Contextures: The Mechanism of Representation Learning
This work provides a foundational theory for representation learning, addressing a critical gap in AI as scaling models yields diminishing returns, with implications for designing more effective pretraining methods across various domains.
The dissertation tackles the lack of scientific understanding of representation learning in foundation models by establishing the contexture theory, which mathematically characterizes how representations are learned from associations between input and context variables, proving that optimal encoders capture maximum information of this association and showing that better contexts, not just larger models, are key for further progress.
This dissertation establishes the contexture theory to mathematically characterize the mechanism of representation learning, or pretraining. Despite the remarkable empirical success of foundation models, it is not very clear what representations they learn, and why these representations are useful for various downstream tasks. A scientific understanding of representation learning is critical, especially at this point when scaling up the model size is producing diminishing returns, and designing new pretraining methods is imperative for further progress. Prior work treated different representation learning methods quite differently, whereas the contexture theory provides a unified framework for analyzing these methods. The central argument is that a representation is learned from the association between the input X and a context variable A. We prove that if an encoder captures the maximum information of this association, in which case we say that the encoder learns the contexture, then it will be optimal on the class of tasks that are compatible with the context. We also show that a context is the most useful when the association between X and A is neither too strong nor too weak. The important implication of the contexture theory is that increasing the model size alone will achieve diminishing returns, and further advancements require better contexts. We demonstrate that many pretraining objectives can learn the contexture, including supervised learning, self-supervised learning, generative models, etc. Then, we introduce two general objectives -- SVME and KISE, for learning the contexture. We also show how to mix multiple contexts together, an effortless way to create better contexts from existing ones. Then, we prove statistical learning bounds for representation learning. Finally, we discuss the effect of the data distribution shift from pretraining to the downstream task.