Title: Unveiling the Uncertainty in Embodied and Operational Carbon of Large AI Models through a Probabilistic Carbon Accounting Model
Venue: NeurIPS 2025
Accepted: yes
Keywords: Carbon footprint

Large AI models

Large language models
Abstract: The rapid growth of large AI models has raised significant environmental concerns due to their substantial carbon footprint. Existing carbon accounting methods for AI models are fundamentally deterministic and fail to account for inherent uncertainties in embodied and operational carbon emissions. Our work aims to investigate the effect of these uncertainties on embodied and operational carbon footprint estimates for large AI models. We propose a Probabilistic Carbon Accounting Model (PCAM), which quantifies uncertainties in the carbon accounting of large AI models. We develop parameter models to quantify key components (processors, memory, storage) in the carbon footprint of AI models. To characterize the distribution of the parameters, we develop a carbon dataset by aggregating related data from various sources. Then, we generate the probabilistic distribution of the parameters from the collected dataset. We compare the performance of PCAM with LLMCarbon, the state-of-the-art carbon accounting method for large AI models. PCAM achieves $\leq7.44\%$ error compared to LLMCarbon’s $\leq108.51\%$.

Unveiling the Uncertainty in Embodied and Operational Carbon of Large AI Models through a Probabilistic Carbon Accounting Model

Abstract

The rapid growth of large AI models has raised significant environmental concerns due to their substantial carbon footprint. Existing carbon accounting methods for AI models are fundamentally deterministic and fail to account for inherent uncertainties in embodied and operational carbon emissions. Our work aims to investigate the effect of these uncertainties on embodied and operational carbon footprint estimates for large AI models. We propose a Probabilistic Carbon Accounting Model (PCAM), which quantifies uncertainties in the carbon accounting of large AI models. We develop parameter models to quantify key components (processors, memory, storage) in the carbon footprint of AI models. To characterize the distribution of the parameters, we develop a carbon dataset by aggregating related data from various sources. Then, we generate the probabilistic distribution of the parameters from the collected dataset. We compare the performance of PCAM with LLMCarbon, the state-of-the-art carbon accounting method for large AI models. PCAM achieves ≤ 7 . 44% error compared to LLMCarbon's ≤ 108 . 51% .

1 Introduction

Large AI models have demonstrated high efficacy across various tasks. However, as model parameters and training datasets expand, the computational demands for training and deploying large-scale models grow significantly, leading to notable carbon emissions. For example, recent studies reveal that training advanced language models like Google's T5 generates 40% more carbon emissions than a transcontinental flight between San Francisco and New York [1]. The AI community is increasingly focused on developing methodologies to tackle social issues [2, 3, 4], particularly in promoting decarbonization and achieving carbon neutrality by 2050 [5, 6, 7, 8]. Carbon accounting, i.e., to estimate the carbon footprint of a product, is crucial for understanding the environmental impact of various operations and for developing strategies to reduce carbon footprints. By quantifying emissions, organizations can set reduction targets, comply with regulations, and demonstrate their commitment to sustainability. The carbon footprint of large AI models encompasses two components: operational carbon (i.e., emissions associated with electricity consumed) and embodied carbon (i.e., emissions associated with AI hardware manufacturing).

While existing studies have initiated carbon accounting for AI models [5, 1], current methodologies exhibit two fundamental limitations. First, they predominantly focus on operational carbon, while neglecting or applying a simple model to account for embodied carbon. They utilize coarse-grained average embodied carbon values for one hardware class (e.g., 14nm CPU) directly from Life Cycle Assessment (LCA) reports, potentially introducing substantial inaccuracies. Second, all existing

carbon models for AI models are single-deterministic and fail to capture the inherent uncertainty in the carbon footprint of AI models. The uncertainty in carbon accounting for AI models comes from (1) geotemporal differences in manufacturing, whereby identical device classes fabricated in different regions and periods embody distinct emissions due to different electricity carbon intensity during production; (2) efficiency evolution over time, as yield improvements, and fabrication energy efficiency gains; and (3) operating context variability, since the operational carbon of AI models can vary significantly depending on the location and time of the operation due to spatiotemporal variations in the carbon intensity of electricity.

In this paper, we propose a P robabilistic C arbon A ccounting M odel (PCAM), which can accurately estimate the carbon footprint of large AI models by capturing the uncertainty in the carbon modeling. Specifically, we develop parameter models for each hardware component (e.g., processors, memory, storage) in the carbon footprint of large AI models. To construct the distribution of the parameters, we make an effort to develop a hardware and electricity dataset by aggregating data from diverse sources, including Environmental, Social, and Governance (ESG) reports from hardware manufacturers, power grid operator statistics, industry reports, and peer-reviewed research publications. Then, we implement a simple yet effective dual-stage distribution modeling (i.e., converting the related collected data into frequency histograms followed by Kernel Density Estimation (KDE)), to generate the continuous probability density functions of the parameters.

We compare the performance of PCAM to LLMCarbon, the state-of-the-art carbon modeling method for large AI models. The evaluation is conducted based on four representative large AI models (XLM, T5, GPT-3, and Switch) [5, 9]. We compare the performance at key distribution percentiles (5th, 10th, 50th, 90th, and 95th) of PCAM's probability density function outputs against the ground truth based on the collected carbon dataset. Our PCAM outperforms LLMCarbon in both embodied and operational carbon on all large AI models. The results of PCAM show differences with the ground truth of only ≤ 2 . 67% for embodied carbon and ≤ 7 . 44% for operation carbon, demonstrating significantly higher accuracy compared to LLMCarbon ( ≤ 23 . 02% and ≤ 108 . 51% , respectively).

Our contributions can be summarised as follows:

We propose a new Probabilistic Carbon Accounting Model (PCAM) for large AI models that can generate distribution-based outputs of carbon footprint instead of singular values, allowing AI developers to make risk-aware and sustainable decisions.

We characterize the uncertainty in the carbon footprint of large AI models across key hardware components by generating the distributions of AI hardware-related parameters through a simple yet effective dual-stage distribution modeling from the collected dataset based on KDE.

