# Towards Semantics Lifting for Scientific Computing: A Case Study on FFT

arXiv: https://arxiv.org/abs/2501.09201 · HTML: https://mlsanity.com/paper/2501.09201/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Leveraging AI for Productive and Trustworthy HPC Software: Challenges and Research Directions](https://mlsanity.com/paper/2505.08135/) (2025)

## Abstract (arXiv)

The rise of automated code generation tools, such as large language models (LLMs), has introduced new challenges in ensuring the correctness and efficiency of scientific software, particularly in complex kernels, where numerical stability, domain-specific optimizations, and precise floating-point arithmetic are critical. We propose a stepwise semantics lifting approach using an extended SPIRAL framework with symbolic execution and theorem proving to statically derive high-level code semantics from LLM-generated kernels. This method establishes a structured path for verifying the source code's correctness via a step-by-step lifting procedure to high-level specification. We conducted preliminary tests on the feasibility of this approach by successfully lifting GPT-generated fast Fourier transform code to high-level specifications.