Abstract: We present a machine unlearning approach that is both retraining- and label-free. Most existing machine unlearning approaches require a model to be fine-tuned to remove information while preserving performance. This is computationally expensive and necessitates the storage of the whole dataset for the lifetime of the model. Retraining-free approaches often utilise Fisher information, which is derived from the loss and requires labelled data which may not be available. Thus, we present an extension to the Selective Synaptic Dampening algorithm, substituting the diagonal of the Fisher information matrix for the gradient of the $l_2$ norm of the model output to approximate sensitivity. We evaluate our method in a range of experiments using ResNet18 and Vision Transformer. Results show our label-free method is competitive with existing state-of-the-art approaches.