Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherence

• URL: http://arxiv.org/abs/2509.00024v1
• Date: Mon, 18 Aug 2025 20:29:34 GMT
• Title: Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherence
• Authors: James Amarel, Nicolas Hengartner, Robyn Miller, Kamaljeet Singh, Siddharth Mansingh, Arvind Mohan, Benjamin Migliori, Emily Casleton, Alexei Skurikhin, Earl Lawrence, Gerd J. Kunde,
• Abstract summary: We apply influence function formalism to characterize how autoregressive PDE surrogates assimilate and propagate information derived from diverse physical scenarios.<n>We provide actionable insights regarding the design of improved surrogates.
• Score: 0.1286280695561924
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Foundation models trained as autoregressive PDE surrogates hold significant promise for accelerating scientific discovery through their capacity to both extrapolate beyond training regimes and efficiently adapt to downstream tasks despite a paucity of examples for fine-tuning. However, reliably achieving genuine generalization - a necessary capability for producing novel scientific insights and robustly performing during deployment - remains a critical challenge. Establishing whether or not these requirements are met demands evaluation metrics capable of clearly distinguishing genuine model generalization from mere memorization. We apply the influence function formalism to systematically characterize how autoregressive PDE surrogates assimilate and propagate information derived from diverse physical scenarios, revealing fundamental limitations of standard models and training routines in addition to providing actionable insights regarding the design of improved surrogates.

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