Neurons in the brain are able to detect and discriminate salient spatiotemporal patterns in the firing activity of presynaptic neurons. It is open how they can learn to achieve this, especially without the help of a supervisor. We show that a well-known unsupervised learning algorithm for linear neurons, slow feature analysis (SFA), is able to acquire the discrimination capability of one of the best algorithms for supervised linear discrimination learning, the Fisher linear discriminant (FLD), given suitable input statistics. We demonstrate the power of this principle by showing that it enables readout neurons from simulated cortical microcircuits to learn without any supervision to discriminate between spoken digits and to detect repeated firing patterns that are embedded into a stream of noise spike trains with the same firing statistics. Both these computer simulations and our theoretical analysis show that slow feature extraction enables neurons to extract and collect information that is spread out over a trajectory of firing states that lasts several hundred ms. In addition, it enables neurons to learn without supervision to keep track of time (relative to a stimulus onset, or the initiation of a motor response). Hence, these results elucidate how the brain could compute with trajectories of firing states rather than only with fixed point attractors. It also provides a theoretical basis for understanding recent experimental results on the emergence of view- and position-invariant classification of visual objects in inferior temporal cortex.

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.

Independent component analysis (or blind source separation) is assumed to be an essential component of sensory processing in the brain and could provide a less redundant representation about the external world. Another powerful processing strategy is the optimization of internal representations according to the information bottleneck method. This method would allow extracting preferentially those components from high-dimensional sensory input streams that are related to other information sources, such as internal predictions or proprioceptive feedback. However, there exists a lack of models that could explain how spiking neurons could learn to execute either of these two processing strategies. We show in this article how stochastically spiking neurons with refractoriness could in principle learn in an unsupervised manner to carry out both information bottleneck optimization and the extraction of independent components. We derive suitable learning rules, which extend the well-known BCM rule, from abstract information optimization principles. These rules will simultaneously keep the firing rate of the neuron within a biologically realistic range.

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 infor- mation bottleneck method. 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 inde- pendent components can in principle be implemented with stochastically spiking neurons with refractoriness. The new learning rule that achieves this is derived from abstract information optimization principles.