Free-energy scaling under domain-wall formation

Key analytical technique used across three model systems to determine constraints on long-range order.

Neighborhood — ranked by edge-count

Frameworks (3)

framework

Autoregressive models
implements
Second model system studied; used to show why flat autoregressive LLMs struggle with long-range coherence.
Potts model
implements
One of three model systems studied to analyze free-energy scaling and domain-wall formation in self-organizing systems.
Hierarchical networks
implements
Third model system studied; shown to support complex pattern formation unlike flat architectures.

Concepts (3)

concept

free energy
associated_with
Thermodynamic potential ΔF = ΔE − TΔS; domain walls form if ΔF < 0
domain wall
associated_with
Boundary between regions of different order; its free-energy cost determines phase stability
Domain-wall formation
studies
Critical phenomenon in determining whether systems can maintain ordered target states; analyzed via free-energy scaling.

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 formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.864
Core result demonstrating topological constraints on self-organization
energy scalingconcept0.763
How the energy gain ΔE scales with perimeter length P; used to assess ordered phase existence
For one-dimensional local Hamiltonian with m>1 stored patterns at non-zero temperature, domain wall formation is thermodynamically favourable (Theorem 2)finding0.761
No ordered phase in 1D with multiple stored patterns
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 learningclaim0.755
Differentiation of the thesis from Friston's FEP to avoid the rock problem
Gradient Descent on Free Energymethod0.746
Optimization procedure for simultaneously updating action selection and perception; uses step size ζ (default 4).
The expected free energy subsumes many existing constructs in science and engineering.claim0.739
Unifying nature of expected free energy claimed in Section 2 and 7.
Expected free energy scores each possible course of action in terms of its ability to reach the range of preferred states of being.claim0.736
Definitional claim from Section 2.
Expected Free Energy Minimizationmethod0.731
Minimizing expected free energy for planning, decision-making, and action selection.