We make an effort to develop a carbon dataset 1 containing AI hardware-related parameters (e.g., yield, etc.) across different technology nodes from various technology reports, ESG reports, LCA reports, and carbon intensity of electricity data across regions from power grid operators.

2 Background

2.1 Large AI models carbon footprint

The carbon footprint of large AI models includes two components, i.e., operational carbon and embodied carbon. The operational carbon of large AI models refers to the emissions stemming from the electricity consumption in the model training or inference. The embodied carbon arises from the manufacturing processes of the hardware used to execute the AI models. The development of large AI models requires not only substantial electricity but also extensive computing hardware resources. For example, training and deploying large AI models require high-performance GPUs (e.g., NVIDIA A100 [10]) and ML accelerators (e.g., Google TPU [11]). These devices are typically manufactured with large processor chips using advanced technologies (e.g., 5nm), which results in significant carbon emissions. This refers to the embodied carbon of large AI models, which is especially notable in the models operated using the latest high-performance devices. As the proportion of green energy in the power grid increases and more and more data centers adopt carbon-free energy, the running

carbon of large AI models will be greatly reduced, resulting in embodied carbon accounting for a non-negligible part of the large AI models' carbon footprint [12, 13].

2.2 Carbon emission factor and carbon intensity

The carbon emission factor (in g/kWh) is defined as the quantity of carbon emission per unit of electricity generated by a specific energy source. The carbon emission factors of brown sources (e.g., coal, gas, etc.) are much higher than those of green sources (e.g., wind, solar, etc.), as Table 1 shows.

The carbon intensity of electricity is the carbon emission rate (in g/kWh ) when the electricity is generated, i.e., the total amount of carbon emitted ( Gram ) as against the electricity generation ( Kilowatt -Hour ). It is the weighted average of carbon emissions by each energy source due to the electricity generated by them. Mathematically, the carbon intensity of electricity generated at any time is as follows:

where ef k is the carbon emission factor and E k is the electricity generated by energy source k .

3 Methodology

3.1 Limitation of existing modeling techniques

The existing carbon modeling techniques for AI models can be summarized as equation 2, where C model denotes the total carbon footprint of the AI models, including embodied carbon ( EC model ) and operational carbon ( OC model ), t is the time the model occupies the hardware system, T is the lifetime of the hardware system, E is the electricity consumed by the hardware system, and CI is the carbon intensity of electricity.

These existing modeling techniques for AI models' carbon footprint are fundamentally deterministic and estimate the carbon emission model as a single deterministic value. These methods typically rely on lifecycle assessment (LCA) reports that generalize embodied carbon estimates ( EC system ) across entire product categories (e.g., 28nm CPUs, LPDDR4 DRAM). However, this paradigm fails to account for critical spatial, temporal, and manufacturing variability that substantially impacts actual carbon emissions. Specifically, the existing carbon models for AI models fail to capture: (1) geotemporal differences in manufacturing, whereby the device instances in identical device classes are fabricated in different regions and periods, e.g., in the winter in Ireland (Intel) or in the summer in Taiwan (TSMC), embody distinct emissions due to different electricity carbon intensity during production; It is known that carbon intensity depends on the electricity generation process, which has spatial and temporal dynamics; (2) efficiency evolution over time, arising from continuous advancements in process yield and the energy efficiency of fabrication methods; and (3) operating context variability, since the operational carbon of AI models can vary significantly depending on the when and where the AI models depoly because of spatiotemporal variations in the carbon intensity of electricity. These characteristics introduce uncertainty into carbon estimates for AI models; however, current carbon accounting methods for AI models fail to account for these uncertainties.

3.2 Embodied carbon modeling

We extend the existing carbon modeling methodology of AI models by giving parameter models for each hardware component and characterizing the uncertainty. Specifically, we analyze the parameter

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value evolution in the fabrication process by collecting data from various sources (e.g., ESG reports, technology reports, power grid operators, etc.). We leverage KDE to generate the distributions of the parameters based on the data we collect. KDE is a standard non-parametric estimation technique used to estimate the probability density function of a random variable by applying a Gaussian kernel weighting technique to data [15]. It is used when the behavior of a sparse data sample is extrapolated to resample data to a larger sample size.

3.2.1 Embodied carbon of processors

We model the embodied carbon of large AI models caused by processors as follows: (1) the operation time of large AI models on processors, denoted as t p , and the processor's lifetime, denoted as T p . (2) the carbon emissions from electricity used during the fabrication process, calculated by multiplying the Electricity consumption Per unit of die Size ( EPS ) by the carbon intensity of electricity during manufacturing CI m ; (3) the emissions associated with the raw materials, denoted as MPS (Material Per Size); and (4) the carbon released by gas (e.g., fluorinated compounds) in the manufacturing process denoted as GPS (Gas Per Size); (5) the die size of the processor, denoted as DizeSize ; (6) fab yield denoted as Y . Then, we can model the embodied carbon of processors for large AI models as follows:

Here, we denote ˜ Y as the probabilistic model of yield Y . Similarly, we have ˜ CI m and ˜ EPS . We will give the detailed uncertainty characterization of the three parameters in the following.

Carbon intensity distribution in the manufacturing process.

CI m denotes the carbon intensity of electricity consumed during semiconductor manufacturing, a critical parameter determined by the energy source mix (e.g., solar, wind, coal, etc.) employed in electricity generation. This metric exhibits spatiotemporal variability due to fluctuations in both manufacturing schedules and geographic locations. The inherent uncertainty in carbon intensity primarily comes from temporal variations throughout annual cycles, driven by seasonal patterns in renewable energy generation and fluctuating electricity demand. When the manufacturing location is specified, regional fabrication facilities demonstrate distinct carbon intensity distribution derived from historical carbon intensity data from 2021 to 2023, as illustrated in Figure 1.

