The Information Complexity of Learning Tasks, their Structure and their Distance
This foundational work provides tools for transfer learning by quantifying task complexity and distance, which is critical for optimizing pre-training and fine-tuning in deep learning.
The paper introduces a framework for measuring the complexity of learning tasks and an asymmetric distance between tasks, addressing the finite nature of training data and distinguishing learning from memorization, with applications to large-scale models and real-world datasets.
We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task, and then fine-tuned for another. The framework we develop is non-asymptotic, captures the finite nature of the training dataset, and allows distinguishing learning from memorization. It encompasses, as special cases, classical notions from Kolmogorov complexity, Shannon, and Fisher Information. However, unlike some of those frameworks, it can be applied to large-scale models and real-world datasets. Our framework is the first to measure complexity in a way that accounts for the effect of the optimization scheme, which is critical in Deep Learning.