Wasserstein-Barycentric Interaction Fields for Spatial Factor Models: Evidence from Language-Model Representations

Battle Count: 51

The paper is primarily a methodological contribution to spatial asset pricing and factor models rather than a direct trading strategy paper. However, it has meaningful relevance to quantitative trading: (1) it provides a novel way to construct peer/interaction matrices from text embeddings that could inform cross-sectional return prediction; (2) the spatial autoregression framework directly models return dependence structure useful for portfolio construction; (3) the barycentric field identifies which firms jointly represent a target's information footprint, relevant for pairs trading and relative value strategies; (4) the attenuation result bounds how much characteristic-implied dispersion survives peer adjustment, relevant for risk management; (5) the joint two-field decomposition separates distributional similarity from news co-mention channels. The 52-firm large-cap sample and conditional (non-causal) interpretation limit direct trading applicability, but the methodology could be extended to broader universes and integrated into factor-model-based strategies.

The implementation involves multiple complex components: (1) article collection, truncation, and embedding with Qwen3-Embedding-8B (4,096 dimensions); (2) balanced assignment problems for pairwise Wasserstein-2 transport between all firm pairs (52×51 ordered pairs); (3) target-anchored simplex optimization for barycentric reconstruction (one per target); (4) construction of RBF diffusion and equal-support comparators; (5) persistent news co-mention matrix construction with multi-year filtering; (6) spatial QMLE with Jacobian determinant computation (eigenvalue spectrum or LU factorization); (7) 2,000 joint-date stationary-bootstrap refits with expected block length 21; (8) boundary-calibrated QLR tests with restricted-null residual simulation; (9) representation sensitivity across 7+ encoders and multiple dimensions; (10) formal verification in Lean 4/mathlib. The mathematical sophistication (optimal transport, Hilbert-space exposures, Neumann series, Perron-Frobenius theory) combined with the computational demands (balanced assignments, repeated bootstrap, grid search with continuous refinement) makes this highly complex to implement and reproduce.

The paper states that a citable public release with versioned code, environment specifications, derived interaction fields, estimation outputs, and scripts will be deposited upon acceptance. Data sources are public (Nasdaq news archive, Yahoo Finance via yfinance). The embedding model (Qwen3-Embedding-8B) is accessible via OpenRouter. Formal verification of algebraic results is done in Lean 4/mathlib v4.31.0. However, the code is not yet publicly available, and the specific article selection, truncation, and alignment procedures require careful replication. The 52-firm sample and 885-date panel are fixed but the construction pipeline involves multiple design choices.