# Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets

arXiv: https://arxiv.org/abs/2601.07687 · HTML: https://mlsanity.com/paper/2601.07687/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 4 of 4)

- [A whitening approach to probabilistic canonical correlation analysis for omics data integration](https://mlsanity.com/paper/1802.03490/) (2018)
- [Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimisation](https://mlsanity.com/paper/2112.07521/) (2021)
- [End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning](https://mlsanity.com/paper/2507.01918/) (2025)
- [Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach](https://mlsanity.com/paper/2508.10776/) (2025)

## Abstract (arXiv)

Recent advances in nonlinear shrinkage yield asymptotically optimal cleaners for large covariance matrices and have been extended to empirical cross-covariances via singular-value shrinkage. However, these approaches rely on stationarity and bounded-spectrum assumptions that are violated by real equity returns, which exhibit dependence drift and macroscopic common modes. We propose a physics-informed neural estimator that parameterizes the cleaned cross-covariance matrix in the empirical singular-vector basis and learns a nonlinear map from empirical singular values and marginal projections to cleaned singular values, recovering the cleaning performances of the analytical solution as a limiting case. On U.S. equity data, the learned correction not only improves out-of-sample cross-covariance prediction but also translates these statistical gains into better tracking-error minimization for portfolio replication. Furthermore, it remains stable in regimes where the analytical cross-covariance estimation deteriorates with universe size, suggesting an interpolation between sample-size denoising and a learned forecast correction under non-stationary dependence.