The mathematical operation of convolution is used as an associative mechanism by several recent influential models of human memory. Convolution can be used to associate two vectors (representing items to be remembered) into a memory trace vector in one operation. An approximation to either of the input vectors can then be retrieved, using the other vector as a probe. Recent convolution-based memory models have accounted for a wide range of data. Connectionist models may have greater potential for providing developmental accounts, but the architectures that have been most widely used to account for developmental phenomena cannot perform one-trial learning and this has limited their use as models of human memory. We show that a connectionist-like architecture can learn, using a gradient-descent algorithm, to perform single-trial learning in a similar manner to convolution. The solution that the network finds leads to less variable retrieval than does convolution. Furthermore, the network can learn to carry out the convolution operation itself. This provides a link between connectionist and convolution approaches, and a basis for models with many of the attractions of both connectionist and convolution approaches.