Mathematical Minimalism
9 hours ago
- #theory of computation
- #deep neural networks
- #elementary functions
- Andrzej Odrzywolek's arXiv article demonstrates that all elementary functions can be derived from the 'elm' function and the constant 1.
- The paper's supplement provides equations to bootstrap basic arithmetic operations: addition, subtraction, multiplication, and division, starting from the 'elm' function.
- The work extends to obtaining constants like π, functions like square and square root, and standard circular and hyperbolic functions.
- This has implications for deep neural networks, as stacking 'elm' functions and 1s can be exact (depending on log and exp precision), contrasting with the universal approximator theorem's epsilon-delta guarantees.