# Dissecting FLOPs along input dimensions for GreenAI cost estimations

arXiv: https://arxiv.org/abs/2107.11949 · HTML: https://mlsanity.com/paper/2107.11949/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 13 of 13)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [Carbontracker: Tracking and Predicting the Carbon Footprint of Training Deep Learning Models](https://mlsanity.com/paper/2007.03051/) (2020)
- [MorphNet: Fast & Simple Resource-Constrained Structure Learning of Deep Networks](https://mlsanity.com/paper/1711.06798/) (2017)
- [Chasing Carbon: The Elusive Environmental Footprint of Computing](https://mlsanity.com/paper/2011.02839/) (2020)
- [Efficient Document Re-Ranking for Transformers by Precomputing Term Representations](https://mlsanity.com/paper/2004.14255/) (2020)
- [Constructing Fast Network through Deconstruction of Convolution](https://mlsanity.com/paper/1806.07370/) (2018)
- [A survey on Variational Autoencoders from a GreenAI perspective](https://mlsanity.com/paper/2103.01071/) (2021)
- [Towards Accurate and Reliable Energy Measurement of NLP Models](https://mlsanity.com/paper/2010.05248/) (2020)
- [A GEMM interface and implementation on NVIDIA GPUs for multiple small matrices](https://mlsanity.com/paper/1304.7053/) (2013)

## Built on by (most cited first, 10 of 10)

- [Lightweight Deep Learning for Resource-Constrained Environments: A Survey](https://mlsanity.com/paper/2404.07236/) (2024)
- [Precipitation nowcasting with generative diffusion models](https://mlsanity.com/paper/2308.06733/) (2023)
- [Accuracy is not the only Metric that matters: Estimating the Energy Consumption of Deep Learning Models](https://mlsanity.com/paper/2304.00897/) (2023)
- [DOCTOR: A Multi-Disease Detection Continual Learning Framework Based on Wearable Medical Sensors](https://mlsanity.com/paper/2305.05738/) (2023)
- [Enhancing variational generation through self-decomposition](https://mlsanity.com/paper/2202.02738/) (2022)
- [Normalizing Energy Consumption for Hardware-Independent Evaluation](https://mlsanity.com/paper/2409.05602/) (2024)
- [COMFORT: A Continual Fine-Tuning Framework for Foundation Models Targeted at Consumer Healthcare](https://mlsanity.com/paper/2409.09549/) (2024)
- [Contrastive Self-Supervised Learning at the Edge: An Energy Perspective](https://mlsanity.com/paper/2510.08374/) (2025)
- [FLOPs vs Real Work: The Importance of Replication in AI Efficiency Assessment](https://mlsanity.com/paper/2608.14550/) (2026)
- [Beyond FLOPs: Energy-Aware Knowledge Distillation for Sustainable LLMs on Code-Related Task](https://mlsanity.com/paper/2608.17515/) (2026)

## Abstract (arXiv)

The term GreenAI refers to a novel approach to Deep Learning, that is more aware of the ecological impact and the computational efficiency of its methods. The promoters of GreenAI suggested the use of Floating Point Operations (FLOPs) as a measure of the computational cost of Neural Networks; however, that measure does not correlate well with the energy consumption of hardware equipped with massively parallel processing units like GPUs or TPUs. In this article, we propose a simple refinement of the formula used to compute floating point operations for convolutional layers, called α-FLOPs, explaining and correcting the traditional discrepancy with respect to different layers, and closer to reality. The notion of α-FLOPs relies on the crucial insight that, in case of inputs with multiple dimensions, there is no reason to believe that the speedup offered by parallelism will be uniform along all different axes.