Deep neural networks have been shown to predict neural responses in higher visual cortex. The mapping from the model to a neuron in the brain occurs through a linear combination of many units in the model, leaving open the question of whether there also exists a correspondence at the level of individual neurons. Here we show that there exist many one-to-one mappings between single units in a deep neural network model and neurons in the brain. We show that this correspondence at the single- unit level is ubiquitous among state-of-the-art deep neural networks, and grows more pronounced for models with higher performance on a large-scale visual recognition task. Comparing matched populations—in the brain and in a model—we demonstrate a further correspondence at the level of the population code: stimulus category can be partially decoded from real neural responses using a classifier trained purely on a matched population of artificial units in a model. This provides a new point of investigation for phenomena which require fine-grained mappings between deep neural networks and the brain.