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New theorem enables neural networks to approximate function derivatives

By PulseAugur Editorial · [2 sources] ·

Researchers have published a paper detailing a generalized universal approximation theorem for neural networks. This new theorem extends previous work by enabling the approximation of not only functions but also their derivatives. The findings are applicable to differentiable maps on infinite-dimensional manifolds and have implications for approximating non-anticipative functionals and path space functionals. AI

IMPACT Extends theoretical understanding of neural network capabilities, potentially enabling more complex function and derivative approximations.

RANK_REASON The cluster contains an academic paper detailing a new theoretical result in machine learning.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Philipp Schmocker, Josef Teichmann ·

    Weighted universal approximation of differentiable maps on infinite-dimensional manifolds

    arXiv:2606.09820v1 Announce Type: cross Abstract: We generalize the universal approximation theorem for functional input neural networks (FNN) to differentiable maps by including the approximation of the derivatives. A FNN maps the input from a possibly infinite-dimensional weigh…

  2. arXiv stat.ML TIER_1 English(EN) · Josef Teichmann ·

    Weighted universal approximation of differentiable maps on infinite-dimensional manifolds

    We generalize the universal approximation theorem for functional input neural networks (FNN) to differentiable maps by including the approximation of the derivatives. A FNN maps the input from a possibly infinite-dimensional weighted manifold to the real-valued hidden layer, on w…

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