Toward Collective Superintelligence

The next-generation architecture paradigm for agent systems

Since 2025, the large-model arms race has rewritten the industry's narrative: more parameters, longer context, more expensive clusters. Once a single model can approach and even surpass human experts at mathematics competitions, code generation, and even research-grade proofs, a clear roadmap seems to have opened up — make one brain big enough, and artificial superintelligence (ASI) will arrive on its own once some threshold of scale is crossed.

A deeper question follows close behind: is "an ever-larger single brain" really the final form of intelligence?

Nature's answer is worth sitting with. Almost none of the most powerful intelligent systems on Earth are centralized. No ant knows the colony's master plan, yet the colony finds the shortest foraging route. No neuron understands language, yet a hundred billion of them give rise to your ability to read this sentence. No trader knows the "right price," yet the market compresses the local knowledge of hundreds of millions of participants into a single, continuously updated signal[1]. Evolution works the same way: no designer, just vast numbers of individuals competing, mutating, and being selected locally — converging in the end on structures so exquisite they have puzzled theologians.

This observation points to a judgment orthogonal to the mainstream narrative: the road to superintelligence may not be making one brain bigger, but making intelligence into a self-organizing, decomposable, parallel, evolvable collective. We call this form the "swarm". This article tries to lay out that road — its theoretical lineage, the wall of mathematics it breaks through, the parts already settled by experiment, the vital question still unproven, and what it ultimately points to.

The Formula for Emergence: Building Blocks, Rules, and Combinatorial Explosion

To understand the swarm, you first have to go back to "emergence" — a word worn out from overuse and almost never explained clearly.

The science writer Emergent Garden once gave a definition that is plain and sharp: an emergent system needs only two things — building blocks and rules[2]. Water molecules are building blocks obeying chemical rules, and out of them emerge surface tension and the fractal snowflake; ants are building blocks obeying pheromone rules, and out of them emerges the architecture of the nest; words are building blocks obeying syntactic rules, and out of them emerges language. This is not mysticism but a scientific lineage half a century deep: in 1970, Conway's "Game of Life" grew structures that move and self-replicate out of three rules; in the 1980s, Wolfram's "Rule 30" looks only at its two immediate neighbors, yet spits out patterns that to this day nobody can predict in advance with a formula — Wolfram put up a 30,000 dollar prize for "finding the shortcut formula," and no one has claimed it[3].

What really makes emergence astonishing is combinatorial explosion: there are vastly more ways to combine things than there are things. The number of distinct bit strings 100 bits can produce exceeds the number of atoms in the observable universe; the value of a Lego set lies not in the model on the instruction sheet but in everything those bricks can build that is not on the sheet. Output exceeds input exponentially.

The swarm is built to exactly this formula. The building block is the cell — an agent that can do work on its own, holding its own small slice of context and its own evolvable set of "strategy genes." The rules are three cellular-automaton-style rules that look only at local information: R1 gossip (broadcast your own verified experience to your neighbors), R2 adopt (take up a better gene), R3 forget (retire the worst gene). There is no privileged cell and no central scheduler; whoever is idle claims a task itself (a stigmergic work-claim, the same indirect coordination as ants leaving pheromone[4]), and when a cell dies, its unfinished work is automatically reclaimed and handed to someone else. The division of labor, the convergence, and the self-healing of the whole are what these local rules produce as they run — not what anyone scheduled.

Why insist on self-organization? Because without it you run into an O(N²) wall — the wall the "single brain" form runs into by its very nature. No matter how much bigger you make the brain, you cannot dodge it.

The Limit of a Single Brain: Hitting the O(N²) Wall

Today's large models rely on "self-attention" to understand context: when a model reads a passage of text, it makes every token look at every other token. N tokens means on the order of N×N relationships to compute. Push the context length from 10,000 to 100,000 and this cost does not grow 10x — it grows 100x. This is not badly written code; it is the mathematical nature of the Transformer architecture. You can buy more expensive cards and brute-force it, but a quadratic curve will eat any budget sooner or later.

