වචන ටැක්සි: Structural Homology, Not Analogy

Saturday, February 7, 2026

Structural Homology, Not Analogy

From Societies of Thought to Eigenmodes of Reasoning

Recent work on reasoning models has revealed something striking: advanced language models do not merely “think longer,” but spontaneously organize internal debates—what has been called societies of thought. These internal processes involve questioning, role differentiation, conflict, and reconciliation, and they causally improve reasoning performance, rather than merely accompanying it.
(Blaise Agüera y Arcas et al., “Reasoning Models Generate Societies of Thought”, arXiv)

This finding is important. But it also raises a familiar risk: the temptation to read emergent coherence as evidence of inner subjectivity or consciousness.

This article takes a different route. It argues that what we are observing is not an analogy to human minds, but a structural homology with a much older mathematical and cognitive logic—one that explains why coherence emerges without requiring consciousness to be present.

What the “Societies of Thought” paper actually shows

The paper demonstrates three key points:

Internal multi-agent discourse emerges spontaneously in reasoning models trained only for accuracy—not through prompting tricks or explicit scaffolding.
Distinct internal roles and conversational behaviors arise, including questioning, critique, conflict, and reconciliation.
This internal organization causally drives reasoning performance, rather than merely correlating with it.

Notably, the paper does not claim:

consciousness,
phenomenal awareness,
moral agency,
or subjective experience.

Its claims are functional and structural, not ontological.

This distinction matters.

Why the “thinking vs. not thinking” debate misses the point

Some responses assert that “LLMs don’t think, they merely do associative pattern matching.” Others counter that thinking need not resemble human cognition to be real.

But this debate prematurely collapses the problem into a binary: thinking versus mimicry. The paper itself does not require either position. What it shows is that reasoning quality can emerge from structured internal plurality, regardless of how one defines thinking.

A more productive question is not whether these systems think, but what kind of structure makes reasoning possible at all.

A structural lens: eigenmodes, not inner voices

Across many domains—structural engineering, wave mechanics, quantum physics, and neural networks—systems under repeated transformation tend to organize themselves along dominant modes.

Mathematically, this is captured by the eigenvalue relation:

\mathbf{T}\mathbf{v} = \lambda \mathbf{v}

Here, a transformation $\mathbf{T}$ acts on a direction $\mathbf{v}$ and reproduces it up to scaling. Such directions—eigenvectors—are not meanings or intentions. They are directions of stability.

In neural networks, similar structures arise implicitly in:

attention matrices,
interaction graphs,
covariance and similarity operators,
and optimization landscapes (e.g., Hessians of loss functions).

They are not “ideas” or “voices.”
They are stable directions of interaction.

This is the missing structural bridge.

From internal debates to collective eigenmodes

The societies of thought described in the paper can be understood structurally as follows:

Each internal agent participates in a network of influence.
Repeated interaction amplifies certain conversational trajectories.
Other trajectories decay.
Over time, the system converges toward dominant patterns of internal coordination.

In mathematical terms, repeated interaction performs a process analogous to iterated application of an interaction operator:

\mathbf{x}_{t+1} = \mathbf{A}\mathbf{x}_t

where $\mathbf{A}$ represents the internal influence structure. As $t$ increases, behavior becomes dominated by the leading eigenmodes of $\mathbf{A}$ .

This is not accidental. It is the same phenomenon that produces:

dominant vibration modes in buildings,
dominant flow patterns in networks,
dominant components in spectral analysis.

In this sense, societies of thought can be understood as social eigenmodes—stable patterns of internal discourse that survive repeated transformation.

This interpretation does not contradict the paper.
It explains its mechanism.

Structural homology, not analogy

At this point, a crucial distinction must be made.

An analogy would say:

“These internal debates are like human consciousness.”

A structural homology says something far more precise:

“Both human collective reasoning and machine reasoning stabilize through dominant relational patterns under constraint.”

The homology lies in form, not in experience.

No inner subject is required for stabilization to occur.

Why coherence is mistaken for subjectivity

As internal societies become more structured:

outputs grow more coherent,
behavior appears more intentional,
attribution of inner life becomes tempting.

But stability is not awareness.
Consistency is not experience.

The paper shows how coherence emerges.
Structural analysis explains why it looks compelling.

The remainder: what stability excludes

Every eigenmode leaves something out.

Minor modes are suppressed.
Alternative trajectories decay.
Residual variance remains unaccounted for.

In reasoning models, this remainder appears as:

brittleness,
hallucinations,
failures outside narrow regimes.

This is not a flaw in the paper’s findings—it is a structural necessity. Where coherence strengthens, exclusion increases.

Why this matters for AI governance and design

If internal societies of thought improve reasoning, they will be increasingly deployed. But richer internal discourse does not grant:

authority,
legitimacy,
or permission to act.

Better reasoning increases, rather than eliminates, the need for boundaries.

This aligns with the paper’s focus on designing internal societies, while adding a necessary constraint: coherence must not be mistaken for mandate.

What the paper enables—and what it does not claim

The Societies of Thought paper makes a genuine advance. It shows that reasoning can emerge from structured internal plurality without central control.

What it does not require—and does not claim—is consciousness.

Seen through the lens of structural homology, the paper fits into a longer intellectual lineage: systems stabilize through dominant modes. What looks like thought is often organization under constraint.

Recognizing this does not diminish the achievement.
It makes it legible—and keeps us honest about where structure ends and projection begins.