Glen Mbeng

Alessandro Achille, Giovanni Paolini, Glen Mbeng et al.

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.

Alessandro Achille, Glen Mbeng, Stefano Soatto

We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model used. This is related to an information theoretic distance function, but is insufficient to predict success in transfer learning, as nearby tasks can be unreachable via fine-tuning. The second factor depends on the ease of traversing the path between two tasks. With this dynamic component, we derive strict lower bounds on the complexity necessary to learn a task starting from the solution to another, which is one of the most common forms of transfer learning.