Separated Signal Libraries: Packing, Saturation, and Joint Spectral Limits

Battle Count: 59

The paper directly addresses the construction and analysis of large signal libraries for cross-sectional return prediction, which is central to quantitative trading. It provides rigorous theoretical foundations for understanding when equally weighted signal ensembles align with principal components, how pairwise correlation constraints affect ensemble properties, and what admission rules (positive IC, IC margins) guarantee target alignment. The motivating example of 3,000 signals over 20 assets is directly relevant to practical quant research. However, the paper is purely theoretical with no empirical validation on market data, and its results describe geometric possibilities rather than guaranteed outcomes for real signal selection processes.

The paper involves advanced mathematics including spherical geometry on product manifolds, packing theory on rectifiable sets, coding theory (Gilbert-Varshamov), exponential tilting and large deviations, Davis-Kahan perturbation theory, and spectral analysis of structured matrices. Implementing the theoretical results requires careful handling of high-dimensional geometry, numerical integration on spheres, and spectral computations. The practical application to signal library construction requires specifying admission rules, computing pairwise correlations over history, and tracking spectral properties. The source bundle provides computational tools but the underlying mathematics is highly specialized.

All results are proved analytically and checked numerically with synthetic data. A source bundle is supplied as ancillary files with the arXiv version, containing packing counts, moment formulas, finite codes, margin spectra, exact quadrature, finite-history gap checks, tilted convolution with grid refinement, fixed-margin correction checks, central-limit regime simulations, and perturbation tests. No market data is used. However, the paper has not undergone independent human peer review.