There has been a lot of interest in understanding what information is captured by hidden representations of language models (LMs). Typically, interpretation methods i) do not guarantee that the model actually uses the information found to be encoded, and ii) do not discover small subsets of neurons responsible for a considered phenomenon. Inspired by causal mediation analysis, we propose a method that discovers a small subset of neurons within a neural LM responsible for a particular linguistic phenomenon, i.e., subsets causing a change in the corresponding token emission probabilities. We use a differentiable relaxation to approximately search through the combinatorial space. An L₀ regularization term ensures that the search converges to discrete and sparse solutions. We apply our method to analyze subject-verb number agreement and gender bias detection in LSTMs. We observe that it is fast and finds better solutions than alternatives such as REINFORCE and Integrated Gradients. Our experiments confirm that each of these phenomena is mediated through a small subset of neurons that do not play any other discernible role.