Connectionist networks are composed of relatively simple, neuron-like processing elements that store all their long-term knowledge in the strengths of the connections between processors. In the last decade there has been considerable progress in developing learning procedures for these networks that allow them to automatically construct their own internal representations [6-8, 10]. The learning procedures are typically applied in networks that map input vectors to output vectors via a few layers of units. The network learns to dedicate particular hidden units to particular pieces or aspects of the input vector that are relevant in determining the output. The network generally learns to use distributed representations [5] in which each input vector is represented by activity in many different hidden units, and each hidden unit is involved in representing many different input vectors. Within the connectionist community, there has been a long and unresolved debate between those who favor localist representations in which each processing element corresponds to a meaningful concept [3, 11] and those who favor distributed representations. The major criticism of distributed representations has been that they cannot handle structured knowledge properly and this criticism has motivated many of the papers in this issue. Another criticism has been the unintelligibility of distributed representations. As soon as there are several hidden layers, it becomes very difficult to say what each hidden unit is representing. Other things being equal, it is clearly desirable to understand how a system performing a task such as medical diagnosis arrives at a particular conclusion and to provide this information to the user. A large pattern of activities or set of learned weights is not a convincing explanation. If, however, the large set of weights performs consistently better than an alternative system that can explain its reasoning, it might be better to settle for the system that works best. Under certain conditions, we can be quite justified in trusting a system even if we have very little understanding of how it arrives at a particular conclusion. Using the probably approximately correct framework developed in [12], Baum and Haussler [1] have shown that if a neural network can be