text: This paper presents a generic unbiased low-rank stochastic approximation to full rank matrices that makes it possible to do online RNN training without the O(n^3) overhead of real-time recurrent learning (RTRL). This is an important and long-sought-after goal of connectionist learning and this paper presents a clear and concise description of why their method is a natural way of achieving that goal, along with experiments on classic toy RNN tasks with medium-range time dependencies for which other low-memory-overhead RNN training heuristics fail. My only major complaint with the paper is that it does not extend the method to large-scale problems on real data, for instance work from the last decade on sequence generation, speech recognition or any of the other RNN success stories that have led to their wide adoption (eg Graves 2013, Sutskever, Martens and Hinton 2011 or Graves, Mohamed and Hinton 2013). However, if the paper does achieve what it claims to achieve, I am sure that many people will soon try out UORO to see if the results are in any way comparable.