Memory can usually be manufactured by multiple manufacturers (e.g., SK Hynix, Samsung, Micron, etc.), unlike processor manufacturers, which have a monopoly (e.g., most GPUs are manufactured by TSMC). For the scenario involving uncertain manufacturing locations, the region selection can be modeled as a discrete random variable. The probability distribution across geographical regions is weighted according to their respective contributions to global IC production capacity for specific process nodes [16]. As detailed in Table 2 from industry reports [17], these capacity allocations serve as probabilistic weights for regional selection. The composite probability distribution for each process node is constructed through a mixture modeling approach, incorporating the following components: (1) regional KDE: non-parametric distributions developed using historical carbon intensity data (20212023) for each major production region; (2) capacity-weighted sampling: a Monte Carlo sampling strategy where regional selection probabilities correspond to normalized production capacities; (3) composite distribution formation: aggregation of weighted regional samples through kernel density smoothing, as visualized in Figure 2. This enables probabilistic modeling of carbon intensity while accounting for both geographical production distributions and temporal energy mix variations.

Yield Distribution . Semiconductor manufacturing yield is defined as the ratio of defect-free semiconductor dies on a wafer to the total number of dies on that wafer. The parameter exhibits inherent uncertainty that stems primarily from temporal variations in defect density observed across fabrication facilities. To systematically investigate this phenomenon, we employ TSMC's historical defect density data across four distinct process nodes [18], coupled with the application of the Poisson yield model [19] for temporal yield computation. Following empirical data collection, we generate yield histograms and subsequently apply KDE [20] to derive comprehensive probability density functions characterizing yield distributions per unit die size, as visually presented in Figure 3.

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EPS Distribution . The inherent uncertainty in EPS is from temporal fluctuations in process energy efficiencies across different fabrication stages. We build the EPS distributions based on the EPS values from the STEC model [13], the ACT model [12], the imec model [21], and the annual energy efficiency improvements data from across the TSMC ESG reports [22] across various technology process nodes (e.g., 5nm, 7nm). To construct the distributions, the analytical procedure involved three key transformations: First, energy efficiency metrics for each process node are temporally normalized relative to their baseline year values. Second, raw EPS values are adjusted through division by these normalized efficiency coefficients to account for technological advancements. Finally, we implement a dual-stage distribution modeling approach, i.e., converting the processed data into frequency histograms followed by KDE to derive continuous probability density functions of ˜ EPS , as visualized in Figure 4.

3.2.2 Embodied carbon of memory

We model the embodied carbon of large AI models caused by memory as follows: (1) the operation time of large AI models on memory t m and the memory's lifetime T m ; (2) the carbon released by the electricity consumed during the process of manufacturing the memory. This is calculated by multiplying the electricity consumption per unit of size ( EPS ) by the carbon intensity of a power grid ( CI m ) then divided by bit density ( BD , in GB/mm 2 ); (3) the carbon released independent of electricity, such as raw materials, distribution, and packaging, denoted as α m ; and (4) the capacity of memory C m . Then, we can model the embodied carbon of memory for large AI models as follows:

Here, the distribution of ˜ CI m and ˜ EPS for memory is similar to that in processors. We develop the distribution based on the data we collect from Hynix [23] as Figure 2 shows.

3.2.3 Embodied carbon of storage

We model the embodied carbon of large AI models caused by storage as follows: (1) the operation time of large AI models on storage t s and the storage's lifetime T s ; (2) the carbon emissions from the process of manufacturing the storage, which is determined by multiplying the electricity consumed per unit of Giga-Byte during the manufacturing process ( EPG ) by the carbon intensity CI m ; (3) the carbon released independent of electricity such as raw materials, denoted as α S . α S can be found in the industry reports [24]; and (4) the capacity of storage, denoted as C s . Then, we can model the embodied carbon of storage for large AI models and omit the distribution derivation as follows:

3.3 Operational carbon

The operational carbon footprint of large AI models ( OC model ) refers to the carbon emissions caused by the electricity used during operation. It is determined by the electricity consumed by the model ( E o ) and the carbon intensity of the electricity ( CI o ) as follows:

where ˜ CI o represents the distribution of the carbon intensity of that electricity. This uncertainty comes from the uncertainty of the time and location of model training or inference. E o can be recorded by hardware during the model operation, or it can be estimated by the following equations:

where P i represents the peak power of hardware i ; eff i denotes the efficiency of hardware i that can be estimated by the hardware efficiency model [1]; n i is the number of hardware i ; and t i refers to the execution time for hardware i that can be estimated according to the existing flop model [1]. These hardware units include CPUs, GPUs, memory, storage, and others.

4 Evaluation

4.1 Setup

To comprehensively evaluate PCAM for the carbon footprint of large AI models, we make an effort to develop a hardware and electricity dataset. This dataset includes hardware-related parameters (e.g., EPS, EPG, MPS, BD, etc.) and electricity-related parameters (e.g., CI), which is constructed by aggregating data from diverse sources, including ESG reports from hardware manufacturers, power grid operator statistics, industry reports, and peer-reviewed research publications

For performance evaluation, we conduct a comparative analysis between PCAM and LLMCarbon, the current state-of-the-art carbon model for large AI models. The evaluation is performed using published training data from four representative large AI models (XLM, T5, GPT-3, and Switch) [5, 9]. We compare the performance at key distribution percentiles (5th, 10th, 50th, 90th, and 95th) by resampling PCAM's probability distribution outputs against the ground truth based on the collected carbon dataset. The evaluation focuses on the training processes of large AI models, as the accounting methodology is identical for both training and inference. Please note that the carbon footprint can not be measured by sensors due to its inherent characteristic. The "ground truth" in the following evaluation is the accounting result based on the carbon dataset we collected without KDE.

4.2 Embodied carbon evaluation

We conduct a comparative analysis of embodied carbon accounting between PACM and LLMcarbon, utilizing the published XLM training data [5]. Notably, to the best of our knowledge, the XLMdataset represents the only publicly available information detailing hardware infrastructure associated with embodied carbon for large AI models training. The hardware configuration, comprising 64 servers with detailed specifications presented in Table 3, is employed for XLM's training process. The training duration lasts 20.4 days, with all hardware components assumed to have a standard operational lifetime of 5 years [5].

