Energy per FLOP Is Not Constant: Measured Dispersion Across FLOP-Matched Training Workloads

The number of floating-point operations (FLOPs) a workload performs is widely used as a proxy for the energy it consumes. This article tests that proxy by direct physical measurement. Five families of neural-network training step, namely dense layers, convolutions, a recurrent cell, embedding lookups, and elementwise updates with sparse products, were each matched to the same FLOP count within two percent and executed on one laptop computer while energy was read from on-chip sensors that had first passed a load-response test: the CPU package through Intel RAPL, and the GPU board through NVIDIA NVML. The hypotheses, decision rules, sample size and analysis were preregistered and fixed by a cryptographic digest before any confirmatory measurement. In the primary session, net CPU package energy per FLOP differed between the most and least efficient families by a factor of 94.43 (95% block-bootstrap interval 78.06 to 119); an independent earlier session gave 93.58, and the GPU board gave 26.05. CPU package power varied little across families, so energy followed runtime: on families withheld from fitting, runtime alone predicted energy with 19.85% mean absolute percentage error, against 63.72% for FLOPs alone, and adding shape-derived estimates of memory traffic did not improve prediction. None of the three sessions satisfied the preregistered stability criterion, because contention on the CPU and clock transitions on the GPU moved a fixed reference kernel by more than ten percent. The study therefore reports a replicated measurement rather than a confirmatory verdict. It documents every deviation from protocol and releases the instrument, the raw measurement windows and the analysis, so that the result can be reproduced or refuted on other hardware.