Local Hamiltonian

Sum of windowed Hamiltonians with same window length; a key construct introduced in the paper to model local interactions on graphs

Neighborhood — ranked by edge-count

framework

AR(ω) model
associated_with
Stochastic process model predicting next token from a context window of length ω; mapped to local Hamiltonian
Windowed Hamiltonian
implements
Core technical concept: a Hamiltonian where spin-spin interactions are defined only within finite windows ω, enabling generic analysis across diverse lattices
graph Hamiltonian
extends
Hamiltonian constructed from adjacency matrix and coupling strengths on a graph

community

finding

concept

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.

LOCAL SYMMETRYconcept0.782
One of Alexander's fifteen properties; appears in birthday table, handshake, and namaste examples
Local Symmetries Transformationconcept0.751
A structure-preserving transformation: introducing symmetries within a center, not globally, to strengthen local order.
Local Symmetriesconcept0.741
The property that living wholes contain many interlocking and overlapping local symmetries rather than overall symmetry; local symmetries act as glue holding space together, and their number predicts cognitive coherence
Localist Representationsconcept0.731
Prior assumption that high-level variables align with disjoint groups of neurons in standard basis; contrasted with distributed representations.
Local-Symmetry Transformationconcept0.718
A transformation that strengthens a center by giving it an internal axis of symmetry, local to the center.
A unique local Hamiltonian with window length ω can be associated to any AR(ω) model (Theorem 3)finding0.714
Mapping autoregressive models to spin systems
locally interacting systemsconcept0.711
Systems on graph vertices with pairwise edge-prescribed interactions
Local learning rulemethod0.710
Learning rule where change in a parameter at point x,t depends only on system state at same or nearby spacetime points, without requiring global cost function computation