The embodied carbon accounting performance of PCAM and LLMCarbon is compared across different hardware components and statistical percentiles, as detailed in Table 4. For total embodied carbon, PCAM demonstrates great alignment with ground truth values across all percentiles, maintaining a maximum deviation of only 2.67% at the 10th percentile and achieving remarkable precision at the median (0.48% deviation). In contrast, LLMCarbon shows substantially larger deviations ranging from 6.03% at the median to 23.02% at the

5th percentile, demonstrating that the single deterministic model fails to capture uncertainty in embodied carbon accounting.

Component-wise analysis shows that PCAM outperforms LLMCarbon at each component. For CPU carbon accounting, PCAM errors are below 2.62% versus LLMCarbon's around 4% - 40% deviations. GPU calculations show PCAM's robust performance with less than 2% deviations across all percentiles, contrasted by LLMCarbon's substantial overestimations reaching around 67% at the 5th percentile. The DRAM and SSD comparison follows similar trends, with PCAM errors remaining

below 1.8% in DRAM (2.1% in SSD) versus LLMCarbon's around 25% - 40% in DRAM (around 2% - 18% in SSD) deviations.

Our analysis reveals that GPUs exhibit a substantially wider absolute uncertainty range (98.69 - 211.05 kg , ∆ = 114.36 kg ) in embodied carbon compared to the cumulative variance of other hardware components, establishing them as the dominant contributor to total embodied carbon variability. This disproportionate impact stems from two key manufacturing characteristics: First, GPU production employs advanced semiconductor fabrication processes that require significantly higher energy, making its embodied carbon particularly sensitive to variations in the carbon intensity of electricity. Second, the combination of larger die sizes and complex architectures results in lower yields with greater variation, amplifying the uncertainty in the embodied carbon of GPUs.

Overall, this significant variance underscores critical limitations in conventional deterministic carbon accounting models like LLMCarbon and highlights the necessity of probabilistic modeling that explicitly accounts for parameter uncertainties in carbon modeling. These findings challenge the validity of current sustainability certification paradigms that rely on deterministic embodied carbon accounting. We propose that comprehensive environmental impact assessments for large AI models should adopt distribution-aware evaluation methodologies and report confidence intervals alongside central estimates to enable more informed decision-making in sustainable large AI models development.

4.3 Operation carbon evaluation

Table 5 presents the operation carbon evaluation results of PCAM for the four large AI models, XLM, T5, GPT3, and Switch, based on their published training information [9]. The training information is listed in Table 5, where 'avg. power (W)' conveys the average system power per computing device (e.g., GPU, TPU, DRAM, etc.); "Num. of device" is the total number of computing devices. We estimate the electricity consumption of large AI models based on the training data and subsequently calculate their operational carbon footprint.

To comprehensively evaluate model performance, we conducted comparative analyses across spatial and temporal dimensions. In the spatial analysis, we maintain a fixed training date while considering global geographical variations (across 90 regions). Conversely, the temporal analysis fixed the training location (the USA) while accounting for time-dependent factors (across 2021-2023 years). Overall, PCAM outperforms LLMCarbon (0.09% - 7.44% vs. 1.54%- 108.51% deviations) in the operational carbon accounting for each AI model. Besides, the absolute error of the LLMCarbon is much larger than that of PCAM, e.g., 372.13 t vs. 3.6 t for GPT3 under the 5th percentile in the spatial dimension.

Besides, spatial variations demonstrate particularly pronounced differences. For example, the deviations of LLMCarbon under the spatial dimension are from 90.43% (5th percentile) to 108.51% (95th percentile), while that is from 16.18% to 16.43% under the temporal dimension.

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This contrast highlights that geographical factors introduce greater uncertainty in operational carbon accounting than temporal variations.

5 Case Study

PCAM delivers practical value by enabling risk-aware decision-making through carbon budget overrun probability assessments, ensuring realistic sustainability targets. It facilitates sensitivity analysis to pinpoint key uncertainty drivers, guiding operational and hardware prioritization while aiding manufacturers in green production optimization. For operational choices, PCAM helps developers schedule computing tasks based on temporal and regional grid carbon intensity. It also supports multi-source hardware comparisons by evaluating embodied carbon distributions to inform procurement. Furthermore, PCAM encourages industry-wide engagement by quantifying supply chain impacts and promoting transparency. Its probabilistic reporting enhances credibility for compliance while aligning with carbon-aware computing trends by providing confidence bounds for auditing and long-term planning.

Figure 5 provides a visual comparison of operational carbon estimates between PCAM and LLMCarbon for XLM training in three regions: California (US), Germany (DE), and Italy (IT). While LLMCarbon suggests the US produces lower emissions than IT and IT has lower emissions than DE, PCAM reveals more nuanced probabilistic outcomes: there is an 81.66% probability of IT's operational carbon footprint exceeding that of the US and a 33.06% probability of surpassing DE's emissions. This probabilistic approach enables PCAM to provide multi-dimensional insights, empowering AI developers to make more informed sustainability decisions.

6 Related Work

The current methodologies for carbon footprint estimation of large AI models predominantly concentrate on operational carbon, which is calculated as the product of electricity consumed and carbon intensity. Most studies predominantly focus on tracking or estimating the electricity consumed. A subset of studies has developed software-integrated instrumentation to monitor real-time CPU/GPU power utilization during inference or training phases [25, 26, 27, 28], while alternative approaches derive energy estimates through the parameters of and hardware (e.g., thermal design power) [29, 30]. However, these methodologies systematically neglect the embodied carbon accounting associated with AI hardware infrastructure, which is non-negligible in the carbon footprint of large AI models, as power grids decarbonize and data centers increasingly adopt zero-carbon energy sources.

