Unified Approximation Theorem for Neural Networks

Ramesh Sighn — Sun, 30 Jun 2024 02:17:35 +0000

For any ( f \in \mathcal{F}(\mathbb{R}^n) ) and any ( \epsilon > 0 ), there exists a neural network ( \mathcal{N}(\mathbf{x}; \theta) ) with parameters ( \theta ) such that: [ \sup_{\mathbf{x} \in K} \left| f(\mathbf{x}) - \mathcal{N}(\mathbf{x}; \theta) \right| < \epsilon, ] where ( K \subset \mathbb{R}^n ) is compact.

Other Collatz conjecture approach

Ramesh Sighn — Sat, 29 Jun 2024 07:11:37 +0000

The Collatz conjecture states that for any positive integer ( n ):
If ( n ) is even, divide it by 2 (i.e., ( n \to \frac{n}{2} )).
If ( n ) is odd, multiply it by 3 and add 1 (i.e., ( n \to 3n + 1 )).

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Unified Approximation Theorem for Neural Networks

Other Collatz conjecture approach