In this paper we show how convolutional neural networks (CNN) fitted to populations of visual sensory neurons improve the performance over GLMs on a simple linear regression problem. Especially for few data but many recorded neurons CNNs win by a large margin. Furthermore, we demonstrate how adding complexity to the problem through more heterogeneous neural types can be easily accounted for through more convolutional features. A final example with mixed population then shows how the neuron-specific weights of shared features in a CNN for a whole neural population can be used to consolidate previously known types as well as suggest new biologically informative ones.