Non-identifiability distinguishes Neural Networks among Parametric Models

• URL: http://arxiv.org/abs/2504.18017v1
• Date: Fri, 25 Apr 2025 01:59:02 GMT
• Title: Non-identifiability distinguishes Neural Networks among Parametric Models
• Authors: Sourav Chatterjee, Timothy Sudijono,
• Abstract summary: We prove a pair of results which distinguish feedforward neural networks among parametric models at the population level.<n>Our results suggest that a lack of identifiability distinguishes neural networks among the class of smooth parametric models.
• Score: 5.678271181959529
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One of the enduring problems surrounding neural networks is to identify the factors that differentiate them from traditional statistical models. We prove a pair of results which distinguish feedforward neural networks among parametric models at the population level, for regression tasks. Firstly, we prove that for any pair of random variables $(X,Y)$, neural networks always learn a nontrivial relationship between $X$ and $Y$, if one exists. Secondly, we prove that for reasonable smooth parametric models, under local and global identifiability conditions, there exists a nontrivial $(X,Y)$ pair for which the parametric model learns the constant predictor $\mathbb{E}[Y]$. Together, our results suggest that a lack of identifiability distinguishes neural networks among the class of smooth parametric models.

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