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arXiv Machine Learning By Isabel Dahlgren, Giovanni Luca Marchetti, Kathl\'en Kohn

Polynomial Residual Networks are Generically Identifiable

Read the original on arXiv Machine Learning →

The paper establishes identifiability results for constant‑width residual networks that use polynomial activations and bias terms. For activations of degree at least five with generic coefficients, the mapping from parameters to network outputs is generically one‑to‑one. For activations of degree at least three that lack a linear term after a suitable input translation, the generic fiber consists of translations of biases combined with scaling of weights and biases by real roots of unity, and these findings also apply to bias‑free networks. Additionally, the authors derive necessary conditions for critical points of the ResNet parametrization, which are important in singular learning theory.

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