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arXiv Machine Learning By Weihan Li, Xinlei Chen, Junhao Wu, Tianshi Zheng

When Should an In-Context Learner Expand Its Hypothesis Space?

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The paper investigates when an in‑context learner should expand its hypothesis space, framing the decision as a costly sequential problem where prediction failures must be translated into structural evidence and then into an action. Using a Structural Revision Environment that allows exact Bayesian analysis, the authors find that the optimal decision to expand is governed by a value boundary rather than a simple evidence threshold, and that this boundary depends on the price of expansion, the remaining horizon, and the specific predictions that cannot be repaired locally. Experiments with transformers and language models show that while these models exhibit a failure‑sensitive signal, they often fail to incorporate cost and horizon considerations into their expansion decisions, and post‑training adjustments to priors or prediction sharpness do not alter the expansion criterion.

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