Large language models show a surprising in-context learning ability—being able to use a prompt to form a prediction for a query, yet without additional training, in stark contrast to old-fashioned supervised learning. Providing a mechanistic interpretation and linking the empirical phenomenon to physics are thus challenging and remain unsolved. We study a simple yet expressive transformer with linear attention and map this structure to a spin glass model with real-valued spins, where the couplings and fields explain the intrinsic disorder in data. The spin glass model explains how the weight parameters interact with each other during pretraining, and further clarifies why an unseen function can be predicted by providing only a prompt yet without further training. Our theory reveals that for single-instance learning, increasing the task diversity leads to the emergence of in-context learning, by allowing the Boltzmann distribution to converge to a unique correct solution of weight parameters. Therefore, the pretrained transformer displays a prediction power in a prompt setting. The proposed analytically tractable model thus offers a promising avenue for thinking about how to interpret many intriguing but puzzling properties of large language models.

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• Spin glasses
• Artificial neural networks
• Cavity methods
• Machine learning models