Energy-based models (EBMs), a.k.a. un-normalized models, have had recent successes in continuous spaces. However, they have not been successfully applied to model text sequences. While decreasing the energy at training samples is straightforward, mining (negative) samples where the energy should be increased is difficult. In part, this is because standard gradient-based methods are not readily applicable when the input is high-dimensional and discrete. Here, we side-step this issue by generating negatives using pre-trained auto-regressive language models. The EBM then works in the residual of the language model; and is trained to discriminate real text from text generated by the auto-regressive models. We investigate the generalization ability of residual EBMs, a pre-requisite for using them in other applications. We extensively analyze generalization for the task of classifying whether an input is machine or human generated, a natural task given the training loss and how we mine negatives. Overall, we observe that EBMs can generalize remarkably well to changes in the architecture of the generators producing negatives. However, EBMs exhibit more sensitivity to the training set used by such generators.