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The Token-Energy Law of LLM Decode: Active Bytes and Realized Time Account for Joules per Token

Chenxu Niu, Batuhan Sencer, Wei Zhang, Yong Chen · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28576 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

El despliegue eficiente de grandes modelos de idiomas requiere comprensión de cómo la arquitectura del modelo, el hardware y las configuraciones de servicio forman energía por token generado. Introducimos la Ley Token-Energy, un modelo compacto e interpretable de energía de la placa de GPU por token de salida para el descifrado denso, de historia completa. Se relaciona la energía del token a dos dimensiones principales: bytes activos y tiempo de descifrado realizado. Los bytes activos describen la demanda lógica de bytes por salida, separando los pesos densos compartidos dentro de una iteración de decodificación de las historias de clave privada-valor (KV) leídas y actualizadas para cada solicitud. El tiempo de decodificación realizado es la duración de decodificación extendida dividida por el número

Machine translation (Meta M2M100); the English original follows.

Abstract

Energy-efficient deployment of large language models requires understanding how model architecture, hardware, and serving settings shape energy per generated token. We introduce the Token-Energy Law, a compact, interpretable model of GPU-board energy per output token for dense, full-history decoding. It relates token energy to two core dimensions: active bytes and realized decode time. Active bytes describe logical byte demand per output, separating dense weights shared within a decode iteration from private key--value (KV) histories read and updated for each request. Realized decode time is the elapsed decode duration divided by the number of output tokens produced. We combine the two byte coordinates and time in a common affine form, with coefficients calibrated for each model and hardware/runtime configuration. This formulation explains how batching amortizes shared-weight work, longer attended histories increase private KV demand, and throughput determines the time-associated cost per output. Our experiments cover three models under BF16 decoding on NVIDIA Hopper and Blackwell GPUs, including two-GPU tensor parallelism on Hopper. Using fixed coefficients and observed decode time, held-out condition-mean energy estimates differ from measurements by at most 3.73%.

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Topics: Byte, Security token, Computer science, Energy (signal processing), Decoding methods, Affine transformation

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