Abstract
We develop a theoretical model that addresses the economic trade-off between cost per token versus serial token generation speed when deploying LLMs for inference at scale. Our model takes into account arithmetic, memory bandwidth, network bandwidth and latency constraints; and optimizes over different parallelism setups and batch sizes to find the ones that optimize serial inference speed at a given cost per token. We use the model to compute Pareto frontiers of serial speed versus cost per token for popular language models.