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It's been said that "Language Models are Unsupervised Multitask Learners." Indeed, self-supervised language models trained on "positive" examples of English text generalize in desirable ways to many natural language tasks. But if such models can stray so far from an initial self-supervision objective, a wayward model might generalize in undesirable ways too, say to nonsensical "negative" examples of unnatural language. A key question in this work is: do language models trained on (positive) training data also generalize to (negative) test data? We use this question as a contrivance to assess the extent to which language models learn undesirable properties of text, such as n-grams, that might interfere with the learning of more desirable properties of text, such as syntax. We find that within a model family, as the number of parameters, training epochs, and data set size increase, so does a model's ability to generalize to negative n-gram data, indicating standard self-supervision generalizes too far. We propose a form of inductive bias that attenuates such undesirable signals with negative data distributions automatically learned from positive data. We apply the method to remove n-gram signals from LSTMs and find that doing so causes them to favor syntactic signals, as demonstrated by large error reductions (up to 46% on the hardest cases) on a syntactic subject-verb agreement task.