Modelling Intelligence From Its Structure

The Problem

A primary goal of current machine learning research is to achieve artificial general intelligence (AGI), and it is being pursued mainly in three ways:

• Scaling laws: training larger models on more data.
• Engineering practice: wrapping those models in agent loops so they can call tools and read their own output.
• Architectural exploration: refining the transformer architecture, or exploring others, such as world models and JEPA.

While these approaches differ, they in fact rest on one shared core bet:

The bet is understandable. Intelligence of a kind has advanced this way in front of us, and one theoretical result is read as support for it. The universal approximation theorem (UAT) states that a wide enough network can approximate any continuous function on a bounded domain to any accuracy required.

However, there is one caveat. The bet carries an assumption that is rarely stated:

The two readings lead to different work:

• Degree. Everything needed is already present, and the remaining task is to supply more of it: more parameters, more data, more compute.
• Kind. No amount of any of those closes the gap, because what is missing was never there in a smaller form. It has to be identified and built, and the only way to identify it is to know what the target is made of.

People do notice this, and alternatives are proposed: Fei Fei Li’s world models, Yann LeCun’s JEPA. These are well specified and seriously built, and they share one move. Each identifies a feature that human intelligence has, a model of the world or prediction inside a representation space, and designs an architecture around it.

Yet, a feature that general intelligence requires is not thereby a feature that produces it. That AGI needs to understand the world does not mean understanding the world is enough to reach it, and neither programme says what the remaining conditions are. So the architecture is fixed in advance and the intelligence is expected to emerge inside it, which leaves the same question standing:

This work is an attempt to answer that question, and doing so reverses the direction of the search. Trying one approach after another and testing whether it arrives is searching for a destination nobody can see. Describing the destination first is what makes it possible to reason about which route could reach it, rather than sampling routes and hoping.

The One Guaranteed Starting Point

What we are looking for is human level intelligence. Without knowing what human intelligence is, nobody can predict whether the approaches above will ever reach it, and the only way left to find out is to spend billions and see. The only system we know of that reaches human level intelligence is human cognition, as it is the source of the definition itself, and every person reading this is running an instance of it.

Intelligence is not a separate faculty that a mind has alongside everything else. It is a product of how that mind is structured, so a structural account of cognition is also an account of the intelligence it produces. That is the object of this work: to give a structural account of cognition, rather than another semantic description of intelligence.

This claim is narrow on purpose. It does not say that a structure resembling cognition is required for intelligence in general. Other kinds of intelligence exist, and what current models have is one of them. It says only that for human level intelligence specifically, the one route known to arrive is the one running through a structure aligned with human cognition, because it is the only route with a working instance at the end of it.

Taking that route is not a matter of preference. Working through the structure of human cognition reveals features that human intelligence depends on but deep learning does not support, and those missing features correspond to the difficulties deep learning keeps meeting: the amount of data a model needs, the absence of any internal structure to interpret, generalization that does not survive a change of context, the inability to build one concept on top of another, and the loss of what was learned before whenever something new is learned.

The Modeling Target

Cognition is an emergent property of the brain, and emergence means the properties of the parts are insufficient to predict the properties of the whole. That has a consequence for how the problem should be attacked, and it is the point on which this work differs from everything else in the field.

Every mainstream approach works on the container and waits for the emergent structure to appear inside it. Architectures are proposed, scaled and patched, and general intelligence is expected to arrive from one of them. But if the properties of the parts are insufficient to predict the properties of the whole, then searching over containers carries no information about which container produces the structure that is wanted.

Some of the foundations of current machine learning do reference the brain, the perceptron most obviously, but that is no guarantee that the same emergence follows. It is entirely possible that on such a family of architectures it just never happens.

This work runs in the opposite direction. What is modelled is the emergent structure itself, and the container is designed afterward to support it. The alignment is in abstract structure, not in biology.

Cognition stands in the same relation to the brain. Once the structure is the thing being built, the container can be designed to fit its running, and the modelling of that structure should not be constrained in advance by an assumed container, which is what the current machine learning paradigm would be.

So this work does not assume anything that is taken for granted under the current paradigm, including deep learning, and instead reasons from first principles and from phenomena that are actually observed.

