Melt rates at the base of Antarctic ice shelves are needed to drive projections of the Antarctic ice sheet mass loss. Current basal melt parameterizations struggle to link open ocean properties to ice‐shelf basal melt rates for the range of current sub‐shelf cavity geometries around Antarctica. We present a proof of concept exploring the potential of simple deep learning techniques to parameterize basal melt. We train a simple feedforward neural network, or multilayer perceptron, acting on each grid cell separately, to emulate the behavior of circum‐Antarctic cavity‐resolving ocean simulations. We find that this kind of emulator produces reasonable basal melt rates for our training ensemble, at least as close as or closer to the reference than traditional parameterizations. On an independent ensemble of simulations that was produced with the same ocean model but with different model parameters, cavity geometries and forcing, the neural network yields similar results to traditional parameterizations on present conditions. In much warmer conditions, both traditional parameterizations and neural network struggle, but the neural network tends to produce basal melt rates closer to the reference than a majority of traditional parameterizations. While this shows that such a neural network is at least as suitable for century‐scale Antarctic ice‐sheet projections as traditional parameterizations, it also highlights that tuning any parameterization on present‐like conditions can introduce biases and should be used with care. Nevertheless, this proof of concept is promising and provides a basis for further development of a deep learning basal melt parameterization.