Formalizing the scaling laws of transformers using fractional order differential equations (FODEs) can provide a more accurate description of learning dynamics, especially in sparse data environments.

Motivation

Traditional ODEs may not capture complex, non-linear dynamics in environments where data is sparse or unevenly distributed. FODEs could provide a more nuanced understanding by accounting for memory effects and anomalies in learning behavior.

Proposed Method

Develop a theoretical framework extending the work's current ODE approach to FODEs. Simulate learning dynamics using FODEs in transformer models trained on sparse datasets and compare convergence and generalization performance against traditional ODE-based models.

Expected Contribution

This research could lead to a new class of scaling laws that better predict model performance in real-world scenarios where data availability is limited or variable.

Required Resources

Access to datasets with varying levels of sparsity, expertise in differential equations, and computational resources to run extensive simulations.

Source Paper

Unifying Learning Dynamics and Generalization in Transformers Scaling Law

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