Regarding embodied carbon modeling, existing frameworks such as SustainableAI [5] estimated the embodied carbon of large AI models through manufacturer-reported emission factors for hardware components, which is an average value. LLMCarbon [1] adopts a deterministic parametric model to estimate the embodied carbon for processors and average values for storage and memory in ESG

reports. However, these approaches lead to oversimplified modeling constrained by two critical limitations: (1) fail to capture the effect of temporal and spatial specificity in hardware instance (e.g., 28nm CPU made in winter in China vs. 28nm CPU made in summer in the US); (2) fail to capture the effect of heterogeneous manufacturing configurations within device class (e.g., yield and fabrication efficiency improvement for certain processors). These characteristics lead to uncertainty in carbon estimates in large AI models, but current large AI models' carbon models fail to capture this uncertainty.

7 Limitations and Discussions

This study examines the carbon footprint of large AI models across four life-cycle stages: (1) Hardware manufacturing, referring to emissions generated during the production of core computing components; (2) Hardware transport, encompassing emissions from shipping hardware to endusers; (3) Operational use, comprising emissions resulting from software execution, primarily due to electricity consumption; and (4) End-of-life processing, involving emissions associated with hardware recycling. Among these, the operational use phase corresponds to the operational carbon of large AI models, while the remaining stages contribute to their embodied carbon. Hardware manufacturing and operational use are the dominant sources of emissions, for instance, over 97% in the case of a Dell R740 server [31]. In contrast, transport and end-of-life stages make negligible contributions and are thus excluded from the current scope. Within hardware manufacturing, we focus specifically on emissions from computer hardware production, such as those arising from material extraction, energy use, and chemical processing, while ancillary factors like infrastructure, cooling systems, and human labor are not considered in this study. We acknowledge that these omitted factors also play a significant role in the overall embodied carbon footprint. A full quantification of their associated uncertainties requires interdisciplinary collaboration and is reserved for future work.

PCAM only considers the uncertainty of some parameters due to the lack of relevant carbon data. Inaccuracy comes from using averaged/aggregated data in various aspects (e.g., raw material, supply chain, packaging, etc.). Intrinsically, carbon data is unique in that it cannot be directly measured by sensors (unlike electricity) and can only be calculated through accounting models, which leads to the fact that perfect carbon modeling is difficult. The increasing focus on carbon emissions considerations among hardware producers drives substantial enhancements in carbon data quality. This trend leads to more accurate and reliable accounting models for the carbon footprint of large AI models.

8 Conclusion

In this paper, we propose PCAM, a Probabilistic Carbon Accounting Model for large AI Models, which systematically captures and quantifies the uncertainties inherent in both embodied and operational carbon emissions. Unlike existing deterministic approaches such as LLMCarbon, PCAM provides distribution-based carbon footprint estimates, enabling AI developers and policymakers to make risk-aware decisions. By moving beyond point estimates to probabilistic carbon accounting, PCAMsupports more robust environmental impact assessments, facilitates compliance with emerging carbon regulations, and promotes transparency in AI sustainability reporting. Future work will expand PCAM to incorporate additional lifecycle stages and supply chain factors, fostering a more holistic and actionable framework for carbon-aware AI development. To facilitate the decarbonization of large AI models, we are open-sourcing the carefully curated carbon dataset compiled in this study, thereby providing the community with the necessary tools to quantify, understand, and mitigate the environmental impact of AI model development. We strongly call for collective action across the industry to enhance the transparency of carbon-related data, including the carbon intensity of power grids and hardware-related data. Establishing a culture of open and standardized emissions reporting is fundamental to driving systemic decarbonization. It enables the establishment of credible baselines, pinpoints optimization hotspots, and paves the way for accountable and verifiable progress across the entire AI ecosystem.

References

Ahmad Faiz, Sotaro Kaneda, Ruhan Wang, Rita Osi, Prateek Sharma, Fan Chen, and Lei Jiang. Llmcarbon: Modeling the end-to-end carbon footprint of large language models. In The Twelfth International Conference on Learning Representations . ICLR, 2024.

Rohan Alur, Loren Laine, Darrick Li, Manish Raghavan, Devavrat Shah, and Dennis Shung. Auditing for human expertise. Advances in Neural Information Processing Systems , 36:7943979468, 2023.

Sander Beckers. Moral responsibility for ai systems. Advances in Neural Information Processing Systems , 36:4295-4308, 2023.

Wentao Gao, Jiuyong Li, Debo Cheng, Lin Liu, Jixue Liu, Thuc Duy Le, Xiaojing Du, Xiongren Chen, Yanchang Zhao, and Yun Chen. A deconfounding approach to climate model bias correction. arXiv preprint arXiv:2408.12063 , 2024.

Carole-Jean Wu, Ramya Raghavendra, Udit Gupta, Bilge Acun, Newsha Ardalani, Kiwan Maeng, Gloria Chang, Fiona Aga, Jinshi Huang, Charles Bai, et al. Sustainable ai: Environmental implications, challenges and opportunities. Proceedings of Machine Learning and Systems , 4:795-813, 2022.

Yiyang Zhao, Yunzhuo Liu, Bo Jiang, and Tian Guo. Ce-nas: An end-to-end carbon-efficient neural architecture search framework. In The Thirty-eighth Annual Conference on Neural Information Processing Systems .

Oussama Boussif, Ghait Boukachab, Dan Assouline, Stefano Massaroli, Tianle Yuan, Loubna Benabbou, and Yoshua Bengio. Improving* day-ahead* solar irradiance time series forecasting by leveraging spatio-temporal context. Advances in Neural Information Processing Systems , 36:2342-2367, 2023.

Ruohan Li, Yiqun Xie, Xiaowei Jia, Dongdong Wang, Yanhua Li, Yingxue Zhang, Zhihao Wang, and Zhili Li. Solarcube: An integrative benchmark dataset harnessing satellite and in-situ observations for large-scale solar energy forecasting. Advances in Neural Information Processing Systems , 37:3499-3513, 2024.

D Patterson, J Gonzalez, Q Le, C Liang, LM Munguia, D Rothchild, D So, M Texier, and J Dean. Carbon emissions and large neural network training. arxiv 2021. arXiv preprint arXiv:2104.10350 , 2021.

