Bidirectional Comparators

Warren Mansell posted a reference to Erling Jorgensen’s paper in Living Control Systems IV on “How the brain gets a roaring campfire: Thalamus through a PCT microscope”. I took a look at the chapter and noticed that there was a section on Bidirectional Comparators. This is an interesting topic to me because, in our models of control, the error signals produced by a comparator can go (and must be able to go) positive or negative. But in real nervous systems, assuming (as in B:CP) that control signals are carried by firing rate, error signals can only be positive. But Erling’s paper suggests that there is some way for a neural control loop to produce bidirectional error signals.

I was unable to understand Erling’s diagrams or descriptions of the process that allows error signals to be bidirectional (a result of my limited mental capabilities, not Erling’s explanations). So I’m posting this to see if someone (like Erling, if he’s still on this forum) could explain how that works so that I can implement it in models of control so as to make them more consistent with the neurophysiology.

Best, Rick

My initial sense is that PCT demos do not necessarily need to implement bidirectional control in the same manner as neural tissue in the brain. We are talking about models of control, and the equations that implement PCT comparators in those models can already go positive or negative. The math takes care of it. It doesn’t need a neurochemical implementation.

However, in the brain, neurophysiology certainly does count. As Rick rightly notes, B:CP’s working assumption is that control loop signals in the brain are carried by the rate of firing itself. And neural action potentials cannot go negative. The most an inhibitory signal can do is to reduce an excitatory signal to zero. The analogy that works for me is that you cannot push on a rope, only pull.

I made the claim in “How the brain gets a roaring campfire: Thalamus through a PCT microscope” (one of the online chapters in The Interdisciplinary Handbook of Perceptual Control Theory: Living Control Systems IV) that thalamic relay cells can function as PCT Comparators. There appears to be Reference input ‘from above’ (specifically, layer 6 neurons in the neocortex), which arrive in thalamic relay nuclei at the same locale as Perceptual input ‘from below’. The standard way that the Reference input is routed is through the thalamic reticular formation, which receives an excitatory signal and sends out an inhibitory signal, down to the thalamic relay neuron. In other words, it reverses the sign of the Reference signal!

So the ‘thalamic comparator’ there now has the equivalent of (p - r), which in the context of control loop equations will tend to decrease subsequent values of p until they approximate the value of r. That is to say, ‘Give me less of p.’ But we also need a way to increase values of p that are too low, i.e., ‘Give me more of p.’ In other words, we need a parallel mechanism providing (r - p ). The thalamus seems to have a way to do that as well.

The mechanism performing this function is called a Dendritic Triad, which essentially reverses the sign of the incoming Perceptual signal! There are fast-acting and slow-acting synapses in the brain. A regular (excitatory) perceptual signal can use the fast form to both excite a relay neuron and excite a nearby (inhibitory) interneuron, which essentially cancels out that perceptual signal. At the same time, the perceptual signal uses the slow-acting form of synapse to pass along an inhibitory version of itself, through the self-same interneuron. These actions typically happen on distal dendrites far from the relay neuron’s cell body.

The descending Reference input also has an alternate route to get to the thalamic relay cell, (without passing through the thalamic reticular formation.) Those neocortical layer-6 cells also make direct connections to the relay cells in the thalamus, specifically onto their distal dendrites. So here we have an excitatory version of the Reference, lining up with an inhibitory version of the Perception, i.e., (r - p).

There are two pieces of important evidence here. These excitatory Reference signals arrive at relay cells that are nearby to the relay cells receiving the inhibitory version of the Reference signals (routed through the thalamic reticular formation). So it looks like adjoining mechanisms, one providing (p - r), & the other providing (r - p). The evidence coming from below is that the Dendritic Triad form of inhibitory signal onto thalamic relay cells seems to be half as common as the regular form of inhibition (doing other things) through interneurons in the thalamus. In other words, that is just the proportion we would expect, if every PCT Comparator there is actually enacted by two mechanisms operating in parallel, but with opposite signs.

There are various other neurophysiological details, in terms of how the synapses actually work. But the gist of it is given above. Again, I don’t necessarily think PCT models have to go into this level of detail, because the implementing language of our models is math, not neurochemistry.

All the best,
Erling Jorgensen

Very interesting, Erling. I’m imagining some excellent conversations with Henry.

There was further discussion & diagrams of these matters back on the CSGnet listserv in August of 2017. It was under the subject heading: “Dealing with the limitation of only positive neural signals”. I’m not sure how to link that material here. I did copy some of the pages from there into a file that I have. The earliest date-stamp among what I have is a diagram by Eetu Pikkarainen, dated 2017/08/16 3:21 AM.

It’s important to be able to link to archived posts without necessarily ‘awakening’ that thread as a current topic, which is what happens if you go there and simply quote from it. To link to an old post:

  1. Go to the top level of Discourse.
  2. Scroll down to the CSGnet archive.
  3. Select CSG2017.
  4. Click the search tool (magnifying glass, top right).
  5. Enter a search string in the search window, in this case “Dealing with the limitation of only positive neural signals”.
  6. The first line that appears searches in all topics; select the second line, which is limited to the CSG2017 archive.
  7. Only the first half dozen or so posts are listed; select More… at the bottom if that’s not enough and you want to see more.

To link to a post there:

  1. Type or copy/paste some text in your own current post that you will use as link text.
  2. Select and copy the URL in your browser’s address field.
  3. Click the link tool at the top of your edit window.
  4. In the popup window, paste the URL that you copied.

Here is an example:

See Fred Nickols (2017.08.15.1537 ET).

Here is a clean diagram of bidirectional comparators that Eetu Pikkarainen made, which captures how I view them.

See [Eetu Pikkarainen (2017/08/16 3:21 AM)] (VS: Dealing with the limitation of only positive neural signals)


I think I just misunderstood what you were describing. I would call the comparators in Eetu’s diagrams unidirectional inasmuch as their error outputs can be only positive. By having the two comparators compute error in opposite ways and having those errors drive outputs that have opposite effects on the value of the references to lower order systems or on a controlled variable (as in Eetu’s diagram), you can produce a control loop that operates in exactly the same way as a control loop that has a true bidirectional comparator, like those in our computer models of control systems.

I’m familiar with (and have built working models of) the “two unidirectional comparator” (positive error signals only) approach to building a system that imitates the function of a system with one bidirectional comprators. I thought perhaps your neurophysiological look at the thalamus showed you how the nervous system could implement a bidirectional comparator like that used in the compuer models – a single comparator that produces bidirectional output even though neural signals are always positive (although they can, of course, have inhibitory effects). But I guess what you may have shown is that the neurophysiology implements bidirectional control using the “two unidirectional comparator” method shown in Eetu’s diagrams. If so, I wish you would more clearly map your diagrams of the neural circuits in the thalamus to Eetu’s diagrams.