> The Crowding Paradox: High-Density States Predict Systemic Risk

Financial ML 高级 2026-04-01 06:41 2026-04-01
#energy-based models #systemic risk #anomaly detection #QUBO #quantum computing #density estimation

Systemic financial risk is predicted by high-density market states — the opposite of anomaly detection. The Fragility Score (density/variance) achieves AUROC 0.931-0.954, far above best anomaly baseline at 0.802. QUBO subset selection with learned lambda achieves 99.7% of oracle quality.

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The Crowding Paradox

Core Insight

Standard anomaly detection assumes rare events are dangerous. Financial markets show the opposite: systemic risk peaks at high-density states when many participants hold similar positions.

\[\text{Fragility Score}(x) = \frac{p(x)}{\text{Var}(\Delta x | x)}\]

Density-variance anticorrelation: \(r = -0.94\) in high-density deciles.

Benchmark Results

Horizon AUROC (FS) Best Anomaly Baseline Gap
5-day 0.931 0.802 +12.9pp
10-day 0.941 0.802 +13.9pp
20-day 0.954 0.802 +15.2pp

Gap widens at longer horizons — crowding is slow-building, not a flash event.

Domain Boundaries

Domain Density Ratio Finding
Financial markets 1.96x Strong crowding paradox
Traffic networks 1.14x Moderate effect
Recommendation systems 0.59x Inverted — high density = popular items, lower risk

The paradox is domain-specific: it arises when high-density creates correlated exit pressure.

Q-Flow: QUBO Subset Selection

Non-submodular optimization (proven): greedy has no polynomial-time guarantee.

Solver Scale Diversity vs Greedy Cost
Simulated Annealing 15-200 +24% to +66% ~44ms-56s
QAOA (Rigetti Ankaa-3) 15-20 Competitive with SA $0.75/task

Learned lambda policy: MLP predicts optimal penalty weight per instance, achieving 99.7% of oracle grid-search quality at zero extra compute.

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