The non-determinism in LLM inference at temperature zero, as described by Thinking Machines Lab, was formalized in Torch Lean to demonstrate how small floating-point arithmetic errors can alter the final argmax output.

Using the Torch Lean framework, it was formally proven that the flash attention mechanism is equivalent to standard attention at the specification level.

AI systems from OpenAI and DeepMind achieved gold medal-level performance at the 2024 International Mathematical Olympiad (IMO).