Nvidia. NVIDIA A100 Tensor Core GPU , 2024. https://www.nvidia.com/en-us/ data-center/a100/ .

Google. Accelerate AI development with Google cloud TPUs , 2024. https://cloud. google.com/tpu .

Udit Gupta, Mariam Elgamal, Gage Hills, Gu-Yeon Wei, Hsien-Hsin S Lee, David Brooks, and Carole-Jean Wu. Act: Designing sustainable computer systems with an architectural carbon modeling tool. In Proceedings of the 49th Annual International Symposium on Computer Architecture , pages 784-799, 2022.

Xiaoyang Zhang, Yijie Yang, and Dan Wang. Spatial-temporal embodied carbon models for the embodied carbon accounting of computer systems. In Proceedings of the 15th ACM International Conference on Future and Sustainable Energy Systems , pages 464-471, 2024.

Xiaoyang Zhang and Dan Wang. A gnn-based day ahead carbon intensity forecasting model for cross-border power grids. In Proceedings of the 14th ACM International Conference on Future Energy Systems , pages 361-373, 2023.

Emanuel Parzen. On estimation of a probability density function and mode. The annals of mathematical statistics , 33(3):1065-1076, 1962.

Anvita Bhagavathula, Leo Han, and Udit Gupta. Understanding the implications of uncertainty in embodied carbon models for sustainable computing. In HotCarbon . 2024.

SIA BCG. EMERGING RESILIENCE IN THE SEMICONDUCTOR SUPPLY CHAIN , 2024. https://www.semiconductors.org/wp-content/uploads/2024/05/ Report_Emerging-Resilience-in-the-Semiconductor-Supply-Chain. pdf .

Ian Cutress. Better yield on 5nm than 7nm: TSMC update on defect rates for N5 , 2020. https://www.anandtech.com/show/16028/ .

EESemi. Test yield model , 2005. https://www.eesemi.com/test-yield-models. htm .

Jake Vanderplas. Density Estimation-scikit-learn.org. , 2024. https://scikit-learn. org/stable/modules/density.html .

L Boakes, M Garcia Bardon, V Schellekens, IY Liu, B Vanhouche, G Mirabelli, F Sebaai, L Van Winckel, E Gallagher, C Rolin, et al. Cradle-to-gate life cycle assessment of cmos logic technologies. In 2023 International Electron Devices Meeting (IEDM) , pages 1-4. IEEE, 2023.

TSMC. Esg reports by tsmc. https://esg.tsmc.com/en-US/resources/ ESG-data-hub?tab=reportbuilder , 2023.

SK Hynix. Sustainability report. https://www.skhynix.com/sustainability/ UI-FR-SA1601/ , 2021.

SEAGATE. Lca product reports by seagate. https://www.seagate.com/esg/ planet/product-sustainability/ , 2024.

Peter Henderson, Jieru Hu, Joshua Romoff, Emma Brunskill, Dan Jurafsky, and Joelle Pineau. Towards the systematic reporting of the energy and carbon footprints of machine learning. Journal of Machine Learning Research , 21(248):1-43, 2020.

Lasse F Wolff Anthony, Benjamin Kanding, and Raghavendra Selvan. Carbontracker: Tracking and predicting the carbon footprint of training deep learning models. arXiv preprint arXiv:2007.03051 , 2020.

Semen Andreevich Budennyy, Vladimir Dmitrievich Lazarev, Nikita Nikolaevich Zakharenko, Aleksei N Korovin, OA Plosskaya, Denis Valer'evich Dimitrov, VS Akhripkin, IV Pavlov, Ivan Valer'evich Oseledets, Ivan Segundovich Barsola, et al. Eco2ai: carbon emissions tracking of machine learning models as the first step towards sustainable ai. In Doklady Mathematics , volume 106, pages S118-S128. Springer, 2022.

Kadan Lottick, Silvia Susai, Sorelle A Friedler, and Jonathan P Wilson. Energy usage reports: Environmental awareness as part of algorithmic accountability. arXiv preprint arXiv:1911.08354 , 2019.

Alexandre Lacoste, Alexandra Luccioni, Victor Schmidt, and Thomas Dandres. Quantifying the carbon emissions of machine learning. arXiv preprint arXiv:1910.09700 , 2019.

Loïc Lannelongue, Jason Grealey, and Michael Inouye. Green algorithms: quantifying the carbon footprint of computation. Advanced science , 8(12):2100707, 2021.

DELL. R740 lca reports. https://www.delltechnologies.com/asset/en-us/ products/servers/technical-support/Full_LCA_Dell_R740.pdf , 2019.

