finding

active

finding:free-energy-scaling-under-domain-wall-formation-in-potts-autoregressive-and-hierarchical-networks-shows-that-combinatorics-of-interactions-on-a-graph-prevent-or-allow-spontaneous-ordering

Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.

Core result demonstrating topological constraints on self-organization

Source paper

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Topological constraints on self-organization in locally interacting systems

(2026) · Francesco Sacco · Dalton Sakthivadivel · Michael Levin

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Claims (2)

claim

All intelligence is collective intelligence, in the sense that it is made of parts that must align with respect to system-level goals.
supports
Central thesis operationalized via free-energy scaling; frames intelligence as alignment problem across multiple scales.
Multiscale systems like those prevalent in biology are capable of organizing into complex patterns, whereas rudimentary language models are challenged by long sequences of outputs.
supports
Conclusion about why biology organizes complexity well and flat LLMs do not

Communities (4)

community

Causal emergence in biological systems
members_of
Examines how macro-scale causal power exceeds micro-scale in living and learning systems.
Hierarchical structure and multiscale coherence in physical systems
members_of
How graph topology and hierarchical interaction patterns enable or prevent phase transitions and ordered states, from statistical mechanics to biological organization.
Hierarchical network ordering & thermodynamics
members_of
Statistical mechanics of clique-structured graphs linking domain walls, free energy, and biological multiscale coherence.
Combinatorial constraints on emergent ordering in networks
members_of
Explores how interaction graph structure and domain-wall formation determine whether systems spontaneously organize into complex patterns across scales.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Free-energy scaling under domain-wall formationmethod0.864
Key analytical technique used across three model systems to determine constraints on long-range order.
For one-dimensional local Hamiltonian with m>1 stored patterns at non-zero temperature, domain wall formation is thermodynamically favourable (Theorem 2)finding0.795
No ordered phase in 1D with multiple stored patterns
Multiscale systems in biology can organize into complex patterns whereas flat autoregressive architectures cannot.hypothesis0.794
Key hypothesis: topological/architectural properties determine capacity for long-range self-organization.
The results generalise readily to non-equilibrium systems where scaling relationships remain similar (e.g., dynamic or localised scaling).claim0.794
Claim about broader applicability of the scaling argument
In hierarchical systems with independent cliques, there exist parameter regimes where individual cliques maintain uniform magnetisation while others flip.finding0.788
Shows how hierarchical topology enables local order within global flexibility; explains biological multiscale organization
Spontaneous ordering in networks of interacting systems can be viewed as a form of self-organization, modelling neural and basal forms of cognition.claim0.787
Claim linking physical self-organization to cognition
The Free Energy Principle applies to all self-organizing systems including rocks, making it too broad; the present thesis restricts consciousness to signed evaluation in the service of learningclaim0.786
Differentiation of the thesis from Friston's FEP to avoid the rock problem
Hierarchical structure in interaction topology enables complex multiscale patterns that cannot exist in flat networks.claim0.782
Explains why biological systems achieve organization across scales while language models struggle; grounds in free energy scaling

Cross-corpus bridges (2)

same_concept_as · Nomic cosine

External markdown files that talk about the same concept as this entity.

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Free Energy Minimizationframeworks/free-energy-minimization.md0.792
aboutblank_kb
Free-Energy Approach To Pattern Regulationframeworks/free-energy-approach-to-pattern-regulation.md0.790