We analyze the asymptotic behavior of autoregressive neural network (AR-NN) processes using techniques from Markov chains and non-linear time series analysis. It is shown that standard AR-NNs without shortcut connections are asymptotically stationary. If linear shortcut connections are allowed, only the shortcut weights determine whether the overall system is stationary, hence standard conditio...

Abstract We show that a group is hyperbolic relative to strongly shortcut groups itself shortcut, thus obtaining new examples of groups. The proof relies on result independent interest: we every relatively acts properly and cocompactly graph in which the parabolic subgroups act convex subgraphs.

Event-related brain potentials were used to investigate the shortcut calculation strategy and nonshortcut calculation strategy in performing addition using mental arithmetic. Results showed that the shortcut calculation strategy elicited a larger P220 than the nonshortcut calculation strategy in the 180-280 ms. Dipole source analysis of the difference wave (shortcut calculation minus nonshortcu...

The Residual Network (ResNet), proposed in He et al. (2015a), utilized shortcut connections to significantly reduce the difficulty of training, which resulted in great performance boosts in terms of both training and generalization error. It was empirically observed in He et al. (2015a) that stacking more layers of residual blocks with shortcut 2 results in smaller training error, while it is n...

Based on research on expertise a person can be said to possess integrated conceptual knowledge when she/he is able to spontaneously identify task relevant information in order to solve a problem efficiently. Despite the lack of instruction or explicit cueing, the person should be able to recognize which shortcut strategy can be applied--even when the task context differs from the one in which p...

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds (F ) and across network shortcuts (f ). For fast shortcuts (f/F 1) and low shortcut densities, traversal time data collapse onto a universal curve, while a crossover behavi...