The swarm's way around it is intuitive enough to draw right on an attention matrix: split one big task into K largely independent subtasks, and let each cell chew on nothing but its own small piece. We compute only those little triangles along the diagonal — the attention inside each cell — and throw away every cross-task square. Total computation drops from quadratic to roughly linear.

The cross-task attention you save is not saved for free — you have to split the task correctly first, and once the work is done you still have to merge the results correctly, and verify that they really are correct. This is exactly where the industry's 2025 wariness of multi-agent systems concentrates: the Cognition team said flatly that "having multiple agents collaborate only gets you fragile systems," and Berkeley's MAST study distilled more than two hundred multi-agent failure trajectories into fourteen failure modes, whose two largest categories are precisely "inter-agent mismatch after the split" and "nobody verifies after the merge"[5].

These criticisms are correct, and they happen to mark out the swarm's real bottleneck and its real barrier to entry: whoever makes splitting and merging solid is the one who realizes the gains this architecture promises. What passes between cells must be verified bounded summaries — about 550 tokens, and not growing with scale — not agents copying each other's answers. The latter is hallucinatory multi-agent work: it looks busy, but it has decomposed nothing.

Two Phase Transitions: The First Layer Is Already Pinned Down

"Cheaper" cannot be left as an intuition. We make the case with two reproducible experiments.

Experiment one (hitting the wall): a single model muscling through a long context pays a cost that grows quadratically with the number of subtasks N; swarm divide-and-conquer pays a cost that grows linearly. By N*=40 subtasks (a single call of roughly 208K tokens), the job exceeds the 200K context window and the single model fails outright with a hard 400 error — past that point only divide-and-conquer can run at all. And even by the attention-quadratic accounting, at N=256 a single long context costs roughly 49.34 million tokens against divide-and-conquer's roughly 1.04 million — a 48x difference.

Experiment two (accuracy collapse): pack more and more subtasks that require genuine reasoning into one model's single context (real model, GSM8K math problems, temperature 0) and accuracy still sits at 0.92 at N=64, collapses from N=96 onward, drops below 0.5 at N*≈128, and is down to 0.28 at N=160; split the same tasks apart, one independent context per subtask, and accuracy stays above 0.96 the whole way, dead flat. The mechanism is visible in the data: inside a long, crowded generation the single model loses the thread — even when you can fit everything into the context, the model cannot use it well.

Both curves share the same shape, and that shape matters: they are phase transitions. Water at 99°C is still water; at 100°C it suddenly boils. Cross N*=40 and the single model flips from finishing the job to hitting the wall and failing it; cross N*≈128 and a single context flips from keeping up to losing the thread. "Split or don't split" is not a smooth continuous judgment — it is whether you have stepped over a critical point. The honest boundary also has to be drawn: the collapse is not caused by "many tokens" — simple arithmetic and retrieval tasks stay perfectly accurate stuffed into tens of thousands of tokens; the accuracy collapse appears only when many items each require genuine reasoning and are forced into one bounded generation together. So don't split because the context is long; split when the task really is decomposable and there is enough of it.

Intelligence Is a Form of Efficiency: From Negative Entropy to Tokens

The two experiments above land on one conclusion: cheaper. But pull the camera back and you find that saving is itself the definition of intelligence.

In What Is Life? Schrödinger said that life "feeds on negative entropy." As a metaphor it is stirring; as physics it is imprecise — life has never violated the second law of thermodynamics. The real ledger reads like this: life takes in low-entropy matter and energy, dumps high-entropy waste and heat back into the environment, its own entropy decreases (ΔS(life) < 0), the environment's entropy increases (ΔS(environment) > 0), and the total is always positive (ΔS(total) > 0). Life is not a container of negative entropy; it is an entropy pump: it buys local order by accelerating the entropy production of the whole universe[11].

