How do neuron signals encode magnitude?

Speaking of sensory-motor neurons for now, (since this is the domain in which the question has most meaning).
Knowing that a neuron can either fire (transmit a signal) or stay mute how is magnitude encoded for example:

  • louder sound than another
  • light intensity - does a retina cell fires more often on higher intensity light?
  • muscle tension - how does a muscle “knows” to pull with higher or lower force?

What I recall from school is that pulses are more frequent for “strong” signals, but is this always the case? Can frequency of firing be considered a general encoding of magnitude?

Can frequency of firing be considered a general encoding of magnitude?

Yeah, this is a commonly used approach in SNN.

Does this make sense in an HTM context though? SNNs use a fundamentally different encoding scheme. As I understand it, in HTM each sequential input encodes a totally new sensory experience and, from the algorithm’s perspective, inputs arrive at a fixed frequency. (Please correct me if I’m wrong here)

“Does this make sense in an HTM context though?“

Yes, in a subtle way.
A given dendrite segment is considered fired if a certain number of adjacent synapses fire in some unit of time.
This collection of synapses can be a larger number firing once (the normal situation in HTM simulation) or a smaller number firing more rapidly.

Using a valued synapse as a proxy for firing rate and rolling integration along the Dendrite would capture this behavior.

Naturally, you would have to spend some time getting the spatial arrangement of the dendrite and synapses right for this to mean anything.

This is also a case where you would have to turn topology on in the simulation- not normally done in HTM. HTM School Episode 10: Topology

Rolling integration?
Given an array of synapses forming a dendrite, each holding an activation value, a related array of integrated synapse values, where these values are the sum of n_size synapses, or the segment activation, this is a simple brute force method:

“a is segment activation, integrated”

For I = 0 to length of dendrite-n_size
A(I) = 0
For n = 0 to n_size
a(I) += dendrite(I+n) “Synapse value”
Next n
Next I

If the activation is more than some value X, the segment is assumed to have fired.

There are several optimizations possible.
We do this sort of thing all the time in signal processing.

Once you get into this can of worms you will have to work out how the main cell body generates a firing rate; the activation value to be transmitted via its axons. More activation in is more activation out.


Ok, going a bit deeper here,

  • Say a neuron fires when a sufficient number of synapses fire “simultaneously”
  • I used quotes because there-s no cpu clock in brain. So “simultaneous” means a sufficiently narrow time window. Could be 10ms or 1000(?) once the time window widens over a threshold there-s almost zero chances the neuron itself will fire.
  • This could be interpreted as neuron having an excitation (or shall be called activation?) level that is increased with every input synapse signalling and once a threshold level is reached the whole neuron fires.
  • of course there should be a gradual decrease of the excitation level to not take the same synapses long after the other as a “match”.

The followup question is - if the above is true - does it matter how many synapses get active?

To make the question more clear, assume a neuron fires if it receives 10 synapse signals in 100ms.
Consider the two following cases:

  • there are 10 synapses fire once within past 100ms, which is sufficient to make the whole neuron fire.
  • only a subset of 2 synapses of the above ten fire within the same time window, but each fires five times (a more intense signal) - will this make the neuron fire too?

I’m asking since I’m curious if a neuron responds not only to given patterns (which are already sparse, the 10 synapses above could be only 1% of all neuron’s synapses) but also to even sparser sub-patterns if they are dense in time (==annoyingly persistent)?

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Please consider that proximity and location on a dendrite matters.

Ten synapses firing, each on a different arm of the proximal dendrite tree won’t fire the main soma body, but ten synapses firming in the same approximate area on a single dendrite will initiate an action potential.

The entire HTM temporal memory theory depends on distal dendrites integrating synapse firing energy and biasing the main soma to fire more readily with proximal dendrite activation.

Yes, sure, but adding dendrite proximity details doesn’t change the underlying question which is still valid - does firing a subset of synapses below the threshold normally needed to elicit a response will result in a response if that subset is sufficiently persistent?

See again: “The entire HTM temporal memory theory depends on distal dendrites integrating synapse firing energy and biasing the main soma to fire more readily with proximal dendrite activation.”
This biasing is below firing potential.

