The vulnerability to adversarial perturbations is a major flaw of Deep Neural Networks (DNNs) that raises question about their reliability when in real-world scenarios. On the other hand, human perception, which DNNs are supposed to emulate, is highly robust to such perturbations, indicating that there may be certain features of the human perception that make it robust but are not represented in the current class of DNNs. One such feature is that the activity of biological neurons is correlated and the structure of this correlation tends to be rather rigid over long spans of times, even if it hampers performance and learning. We hypothesize that integrating such constraints on the activations of a DNN would improve its adversarial robustness, and, to test this hypothesis, we have developed the Self-Consistent Activation (SCA) layer, which comprises of neurons whose activations are consistent with each other, as they conform to a fixed, but learned, covariability pattern. When evaluated on image and sound recognition tasks, the models with a SCA layer achieved high accuracy, and exhibited significantly greater robustness than multi-layer perceptron models to state-of-the-art Auto-PGD adversarial attacks \textit{without being trained on adversarially perturbed data