And what really matters is not "low entropy" — it is being far from equilibrium. Prigogine's theory of dissipative structures says it plainly: order is sustained by gradients — the chemical potential difference between ATP and ADP, the ion concentration difference across a cell membrane, the proton gradient in a mitochondrion, the radiative flux difference between the sun and deep space. A gradient is free energy available to do work. Stop that flow, the gradient disappears, and the structure collapses immediately. That is death[12].

But order has levels. A crystal is highly ordered and does nothing at all. Life can sustain and replicate itself. Intelligence does a third thing — it learns, predicts, plans, and creates new order, which is to say it actively reduces future uncertainty. What distinguishes these three levels is not the total amount of order but efficiency.

Hence a definition:

Intelligence is the efficiency with which life (or an agent) uses finite free energy to sustain and create ordered structure over the long run.

Written as a crude but instructive proportionality:

The "information" in the numerator is not a count of Shannon bits — a brick and a textbook can hold roughly the same number of bits, but the information usable for prediction, decision, and adaptation differs by orders of magnitude; order carries semantics (brick < textbook < model weights < DNA). This direction resonates naturally with Friston's free energy principle: an agent's behavior can be characterized uniformly as minimizing its own prediction error about the world[13]. And what keeps this machine running is four verbs — accumulate (acquire order), compress (turn order into a shorter representation), inherit (hand the compressed order to the next generation), and exploit (trade it back for more free energy). Life's medium of inheritance is DNA; human civilization's is language and writing; today it is code and model weights.

That brings the 48x back to the point. In engineering terms the definition converts directly into a computable ratio — call it AIR (Agent Intelligence Ratio):

The "capability" in the numerator is a composite of success rate, robustness, generalization, and novelty. This metric sits far closer to the essence of intelligence than parameter counts or leaderboard scores — Intelligence per Compute. That gives a second statement:

If an agent achieves the same result with fewer tokens, that counts as higher reasoning efficiency.

That statement comes with a boundary that must be drawn without wobble: it holds only when task, success rate, robustness, and generalization are all held fixed, and the gain comes from better internal representations. If the drop in tokens comes from data leakage, leaderboard overfitting, or a quiet sacrifice of robustness, that is not an efficiency gain — it is metric gaming.

And the swarm's strategy genes are exactly this compressor made concrete. If a gene preserves capability while cutting tokens by thirty percent, what it has done is policy compression: folding "observe → reason → reason → reason → reason → act" into "observe → act." This is the same thing as chunking in neuroscience, and the same thing as a senior programmer who glances at an error message and knows where the problem is — a long reasoning chain compressed into short-path intuition. Memory, skills, reflection, and genes in the swarm are all different stations on this compressor; the three rules R1/R2/R3 are what let the fruits of compression be inherited and spread through the population.

So the third statement joins the first two:

Improving intelligence is, at bottom, continually compressing the compute, energy, and time cost required to reach a given capability, while holding or raising that capability.

This is also why that 48x is not just a cheaper invoice: it is the same capability, produced with less free energy.

Three Layers of Claim and Three Generations of Topology: From Crystal to Life

Let us draw the boundary clearly. The swarm's complete claim comes in three layers, each harder than the one beneath it:

① Cost savings (proven) — trade expensive quadratic attention for cheap communication overhead; the two experiments above have already landed this.

② Emergence (the argument in progress) — a group of models that divides labor and collaborates outperforms a single model at equivalent compute.

③ ASI (the vision) — approaching superintelligence by way of the swarm.

Today the third layer is a direction, not a conclusion; a pragmatic judgment should rest on ① being proven and on an independent read of ②.

Mapping onto those three layers is a three-generation roadmap of topologies: 1.0 parallel divide-and-conquer (everyone works alone, results are aggregated — deliverable today); 2.0 mesh topology (cells pass verified strategies sideways and calibrate against one another, moving from mere parallelism to genuine collaboration); 3.0 spatial / cross-disciplinary topology (composing mathematical, physical, biological, and engineering capability inside a single spatial structure, so that cross-disciplinary new solutions emerge).

