Transformer tricks: Precomputing the first layer

This micro-paper describes a trick to speed up inference of transformers with RoPE (such as LLaMA, Mistral, PaLM, and Gemma). For these models, a large portion of the first transformer layer can be precomputed, which results in slightly lower latency and lower cost-per-token. Because this trick optimizes only one layer, the relative savings depend on the total number of layers. For example, the maximum savings for a model with only 4 layers (such as Whisper tiny) is limited to 25%, while a 32-layer model (such as Mistral-7B) is limited to 3% savings.