A Definition of AGI

AGI means different things to different people. An argument that turns on which meaning a term carries is an argument about the word rather than about what it refers to, so the convention here is to state what a term means before using it.

As mentioned above, the only thing we can confirm to have reached general intelligence is a person, so the definition of AGI used here is anchored to that and is deliberately conservative:

The second half follows from the first rather than being added to it. Once the structure is the thing being built, rather than a set of weights being trained until a score improves, the internal state can be read while it runs, edited, copied, forked and rejoined, and run at whatever rate the hardware allows. None of that is available in a brain, and none of it needed a separate assumption.

Methodology

Neurons are the wrong level at which to read the structure of cognition, for the reason given above, which is why decades of work on neural mechanism have not produced a derivation of it. This work models cognition at its own level and treats neuroscience as corroboration rather than as the foundation.

That choice is what makes the model independent of what it runs on, and everything after it depends on that being true. If structure is what constitutes cognition, then any platform that can carry the structure carries cognition, and a machine learning implementation is a real possibility rather than a metaphor.

The Thing Being Modelled

As few assumptions as possible are made about what is being modelled, which matters most where the terms are vague enough that no universally agreed definition exists. The minimal structure is a coupled pair.

The pair is coupled in both directions.

• Cognition decides how awareness moves when nothing is arriving from outside.

  Two people meeting the same event think along different paths, because what each of them holds in cognition differs.

• The path awareness takes reshapes cognition.

  You remember what you were just thinking about.

Two ways of observing, and why both are needed

The object of study is subjective, and that creates a specific difficulty: everything objective that can be measured about a mind is already a projection of it.

• First person. Introspection is the only instrument that reaches inside a subjectivity at all. It gives a detailed account of what depends on what, what happens in what order, and what rearranges what. What it cannot give is reproducibility, so it is used as a source of candidates and never as a source of conclusions. It proposes; formalisation decides which proposals survive.
• Third person. Behaviour across many people, development from infancy, variation across cultures and languages, and the phenomena psychology has catalogued. Reproducible, because anyone can look. But each observation is a reading taken from outside a closed system, so the structure that produced it has to be inferred rather than seen.

One instance in high detail, constrained by many instances observed from outside. A structure derived from the first has to explain the phenomena of the second across people whose cognitive contents differ completely, and any phenomenon it cannot explain forces a revision rather than an exception.

What can actually be measured

Nothing is assumed about the inside. A person’s cognition is not open to inspection, so the only honest move is to treat it as closed and describe it by what it does under test. Ask a question and what comes back is one reading: not the state itself, but a boundary the state has to sit inside.

A single reading says little. Put readings in series and they say a great deal, because what is then being watched is not an answer but a change. How far the responses agree with one another across repeats. How that agreement moves after something is learned. How long the reaction takes, and whether the delay shortens with exposure. Each probe narrows the range of structures that could have produced the whole sequence, and a structure is admitted only if it can produce every reading in it.

Why a hypergraph

A description of what a mind holds needs a formalism to be written in. Ontology, the study of what exists and how it is categorised, hands you substances and the relations between them. Modelled directly that becomes a typed directed graph, where things are nodes and relations are edges, and it brings two problems. Relations have to be a different kind of object from the things they relate, so they need machinery of their own. And there is nowhere to put a relation between two relations, though those plainly exist: over the real numbers, is greater than and is less than are mutually exclusive, and that exclusivity is itself a relation holding between two relations.

A directed hypergraph removes the distinction between the two kinds of object. Anything that can interact with anything else is a hypernode, relations included, and a hyperedge points from a set of hypernodes to a set of hypernodes with no internal structure of its own. A relation R holding from A to B is the edge from the set containing A and R to the set containing B, and relations between relations then follow without anything being added. Everything is a primitive of the same kind, and the structure is free to recurse.

It also stays refinable. A hypernode can itself be a set of smaller hypernodes, so a description can be made finer indefinitely without changing the formalism and without rewriting what was already said at the coarser level.

What reasoning looks like in it

The first test of a formalism is whether the things people already do with thought can be written in it without special cases. Deduction, induction and abduction turn out to be three ways of moving on one structure rather than three separate faculties.

