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#universal-approximation News & Analysis

2 articles tagged with #universal-approximation. AI-curated summaries with sentiment analysis and key takeaways from 50+ sources.

2 articles
AIBullisharXiv – CS AI · Mar 46/103
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On the Expressive Power of Transformers for Maxout Networks and Continuous Piecewise Linear Functions

Researchers establish theoretical foundations for Transformer networks' expressive power by connecting them to maxout networks and continuous piecewise linear functions. The study proves Transformers inherit universal approximation capabilities of ReLU networks while revealing that self-attention layers implement max-type operations and feedforward layers perform token-wise affine transformations.

AINeutralarXiv – CS AI · Jun 236/10
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Universal Approximation of Nonlinear Operators and Their Derivatives

Researchers have proven the first Universal Approximation Theorems for k-times differentiable nonlinear operators and their derivatives in infinite-dimensional Banach spaces, establishing theoretical foundations for Derivative-Informed Operator Learning (DIOL). This breakthrough extends classical approximation theory to operator learning architectures like DeepONets and enables applications in optimal control, PDEs, and inverse problems.