Ruoran Bai | Searcharxiv

arXiv2026

Solvable dynamics model of in-context learning

Pretrained Transformer architectures display a surprising in-context learning ability without additional training. How the learning process guides the network to achieve this intriguing capability remains unsolved. In this study, we focus on a single-layer, single-head linear attention model, where empirical risk minimization is defined for learning. Given a finite amount of training examples, we determine the exact solution of network parameter dynamics, which is linked to the training error and generalization error, characterizing how memorization and generalization emerge from learning and how these transitions are related to curvatures of the empirical risk landscape. Furthermore, we calculate a data-dependent free energy, from which the training and generalization errors in the long-time limit of learning dynamics can be well predicted. Our work adds insights toward understanding the mechanism of in-context learning, especially from a learning dynamics perspective.

cs.LG↗

arXiv2025

Spin glass model of in-context learning

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 pre-training, 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 pre-trained transformer displays a prediction power in a novel 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.

cond-mat.dis-nn↗