Recurrent: Liquid/ Echo State Machines/Random reservoir networks
This sounds deliciously lazy; Roughly speaking, your first layer is a reservoir of random saturating IIR filters. You fit a classifier on the outputs of this - possibly even allowing the network to converged to a steady state in some sense, so that the oscillations of the reservoir are not coupled to time.
Easy to implement, that. I wonder when it actually works, constraints on topology etc.
I wonder if you can use some kind of sparsifying transform on the recurrence operator?
These claim to be based on spiking (i.e. even-driven) models, but AFAICT this is not necessary, although it might be convenient for convergence.
Various claims are made about how hard they avoid the training difficulty of similarly basic RNNs by being essentially untrained; you use them as a feature factory for another supervised output algorithm.
Suggestive parallel with random projections. Not strictly recurrent, but same general idea: He, Wang, and Hopcroft (2016).
Lukoševičius and Jaeger (2009) has maps out the various types, as much as that is possible in the shifting buzzword sand of neural network research.
From a dynamical systems perspective, there are two main classes of RNNs. Models from the first class are characterized by an energy-minimizing stochastic dynamics and symmetric connections. The best known instantiations are Hopfield networks, Boltzmann machines, and the recently emerging Deep Belief Networks. These networks are mostly trained in some unsupervised learning scheme. Typical targeted network functionalities in this field are associative memories, data compression, the unsupervised modeling of data distributions, and static pattern classification, where the model is run for multiple time steps per single input instance to reach some type of convergence or equilibrium (but see e.g., Taylor, Hinton, and Roweis (2006) for extension to temporal data). The mathematical background is rooted in statistical physics. In contrast, the second big class of RNN models typically features a deterministic update dynamics and directed connections. Systems from this class implement nonlinear filters, which transform an input time series into an output time series. The mathematical background here is nonlinear dynamical systems. The standard training mode is supervised.
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