Unveiling the Uncertainty in Embodied and Operational Carbon of Large AI Models through a Probabilistic Carbon Accounting Model
Authors: Xiaoyang Zhang
He Fang
Yang Deng
Dan Wang
Venue: NeurIPS 2025 poster ()
Keywords: Carbon footprint
Large AI models
Large language models
Primary area: social_and_economic_aspects_of_machine_learning

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
Xiaoyang Zhang', Fang He', Yang Deng', and Dan Wang
Department of Computing, Hong Kong Polytechnic University Division of Environment and Sustainability, Hong Kong University of Science and Technology (xiaoyang. zhang, fangf he, yang2. deng) @connect. pol yu. hk, wangdan uust. hk
Abstract
The rapid growth of large Al models has raised significant environmental concerns due to their substantial carbon footprint. Existing carbon accounting methods for AI models are fundamentally deterministic and fail account for inherent uncertainties in embodied and operational carbon emissions. Our work aims to investigate the effect of these uncertainties embodied and operational carbon footprint estimates for large AI models. We propose a Probabilistic Carbon Ac- counting Model (PCAM), which quantifies uncertainties the carbon accounting of large AI models. We develop parameter models to quantify key components (pro- cessors, memory, storage) in the carbon footprint of AI models. To characterize the distribution of the parameters, we develop 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-an carbon accounting method for large Al models. PCAM achieves S 7.44% error compared to LLMCarbon's 's < 108.51%.
Introduction
Large Al 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 (.. The AI community is increasingly
focused developing methodologies to tackle social issues 12 3 4 particularly in promoting g Carbon accounting, i.e., to
decarbonization and achieving carbon neutrality by 2050 5S 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 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).
emissions, organizations
While existing studies have initiated carbon accounting for AI models [5] D. current methodologies exhibit two fundamental limitations. First, they predominantly focus on operational carbon, while neglecting or applying 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
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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carbon models for Al models are single-deterministic and fail to capture the inherent uncertainty in the carbon footprint of AI models. The uncertainty in carbon accounting for Al 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 Probabilistic Carbon Accounting Model (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) the carbon footprint of large Al 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 statisties, 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 ofte-of-iie of-the-art carbon modeling method for large Al 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 (S 23.02% and S 108.51%, respectively).
Our contributions can be summarised as follows:
We propose a new Probabilistic Carbon Accounting Model (PCAM) for large Al models that can generate distribution-bast based outputs of carbon footprint instead of singular values, allowing Al developers to make risk-aware and sustainable decisions.
We characterize the uncertainty in the carbon footprint of large Al models across key hardware components by generating the distributions of AI hardware-relater 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 PaanettCcottttn 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 Al models carbon footprint
The carbon footprint of large AI models includes two components, i.c., operational carbon and embodied carbon. The operational carbon of large Al 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 Al 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 A 110 (00) and MI accelerators (e.g., Google TPU (TT.. 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 Al 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
Available https://gihubb.oo//uuuaaccce

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Table 1: Carbon emission factors (g/kWh) for energy sources
14
Emissiio factors
Coal
Natural gas
Nuclear
Wind
Solar
Hydro
Geothermal
Biomass
Other
Life-cycle emissions
650
24
230
carbon of large Al models will be greatly reduced, resulting in embodied carbon accounting for non-negligible part of the large Al 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.) much higher than those of green sources (e.g., wind, solar, etc.), as Table shows.
The carbon intensity of electricity is the carbon emission rate (in g/ g/kWh) when the electricity is generated, i.e., the total amount of carbon emitted (Gram) as against the electricity generation (Kilowall Hour). 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:
Eeth E Σ Eb
Carbon Intensity
where ef is the carbon emission factor and E 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 equation 2 where Cmoddt denotes the total carbon footprint of the Al models, including embodied carbon (EC model)) and operational carbon (OCmodet), é 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 CT is the carbon intensity of electricity.
Cmodei ECmodel + OCmomel t/T E.TT-ECsysten ECsystem + E CT
(2)
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 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 account for critical spatial, temporal, and manufacturing variability that substantially impacts actual carbon emissions. Specifically, the existing carbon models for Al 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 distinet emissions due different electricity carbon intensity during production; 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 AI models can vary significantly depending on the when and where the Al models depoly because of spatiotemporal variations in the carbon intensity of electricity. These characteristics introduce uncertainty into carbon estimates for Al models; however, current carbon accounting methods for Al models fail to account for these uncertainties.
3.2 Embodied carbon modeling
We extend the existing carbon modeling methodology of models by giving parameter models for each hardware component and characterizing the uncertainty. Specifically, analyze the parameter

