Final coverage
1.00%
The selected final models for both ETH and BTC achieve the target 1% realized tail-hit rate over the full out-of-sample evaluation while clearing Kupiec and Christoffersen coverage tests across the reported sub-periods.
Quantitative Finance · Machine Learning
Deep Sparse Canonical Schrödinger Networks: Learning Continuous Liquidity Manifolds from High-Dimensional Market Microstructure
A liquidity-driven, physics-constrained Value-at-Risk architecture built from public Uniswap V3 microstructure and cross-chain capital-flow data.
Working Paper · Forthcoming
Full Article ↗The paper asks whether the spatial structure of decentralized-market liquidity can be converted into an auditable tail-risk model rather than treated as a descriptive market statistic. It uses the fact that Uniswap V3 exposes standing liquidity across the price grid, then combines that geometry with cross-chain stablecoin and DeFi capital flows to learn a conditional risk distribution for Ethereum and Bitcoin.
Research question
Can directly observable liquidity geometry from a decentralized exchange be transformed into a Value-at-Risk model that passes formal coverage tests across assets and market regimes using only real, permissionless data?
Method
The architecture couples a 50-variable systemic-flow manifold to a 100-bin liquidity manifold through dynamic deep sparse canonical correlation, then learns a Schrödinger-constrained conditional density with a SIREN network. A separate online calibration layer uses adaptive conformal and power-calibration mechanisms so statistical coverage can be tested independently of the physics layer.
Main findings
Regulatory backtest
Green zone
Over the most recent 250 out-of-sample days, ETH records 3 violations and BTC 2, placing both final models in the Basel traffic-light Green zone.
Liquidity sparsity
50 / 100
For BTC, half of the liquidity-manifold features can be pruned at the best-fit checkpoint without degrading the information criterion, while ETH shows a genuine sparsity-versus-fit trade-off.
Full-OOS Kupiec
0.669 / 0.951
The final ETH and BTC models reach full-out-of-sample Kupiec p-values of 0.6691 and 0.9508 respectively, after the paper's diagnosed online recalibration sequence.
Why it matters
The central result is not that a physics-inspired model replaces statistical calibration. It is that the two can be separated and audited independently: the liquidity and Schrödinger layers learn a rich conditional density, while the online statistical layer guarantees that the reported tail behaves as claimed. The asset-specific sparsity result also shows that Bitcoin and Ethereum expose materially different liquidity-risk structures under one shared architecture.
Full research record
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