# A note on computing with neural synchrony

In a recent paper, I explained how to compute with neural synchrony, by relating synchrony with the Gibsonian notion of sensory invariants. Here I will briefly recapitulate the arguments and try to explain what can and cannot be done with this approach.

First of all, neural synchrony, as any other concept of neural code, should be defined from the observer point of view, that is, from the postsynaptic point of view. Detecting synchrony is detecting coincidences. That is, a neural observer of neural synchrony is a coincidence detector. Now coincidences are observed when they occur in the postsynaptic neuron, not when the spikes are produced by the presynaptic neurons. Spikes travel along axons and therefore generally arrive after some delay, which we may consider fixed. This means that in fact, coincidence detectors do not detect synchrony but rather specific time differences between spike trains.

I will call these spike trains Ti(t), where i is the index of the presynaptic neuron. Detecting coincidences means detecting relationships Ti(t)=Tj(t-d), where d is a delay (for all t). Of course we may interpret this relationship in a probabilistic (approximate) way. Now if one assumes that the neuron is a somewhat deterministic device that transforms a time-varying signal S(t) into a spike train T(t), then detecting coincidences is about detecting relationships Si(t)=Sj(t-d) between analog input signals.

To make the connection with perception, I then assume that the input signals are determined by the sensory input X(t) (which could be a vector of inputs), so that Si(t)=Fi(X)(t). So computing with neural synchrony means detecting relationships Fi(X)(t)=Fj(X)(t-d), that is, specific properties of the stimulus X (Fi is a linear or nonlinear filter). You could see this as a sensory law that the stimulus X(t) follows, or with Gibson’s terminology, a sensory invariant (some property of the sensory inputs that does not change with time).

So this theory describes computing with synchrony as the extraction sensory invariants. The first question is, can we extract all sensory invariants in this way? The answer is no, only those relationships that can be written as Fi(X)(t) = Fj(X)(t-d) can be detected. But then isn’t the computation already done by the primary neurons themselves, through the filters Fi? This would imply that synchrony does not achieve anything, computationally speaking. But this is not true. The set of relationships between signals Fi(X)(t) is not the same thing as the set of signals themselves. For once, there are more relationships than signals: if there are N encoding neurons, then there are N2 relationships, times the number of allowed delays. But more importantly, a relationship between signals does not have the same nature as a signal. To see this, consider just two auditory neurons, one that responds to sounds from the left ear only, and one that responds to sounds from the right ear (and neglect sound diffraction by the head to simplify things). None of these neurons is sensitive at all to the location of the sound source. But the relationships between the input signals to these two neurons are informative of sound location. Relationships and signals are two different things: a signal is a stream of numbers, while a relationship is a universal statement on these numbers (aka “invariant”). So to summarize: synchrony represents sensory invariants, which are not represented in the individual neurons, but only a limited number of sensory invariants. For example, if the filters Fi are linear, then only linear properties of the sensory input can be detected. Thus, sensory laws are not produced but rather detected, among a set of possible laws.

Now the second question: is computing with synchrony only about extracting sensory invariants? The answer is also no, because the theory is based on the assumption that the input signals to the neurons and their synchrony are mostly determined by the sensory inputs. But they could also depend on “top-down” signals. Synchrony could be generated by recurrent connections, that is, synchrony could be the result of a computation rather than (or in addition to) the basis of computation. Thus, to be more precise, this theory describes what can be computed with stimulus-induced synchrony. In Gibson’s terminology, this would correspond to the “pick-up” of information, i.e., the information is present in the primary input, preexisting in the form of the relationships between transformed sensory signals (Fi(X)), and one just needs to observe these relationships.

But there is an entire part of the field that is concerned with the computational role of neural oscillations, for example. If oscillations are spatially homogeneous, then it does not affect the theory – it may in fact be simply a way to transform similarity of slowly varying signals into synchrony (this mechanism is the basis of Hopfield and Brody’s olfactory model). If they are not, in particular if they result from interactions between neurons, then this is a different thing.