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Appendix

We provide additional experiments to compare PCAM with STEC [13], which is an embodied carbon accounting model for computer systems. STEC incorporates spatiotemporal variability in the carbon intensity of electricity used during hardware manufacturing. However, it remains a fundamentally deterministic model and does not probabilistically account for other key sources of uncertainty, such as geotemporal manufacturing capacity distribution or efficiency evolution over time (e.g., yield and fabrication efficiency improvements). To enable a direct quantitative comparison with PCAM at the AI model level, we extended the STEC methodology by scaling its hardware-level carbon accounting using the foundational equation (Eq. 2 from the main text) and generating a distribution of embodied carbon based on the regional electricity carbon intensity frequency data. PCAM outperforms STEC consistently across all percentiles, with errors under 3% compared to STEC's under 24%, as Table 6 shows.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the critical issue of carbon emissions associated with large AI models, encompassing both operational and embodied carbon footprints. While prior studies have largely relied on deterministic estimates, this work identifies and models three key sources of uncertainty that affect carbon accounting: (1) geotemporal variability in manufacturing, (2) temporal evolution of manufacturing practices, and (3) dynamic operational conditions. To capture these factors, the authors propose a Probabilistic Carbon Accounting Model (PCAM) that integrates a dual-stage distribution modeling approach using Kernel Density Estimation (KDE) on a curated dataset of carbon-relevant parameters from diverse sources. Experimental results demonstrate that PCAM significantly improves estimation accuracy, achieving ≤ 7.44% error compared to LLMCarbon’s ≤ 108.51%.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n1. **Timely and Impactful Topic**.\n   The paper addresses a critical and timely problem—the carbon footprint of large AI models—at a moment when environmental sustainability in AI is garnering significant attention across academia, industry, and policy-making. By focusing on both *operational* and *embodied* carbon emissions, the work reflects a holistic view of AI's environmental impact, aligning with recent calls for more transparent and accountable AI development practices.\n\n2. **Quantitative Evaluation with Clear Metrics**.\n   The empirical evaluation is well-structured and includes a comparative benchmark against a widely cited prior method, **LLMCarbon**. The results, indicating a ≤ 7.44% estimation error for PCAM versus ≤ 108.51% for LLMCarbon, are compelling and underscore the effectiveness of the proposed probabilistic modeling approach.\n\n3. **Well-Structured and Coherent Presentation**.\n   The paper is clearly written and logically organized. Each section transitions smoothly into the next, and technical components are introduced with sufficient motivation and clarity. This makes the paper accessible not only to sustainability researchers but also to a broader machine learning audience concerned with AI's environmental footprint.\n\n\n## Weaknesses\n\n1. **No comparison against a highly-related prior work**.\n  The paper does not compare PCAM with the method proposed in Zhang et al. [12] (\"Spatial-temporal embodied carbon models for the embodied carbon accounting of computer systems\", e-Energy 2024). This prior work also addresses uncertainties in embodied carbon and should serve as a critical baseline. I strongly encourage the authors to include a quantitative comparison with [12] in the experimental section. Doing so would more rigorously establish the novelty and practical advantage of PCAM in capturing embodied carbon uncertainty.\n\nQUESTIONS:\n1. Zhang et al. [12] present a spatial-temporal model for embodied carbon that also addresses uncertainty, making it a strong baseline for comparison. Could you clarify why this work was not included in your experimental evaluation? Additionally, is there a technical limitation or incompatibility that prevents a direct quantitative comparison between PCAM and [12]? Including such a comparison would significantly strengthen your claims regarding PCAM’s accuracy and novelty.\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors proposed probabilistic carbon accounting model (PCAM) to accurately estimate the carbon footprint of large AI models by capturing the uncertainties in carbon modeling. The uncertainties are: 1) geotemporal manufacturing variability, 2) dynamic manufacturing evolution, 3) dynamic operating context. PCAM will report a distribution instead of a single number that helps make more risk-aware decisions in sustainable AI. They proposed novel approaches to construct distributions for parameters like embodied carbon of processors, embodied carbon of memory, embodied carbon of storage, etc.\n\nTo evaluate their proposed method, the authors crafted a dataset including ESG reports, power grid data, etc. They evaluated PCAM on 4 large AI models, XLM, T5, GPT3, Switch, and the results showed that PCAM outperformed LLM Carbon, achieving less than 8% error in both embodied and operational carbon predictions.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1) Proposed a novel approach for accounting embodied carbon and report a distribution instead of just a number which captures the uncertainty in embodied carbon uncertainty.\n2) Significant improvement over the current benchmark (LLM Carbon) in embodied and operational carbon accounting\n3) Provide important insight on GPUs are major contributors to carbon uncertainty.\n4) The paper is well organized and clear.\n\nWeakness:\n1) For operational carbon accounting, the sampling may not capture the temporal characteristics. for example, from 12pm to 2pm in California when solar is abundant, we have low carbon intensity for the electricity, however, by sampling from a distribution, you may get high values of carbon emissions for this time period which makes the operational carbon accounting inaccurate.\n2) Other factors like cooling infrastructure in data centers are neglected which plays a pivotal role in carbon accounting\n\nQUESTIONS:\n1) Why didn't you just use electricity maps data for operational carbon accounting instead of sampling from a distribution. my question is related to comment 1 on weakness.\n2) Can the cooling infrastructure's embodied and operational carbon accounting be modeled with PCAM?\n3) How do you think PCAM can be used in practice by AI engineers? How can it be informative and insightful to be able to change the manufacturing process of the parts like processors, memory, etc?\n\nLIMITATIONS:\nThe limitation were addressed adequately; however, they can also argue in their discussion about the hidden carbon emissions that is often neglected like labor.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper reports the development of a new model to estimate the carbon emissions of LLMs. By using a novel dataset assembled by the authors containing semiconductor production data and electricity emissions, the authors estimate parameter distributions for relevant sources of variation in emissions and integrate them into a single predictive model for LLM carbon emissions. The authors report a test of this model compared to LLMCarbon, finding favorable performance.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Improving the understanding of GHG emissions of LLMs is an important endeavor. The paper suggests ways to better model several different parts of the overall emissions of LLMs, focusing on including uncertainty quantification.\n- The authors intend to release a dataset they have assembled with information relevant to performing LCAs for LLMs. From the brief description in the paper, this dataset would seem to be valuable for other LCA practitioners. \n- The authors have attempted to test their model against values derived from reported data regarding LLM training.\nWeaknesses\n- No machine learning is used in the paper. It might be more appropriate for a conference focusing on LCA, supply chain emissions, or data center sustainability.