In-context learning and Occam's razor
Keywords: generalization, complexity, compression, in-context learning, meta-learning
TL;DR: The next-datapoint prediction error objective used in models that exhibit in-context learning can be seen as a meta-objective that optimizes for learners that not only explain their training data, but do so using the simplest model.
Abstract: A central goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees for generalization without further assumptions, in practice we observe that simple models which explain the training data generalize best—a principle called Occam's razor. Despite the need for simple models, most current approaches in machine learning only minimize the training error, and at best indirectly promote simplicity through regularization or architecture design. Here, we draw a connection between Occam's razor and in-context learning—an emergent ability of certain sequence models like Transformers to learn at inference time from past observations in a sequence. In particular, we show that the next-token prediction loss used to train in-context learners is directly equivalent to a data compression technique called prequential coding, and that minimizing this loss amounts to jointly minimizing both the training error and the complexity of the model that was implicitly learned from context. Our theory and the empirical experiments we use to support it not only provide a normative account of in-context learning, but also elucidate the shortcomings of current in-context learning methods, suggesting ways in which they can be improved.
Primary Area: transfer learning, meta learning, and lifelong learning
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Submission Number: 531
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