Abstract Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network architectures and learning algorithms even as the basic premise of a convolutional layer has remained unchanged. In this paper, we seek to revisit the convolutional layer that has been the workhorse of state-of-the-art visual recognition models. We introduce a very simple, yet effective, module called a perturbation layer as an alternative to a convolutional layer. The perturbation layer does away with convolution in the traditional sense and instead computes its response as a weighted linear combination of non-linearly activated additive noise perturbed inputs. We demonstrate both analytically and empirically that this perturbation layer can be an effective replacement for a standard convolutional layer. Empirically, deep neural networks with perturbation layers, called Perturbative Neural Networks (PNNs), in lieu of convolutional layers perform comparably with standard CNNs on a range of visual datasets (MNIST, CIFAR-10, PASCAL VOC, and ImageNet) with fewer parameters