Many models for computations in recurrent networks of neurons assume that the network state moves from some initial state to some fixed point attractor or limit cycle that represents the output of the computation. However experimental data show that in response to a sensory stimulus the network state moves from its initial state through a trajectory of network states and eventually returns to the initial state, without reaching an attractor or limit cycle in between. This type of network response, where salient information about external stimuli is encoded in characteristic trajectories of continuously varying network states, raises the question how a neural system could compute with such code, and arrive for example at a temporally stable classification of the external stimulus. We show that a known unsupervised learning algorithm, Slow Feature Analysis (SFA), could be an important ingredient for extracting stable information from these network trajectories. In fact, if sensory stimuli are more often followed by another stimulus from the same class than by a stimulus from another class, SFA approaches the classification capability of Fishers Linear Discriminant (FLD), a powerful algorithm for supervised learning. We apply this principle to simulated cortical microcircuits, and show that it enables readout neurons to learn discrimination of spoken digits and detection of repeating firing patterns within a stream of spike trains with the same firing statistics, without requiring any supervision for learning.

The extraction of statistically independent components from high-dimensional multi-sensory input streams is assumed to be an essential component of sensory processing in the brain. Such independent component analysis (or blind source separation) could provide a less redundant representation of information about the external world. Another powerful processing strategy is to extract preferentially those components from high-dimensional input streams that are related to other information sources, such as internal predictions or proprioceptive feedback. This strategy allows the optimization of internal representation according to the information bottleneckmethod. However, concrete learning rules that implement these general unsupervised learning principles for spiking neurons are still missing. We show how both information bottleneck optimization and the extraction of independent componentscan in principle be implemented with stochastically spiking neurons with refractoriness. The new learning rule that achieves this is derived from abstract information optimization principles.