arXiv:2312.08472v2 Announce Type: replace-cross Abstract: Transcendental functions, such as the exponential, are central to scientific computing, yet they cannot be natively calculated by digital hardware. Instead, computers must approximate these functions by combining basic operations, such as $\{+, -, \times, \div\}$, using methods like Taylor series. These methods were developed over centuries by mathematicians, who focused on approaches that could attain arbitrary accuracy. However, computers can handle most applications by using only finite-precision types, like float32, where any accura
The proliferation of AI and the increasing demand for computational efficiency in various applications are driving innovations in fundamental mathematical operations, pushing for automated discovery of more optimized functions.
This development could significantly improve the performance and energy efficiency of all digital hardware by optimizing the very core mathematical functions they rely on, impacting everything from scientific computing to everyday devices.
The reliance on centuries-old, human-derived approximation methods for transcendental functions may be replaced by AI-discovered, highly optimized functions tailored for specific finite-precision hardware.
- · AI/ML hardware manufacturers
- · High-performance computing sectors
- · Software developers
- · Scientific research institutions
- · Traditional numerical methods specialists (potentially requiring reskilling)
- · Hardware designs optimized around existing function approximations
Increased computational speed and reduced power consumption across a wide range of computational tasks.
Accelerated progress in other AI fields and scientific discovery due to more efficient foundational numerical operations.
Potential for new hardware architectures designed specifically to leverage these AI-optimized mathematical functions, creating a co-evolution of software and hardware.
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Read at arXiv cs.LG