Deduction follows edges that already exist

Take the syllogism: Socrates is a man, every man is mortal, therefore Socrates is mortal. Both premises are written the same way the formalism writes everything else. The first is the edge from the set containing Socrates and the relation is a to the set containing man. The second is the edge from the set containing man and the relation implies to the set containing mortal. Deduction is following the one and then the other, and the conclusion is the composite edge from Socrates and is a to mortal. It was reachable before anyone stated it, which is the precise sense in which a valid deduction tells you nothing you did not already have.

Induction builds a hypernode that was not there

Several cases carry the same edge: this swan is white, that swan is white, the next one too. Induction forms a hypernode covering those cases and attaches the edge to that instead of to each case separately. What is new is the hypernode, not the edge, which is why induction adds something where deduction does not, and also why induction can be wrong: the hypernode is a claim that those cases belong together.

Abduction reads an edge from the wrong end

The ground is wet; rain causes wet ground; so rain is proposed. The edge from rain to wet ground is the one that already exists, and abduction enters at its destination and names a source. The formalism says in one line why this is not valid: an edge points from a set to a set, and several different sources can point at the same destination, so running one backwards returns a candidate rather than a conclusion. What makes one candidate better than another is how much else in the structure it already connects to.

The three are not equally basic, and the order between them matters for what follows. Deduction moves through structure that already exists. Induction is what puts that structure there, and the section on self assembly below is an account of how it happens with nobody supplying the categories. Abduction is an existing edge read backwards, and it is what produces the guesses induction then has to confirm or drop. A system that has only the first of the three can rearrange what it was given and nothing else.

One more consequence, because it connects the formalism to the rest of the page. A deduction walked often enough stops being walked: the composite edge from Socrates to being mortal becomes an edge in its own right, and the two steps that produced it are no longer traversed. That is the operation Figure 6 draws, and it is what it feels like to know something immediately and be unable to say how you got there.

Where deep learning cannot follow

One assumption sits under every mainstream model whatever its architecture: that intelligence is the approximation of a mapping from a start state to an end state. Supervised models map inputs to labels. Diffusion and flow matching look like a departure from that, but they only move the two endpoints, with noise as the start state and a sample from the data distribution as the end state. Computation is defined as transporting a given input toward a given target.

Cognition does not have that shape. It runs continuously in time and carries its own state, with nothing resetting it between one input and the next. An input arriving and an output being produced are two separate events happening against an internal evolution that was already under way, and people do not take input in order to produce output. Binding the two into a single mapping is an artefact of the assumption rather than something observed.

Why approximation results do not settle it

A universal approximation theorem says that a wide enough network can approximate any continuous function, and that result is the formal comfort underneath a great deal of confidence in scale. Stated properly it is an existence result about one fixed function.

Two things sit outside what that result covers.

• The function it approximates is static. Cognition is not a fixed mapping being estimated more and more closely. The object here is f_t, rewritten every second by its own operation, so getting within ε of the version present at one moment says nothing about the next one, and the sequence of approximations converges on nothing.
• Recurrence puts structure at every scale. When a state routes back through structure that its own passage has just altered, the result has detail at arbitrarily fine scale rather than a fixed smoothness. Approximating something like that with a fixed layered form takes capacity that grows far faster than the description of it does, which is one reason scale keeps buying less than expected. A model whose shape is unlike the shape of what it is approximating does not get close to it cheaply at any size.

What follows in training

Layered structure forces a backward pass to assign credit, and backpropagation is the method almost universally used for it. Any gradient needs an objective, and the objective has to come from somewhere. The deeper commitment is that the feedback comes from outside the system: a label in supervised learning, a reward function in reinforcement learning, a target distribution in a generative model. Fixed, external, and unaffected by whatever the model does.

In a person only a small set of bodily signals are given from birth. Everything else that feels good or bad is built on top of those, which is to say it is learned.

That follows from the assumption rather than being an engineering choice: a mapping needs a target, and a target has to be specified from outside. Methods that do without gradients keep the commitment anyway. Forward Forward’s goodness function, predictive coding’s prediction target and an evolutionary method’s fitness score are all supplied by a designer. The thing a mind builds first is the one thing the model is never allowed to build.

