A book about dendritic computation and cortical layers

Hey all, Sergey here. I have been away for a while, because I have been writing a book called Cortical Circuitry. It’s out now, and I’d love for people here to check it out and give feedback.

The book largely agrees with HTM as far as the general function of the cortex goes, but presents a different view on the function of individual neurons and cortical layers. The differences start in Chapter 4, which is probably where most of you would want to start.

If you’re interested - Cortical Circuitry is on Amazon - https://www.amazon.com/dp/B075G4GYNV,

Edit: PDF link - https://www.dropbox.com/s/xpvl5xif18t95e2/Cortical_Circuitry.pdf?dl=1


Thanks Sergey!

I have it now in my kindle!

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Thank you. May I ask you the PDF version?

Hey Sergey, cool project. I’ve skimmed a bit on the Amazon version and it looks like certain things (the algorithms in particular) are very poorly typeset in the Kindle format. Could you make a PDF link available?


Oops - I’ll fix that, thanks.

Here’s a PDF https://www.dropbox.com/s/xpvl5xif18t95e2/Cortical_Circuitry.pdf?dl=1


I just started chapter 4, and have a few questions. Are you saying there are 3 types of spike - a basal dendrite NMDA spike, a tuft dendrite NMDA spike, and a Calcium spike that is not an action potential?
If so: where is the Calcium spike?
Also: you seem to have some divergence from numenta temporal memory theory. According to you, a burst is when a prediction (at the apical dendrite) coincides with spikes at the basal dendrite. (I think basal in your case is the equivalent of both proximal and distal in numenta theory). So if I understand you correctly, which I probably don’t, bursting happens when an input is predicted. By contrast, bursting in numenta temporal memory happens when an input is not predicted.
That’s a big difference. You point out that bursting of a neuron means many successive impulses to its target neurons in a short time. So predicted inputs leads to cortical activity. While in the case of numenta theory, its the surprise of an unexpected input that leads to the cortical activity.
Could you clarify?


Hey, good question.

About the 3 types of spikes - I don’t think about it that way. Concurrent input on a dendritic segment causes an NMDA spike. Enough NMDA spikes (2+ or 1 and some input) in tuft dendrites causes a calcium spike. Enough NMDA spikes in basal dendrites cause an action potential or a burst if there has been a calcium spike recently.

Check out figure 4(G,H) here - https://www.projekte.hu-berlin.de/en/larkum/publications/larkum_science_2009

and figure 2 here - https://www.projekte.hu-berlin.de/en/larkum/publications/larkum_tins_2013

Yes, you understand me correctly. I think that predicted input causes bursts. The second paper I linked is an opinion piece by Matthew Larkum about this exact issue. I highly recommend it, especially figure 3.


Hi @gidmeister, I think HTM and @s.aleksashenko uses the term bursting differently. For HTM, bursting means neurons of a minicolumn becoming active if they are not predicted. So bursting refers to the total activation of a minicolumn, not the firing characteristics of a specific neuron. From what I understand, @s.aleksashenko uses bursting in the sense that a specific neuron fires frequently in case of a predicted activation.

In addition, according to BAMI page 28:

One condition that can cause a mini-burst is when a cell starts firing from a previously depolarized state. A mini-burst activates metabotropic receptors in the post-synaptic cell, which leads to long lasting depolarization and learning effects.

So HTM itself states a similar thing that a predicted active cell bursts (they call it mini-burst). If I am not wrong, Numenta specifically explored whether there is a firing difference between just an active cell (resulting from a bursted minicolumn) or a predicted active cell. For their temporal pooling theory to work, they needed predicted active cells to fire differently than just neurons that are active because their minicolumn is bursted. Their best answer was the functional difference between metabotropic and ionotropic receptors of neurons. So predicted active cells lead to the activation of the metabotropic receptors of the target cell because of the firing characteristics of the predicted active cell which they call mini-burst above and corresponds to what @s.aleksashenko refers as bursting. On the other hand, bursting in HTM refers to neurons of a mini-column getting all active. So this is where the confusion originates but I am almost sure that they are saying the same thing with different words.


Fair point about columns vs neurons. In neuroscience the term “bursting” pretty much always refers to neurons. Columns “bursting” is, I think, an exclusively Numenta term (at least I haven’t been able to find it on Google Scholar).

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I agree with that in my experience and initially pointed that out in my answer but I am not a neuroscientist so I gave it the benefit of doubt. It would definitely be better if the HTM terms had more precise counterparts in neuroscience material. The other one that confuses a lot of people is the usage of column in the context of Spatial Pooler and Temporal Memory which refers to the minicolumn in neuroscience. On the other hand, in the recent HTM sensorimotor research, column refers to 2 HTM layers of minicolumns on top of each other (probably macrocolumn in neuroscience?). I am sure these create frustrating gaps in the understanding of the newcomers and community members as is the case.


This book is really fun. It’s clear you put a lot of thought and time into it. I like the way the tone is so human while discussing something so complex. Thanks for sharing this with everyone.


Thanks for the explanation. I re-read BAMI page 28, and they say the state of “active-after-predicted” is a bursting neuron. So a bursting column in HTM terminology stops being a bursting column once a neuron in it has mini-bursted and has learned to fire. I suppose it suppresses the other cells of its own column.


