In a synfire chain, activity propagates synchronously from one layer to the next. Transmission delays are identical for all synaptic connections between two layers. Bienenstock proposed the notion of synfire braid for the case when transmission delays are heterogeneous (Bienenstock (1994), A model of neocortex, see Appendix A). The idea was expanded by Izhikevich with the terminology “polychronization” (Izhikevich, Neural Comp 2006; Szatmary and Izhikevich, PLoS CB 2010), and related to Edelman’s theory of neural darwinism (see his 1988 book).
Polychronization relies on the same propagation mechanism as synfire chains, but a polychronous group differs from a synfire chain in that there are no layers per se. When a set of neurons fire spikes at times such that, added to the transmission delays, they arrive simultaneously at a common target neuron, this neuron may fire. A spatio-temporal pattern of activity congruent with synaptic delays may then propagate along the “polychronous group”. Polychronization is a natural generalization of synfire chains, but there are interesting new properties. First, in a recurrent neural network, there are potentially many more polychronous groups than neurons, unlike synfire chains, and each neuron may participate in many such groups. In fact, in theory, the exact same set of neurons can participate in two different groups, but in a different activation order. In a recurrent network, polychronous groups spontaneously ignite at random times and for short durations. This means in particular that repeating spatiotemporal patterns would be very difficult to observe in spontaneous activity. It is important to emphasize that “polychronization” is not a specific mechanism, in that it does not rely on particular anatomical or physiological mechanisms other than what is currently generally accepted. It occurs in balanced excitatory-inhibitory networks with irregular activity and standard spike-timing-dependent plasticity, and in such conditions neurons are known to be highly sensitive to coincidences. In other words, it is a particular perspective on the dynamics of such networks.
The interesting application of polychronization is working memory (Szatmary and Izhikevich 2010). As I mentioned, the general theoretical context is Edelman’s theory of neural darwinism. Edelman got the Nobel prize in the 1970s for his work on the immune system, and he then moved to neuroscience where he developed a theory that relies on an analogy with the immune system. In that system, there is a preexisting repertoire of antibodies, which are more or less random. When a foreign antigen is introduced, it binds to some of these antibodies, and the response is then amplified with clonal multiplication – much like in Darwinian evolution theory. Here a memory item is presented under the form of a specific spatiotemporal pattern of activation. This pattern may be congruent with some of the connection delays of the network, i.e., it may correspond to a polychronous group (or part of one): this corresponds to the binding of antibodies to an antigen. It is then hypothesized that these connections are amplified through quick associative plasticity, i.e., STDP acting on a short time scale, fading over about 10 seconds (one hypothesis relies on NMDA spikes). Note that this is very similar in spirit to von der Malsburg’s “dynamic link matching”. This step corresponds to clonal amplification in the immune system. Because of the reinforcement of the connections, the polychronous group is spontaneously reactivated at random times, until it ultimately fades out. In this way the spatiotemporal pattern is replayed for a few tens of seconds.
The articulation of this theory with empirical evidence is rather interesting in the context of the rate vs. timing debate. First, it builds on generally accepted empirical evidence, including irregular firing statistics and excitatory-inhibitory balance. The theory is based on precise spike timing, but spike timing is not reproducible. Indeed spike timing is not locked to the stimulus, and only relative spike timing matters. What is more, in different trials, different polychronous groups may be selected and therefore even relative spike timing may not be reproducible across trials (but probably within a trial). Another interesting observation is that it predicts that the firing rate of some neurons should show an increasing (ramping) firing rate after stimulus presentation. This is not because these neurons “encode duration” with their rate, but because as the polychronous group is spontaneously reactivated, its length progressively increases, which means that neurons in the group’s tail fire more and more often through the course of reactivation.
Without judging the validity of the polychronization theory, I note that it provides a concrete example of a spike-based theory that appears consistent with many aspects of neural statistics (irregularity, lack of reproducibility, etc). This fact demonstrates once more that these aspects cannot be used as arguments in support of rate-based theories.