L1 regularization is better than L2 for learning and predicting chaotic   systems
  Emergent behaviors are in the focus of recent research interest. It is then of considerable importance to investigate what optimizations suit the learning and prediction of chaotic systems, the putative candidates for emergence. We have compared L1 and L2 regularizations on predicting chaotic time series using linear recurrent neural networks. The internal representation and the weights of the networks were optimized in a unifying framework. Computational tests on different problems indicate considerable advantages for the L1 regularization: It had considerably better learning time and better interpolating capabilities. We shall argue that optimization viewed as a maximum likelihood estimation justifies our results, because L1 regularization fits heavy-tailed distributions -- an apparently general feature of emergent systems -- better. 
Z. Szabo and A. Lorincz