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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

French

Le déploiement économe en énergie de grands modèles linguistiques nécessite la compréhension de la façon dont l'architecture de modèle, le matériel et les paramètres de service forment l'énergie par jeton généré. Nous présentons la loi Token-Energy, un modèle compact et interprétable de l'énergie de la carte GPU par jeton de sortie pour le décodage dense et complet. Il relie l'énergie de jeton à deux dimensions de base: les octets actifs et le temps de décodage réalisé. Les octets actifs décrivent la demande logique de octets par sortie, séparant les poids denses partagés dans une itération de décodage des histoires de clé privée-valeur (KV) lues et mises à jour pour chaque

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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