Why must this move toward structure, instead of simply laying the 1.0 ring out wider? Wolfram's four-class taxonomy of complex systems has the answer: a perfectly symmetric, uniform structure in which everyone runs the same parameters either collapses into a dead homogeneous state (Class 1, like pure steel) or locks into a neat repeating pattern (Class 2, like a crystal) — neither one ever grows the durable division of labor where "this cell specializes in mathematics, that one in biology"[3].

What actually lets organization emerge is Class 4: a mixture of order and randomness, wedged into the narrow seam known as the "edge of chaos" — complex crystals, spiral galaxies, and life and thought itself all belong to this class[3]. A crystal, however large it grows, is still a crystal; it will never turn itself into life. To grow a division of labor, the structure itself must be non-uniform. The modular topologies of 2.0 and 3.0 are, at bottom, a way of pushing the system out of its cage of symmetry and toward the edge of chaos. And this judgment can be turned into a falsifiable engineering metric: self-organized criticality (SOC) theory predicts that in a healthy critical system the sizes of propagating perturbations follow a power law, with an exponent falling between 1.5–3.0[6] — fit the swarm with a power-law gauge on "avalanche size," and "sitting at the edge of chaos" turns from a slogan into a measurable proposition.

From Drawing Topology Diagrams to Designing the Interaction Kernel: The Echo of a Century-Old Problem

The swarm's deeper methodology echoes, unexpectedly, a problem posed in 1900.

Hilbert's sixth problem asks for macroscopic physical laws to be derived rigorously from the axioms of microscopic mechanics. In 2025, Yu Deng, Zaher Hani, and Xiao Ma closed the critical link in that chain: starting from pairwise collisions of Newtonian hard-sphere particles, passing through the Boltzmann kinetic equation, they rigorously derived the Navier–Stokes fluid equations[7]. Micro is particles and collisions, meso is distributions and their evolution, macro is flow fields and pressure — three scales, one rigorous bridge.

For agent systems the lesson is paradigm-level: a multi-agent network should not be seen as a static architecture diagram, but as a kinetic system generated over time by a great many local "collisions." A single cell is a particle; the messages, mutual critiques, and experience exchanges between cells are collisions; the interaction rules are the collision kernel; and task density, congestion pressure, and opinion temperature are the macroscopic information fluid. The design question therefore undergoes a deep inversion — the question is no longer "tree or mesh," but "what kind of interaction kernel generates a stable, high-throughput, low-redundancy macroscopic collaboration network under sparse scaling." Macroscopic topology is not drawn; it is the evolutionary product of local rules, to be observed, evaluated, and controlled.

Hidden inside this correspondence are two laws that are life-or-death for the swarm.

The first is Boltzmann-Grad scaling: the kinetic equation holds only if the average collision rate is held constant as the particle count goes to infinity. Translated into engineering terms — as the system scales out, the average communication rate per cell must stay constant-order, and fully connected broadcast, which pushes message volume toward O(N²), is never permitted. This is precisely the mathematical pedigree of the swarm's "bounded summary" design.

The second is propagation of chaos: in the sparse limit, particles do collide, yet the many-particle distribution still factorizes approximately into a product of single-particle distributions — individuals remain statistically independent. Carried over to agent networks, this lands like a hammer: many multi-agent systems have several agents on the surface, but in fact those agents share the same prompt, the same retrieval results, the same intermediate summary, and their outputs are highly correlated. Adding agents then buys no linear gain in quality; it is repeated sampling of one and the same bias. Preserving independence must become a first-class metric of topology design.

