Neural Scaling Laws for Deep Regression
This work addresses the problem of understanding and predicting performance scaling in deep regression for researchers and practitioners, though it is incremental as it extends known scaling laws to a new domain.
The paper empirically investigates neural scaling laws for deep regression models, finding power-law relationships between loss and training dataset size or model capacity, with scaling exponents ranging from 1 to 2, indicating substantial performance improvements with more data.
Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language models highlights the importance of these laws, their application to deep regression models remains largely unexplored. Here, we empirically investigate neural scaling laws in deep regression using a parameter estimation model for twisted van der Waals magnets. We observe power-law relationships between the loss and both training dataset size and model capacity across a wide range of values, employing various architectures--including fully connected networks, residual networks, and vision transformers. Furthermore, the scaling exponents governing these relationships range from 1 to 2, with specific values depending on the regressed parameters and model details. The consistent scaling behaviors and their large scaling exponents suggest that the performance of deep regression models can improve substantially with increasing data size.