Transitional accounts of evolution emphasise a few changes that shape what is evolvable, with dramatic consequences for derived lineages. More recently it has been proposed that cognition might also have evolved via a series of major transitions that manipulate the structure of biological neural networks, fundamentally changing the flow of information. We used idealised models of information flow, artificial neural networks (ANNs), to evaluate whether changes in information flow in a network can yield a transitional change in cognitive performance. We compared networks with feed-forward, recurrent and laminated topologies, and tested their performance learning artificial grammars that differed in complexity, controlling for network size and resources. We documented a qualitative expansion in the types of input that recurrent networks can process compared to feed-forward networks, and a related qualitative increase in performance for learning the most complex grammars. We also noted how the difficulty in training recurrent networks poses a form of transition barrier and contingent irreversibility -- other key features of evolutionary transitions. Not all changes in network topology confer a performance advantage in this task set. Laminated networks did not outperform non-laminated networks in grammar learning. Overall, our findings show how some changes in information flow can yield transitions in cognitive performance.