I will now give a brief overview of different spike-based theories. This is not meant to be an exhaustive review – although I would be very glad to have some feedback on what other theories would deserve to be mentioned. My aim is rather to highlight a common theme in these theories, which distinguishes them from rate-based theories. At the same time, I also want to emphasize the diversity of these theories.

“Synfire chains” were introduced by Moshe Abeles in the 1980s (see his 1991 book: Corticonics: Neural Circuits of the Cerebral Cortex), although in fact the concept can be traced back to 1963 (Griffith, Biophysical Journal 1963). It is based on the observation that neurons are extremely sensitive to coincidences in their inputs (in the fluctuation-driven regime) - I commented on this fact in a previous post. So if a small number of input spikes are received synchronously in one neuron (on the order of ten), then the neuron spikes. Now if these presynaptic neurons also have postsynaptic neurons in common, then these postsynaptic neurons will also fire synchronously. By this mechanism, synchronous activity propagates from one group of neurons to another group. This is a feedforward mode of synchronous propagation along a chain of layers (hence the terms “synfire chains”), but note that this feedforward mode of propagation may be anatomically embedded in a recurrent network of neurons. It is important to note that this propagation mode 1) can only be stable in the fluctuation-driven regime (as opposed to the mean-driven regime), 2) is never stable for perfect integrators (without the leak current). A simple explanation of the phenomenon was presented by Diesmann et al. (Nature 1999), in terms of dynamical systems theory (synchronous propagation is a stable fixed point of the dynamics). In that paper, neurons are modeled with background noise – it is not a deterministic model. Much earlier, in 1963, Griffith presented the deterministic theory of synfire chains (without the name) in discrete time and with binary neurons (although he did consider continuous time at the end of the paper). He also considered the inclusion of inhibitory neurons in the chain, and showed that it could yield stable propagation modes with only a fraction of neurons active in each layer. Izhikevich extended the theory of synfire chains to synchronous propagation with heterogeneous delays, which he termed “polychronization” (I will discuss it later).

As I have described them so far, synfire chains are postulated to result from the dynamics of neural networks, given what we know of the physiology of neurons. This raises two questions: 1) do they actually exist in the brain? and 2) are they important? I do not think there is a definite empirical answer to the first question (especially considering possible variations of the theory), but it is interesting to consider its rejection. If one concludes, on the basis of empirical evidence, that synfire chains do not exist, then another question pops up: why are they not observed, given that they seem to be implied by what we know of neural physiology? Possibly then, there could be specific mechanisms to avoid the propagation of synchronous activity (e.g. cancellation of expected correlations with inhibition, which I mentioned in a previous post). I am not taking side here, but I would simply like to point out that, because the existence of synfire chains is deduced from generally accepted knowledge, the burden of proof should in fact be shared between the tenants of synfire chains and their opponents: either synfire chains exist, or there is a mechanism to prevent them from existing (or at least their non-existence deserves an explanation). Before someone objects that models of recurrent spiking neural networks do not generally display synfire activity, I would like to point out that these are generally sparse random networks (i.e., with no short cycle in the connectivity graph) in which the existence of the irregular state is artificially maintained by external noisy input (e.g. Brunel (2000)), or by a suprathreshold intrinsic current (e.g. Vogels and Abbott 2005).

The second question is functional: what might be the computational advantage of synfire chains? As I understand it, they were not introduced for computational reasons. However, a computational motivation was later proposed in reference to the binding problem, or more generally compositionality by Bienenstock (1996, in Brain Theory). A similar proposition was also made by Christof von der Marlsburg and Wolf Singer, although in the context of oscillatory synchrony, not synfire chains. A scene is composed of objects that have relationships to each other. Processing such a scene requires identifying the properties of objects, but also identifying the relationships between these objects, e.g. that different features belong to the same object. In a rate-based framework, the state of the network at a given time is given a vector of rates (one scalar value per neuron). If the activation of each neuron or set of neurons represents a given property, then the network can only represent an unstructured set of properties. The temporal organization of neural activity may then provide the required structure. Neurons firing in synchrony (at a given timescale) may then represent properties of the same object. The proposition makes sense physiologically because presynaptic neurons can only influence a postsynaptic target if they fire together within the temporal integration window of the postsynaptic neuron (where synchrony is seen from the postsynaptic viewpoint, i.e., after axonal propagation delays). In my recent paper on computing with neural synchrony (which is not based on synfire chains but on stimulus-specific synchrony), I show on an olfactory example how properties of the same object can indeed be bound together by synchrony. I also note that it also provides a way to filter out irrelevant signals (noise), because these are not temporally coherent.

Apart from compositionality, the type of information processing performed by synfire chains is very similar to those of feedforward networks in classical neural network theory. That is, the activation (probability of firing) of a given unit is essentially a sigmoidal function of a weighted sum of activations in the preceding layer (if heterogeneous synaptic weights are included) – neglecting the temporal dispersion of spikes. But there may be another potential computational interest of synfire chains, compared to traditional rate-based feedforward models, which is processing speed. Indeed, in synfire chains, the propagation speed is limited by axonal conduction delays, not by neural integration time.

In the next post, I will comment on polychronization, an extension of synfire chains that includes heterogeneous delays.