ResearchResearch paperLarge Language Models · Training & Scaling · Reinforcement Learning1 source · Oct 7, 2026

Residual Learning in Empirical Asset Pricing

Residual learning allows neural network models in asset pricing to go deeper by preserving and refining their shallow counterparts.

Key points

  • Shallow models are special cases of deep models, and deep models theoretically have the potential to outperform the shallow ones.
  • However, the existing empirical asset pricing literature provides strong benchmarks for shallow models.
  • The out-of-sample Sharpe ratio for value-weighted long-short portfolios of deep residual models (2.07) is higher than that for the corresponding shallow ones (1.92) and more than twice that of the deep feedforward models (0.89).
  • We show that model depth is a source of additional economic value in asset pricing.

Sources (1)

  • [1]Residual Learning in Empirical Asset Pricing
    arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 07:55 AM
    Residual learning allows neural network models in asset pricing to go deeper by preserving and refining their shallow counterparts.
    Shallow models are special cases of deep models, and deep models theoretically have the potential to outperform the shallow ones.

Extractive summary: sentences quoted from the sources.

Related