[Paper Review] Towards a theory of out-of-distribution learning

Ali Geisa, Ronak Mehta+5 more|arXiv (Cornell University)|Sep 29, 2021

Machine Learning and Algorithms60 references4 citations

TL;DR

This paper proposes a generalized theory of out-of-distribution (OOD) learning by relaxing the traditional in-distribution assumption in learning theory. It introduces learning efficiency (LE) as a metric to quantify data utilization and unifies transfer, multitask, meta, continual, and lifelong learning under a common framework, offering theoretical grounding for real-world OOD challenges in AI.

ABSTRACT

What is learning? 20 century formalizations of learning theory -- which precipitated revolutions in artificial intelligence -- focus primarily on extit{in-distribution} learning, that is, learning under the assumption that the training data are sampled from the same distribution as the evaluation distribution. This assumption renders these theories inadequate for characterizing 21$^{st}$ century real world data problems, which are typically characterized by evaluation distributions that differ from the training data distributions (referred to as out-of-distribution learning). We therefore make a small change to existing formal definitions of learnability by relaxing that assumption. We then introduce extbf{learning efficiency} (LE) to quantify the amount a learner is able to leverage data for a given problem, regardless of whether it is an in- or out-of-distribution problem. We then define and prove the relationship between generalized notions of learnability, and show how this framework is sufficiently general to characterize transfer, multitask, meta, continual, and lifelong learning. We hope this unification helps bridge the gap between empirical practice and theoretical guidance in real world problems. Finally, because biological learning continues to outperform machine learning algorithms on certain OOD challenges, we discuss the limitations of this framework vis-a-vis its ability to formalize biological learning, suggesting multiple avenues for future research.

Motivation & Objective

• To address the limitations of traditional in-distribution learning theories in modeling real-world data shifts.
• To formalize out-of-distribution learning by relaxing the assumption that training and evaluation data follow the same distribution.
• To introduce learning efficiency (LE) as a measure of how effectively a learner uses data, regardless of distribution shift.
• To unify diverse learning paradigms—transfer, multitask, meta, continual, and lifelong learning—under a generalized learnability framework.
• To identify theoretical gaps in modeling biological learning and suggest directions for future research.

Proposed method

• Relaxes the standard learnability definition by removing the in-distribution assumption, enabling analysis of distribution shift.
• Introduces learning efficiency (LE) as a quantitative measure of data utilization in both in- and out-of-distribution settings.
• Defines generalized learnability using LE and establishes mathematical relationships between different learning regimes.
• Applies the framework to analyze transfer, multitask, meta, continual, and lifelong learning as special cases of the generalized theory.
• Uses formal definitions and proofs to demonstrate consistency and generality across learning paradigms.
• Compares the framework’s limitations in modeling biological learning, highlighting open challenges.

Experimental results

Research questions

• RQ1 How can existing learning theories be extended to handle out-of-distribution generalization?
• RQ2 What metrics can effectively quantify data utilization in out-of-distribution learning scenarios?
• RQ3 In what ways can transfer, multitask, meta, continual, and lifelong learning be unified under a single theoretical framework?
• RQ4 How does learning efficiency (LE) relate to generalized learnability across different learning regimes?
• RQ5 What are the theoretical limitations of this framework in modeling biological learning processes?

Key findings

• The proposed framework generalizes traditional learnability theory by removing the in-distribution assumption, enabling analysis of real-world distribution shifts.
• Learning efficiency (LE) is introduced as a robust metric to quantify how effectively a learner leverages data, irrespective of distributional shift.
• The framework successfully unifies transfer, multitask, meta, continual, and lifelong learning under a single theoretical umbrella.
• Formal proofs establish the relationship between generalized learnability and learning efficiency, validating the framework’s consistency.
• The theory identifies key limitations in modeling biological learning, suggesting that current formalizations fall short in capturing the full scope of biological inductive biases.
• The work provides a foundation for aligning theoretical guidance with empirical practice in real-world AI applications involving distribution shift.