False Consensus: Collective Intelligence's Most Insidious Enemy

The hardest obstacle Boltzmann's derivation runs into on a periodic domain is recollision: particles meet again and again, and their collision histories tangle into loops that resist untangling. The swarm is haunted by exactly the same ghost — A generates a hypothesis, B critiques A, C summarizes B's critique, and then A reads C's summary and takes it as independent corroboration. One piece of information circles back under three different names, five agents "unanimously agree," and in reality there was only ever one source. This is false consensus: it looks like collective wisdom, and it is an echo chamber.

The antidote is to upgrade the "current communication graph" into an "interaction history graph": every message, every tool call, every merged conclusion records its parent nodes, forming a timestamped causal lineage. With lineage in hand you can detect cycles, down-weight information that has already circled back, and impose a cooldown on repeated mutual evaluation between the same pair of agents — and at final merge time, report the number of independent sources behind a conclusion, not the number of participating agents.

This discipline shares a root with the lesson of Schelling's segregation model: the micro-rules of a self-organizing system emerge into macro-level harms you never intended — individuals want nothing more than "not too many unlike me next door," and the macro outcome is complete segregation[8]. The swarm's work-claim rules will just as quietly starve some fraction of its cells; the swarm's mutual-evaluation rules will just as quietly manufacture an echo chamber. What you don't audit, you can't see. Designing through emergence presupposes bolting an observable, falsifiable instrument panel onto the emergence.

The Verification Bottleneck: When Answers Get Cheap, What Gets Expensive

Suppose the swarm really is running — thousands upon thousands of cells producing answers, code, and proofs in parallel. What happens next?

Terence Tao's ICM 2026 lecture offers a remarkably penetrating preview[9]. He assumes AI can do a substantial share of research-level mathematics at reasonable cost, then asks: what becomes of the mathematical community? The answer is that mathematics moves from "proof scarcity" to "proof abundance" — and congestion shows up, in order, at verification, readable exposition, peer review, and the settling of results into final form. His knowledge lifecycle model deserves to be on the wall of everyone building collective intelligence: a proof becomes knowledge only after passing through generation → verification → exposition → community acceptance → digestion → canonization. Speeding up generation at the head of the chain a hundredfold does not speed up the chain — effective throughput ≈ min(generation, verification, exposition, acceptance, digestion), set by the slowest link.

This is the deeper reason the swarm architecture has to make provenance and verification labeling a foundation rather than an afterthought plugin. When the marginal cost of an answer approaches zero, verification, provenance, and digestion become the new scarce resources. So the swarm makes "who to trust" an always-on foundation: every adopted experience is labeled by whether its score is self-reported or independently verified, every conclusion is labeled with its number of independent sources, and the over-claim gap is measured continuously; on top of that, an independent merge-verification action is built in as an opt-in first-class capability that takes over gene scoring once enabled — this is not engineering fussiness, it is the survival law of an age of proof abundance.

Tao's other warning applies just as well: Goodhart's law says that when a measure becomes a target, it stops being a good measure. The swarm's fitness scores, adoption rates, and problems-solved counts are all proxy metrics; over-optimize against a single number and the swarm grows into a monster that scores high and can do nothing. Measuring emergence requires continuous metrics plus ablation studies — the literature has already shown that many so-called "emergent abilities" are an artifact of poorly chosen metrics[10].

The Structural Bet: A Corroboration from Investing

Curiously, the investment theory of complex systems offers an independent corroboration of this route.

In a power-law-dominated market, the overwhelming majority of returns come from a tiny handful of right-tail winners. The rational strategy is not to predict precisely which single point will win — that is very nearly impossible — but to identify the structures value flows through, occupy the key nodes, keep exposure broad enough, and make sure you survive long enough for the logic to pay off.

Translate that language onto AI's technical routes: a single super-model puts every chip on one position; the swarm makes intelligence into a structure. It does not predict which cell will produce the brilliant solution; it guarantees that the system stays present across the enormous solution space that combinatorial explosion opens up, and lets the verification mechanism capture the right tail. Markets beat central planning over the long run not because some trader is smarter, but because the price mechanism distributes an immense amount of local computation out to the participants. If the swarm has a decisive edge over the single big brain, it will be that same one: the structural advantage of distributed computational structure over centralized computational structure.

