arXiv:2602.09405v2 Announce Type: replace-cross Abstract: We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to the prior distribution $\pi$, giving explicit conditions under which optimal generalization necessitates that the training error be (i) near interpolating relative to the noise size (i.e., memorization is necessary), or (ii) close to the noise level (i.e., overfitting is harmful). Remarkably, these phen
This research provides a theoretical framework for understanding the interplay between memorization and generalization in overparameterized models, a critical topic given the widespread adoption of large AI systems.
Understanding when memorization is beneficial versus harmful is crucial for developing more efficient, reliable, and interpretable AI models, impacting design choices across the AI industry.
The explicit conditions for optimal generalization now provide clearer guidance on whether to encourage or prevent memorization based on prior information within a Bayesian setup.
- · AI researchers
- · Machine learning framework developers
- · Industries relying on AI model performance
- · Developers using 'black box' approaches
- · Inefficient AI training methodologies
Improved understanding and design of AI model architectures for better generalization.
Development of adaptive training algorithms that dynamically adjust memorization strategies based on data priors.
More robust and explainable AI systems leading to broader adoption in sensitive applications like medicine and autonomous systems.
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