Boltzmann RBM Credit Risk Model: 1,000 synthetic borrowers scored by energy state, showing default probability and credit tier using Boltzmann distribution
Total borrowers
1,000
Overall default rate
—
Average energy (Ē)
—
High-risk count
—
Each dot = one borrower. X = debt-to-income ratio, Y = payment history. The bottom-right corner is the "danger zone" — high DTI + poor payment history → high Boltzmann energy → high default risk.
Prime (A)Near-prime (B)Subprime (C)High-risk (D)
Bars = borrower count per energy bin (left axis). Orange line = Boltzmann P(default) curve (right axis) — a sigmoid rising steeply around equilibrium energy E₀ = 4.0. The "phase transition" is the steep zone where safe borrowers become risky.
Default rates rise sharply from near-zero in Prime to severe in High-risk — the Boltzmann model captures this non-linear jump that linear credit scores miss.
Borrowers per tier
Observed default rate per tier (%)
Borrower inputs
Debt-to-income ratio
0.35
Payment history score
0.80
Employment stability
0.85
Energy formula:
E = 2.5 × DTI + 2.0 × (1 − Pay) + 1.5 × (1 − Emp)
P(default) = sigmoid( β × (E − E₀) )
where β = 3.0, E₀ = 4.0