\n- Although presented as an LCA analysis, the paper does not include several important aspects of LCA that are specified in ISO 14040. One example is a failure to clearly specify the system boundary. The electricity consumption and IT hardware are included, but the data center physical building and other potential sources of emissions are omitted, without discussion. Another example is a failure to include the full life-cycle of IT components, which encompasses end-of-life disposal.\n- The reported evaluation with “ground truth” from published LLM training information is unclear and difficult to follow, but it appears to only compare emissions estimates of the training phase of AI models, not inference. \n- The paper strongly asserts the value of uncertainty modeling in LCA. While it’s true that this can provide confidence intervals (as mentioned), that doesn’t translate to enabling AI model developers to make choices about lower-emitting options. For example, yield variation impacts this uncertainty, but there is no practical way AI model developers can directly make business choices to change yield.\n- In order to accept this paper for publication, I recommend the following changes. First, a clearer specification of the system boundary and the “life stages” of the LLM that are included / excluded and a discussion of the reasons. Second, a clearer description of how published training data were used to develop a distribution of embodied carbon emission estimates (as “ground truth”), and a clear discussion about whether and how this applies to the inference phase vs the training phase. Third, a clearer discussion about what insights this type of uncertainty-based LCA modeling of LLMs could actually provide to decision-makers developing LLMs, and which of these are practically feasible. With these changes I would be willing to consider revising my recommendation to “accept”.\n\nQUESTIONS:\n•\t[Line 63] Why are you reporting results with three or more significant figures, when a substantial part of this work is highlighting uncertainty ranges? This seems to be false precision, and I would recommend no more than 2 sig figs be used. \n•\t[Line 97] Where did you source the carbon emission factors for Table 1? They are approximately right, but there are significant variations by region and by sub-technology.\n•\t[Line 141] It’s good that you’ve included the F-gas emissions and the raw material extraction emissions. However, they don’t seem to be addressed in the following discussion. How did you handle those uncertainties?\n•\t[Line 155] Grids are evolving across the world, and the share of low-carbon electricity is typically increasing in them. Yet you are using data from 2021 and 2023 to estimate carbon intensity of electricity consumption. How can your approach be efficiently kept up-to-date with changing grid generation mixes?\n•\t[Line 203] The energy efficiency appears to be treated as a variable that improved by a fixed percentage every year, ad infimum. Has this been true of observed efficiency gains in fabs?\n•\t[Line 247] Your evaluation appears to take published information on training hardware and duration for select LLMs, and convert that into an embodied carbon value. It’s not clear how you’re doing this, or how you’re obtaining a distribution. How do you determine the geographic region where training occurred? How do you determine the emissions associated with manufacturing for hardware used in training? Further, given the input data, this test only speaks to the emissions for training a model, not for inference.\n•\t[Line 267] Why do you conclude that the large deviation between LLMCarbon and the ground truth data demonstrates a failure to capture uncertainty? The primary conclusion seems to be that LLMCarbon is based on inaccurate or insufficient data. Incorporating uncertainty would presumably not change the median value estimated by LLMCarbon unless distributions of relevant parameters were significantly skewed. Do you think that’s the case?\n•\t[Line 295] Given geopolitical and economic realities, why do you feel it is feasible for companies training AI models to select different manufacturing timelines and geographic locations for their GPUs? This would appear to be highly impractical.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents PCAM, a Probabilistic Carbon Accounting Model for estimating the carbon footprint of large AI models. It addresses a key limitation in prior work like LLMCarbon by modeling uncertainty in both embodied and operational carbon—specifically due to geo-temporal variability, manufacturing evolution, and operating context. PCAM uses KDE-based parameter distributions and a carbon dataset compiled from ESG reports and energy statistics. Compared to LLMCarbon, PCAM achieves significant error reductions. The work is well-motivated and timely in light of increasing interest in AI sustainability.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- Important problem: The paper tackles a meaningful and underexplored issue—quantifying uncertainty in AI carbon footprint estimation—which has practical implications for sustainability-aware system design and policy compliance.\n- Novel contribution: Introduces a probabilistic modeling approach (PCAM) that goes beyond deterministic estimates, enabling risk-aware decision-making.\n- Dataset contribution: Authors commit to release a comprehensive dataset for embodied carbon estimations along with the code\n\n**Weaknesses**\n- Lack of component attribution analysis: While the paper models distributions over multiple factors (e.g., yield, carbon intensity), it does not perform an attribution analysis to assess which parameter contributes most to overall variance. Such sensitivity analysis would be valuable to guide optimization or intervention.\n\n- Ground truth ambiguity: In Table 5, it's unclear how the \"ground truth\" embodied carbon values were calculated. Are these empirical measurements, model-derived, or based on re-aggregated estimates?\n\n- Power estimation unclear: Section 4.3 mentions estimating electricity consumption from training data, but the method for computing “Ave. Power” in Table 6 is not described. Is it measured, averaged across hardware, or estimated from spec sheets?\n\n- Geographic granularity concerns: The operational carbon analysis seems to aggregate carbon intensity at the country level. For a geographically diverse region like the US, this averaging may obscure intra-country variance. Figure 5 suggests lower variance for the US, but it’s unclear if this is due to temporal-only variation or over-averaging. Tools like ElectricityMaps offer balancing-authority-level granularity that may yield more accurate results.\n\n- Hardware lifespan effects: While lifespan is modeled in the formulas, its role in uncertainty or sensitivity is not discussed in the evaluation. Additionally, environmental factors (e.g., temperature, humidity) that affect hardware degradation and embodied carbon are not modeled.\n\n- Typos and presentation issues: There are a number of typos and formatting issues (e.g., “Trainin Day” in Table 6), which detract from polish and clarity.\n\n- Fit for NeurIPS: While the work is high-quality, it may be better suited for venues in systems, sustainability, or hardware design (e.g., HPCA, ISCA, or HotCarbon), as the paper’s core technical contribution lies in accounting methodology rather than ML algorithmics.\n\nQUESTIONS:\nIn terms of quantification method and evaluation, some important points are not clear to me:\nQuestions:\n- It is not clear how’s the ground truth embodied carbon data is calculated in Table 5? \n- Section 4.3 “We estimate the electricity consumption of AI models based on the training data” -> How’s this estimation done? i.e. How’s the “Ave. Power” of the different models calculated in Table 6? \n- What’s the geographic granularity used for operational carbon analysis in the US? US is much larger compared to Germany/Italy geographic and there is a lot of differences between each Balancing Authorities in the US. In Figure 5, is the variability only caused by temporal differences? If so it means data is averaged significantly for US and that’s probably the reason for why the density function has less variance compared to other countries. Operational carbon estimation tools such as ElectricityMaps provide finer granularity than country level geographic granularity.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-15"}