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I'm working through the tutorial of section 2.4 of "How to Build a Brain" and I've encountered this graph of a neuron tuning curve.


I understand the Y axis is the firing rate of the neuron, that each curve is the response of a single neuron (there are 100 neurons represented here) and that this plot shows a variety of "on" and "off" neurons, but what does the X axis represent? Is it the action potential input? Is X the value that the neuron represents by firing at that rate?

Please allow me to give some context around the tutorial. You first create a population of 100 neurons to represent an input that will vary from -1 to 1. You notice that this works well, but that the representation degrades when you exceed this range falls apart and you cannot represent anything the range past -2 to 2.

You then use a new population of neurons to build upon this newly acquired knowledge of how neurons can represent functions, to make them represent a 2-dimensional vector similar to the monkey-arm motor experiment performed by Georgopolous.

I could take the leap of faith here and just take for granted that neurons can represent functions and that the more neurons you have, the better approximation of the function you can get, but I feel like understanding these fundamental concepts are important.


I'm currently still working on this, but in case someone else is also stuck on this, it should probably be noted that "How to Build a Brain" is based on the Neurological Engineering Framework (NEF) and Nengo. Resources in regards to this can be found here.

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I'm going to hazard a guess that these are neurons that are tuned to a particular direction in space and that the x-axis is the angle in multiples of $\pi$ radians. –  Chuck Sherrington Apr 19 at 12:42
(especially if there are Georgopoulos and colleagues - neurosci.umn.edu/faculty/georgopoulos.html - papers cited in the background work) –  Chuck Sherrington Apr 19 at 12:44
@ChuckSherrington Are you saying that it is impossible to read a neuron tuning graph without being first given the context that neurons are firing under? –  Seanny123 Apr 19 at 12:47
@ChuckSherrington You are however correct that this tutorial I'm following is leading up to modeling Georgopoulos work with motor neurons and the preferred direction. –  Seanny123 Apr 19 at 12:54
Yes, otherwise it's impossible to know what the particular cell (or groups of cells) are tuning to. See en.wikipedia.org/wiki/Neural_coding#Position_coding for some other examples. –  Chuck Sherrington Apr 19 at 12:54

1 Answer 1

From the comments:

I'm going to hazard a guess that these are neurons that are tuned to a particular direction in space and that the x-axis is the angle in multiples of π radians, particularly since these are related to the work of Georgopoulos and colleagues.

Since we know these are positionally tuned neurons, you can see some other examples in this Wikipedia page for some other examples.

A typical population code involves neurons with a Gaussian tuning curve whose means vary linearly with the stimulus intensity, meaning that the neuron responds most strongly (in terms of spikes per second) to a stimulus near the mean.

So, as mentioned above, the independent variable here is the stimulus "intensity" (in this case abstracted by the quantity of direction) and the firing rate is the dependent variable, hence their positions on the axes in the plot.

For some of the more theoretical studies of this type of phenomenon, I would definitely check out the work of Emo Todorov, among many others, as well.

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