Belief Propagation — Cavity Method
BP on sparse random Ising graph: cavity messages h_{i→j}, magnetization, convergence
Graph & Model
Nodes N:
30
Avg degree c:
3.0
Coupling J:
0.50
External field h:
0.00
Temperature β⁻¹:
1.00
▶ Run BP
↺ New Graph
Iteration:
0
Max Δh:
—
Converged:
No
Avg |magnetization|:
—
Free energy:
—
Cavity/BP equations:
h_{i→j} = h + Σ_{k∈∂i\j} atanh(tanh(βJ)·tanh(βh_{k→i}))
m_i = tanh(βh_i) where h_i = h + Σ_{k∈∂i} atanh(tanh(βJ)·tanh(βh_{k→i}))
Edges colored by cavity field magnitude.