Neuron: physical base for AND functionality?

There is the UNION operation on SDRs.
The problem with that is it has limited capacity to distinguish patterns and only support ORing items.
Also it doesn’t allow more complex activation.

In logical terms UNION is like an OR operation.

   IF pattern1 OR pattern2 OR ... THEN depolarize 

From physical standpoint it seem feasible to SUM (OR) all the distal synapses signals.

So I’m speculating/expecting/deducing :wink: the neuron should also support AND functionality.
What do I mean by that :

  IF pattern1 AND pattern2 AND ... THEN depolarize 

I can imagine two ways of neuron doing this :

  1. A dendrite switches ON/OFF all synapses that are on it via some chemical process !!
  2. An inhibitor neuron impeding dendrite region i.e. switching it ON/OFF
    A and B = NOT( NOT(A) OR NOT(B) )
  3. Some other mechanism ?
  4. External mechanism ?

IS there a mechanism for this ??

The analog in SDR parlance is CONCATENATION, so you still can have UNIONS combined in CONCATENATION.

BTW I’m looking probably for AND-capacity in the REPRESENTATION level, less in the neuron level, because the former will indicate intrinsic capability and the latter will require neurons-functional grouping (something akin to mini column)

after gmirey post something lit … having a UNION of SDRs f.e. A, B, I can check for both A OR B, which if both are in the union should return False , but may return True if i check for A AND B. So it seem we have to distinguish between two operations STORING conj and disj … vs CHECKING for conj and disj

So a UNION can store a conjunction and we can check for conjunction, but can not store/check a dis-junction (may be only if we mutate/permute the items)

let me see if i got it right :slight_smile:

u = a | b
a in u AND b in u => true
a in u OR b in u => true

u = ab
a in u AND b in u => true 
a in u OR b in u => false << not possible with union

You may ask what is this good for ?!

Let say you are storing a state S in an SDR … if you add it in a union you can check for a state in a union of states.
Now you want to add a different context C to different states but still add them to a union and check for Ctx1-StateX or Ctx2-StateX (currently checking for just StateX will return true) … they are anded patterns … hmm may be doable with permutations!!

So something like this become possible :

    IF ( (Ctx1 AND StateX) OR (Ctx2 AND StateX) ) in UNION THEN depolarize 

but not this :

    IF ((Ctx3 AND StateX) OR StateX) in UNION   THEN depolarize 

because the partially overlap

hmm…permutations may be, but there is no way to know in advance what to permute before the check !!

A while back we had a discussion about HTM’s ability to learn the XOR operation. AND could be learned in a similar way. The key is to consider receptive fields and inhibition.

@gmirey pointed out that much of the sensory apparatus send both polarities of signals. This implies that both signal and /signal are available for logical operations.

can you elaborate ?

I elaborated on it in the thread that I linked to. From there, this visualization is probably the easiest to understand. This depicts the receptive fields of some minicolumns, and you can see that some minicolumns can align better to just X or just Y, while others can align better to both X and Y. Add inhibition (such as k-winner step in the SP algorithm), and you will get different activations for X and Y versus just X or Y alone.


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i see, thank you
i was confused about the word “receptive fields”

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Ah, yes, another way to think of that is the “potential pool”. Basically the possible cells that a particular minicolumn might be able to connect with. May or may not be topologically biased.

trying to put “square peg in a circle” going the opposite way… from logic to biology :

 A and B = NOT( NOT(A) OR NOT(B) )

I dont see biologically plausible way to implement Double-negative !

BTW there is no dendrite segment inhibition, ONLY FULL neuron inhibition , right ?

Good point. It’s probably both and the voting accross modalities or columns are all equivalent to this. They implement ‘and’ and ‘or’.
It’s a very good example of repetition or reuse of patterns in biology specific to the brain.

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Jeff Hawkins once said the recursion isn’t understood but that is very simple wiring and fortunately basic logic. Neurologically though? That would be nice to know.

My own reaction rests on parentheses rather than negation. Nested functions needs a hierarchy and essentially recursion. It sounds like an interaction between layers of cell types.
It occurs to me that negation can even be the absence of an signal even when lacking inhibition. Logically, given you can’t invert a spike it must involve multiple cells.

yeah i’ve seen he mention recursion in at least 2 videos, but never what is the mechanism.
(… cup in a logo in a cup)

Would be good to know !

Sure and you folks study repeating patterns in biology within your domain. I hear of
Cell types tweaked with small variations.
The early brain development and formation of layers and perhaps pruning.
Much of Chomsky’s work around linguistics and his Merge challenge.
Both in neurologically and psychologically we can look at voting vs nosiy decision making.
From a Kantian view we see recursion around object identity and catagories. In any ontology existentially.
In math there is an interpretive relationship between self reference, identity and recursion.
It shows up in Numenta’s temporal work and NN learning.
More recently in advisarial networks which is at a higher level.
Continous learning too.
In my view the mini-column theory shows internal and hierarchical recursion but organic.
My simple definition of consciousness is recursive.
And Jeff spoke at length about recursion in visual perception and object composition as fully integrated across modalities.
Feedback (rather than forward) is often recursive but both can have recursive layers.
That’s all I can think of at the moment but what list! That’s just brain. Nature is a wonder.
Chomsky’s Merge is a cross cutting utility function appearing in many places. It is necessary but insufficient from one view.
More importantly we should speak to his view here around Occam’s Razor. The medium where we find the brain is built of neurons.
This simple design and it’s growth create an emergent complexity and power I needn’t explain here.
We do find Chomsky’s merge hidden in the mini-columns but the simplest building block he rightly searches for in linguistics is of enormous complexity. The neuron.
At a linguistic level we see something similar but more abstract. It’s not Merge but the ontological object (concept) that is a worthy building block.
I agree it can be further reduced and ultimately ties to this work. So I see Merge as important but the wrong place to focus. It is more of a toy experiment and example of methodology.

From HTM’s theory point of view:
Each cell ANDs at the distal segment level (pattern recognition)… or a fuzzy-AND if you wish, since it could go with 10 among 15 or something.
Each cell ORs those ANDed segments to predict (or even fire, if you inject a minimal proximal signal).
This is already enough to represent any sentence of propositional logic, I guess…

But if you want to AND several patterns in a simple way, then maybe just consider a cell sampling from those first pattern detectors ?
…since it can sample by ANDing (at least fuzzy-ANDing) the first row of pattern recognizers on its own segments.


that will ok, but what you have here is bit-ANDing not pattern-ANDing

didnt understood this, can u elaborate ?

Well, it’s as in your first concern: Your segments ANDs so-called “bits”, at first, right?

But then that whole cell fires in turn, what does its action potential represent ?
Well, “patterns” of your first order “bits”
Thus, just add one more layer of cells afterwards, and each of the “bits” inputs of those are semantically, “patterns” of the previous layer…
And by virtue of the per-segment mechanism, you’ll AND between them when sampling them.

Does that make more sense?


oo , so you where saying implementing AND by multiple neurons/layers ?

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Well, yes.

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