A Possible Approach to AGI.pdf (2.2 MB)
As promised.
Thoughts appreciated.
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Interesting read, I particularly like the concept of hyper-tetrahedrons as the optimal solution
in an n-dimensional problem space, if I am understanding it correctly. Does rather beg the question
âwhy arenât all fund managers running this algorithm, sitting back and raking in the profitsâ,
or perhaps they are.
I struggle with how to get from sensory nerve signals, to hyper-tetrahedrons and back
to motor nerve signals.
A short thought experiment:
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Driving a car requires intelligence we presume, itâs not something even the smartest ape could do.
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If I train an LLM on all the information on cars, roads and driving there is in the world it will
be able to correctly answer any question about driving a car you ask. Does it know how to drive a car ? -
I expect the answers will be yes to part 1 and no to part 2. Driving a car requires muscle memory and extensive situational awareness only acquirable through practical experience. The intelligence required and acquired eventually gets utilised at an almost subconscious level without the driver being aware of it at the fully conscious level a learner driver must use.
So, I have an artificial creature with a whole bunch of sensory nerves from all of the artificial muscles and eyes and ears and balance organs, and another bunch of motor nerves stimulating the artificial muscles. What goes in between is the AGI system, Monty, Cover or some such. But lower down itâs not an n-dimensional problem to optimise. Itâs a hole where I went to place the foot, a step to climb over, a room to navigate. This feels more like an n-dimensional feedback control loop, something I like to call behavioural intelligence. Unfortunately the term is commonly used to mean intelligence about human behaviour, whereas I refer to creating behaviour in an artificial creature, which could be said to be intelligent behaviour. This control loop could be implemented in the form of a recurrent neural network with pliable hidden states.
The higher functions would then be built on top of the n-dimensional feedback control loop, modifying the control as it extracts more complex patterns from the sensory data and formulates more sophisticated responses. I think what I am saying is that something like an old brain implementation is required as an interface between a neocortex model and the real world, and itâs real world behaviour that we perceive, not unreasonably, as intelligence.
Fund managers operate primarily as risk takers and speculators imagining (against mountains of evidence) that they can beat markets. The most sophisticated ones attempt to lay risk off on other participants (this often looks like market manipulation, e.g., high frequency trading accessing information not yet available to the public).
Coverâs universal portfolio doesnât have any excitement to it. It just works, positioning one to do as well as one can reasonably do and to do so with low volatility over the long run.
I think A Thousand Brains (or some Cover variant of it) does operate via n-dimensional feedback control loops. In my understanding, process wise they differ in the order of operations.
A Thousand Brains:
- encounters something,
- models the input,
- identifies (applying the just created model).
Cover variant:
- encounters something,
- identifies (applying the last created model), then
- updates the model for the next encounter.
A Cover approach operates faster in real time with the trade off of accuracy. That said, over the longer run, it gets to the same success in respect to the unknowable future. Coverâs algorithms operate like evolution, over time.
I think lots of high-level intelligence operates at a subconscious level.
Psychiatrist, Anton Ehrenzweig published The Hidden Order of Art: A Study in the Psychology of Artistic Imagination, in 1967. In sections of the work, he posits that complexity of certain tasks go beyond the capacity of a conscious mind to do them efficiently, effectively, or practically at all.
Yet we (humans) do them. Ehrenzweig observes that those that can get out of their own way access the deeper and broader capacity of our sub-conscious minds - the organizational powers of the sub-conscious do extraordinary things. We all have experiences of this. Creativity. Lateral thinking. Flow states. Inspiration. Epiphanies.
Federico GarcĂa Lorca famously described Flamingoâs idea of duende as ââŠa power, not a work; a struggle, not a thought,â something outside of the individuals consciousness.
âNo mind states,â or the concept of âno-mindâ, from meditative traditions like Zen and Daoism (mushin or wuxin) described a state as not an absence of awareness or a complete cessation of all brain activity, but rather a state of pure consciousness, freedom from conceptual thought, emotional attachment, and the ego-based âthinking mindâ which accesses the whole mind.
