The brain represents sensory and motor variables through the activity of large populations of neurons. It is not understood how the nervous system computes with these population codes, given that individual neurons are noisy and thus unreliable. We focus here on two general types of computation, function approximation and cue integration, as these are powerful enough to handle a range of tasks, including sensorimotor transformations, feature extraction in sensory systems and multisensory integration. We demonstrate that a particular class of neural networks, basis function networks with multidimensional attractors, can perform both types of computation optimally with noisy neurons. Moreover, neurons in the intermediate layers of our model show response properties similar to those observed in several multimodal cortical areas. Thus, basis function networks with multidimensional attractors may be used by the brain to compute efficiently with population codes.