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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

Indonesian

Pengembangan efisiensi energi dari model bahasa besar membutuhkan pemahaman tentang bagaimana arsitektur model, perangkat keras, dan pengaturan layanan membentuk energi per token yang dihasilkan. Kami memperkenalkan Token-Energy Law, model yang kompak dan dapat ditafsirkan dari energi GPU-board per token output untuk dekoding yang padat, penuh sejarah. Ini menghubungkan energi token ke dua dimensi inti: byte aktif dan waktu dekoding yang terwujud. Byte aktif menggambarkan permintaan byte logis per output, memisahkan beban padat yang dibagikan dalam iterasi dekoding dari sejarah key-value (KV) pribadi yang dibaca dan diperbarui untuk setiap permintaan. Waktu dekoding yang terwujud adalah durasi dekoding yang telah berlalu dibagi oleh jumlah token output yang dihasilkan. Kami menggabungkan dua koordinat dan waktu dalam bentuk

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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