What follows in architecture

The structure of a network is fixed before training begins. Training changes the weights; the topology along which information flows never rearranges. Residual connections are wiring a designer chose, not a rerouting the system performed. A feature holds a fixed relation to the features it connects to, so it is bound to its layer and cannot drift, merge with a neighbour, or split in two. A long path traversed many times never becomes a short one.

It also means the structure cannot be fixed in advance. When a path shortens, the manifolds the states lie on drift, merge and rearrange. The point is sharper for a neural network, where each layer’s latent space is itself a manifold rather than a single point standing for a single state. A retrieval store attached to the side is not the same thing either: intuition has to live inside the structure, because it is a change to the structure.

The consequence is about dependency. A simple idea and a harder one built on top of it have a relationship, but a trained network holds no structural dependency between them, so the harder one cannot be learned through the simpler one. Before a person understands the simple thing, the hard thing arrives closer to noise than to information. Once they hold the simple thing, the hard thing is processed through it first and arrives as a pattern, carrying far less that is new.

A latent space is not a substitute for that. It does not change over time, and the relations between features are folded into the geometry of the coordinates rather than held as structure that can be revised.

What follows in theory

Learning theory speaks in distributions, convergence rates, generalisation bounds and scaling laws, all of which are statistical descriptions of a model seen from outside it. None of them says how intelligence forms or how it changes over time.

The theories of consciousness have the mirror image of that problem. Global Workspace Theory describes an arrangement, a broadcast and a spotlight, without saying what the workspace is made of or how it comes to exist. Integrated Information Theory assigns a quantity to a system without giving a structure that says how any of it forms, evolves or breaks. Both describe a result. Neither gives a mechanism anyone could build from.

The black box problem is the same absence seen from the inside. When every parameter is shaped by gradient flow there is no internal structure left to interpret. Opacity is not a missing tool that better probes would supply. It is the default state of a system that was never given a structural organisation in the first place.

What it costs in capability

Two abilities that define human intelligence are absent, and both follow from what is above rather than being separate shortcomings. The first is continual learning. New knowledge competes with old knowledge instead of building on it, because nothing can be placed anywhere structurally and everything enters as undifferentiated gradient flow. Catastrophic forgetting is the visible symptom.

The second is thinking, and it is the one that is rarely counted as a capability at all.

What happened is that knowledge you were holding as separate pieces was taken apart and put back together with different connections between them. It is the operation that separates understanding something from having memorized it, and it costs no data at all. What it costs is thinking, and the time thinking takes. Current models go the other way: to become more intelligent they need more data.

A model can be given somewhere to write into, a retrieval store for instance, and that is still not the same thing. Even with somewhere to write, a model needs data to learn from, some form of input and usually a target to move toward. Thinking in a person is an internal process. It involves no interaction with the external world at all.

Structure that assembles itself

Before anything can be related to anything else, there has to be a thing there to relate. Ontology asks what exists; the question before it is how a mind comes to have anything at all that it can point at. Not how a category is learned once someone hands you the categories, but how something becomes recognisable when nothing yet plays that role.

A representation is not an object placed somewhere. It is what is left when the spread of where a state can go next collapses from high uncertainty to low, continuously, until a region of states is reliable enough to be treated as one thing.

• Situations arrive that share part of a patternTwo situations are not identical but resemble each other, and the relation between their parts is similar in both. Physical time is continuous, so what arrives is continuous too.
• The shared part is reinforced on every passEach situation activates a region of states that partly overlaps with the region the other one activates. The overlapping part is present every time. The parts that vary are present occasionally.
• Only the shared part survivesThe link from one overlap to the next is reinforced on every exposure, while the links off the overlap are reinforced rarely and stay weak. What is left standing is the structure the situations had in common.
• That is the representationNothing selected it, labelled it or rewarded it. It precipitated out. No feedback of any kind was involved, which makes this unsupervised in a way that no pretext task is.

This is induction happening physically rather than being applied as a rule. The region that survives is the hypernode that Figure 4 shows induction forming, and nothing had to supply the category it stands for.

