Paper: arXiv 2507.16548

Authors: Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk

Abstract

The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for training, validation, estimation purposes, and hyperparameter tuning. Therefore, in this research, through empirical experiments on equity and cryptocurrency assets, we apply the Mean Absolute Directional Loss (MADL) function, which is more adequate for optimizing forecast-generating models used in algorithmic investment strategies. The MADL function results are compared between Transformer and LSTM models, and we show that in almost every case, Transformer results are significantly better than those obtained with LSTM.

Complexity vs Empirical Score

  • Math Complexity: 6.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced neural network architecture mathematics (Transformer attention mechanisms with formal equations) and demonstrates rigorous empirical testing including walk-forward procedures, extended out-of-sample periods, and risk-adjusted performance metrics across multiple asset classes.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Design ML testing for Finance"] --> B["Data Sources<br>(Equity & Crypto Assets)"]
  B --> C{"Model Training & Tuning"}
  C --> D["Transformer Model"]
  C --> E["LSTM Model"]
  D & E --> F["Apply MADL<br>Loss Function"]
  F --> G["Comparison &<br>Evaluation Results"]
  G --> H["Outcome:<br>Transformer outperforms LSTM"]