As far as “persistent” activity, activation from a spike input decays over time. There is always some background firing of cells as a maintenance thing - trading activation between the cells in the cortical fabric. The whole balance between inhibitory and excitory firing acts to stabilize the cells to an operating point close to firing but “idling” at minimal energy consumption; a few synapses firing here and there would be lost in this “noise”

So can’t the same synapse spike again before the activation decays? (that’s what I meant by “persistent”)
Or a quick consecutive spike from the same input synapse won’t be “received” during the same activation period?

You are asking about spike trains.

The basic mechanism of generation and conduction of a spike is nicely covered here:

I have been meaning to read this paper but alas, it sits with thousands in the “to be read in detail” pile.

It does suggest that the upper end of the spike firing rate is just under 200 Hz.

In the 10 Hz window of the alpha cycle that would be integrated as many firing vs a larger number of local synapses firing more slowly. It would go to reason that the fast firing axon would have more effect.

I don’t know how much a single junction can affect depolarization vs the combined action of many junctions. I know that I have read papers on that but I can’t lay my hands on that at the moment. These sit in the vast “to be filed” stack.

What I also don’t know is how quickly the synapse driver exhausts the store of chemical messenger so as to reduce the effect on the receiving dendrite. From my reading, there is clearly a limited amount of messenger chemical available, depending on the size of the synaptic junction. This goes well beyond the refractory period where the cell pumps out ions to reset to fire again.

I don’t currently have enough interest to dig through my paper collection to resolve this question but if you do research this topic please report on what you find.

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Phew, you dug more than enough for me thanks alot!

The picture that answers even more than I asked for is in the wikipedia page you linked:
That’s a great picture because even though it looks like an average image of a “typical” neuron, who made it put a real effort to plot it in milliseconds by millivolts. I’m pretty sure the proportions are accurate.

There is entirely clear that:

  • a neuron has a lower bound limit of ~5ms between consecutive firings, which is consistent with the upper limit of 200hz firing rate.
  • which means a single synapse cannot fire faster than every 5ms = the upper rate of its upstream neuron.
  • and from the same chart those pesky “Failed initiations” bumps in activation potential are smaller than 1ms
  • Also I would assume the smaller bump is a single synapse fire, while the double sized bump is produced be two synapses firing very close to each other.

Hence the “firing opportunity” for one synapse is sparsely occurring less than 5% of the times within a pulse train of e.g. 50Hz of a single synapse

What leads to the idea of neurons talking with each other in “chirps” rather than single spikes.

What does that mean exactly? A chirp is (received as) a train of <1ms short bumps in action potential - the train can be shorter or longer and can have bumps closer or farther apart (== higher or lower frequency)

Let’s consider only two input synapses with overlapping chirps - one chirps at an average 100 hz another at 120hz - so bumps from both overlap at no more than 20 times / sec rate.
But 2 overlaps is not sufficient to reach activation potential, it requires both more nearby synapses to chirp too, and the chance of overlapping 3-5 bumps in order to reach activation potential increases with frequency of each individual synapse and with number of synapses chirping together.
When more synapses chirp “louder” together the receiving neuron chirps itself “louder”.

This is a very different perspective from that of binary on/off individual pulse encodings.

Furthermore see this very nice neuron firing footage from Subutai’s presentation:

Initially I thought that each “flash” is a single neuron activation spike and the film is slowed down so we can have time to notice on-off short spike of each neuron, but now I would bet those firings are shown in real time and each neuron pulse there are “chirps” of dozens of ms length, and the brighter the “firing” means the stronger (higher frequency) chirp is.

What is also amazing is the noticeable rhythm each neuron has, the flashes repeat with regularities, and we can see different neurons with similar but slightly different rythms.

Because what applies to overlapping individual spikes could also apply to overlapping of chirps. Overlapping of slightly different “rhythms” on receiving synapses could produce a different rhythm of chirping with a specific strength for the receiving neuron.

That could explain our attraction for both sound and geometric patterns - flowers, mandalas, geometric tiles and music. We don’t usually eat flowers, why are we fascinated by them?
Maybe because they trigger meaning/correlations without any underlying conditioning derived from the hard coded priors/needs for food, safety or water.

They just correlate with the underlying functioning of the brain.

PS and the “pleasure” they produce is simply because brain rewards itself for noticing a new, unexpected pattern