The humility of prediction applies to us as well. The direction can be judged (the quadratic wall is mathematics; the payoff of divide-and-conquer is proven), the magnitude is harder, the timing is close to unpredictable — and "can emergence be delivered" is a genuinely open question. Systems like this are most likely computationally irreducible: no shortcut formula can compute in advance whether a group of models will grow a capability no single model has. You can only run it and measure it with ablation studies. That is not a disclaimer. That is evidence of understanding the problem deeply enough.

Conclusion: Cultivating a Garden

In the end, this is a difference of temperament between two ways of building things.

"Make the model bigger" is building a tower: you fill in the blueprint first, and the ceiling on its capability is whatever you drew into that blueprint. The swarm is something else: design one building block, one set of local rules, one evolutionary loop — then let go and let the outcome run itself out.

You do not invent what the swarm will become; you invent only the rules it obeys, and then go discover the consequences those rules produce — and if you don't like them, you change the rules and iterate again. This is closer to growing a plant than to putting up a house. Whoever invented chess did not have to invent every opening and every mating pattern; those emerged from the rules. That has always been the payoff formula of designing through emergence: you design a small part, and you harvest far more than you drew into the blueprint by hand.

The price is control. You cannot both permit unanticipated outcomes and decide in advance what those outcomes will be; pray for rain and you deal with the mud. So the whole discipline of this path condenses into three things: make the splitting and the merging solid, put a falsifiable instrument panel on emergence, and post heavy defenses at the verification bottleneck. The rest you hand over to combinatorial explosion.

What a single brain runs into is a quadratic wall; a hundred billion neurons already proved there is another road. This time we swap the neurons for cells that think, the synapses for verified experience, and compress four billion years of evolution into a loop measured in hours. And there has only ever been one yardstick for how well this garden is growing: does the same capability now cost less free energy? Not thinking more, but doing less and less ineffective thinking.

References

[1] Hayek, F. A. (1945). The Use of Knowledge in Society. American Economic Review, 35(4), 519–530.

[2] Emergent Garden, "Emergent Complexity," YouTube, Nov. 22, 2025. [Online]. Available: https://www.youtube.com/watch?v=0HqUYpGQIfs.

[3] S. Wolfram, A New Kind of Science. Champaign, IL, USA: Wolfram Media, 2002.

[4] Grassé, P.-P. (1959). La reconstruction du nid et les coordinations interindividuelles chez Bellicositermes natalensis et Cubitermes sp. La théorie de la stigmergie: Essai d'interprétation du comportement des termites constructeurs. Insectes Sociaux, 6, 41–80.

[5] Cemri, M., Pan, M. Z., Yang, S., et al. (2025). Why do multi-agent LLM systems fail? Advances in Neural Information Processing Systems, 38. arXiv:2503.13657.

[6] Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of 1/f noise. Physical Review Letters, 59(4), 381–384.

[7] Deng, Y., Hani, Z., & Ma, X. (2025). Hilbert's Sixth Problem: Derivation of Fluid Equations via Boltzmann's Kinetic Theory. arXiv:2503.01800.

[8] Schelling, T. C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1(2), 143–186.

[9] Tao, T. (2026, July 24). Mathematics in the age of AI [Public lecture slides]. International Congress of Mathematicians 2026.

[10] Schaeffer, R., Miranda, B., & Koyejo, S. (2023). Are Emergent Abilities of Large Language Models a Mirage? NeurIPS 2023.

[11] Schrödinger, E. (1944). What Is Life? Cambridge University Press.

[12] Prigogine, I., & Stengers, I. (1984). Order Out of Chaos: Man's New Dialogue with Nature. Bantam Books.

[13] Friston, K. (2010). The free-energy principle: a unified brain theory? Nature Reviews Neuroscience, 11(2), 127–138.