The starting conditions are close to nothing: continuity in what arrives, so that similar situations produce similar states, and some initial pathways carrying that input inward. Given those two, structure deepens on its own, and each layer that forms becomes the material the next one is built from. That recursion is the whole engine, and it is why the process needs no designer to say what the features should be at any level.

Why unsupervised, reinforcement and supervised learning are not three algorithms

They are three boxes a designer chooses between before training starts. In a person they are stages of one process, and the order between them is a dependency rather than a curriculum: each stage cannot run until the one before it has produced what it needs.

• Features form, with no feedback at allThe self assembly described above. Structure precipitates out of the temporal structure of what arrives. Nothing is being optimised and nothing is being told.
• Routing between features gets laid downOnce features exist, the temporal relations between them are learned: this region tends to be followed by that one. Some of those chains terminate at the bodily signals given from birth. A feature several steps away from anything biological therefore acquires a good or bad sense through the chain it sits on. This is learning the causal relations between features, which is a separate thing from feedback then acting on the route.
• Only then can anything be supervisedBeing taught requires that my answer matches the given answer is itself a state the learner can identify, and that identifying it already produces something positive or negative. The second of those is built from experience: answering correctly earns a sweet, and the child has already connected a sweet to the taste of sugar, so answering correctly inherits that feedback along the route. Both have to be in place first. Before that, a teacher’s reaction carries no weight at all, every outcome is worth the same, and nothing converges.

Where it sits

This is not supervised, unsupervised or reinforcement learning. That three way split classifies approaches to function approximation, and this is not one of them, which is as much a problem as a distinction: no existing benchmark is waiting for it. The nearest work, and where it parts company with each:

• Hebbian learning, STDP

  Sharesa local update rule driven by timing, with no backward pass

  Differsthey operate on physical connections between neurons, while this operates on abstract states and the regions they fall into, which is a different level of description

• Forward Forward

  Sharesgenuinely no backward pass

  Differslayers are trained independently against a goodness function a designer supplies, so the objective is still fixed and still external

• Predictive coding

  Sharesno chain rule backward pass, and an internally generated signal

  Differsit takes expectation as a primitive without defining it, keeps top down prediction and iterative settling, and converges numerically toward the gradients backpropagation would have produced

• Free Energy Principle

  Sharesa self updating internal model with no external supervisor

  Differsit rests on an explicit generative model and variational inference, both assumed rather than derived from observation

• Heteroclinic network models

  Sharesthe vocabulary of saddles, trajectories and phase space

  Differsthe network of saddles is fixed and the question is how a trajectory moves through it, whereas here the structure is itself the thing that evolves

• World models, JEPA

  Sharesan internal model of how the environment unfolds in time

  Differsthe architecture carrying that model is designed in advance, rather than emerging out of the temporal structure of the input

• Global Workspace, IIT

  Sharesconsciousness treated as the object of study rather than a side effect

  Differsthey describe a functional arrangement or assign a scalar to it, without a structure that says how any of it forms or changes

Locality, forward only training and a recurrent state of constant size are properties a good deal of this field already shares. None of them is presented here as an invention.

What comes with it

Because the framework describes cognition rather than a model architecture, it reaches things machine learning normally has no contact with. A great many psychological phenomena follow from the same small set of structural rules, without a separate account for each: how a preference forms, why views on one subject diverge systematically between people, why a learned reaction persists after its original cause has become untraceable. The same holds for several long standing questions in philosophy, which turn out to be questions about the structure doing the asking.

Where it stands

The present work is the theory: the structural observations, the formal objects that carry them, and whether the whole stays consistent while covering more of what is actually observed in people. That is a demanding bar. Every phenomenon the framework cannot produce forces a structural revision rather than an exception, and it has been rebuilt more than once on that basis.

What it describes is implementable rather than an abstraction with no route to hardware. Updates are local in time and space, the computation is purely forward, and it maps onto parallel, distributed and analog hardware rather than requiring a global backward pass.

Work with me

I work on this full time and independently. The most useful thing anyone can send is an objection. If you work on anything adjacent, whether local learning rules, dynamical systems accounts of cognition, computational cognitive science or philosophy of mind, I would like to hear where you think this breaks.

If you invest in early foundational work, there is considerably more detail than belongs on a public page, including the parts held back here, and I am glad to go through it properly.