Sobolev spaces
PulseAugur coverage of Sobolev spaces — every cluster mentioning Sobolev spaces across labs, papers, and developer communities, ranked by signal.
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New Metaplectic Neural Networks Show Promise for Schrödinger Equation Approximation
Researchers have developed a new type of shallow neural network utilizing a dictionary based on metaplectic operators. This approach extends the concept of Barron spaces by incorporating a metaplectic transform, a sympl…
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New neural network architecture improves function approximation
Researchers have developed a new type of neural network that utilizes metaplectic operators, extending the concept of Barron spaces. This approach, termed neural metaplectic dictionaries, allows for more efficient appro…
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New criterion for conditional expectation operators in machine learning
A new paper introduces a verifiable criterion for understanding conditional expectation operators (CEOs) and conditional mean embeddings (CMEs). These concepts are crucial in areas like nonparametric regression, Bayesia…
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New research defines limits for learning linear operators
Researchers have established the statistical and computational limits for learning bounded linear operators between Sobolev spaces using noisy input-output data. The problem is reframed as an infinite-dimensional matrix…
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Random feature models including neural networks achieve universal approximation
Researchers have introduced a new framework for random feature learning, extending it to Banach spaces. This approach allows for significant reductions in computational complexity by only training a linear readout after…