I donât see that one needs much beyond the operation of reference frames (maybe + Cover) in silicon to replicate this.
Unless Iâm mistaken, Monty doesnât actually build a fresh model prior to object identification. It uses existing hypotheses to interpret sensation immediately, then updates the model if and when appropriate. So Montyâs operation order, to me, seems closer to the Cover variant you described.
That said, I like your framing of Cortical Columns as a kind of distrobuted MoE network. Thats a fun way of viewing it. Using simplex-geometry to model module concensus is also clever.
As for thoughts⊠Iâd love to see an expansion of the memoâs âInnovation and Creativityâ section. To me, evolution-style reweighting optimizes that which already exists, but it doesnât really explain how the system invents new experts. So from within this framework, where would you say abstration comes from? How is it achieved?
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The same way brains already do it â extending a reference frame to incorporate some combination of stuff that we hadnât previously combined, which, in being combined, enables something or solves a problem we or even experts in a field have previously failed to solve.
We donât create ex nihilo. We can only combine things or ideas about things that already exist in the world (world certainly includes the body of human knowledge about the world).
A story came down to me that illustrates this. P&G sent a group of summer interns to Washington, D.C. to look for things at the US Patent Office the company could use.
An intern, a young woman in her teens, came across a patent that described a paper âgortexâ like material that water could pass through in only one direction. Being just paper she didnât think it had sufficient substance to use for anything, e.g., you couldnât make space suits out of it or waterproof shoes or jackets. She set the patent aside.
Later that day, the same intern came across a 2nd patent. This patentâs illustration looked like a cloud and it described a material that could absorb thousands of times its weight in water.
The intern, an experienced expert as a baby sitter, reportedly picked up the two patents, put them together, and invented Pampers and - as told to me - received a patent even though it incorporated two patents already filed.
Not certain if it really happened this way, but the story makes the point.
Certainly, innovation/invention/originality in any area of human endeavor can seem strange, when we donât know all the bits that someone accessed to arrive at the innovation.
Patent applications require a review of âprior artâ.
Magic tricks canât do anything beyond physics, they just hide or divert us from seeing all the pieces.
I still find Shakespeare strange and wonderful.
I feel the same way about A Thousand Brains.
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Great. I had only come to A Thousand Brains via the book and have only begun to dig into the more recent work.
I think I phrased this poorly. I agree with your stance here, I was more probing for how youâd propose doing it (or how you think the brain does it).
Itâs been a minute since I really thought about it myself, but personally, I suspect the brain employs a kind of resting state manifold learning function, potentially observed in things such as DMN activity.
Your questions have had me thinking the past several months. The following attempts to make sense of it.
Innovation, abstraction, creativity, even the capacity to generate explanations evolved.
Cover fits into this as the mathematician of Darwinian competence. Tom formalized why blind variation plus selection works so well, while remaining largely silent on knowledge, meaning, or explanation.
The mathematics of blind success
Coverâs theorem (1965) stated informally:
A complex pattern classification problem that is not linearly separable in low dimensions is likely to become linearly separable when projected into a sufficiently high-dimensional space.
Thereby:
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You do not need insight, understanding, or foresight to solve hard problems.
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You need rich variation and a simple selection rule.
Cover proved:
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High-dimensional representations make discrimination easy
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The power of random feature expansion
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Selection (error minimization) does the organizing
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Performance can arise without comprehension
Cover expresses Darwinâs algorithm in geometry, explaining why:
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Evolution works
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Machine learning works
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Scaling beats cleverness
He never published anything that claimed these systems understand anything, although I had conversations with him that pointed the way.
Essentially Cover formalized Dawkinsâs âBlind Watchmakerâ
Richard Dawkins explains conceptually what Cover shows mathematically.
Creativity: Innovation, Abstraction, and Explanation in Cover:
Some questions:
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Can brains evolve the capacity to expand a solution space?
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What constitutes abstraction?
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Where does the capacity to form explanations evolve?
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Could abstraction = explanation?
Innovation combines things and/or processes (nouns and verbs) not previously combined to solve problems not previously solvable.
