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Quantify closeness between mean field models and practical deep networks

Determine how closely the behavior of deep neural networks in asymptotically equivalent mean field models matches the behavior of practical deep neural networks used in applications, by providing quantitative comparisons or conditions under which the equivalence accurately reflects optimization and generalization behavior.

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Background

The paper reviews mean field approaches that provide asymptotic models for multilayer neural networks and notes that conclusions depend on approximations (e.g., asymptotic expansions).

The authors explicitly state that it is unclear how closely these equivalent models reflect real network behavior, indicating a need for rigorous quantitative validation of the equivalence in practical regimes.

References

Here it is again unclear how close the behaviour of the deep networks in the equivalent model is to the behaviour of the deep networks in the applications, because the equivalent model is based on some approximation of the deep neural networks using, e.g., some asymptotic expansions.

— Statistically guided deep learning (2504.08489 - Kohler et al., 11 Apr 2025) in Section 1.9 (Discussion of related results), Mean field approach