Peter Tino (joint work with Barbara Hammer and Alessio Micheli) Recurrent/recursive networks as non-autonomous dynamical systems - lessons learnt A large body of work has been done on the connection between recurrent neural networks and dynamical systems. For example, we were able to better understand why it is so difficult to learn to latch an important information that appeared in the past, and consequently construct models that are less prone to the "curse of long time spans". Basic tools of dynamical systems such as linearization of the dynamics around fixed points and bifurcation analysis enabled us to study learning and representational issues in recurrent networks. We have better understood the impact of various forms of dynamic noise on the computational power of recurrent networks. There are several lessons to be learnt from realizing that prior to training, recurrent nets are often initialized as contractive (Lipschitz continuous) systems that readily represent Markov models. This has direct consequences for the style of reporting of experimental results. For example, in certain circumstances variable memory length Markov models should be employed as the null hypothesis against which recurrent networks should be tested. Also, a detailed theoretical learnability analysis in the PAC framework, as well as fractal analysis of the dynamic activations patterns is possible. Similar analysis can be performed on recursive networks capable of processing more complex data structures such as trees. I will report some preliminary results showing that - the Markovian architectural bias still holds and - detailed fixed point analysis of the dynamic maps is very helpful for understanding typical patterns of internal representations of structured data. What new lessons are there to be learnt from viewing recurrent/recursive networks as dynamical systems?