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Keeping a memory of evolving stimuli is ubiquitous in biology, an example ofwhich is immune memory for evolving pathogens. However, learning and memorystorage for dynamic patterns still pose challenges in machine learning. Here,we introduce an analytical energy-based framework to address this problem. Byaccounting for the tradeoff between utility in keeping a high-affinity memoryand the risk in forgetting some of the diverse stimuli, we show that a moderatetolerance for risk enables a repertoire to robustly classify evolving patterns,without much fine-tuning. Our approach offers a general guideline for learningand memory storage in systems interacting with diverse and evolving stimuli.

Risk-utility tradeoff shapes memory strategies for evolving patterns