The information complexity of learning tasks, their structure and their distance
Abstract
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 and 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 04, 2021
- Source ID
- 10.1093/imaiai/iaaa033
Entities
People
- Alessandro Achille
- Giovanni Paolini
- Glen Bigan Mbeng
- Stefano Soatto
Organizations
- Army Research Office
- Office of Naval Research
- Scuola Normale Superiore
- University of California