Abstraction works in an almost opposite direction, identifying something common to a class of things or processes.
Innovation combining abstractions not previously combined might get us to explanation.
Prior to his death, Tom Cover and I spoke at length about expanding solution spaces e.g. , adding new experts (models). Tom saw no issue with his universal processes incorporating new experts into their optimization framework. Neither did he think doing so would de-optimize the process.
The question becomes, how does a brain add new experts?
Evolution already solved this question.
Conjecture:
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Abstraction always (and naturally) emerges as one or more experts/models within a cluster of cortical columns.
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As example, in a reference frame considering a cup, one expert/model casts its âvoteâ as an abstraction of a cup, a vessel.
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The abstraction (vessel) then becomes available in the modeling of bowls, vases, bottles, even variation like stainers operating across multiple reference frames.
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Participation of abstractions across multiple reference frames introduces innovation.
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Innovation yields a new expert/model that could participate across new reference frames or even across the reference frames from which its components reside.
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The innovation, as any expert/model, gets assessed time step after time step for fitness/usefulness.
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Abstraction and innovation emerge/evolve.
I donât think one needs anything other than this sort of evolutionary innovation to get to abstraction.
How does one then get to explanation?
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Abstraction extracts invariants across instances.
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Explanation organizes abstractions into a generative constraint structure that answers counterfactuals.
(I rely on Popper and Deutsch in this.)
Abstraction compresses. Explanation constrains.
An abstraction like âvesselâ compresses cups, bowls, bottles.
An explanation adds mechanism and counterfactual reach:
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vessels hold fluids because geometry + containment constraints
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if you puncture containment, holding fails
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if gravity changes, vessel behavior changes
So abstraction alone does not equal explanationâŠ
Explanation requires abstraction plus a structure that governs behavior across interventions.
What mechanism generates new experts?
Restating the above conjecture:
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cortical columns act as local modelers (Hawkins),
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clusters of columns produce candidate models,
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some models compress variation across contexts â abstractions,
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abstractions become reusable modeling primitives,
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cross-frame participation of abstractions enables innovation,
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innovations spawn new experts,
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universal selection evaluates them over time.
An evolutionary learning loop looks like this:
variation â abstraction â recombination â new expert â selection
Essentially, a cognitive analog of Darwin + Cover.
The âvesselâ example illustrates it (again repetitive, but maybe worth the repetition):
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object-centric columns encode cups, bowls, bottles
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clustering reveals invariant containment geometry
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one column (or small ensemble) stabilizes that invariant â abstraction âvesselâ
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abstraction participates across reference frames â compositional reuse
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recombination yields new experts (e. g. , strainer as constrained vessel)
Nothing mystical enters. Abstraction emerges as a byproduct of compressive modeling pressure, evolutionary natural selection.
Does abstraction + solution-space expansion yield explanation?
The conjecture captures two necessary ingredients:
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expansion of the expert space (innovation)
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compression across instances (abstraction)
Together they create the raw material for explanation.
But explanation requires one additional step:
Explanation = abstraction embedded in a constraint network
It seems that abstractions become explanations when they:
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govern behavior under intervention,
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unify multiple phenomena under shared constraints,
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survive criticism across contexts.
So the evolutionary loop naturally generates abstraction.
But explanation emerges only when selection pressures favor:
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counterfactual robustness,
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cross-context invariance,
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minimal generative structure.
It seems as if:
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abstraction provides the vocabulary of explanation
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selection over counterfactual performance provides the grammar.
Innovation as cross-reference-frame abstraction recombination
The key idea lies in:
Innovation combining abstractions across reference frames yields new experts.
This gives a mechanistic account of creativity:
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each reference frame develops local abstractions,
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cross-frame interaction reveals compatibility or analogy,
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recombination creates candidate generative structures,
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selection filters for usefulness.
That mechanism naturally yields explanation because cross-frame consistency imposes constraints. If an abstraction works across many frames, it likely captures a real invariant.
I think Daniel Dennett would view this as a real pattern.
I further suggest that David Deutsch (see David Deutsch, Aeon, Creative blocks, 2012) would view this as an explanation with reach (I emailed him when the Aeon piece came out. He graciously responded. He might have an interest in chiming in on this).
