  Transfer learning seeks to improve the generalization performance of a target
task by exploiting the knowledge learned from a related source task. Central
questions include deciding what information one should transfer and when
transfer can be beneficial. The latter question is related to the so-called
negative transfer phenomenon, where the transferred source information actually
reduces the generalization performance of the target task. This happens when
the two tasks are sufficiently dissimilar. In this paper, we present a
theoretical analysis of transfer learning by studying a pair of related
perceptron learning tasks. Despite the simplicity of our model, it reproduces
several key phenomena observed in practice. Specifically, our asymptotic
analysis reveals a phase transition from negative transfer to positive transfer
as the similarity of the two tasks moves past a well-defined threshold.
