This post starts a series on the debate between rate-based and spike-based theories of neural computation and coding. My primary goal is to clarify the concepts. I will start by addressing a few common misconceptions about the debate.

Misconception #1: “Both rate and spike timing are important for coding, so the truth is in between”. This statement, I will argue, is what philosophers would call a “category error”: it is not that only one of the alternatives can be right, it is just that the two alternatives belong to different categories.

Neurons mainly communicate with each other using trains of spikes – at least this is what the rate-timing debate is concerned about. A spike train can be completely characterized by the timing of its spikes. The firing rate, on the other hand, is an abstract definition, that is only valid in a limit, which involves an infinite number of spikes. For example, it can be defined for a single neuron as a temporal average: the inverse of the mean inter-spike interval. It appears that rate is defined from the timing of spikes. Thus these are two different concepts: spike timing is what defines spike trains, whereas rate is an abstract mathematical construction on spike trains. Therefore the rate vs. timing debate is not about which one is right, but about whether rate is a sufficiently good description of neural activity. Spike-based theories do not necessarily claim that rate does not matter, they refute the notion that rate is the essential quantity that matters.

There are different ways to define the firing rate: over time (number of spikes divided by the duration, in the limit of infinite duration), over neurons (average number of spikes in a population of neurons, in the limit of an infinite number of neurons) or over trials (average number of spikes over an infinite number of trials). In the third definition (which might be the prevailing view), the rate is seen as an intrinsic time-varying signal r(t) and spikes are seen as random events occurring at rate r(t). In all these definitions, rate is an abstract quantity defined on the spike trains. Therefore when stating that the neural “code” is based on rates rather than spike timing, what is meant is that the concept of rate captures most of the important details of neural activity and computation, while precise spike timing is essentially meaningless. On the other hand, when stating that spike timing matters, it is not meant that rate is meaningless; it simply means that precise timing information cannot be discarded. Thus, these are not two symmetrical views: the stronger assumptions are on the side of the rate-based view. Now of course each specific spike-based theory makes a number of possibly strong assumptions. But the general idea that the neural “code” is based on individual spikes and not just rates is not based on strong assumptions. The rate-based view is based on an approximation, which may be a good one or a bad one. This is the nature of the rate vs. timing debate.