A 4-parameter law predicts LLM inference energy with R²=0.969 across 13 models
ecs-lab · hf · 2026-11-06
Researchers from University of Bologna and CINECA derive the SIMPLE Law, a four-parameter analytical law predicting LLM inference energy directly from architectural hyperparameters—no per-LLM fitting needed—separating prefill from decode (KV-cache + next-token) costs.
Key findings:
- Validated on NVIDIA H100 across 13 LLMs from 6 families (OPT, LLaMA, Gemma, Falcon, Qwen2, Granite): R²=0.969, 11.97% MAPE—3.1–3.5× below per-LLM SOTA;
- Inference energy grows quadratically with hidden dimension, so larger LLMs suffer most from long inputs;
- More aggressive GQA KV grouping cuts per-token energy up to 3× vs standard MHA;
- Reasoning budgets drive super-linear energy growth: Intelligence per Joule peaks at an intermediate budget and falls up to 3.14× at a 4× reasoning budget.
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