—Recurrent neural networks processing symbolic strings can be regarded as adaptive neural parsers. Given a set of positive and negative examples, picked up from a given language, adaptive neural parsers can effectively be trained to infer the language grammar. In this paper we use adaptive neural parsers to face the problem of inferring grammars from examples that are corrupted by a kind of noise that simply changes their membership. We propose a training algorithm, referred to as hybrid finite state filter (HFF), which is based on a parsimony principle that penalizes the development of complex rules. We report very promising experimental results showing that the proposed inductive inference scheme is indeed capable of capturing rules, while removing noise.