Summary
The evolutionary abstraction-innovation loop can generate explanation, but only under one added pressure:
**selection must reward counterfactual stability, not only predictive fit.**
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Innovation expands the hypothesis space.
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Abstraction compresses variation.
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Selection across contexts filters abstractions.
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Cross-frame reuse imposes invariance.
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Counterfactual robustness elevates abstraction into explanation.
Thus explanation emerges as an evolutionary equilibrium in the space of abstractions.
Concisely
A brain expands its solution space by generating new experts through recombination and structural mutation. Some experts compress variation across instances and stabilize as abstractions. Abstractions participate across multiple reference frames, enabling innovation through recombination. Universal selection evaluates innovations over time. When an abstraction survives cross-context criticism and supports reliable counterfactual reasoning, the abstraction functions as an explanation. Computational irreducibility limits how far explanations compress dynamics, but it does not prevent abstractions from emerging. Explanation therefore appears as a selected subset of abstractions that achieve invariant generative reach.
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I like this.
I think youâre probably correct here. I actually think one of the core functions of the default mode network is to compress high-dimensional information into a low-dimensional state (e.g., generalizing it). At one point, I think I used the term âresting-state manifold learnerâ to describe the DMN in more ML-specific terms.
The CEN and saliance networks, I would suspect, also have a role to play in generating explantion.
Regarding the selection pressure: You assert that explanation emerges when selection rewards counterfactual stability rather than just predictive fit. But what generates that pressure? Predictive fit is metabolically cheap to evaluate. But counterfactual robustness isnât. Youâre essentially simulating interventions which havenât happened yet. So why might a brainâone which evolved under tight energy constraintsâseem to prefer this?
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Iâve been rereading Darwin, Dawkins, and Dennet, so I may have a kind of contact bias. Apologies if Iâve missed something in your questions.
At the highest level, evolutionary survival of the fittest within the environment the human species found itself.
Donât all internally referencing reference frames do this? We visualize things not in front of us. We can visualize things in our heads that weâve never seen in real life. Our brains evolved these capacities. They must have provided fitness advantages.
Counterfactual robustness and the accompanying capacity to form explanations more distinguishes humansâfrom all other beingsâthan anything else (I first encountered this idea in David Deutschâs The Beginning of Infinity). More so even than language or tool making which apparently lots of creatures do.
Why human brains evolved this under the environmental (including energy) constraints they faced, seems less important than that they evolved to do so.
While we may not have identified the exact biological mechanism enabling this (although Thousand Brains seems plausible and very close), we certainly know that one exists. While we may not understand the step-by-step process that evolved the mechanism, we certainly know that it occurred.
Evolution deems counterfactual robustness as worth the cost. It could only do so, because it conferred fitness.
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I think your idea aligns directly with Thousand Brains consensus formation (whether a Cover implementation or Monty).
During rest (especially DMN activity), the brain can internally explore and reorganize the geometric structures (e.g., reference frames) of its learned representations, refining the latent manifold that supports perception, imagination, and abstraction. Consistent with the brain reflecting on itself.
Rest = geometric self-organization of experience.
Different sleep states may support different access to these capacities.
Matthew Walkerâs, Why We Sleep, provides a useful lay-person description of all of this,
I think the experience of coming to insights during phases of light sleep coping up into consciousness, enables some memory of the process.
The Sufi poet, JalÄl al-DÄ«n Muáž„ammad RĆ«mÄ«, advised (paraphrased):
Should you wake in the night, welcome the early hours, the morning winds have messages for you.
Given a Cover | Universal Portfolio | epistemic framing:
- DMN manifold exploration resembles expert weighting over hypotheses
- Replay and simulation approximate Cover-style universal search
- Consensus across cortical columns parallels Hawkinsâs ensemble voting
Pretty direct link:
DMN dynamics â evolutionary manifold search â Thousand Brains consensus formation
Evolution selected for us to spend nearly 1/3 of our lives asleep - a huge cost, but maybe that sleep pushes everything else.
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