper. This approach shows that codes composed of nonmonotonic perceptrons can provide the optimal exponents with the Hamming distortion, when the transfer function of perceptron is optimized.