This research provides the first comprehensive theoretical analysis of how round-off errors affect transformer-based language models during computation.

• Establishes fundamental bounds for numerical error propagation in transformer architectures
• Identifies how errors accumulate during the forward pass of model execution
• Offers insights for optimizing hyperparameters to improve computational stability
• Suggests practical approaches to mitigate numerical instabilities in LLM training

For engineering teams, this work provides critical understanding of why training instabilities occur and how to design more reliable, efficient LLM architectures with improved numerical precision considerations.

Numerical Error Analysis of Large Language Models