Yes that’s how they explain it with one small difference. A column bursts when it gets activated without any predictive cells in it. So the column doesn’t always start in a bursting state when it gets activated. The predictive cell of the active column is closer to firing than the rest, so it fires earlier than the rest of the cells. This timing difference results in the predicted active cell inhibiting the rest and not allowing them to fire, so the column never bursts in this case. This mechanism is attributed to the functionality of fast spiking basket cells in neuroscience if I am not mistaken.


I finished your book, and have a few questions.
In the chapter with the pseudocode, by ‘nearby_dendrites’, do you mean areas on the same dendrite branch that have synapses connecting to them?
What is the difference between a ‘connected’ and a ‘nearby’ dendritic segment?
How do you make the neuron spike regularly? Does the ‘neuron.regular_spiking’ flag make a spike happen every so often? If so, is it ever turned off?
You say that a homeostatic method maintains a certain number of synapses for a neuron, and if the number drops below some threshold, the neuron forms new synapses. It forms synapses with axons that fire close in time to its own spikes (dendrite spikes). Are these axons nearby? Suppose no axons in the vicinity are firing?
You talk about the “what” vs “where” streams in the brain. “What” tells us what an object is, “where” tells us where it is. You say that the main difference between the two streams is that there is an additional piece of information coming into the “where” stream, and that is information about the movement of the eyes or hand or sensors. On the other hand, Numenta seems to be finding out that information about location of sensors is required even if you are just finding out WHAT an object, is, never mind WHERE it is. Perhaps additional information is needed to distinguish the two streams?
From a machine learning point of view, what do you think can be accomplished by a very simple architecture (not large numbers of regions and layers within regions) of your type of sequence neurons?

Any answers are appreciated.


What are your thoughts on the burst that comes before and seems to trigger movements, which seems to be predictive of the movement or movement result?
Presaccadic predictive remapping occurs in L5 cells which project to the superior colliculus and peaks at burst-like firing rates on average milliseconds before the saccade, so it seems like predicting the visual result triggers the movement, once activity becomes strong enough to indicate a decision and/or proper timing. There are bursts in response to sensory input, but most research on bursting is on layer 5 thick-tufted cells, which have more electrically separated tuft dendrites and so are different burst-wise from other cells. Bursting of these cells also causes widespread inhibition of their tuft dendrites, so long as martinotti cells aren’t inhibited by other circuits, and, although based on slices and maybe current injection, strong inputs might cause plateau potentials which prevent bursting but can generate sustained regular spiking.

I still think bursting as a result of a predicted input is possible or even likely, but I’m not sure about the details


Hi, thank you for reading and for awesome questions!

  1. Yes.

  2. Same thing. I realize now that I used the terms clumsily in a sentence once - both of them are meant to mean a dendritic segment on the same branch next to the original one.

  3. Yes, it does, but the frequency decays over time. If the frequency falls bellow a threshold, the regular spiking stops. If you look at spike trains of real neurons, you can see that happening.

  4. Yes, synapses are formed with axons in close proximity. If there are no such axons, the neuron grows new dendrites. Excitatory neurons in the cortex grow and retract branches all the time.

  5. Maybe. There are some ideas out there about the two streams getting different types of visual information from V1. I am still thinking about this, would definitely want to experiment.

  6. I don’t know! I am going to be assembling a team to build such networks next, so hopefully, we’ll find out. My goal is to build brains for robots that operate in the physical world, not software that works on labeled data. The dream is to build robots for the SpaceX 2022 Mars mission, however improbable it might be. I am not sure if it would be appropriate for me to post about new developments here, but if you want to keep in touch and see how this goes - shoot me a message!


I wrote a fair bit about this in the book. I think that the feedback information that comes to L5 neurons is goals. So when goals and ways to achieve them are combined, the neuron bursts and causes the saccade. Seems consistent with pre-saccadic bursts.

L3 neurons, however, receive predictions as their feedback information. So when they burst - it’s identifying predicted sensory information.

P.S. The reason that most research is on Layer 5 thick-tufted cells is that they are easier to study, not that they are more important, as far as I understand it.


Hi gidmeister and sergey

I am new here. It caught my interest that you mentioned the “what” and “where” streams…can I interfere with some additionals:
The “where” system is the allocentric system (the Moser nobel prize last year) creating possible “whats” (targets) and the “when” system is the egocentric system (fixation on the target).

If we say “where” and “what” we accept that doubt (=entropy) is the fundamental premise for the brain: Asking to answer “what to do now, now now…”

Taking this road based on doubt, we must accept questions in a learning process called query:
it seems there is an afferent sequence of questions:
What (target)
Which (goal)
And an efferent sequence:
Why (this goal and target)
When (this goal and target)
How (to restrict, modify, regulate, control, start/stop) the current movement…

I just described all that in my model (on the tangential) called The Human Decision System.
In here, the brain has six layers handling time (six different learning processes learning from data streams: doubt, past, future, present, moment, now) and six layers handling space (doubt): where, what, which, why, when how…

The six layers in each dimension is a result of minimizing entropy by partitioning…

Does this help in clarifying the foundation for partitioning ?


Now I really want to read it. Sorry I missed that, just busy with classes.

Thanks, that helps a lot!