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China
Taiwan
Japan
131h
5317
6954
0.03
tatre
1:11
X:06-
1302
6083
200
1300
163 Carbon inconsity (g/WW)))
450
(graWh))
8:00
To
Corbon (grath)
Figure 1: Histograms of hourly carbon intensity data (monthly data in China) from five major IC production regions between 2021-2023 with their individual kernel density estimates (KDEs).
Processors Mixture KDE Carbon Intensity Fabrication 2021-2023
SSD and DRAM Mixture KDE Carbon
Intensity of Fabrication 2021 1-20
28+ nm
SSD DRAM
8.008
10-22 nm
<10 nm
Density
Density
0.006
0.004
0.002
0.000
300
400
500
600
700
300
400
500
600
700
Carbon Intensity (g/kWh)
Carbon Intensity (g/kWh)
Figure 2: The distribution of carbon Intensity of processors, memory (DRAM), and storage (DRAM) fabrication 2021-2023.
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 estimate the probability density function of random variable by applying Gaussian kernel weighting technique to data [15]. is used when the behavior of a sparse data sample is extrapolated resample data larger sample size.
3.2.1 Embodied carbon of processors
We model the embodied carbon of large Al models caused by processors as follows: (1) the operation time of large AI models on processors, denoted t,. and the processor's lifetime, denoted Tp- (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 Cl (3) the emissions associated with the raw materials, denoted as M PS (Material
Per Size); and (4) the carbon released by gas (e.g., fluorinated compounds) in the manufacturing process denoted as G PS (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 Al models as follows:
model lp DicSize Tp T
ECº
(Clm - GPS MPS)
(3)
Here, denote Ý the probabilistic model of yield Y. Similarly, have Cîn, and EPS. We will give the detailed uncertainty characterization of the three parameters in the following.
Carbon intensity distribution in the manufacturing process.
CIn,, denotes the carbon intensity of electricity consumed during semiconductor manufacturing, critical parameter determined by the energy source mix (e.g., solar, wind, coal, etc.) employed in electricity generation. This metric exhibits spatiotemporal variability due 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 specified, regional fabrication facilities demonstrate distinct carbon intensity distribution derived from historical carbon intensity data from 2021 2023, as illustrated in Figure] [

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Table 2: Global wafer fabrication capacity by technology by regions in 2020.
Regions
US
China
Taiwan
Korea
Japan
Others
<10mm Logic
0%
0%
69%
31%
0%
0%
10-22nm Logic
28%
6%
40%
9%
5%
12%
28nm+ Logic
8%
33%
30%
5%
10%
14%
Memory(DRAM)
3%
18%
20%
52%
7%
0%
Storage(NAND)
3%
26%
4%
30%
30%
7%
Memory can usually be manufactured by multiple manufacturers (e.g., SK Hynix, Samsung, Micron, etc.), unlike processor manufacturers, which have monopoly (e.g., most GPUs manufactured by TSMC). For the scenario involving uncertain manufacturing locations, the region selection can be modeled 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 from industry reports 117. these capacity allocations serve as probabilistic weights for regional selection. The composite probability distribution for each process node constructed through mixture modeling approach, incorporating the following components: (1) regional KDE; non-parametric distributions developed using historical carbon intensity data (2021- 2023) for each major production region; (2) capacity- weiighed sampling: 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 semi- conductor dies wafer to the total number of dies that wafer. The parameter exhibits inherent uncertainty that stems primarily from temporal variations in defect density observed across fabrica- tion facilities. To systematically investigate this phenomenon, we employ TSMC's historical defect density data across four distinct process nodes [88. coupled with the application of the Poisson yield model [9] 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
Kernel Density Estimation of Yield
16.
5mm
7am
40
10mm
Donsity
Qvenitt
18
6.50
3.86
6:38
pper cm/!
EPS (WWh on")
Figure 3: The Kernel Density Estimation of
Figure 4: The kernel density estimation of EPS across different technology nodes.
Yield Y.
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 [3]. the ACT model [[2], the imec model (2T) 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
5

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3.2.2 Embodied carbon of memory
We model the embodied carbon of large AI models caused by memory follows: (I) the operation time large Al models on memory im and the memory's lifetime Tm: (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 size (EPS) by the carbon intensity of a power grid (CIIm) then divided by bit density (BD, in GB GB/mm'* )) (3) the carbon released independent of electricity, such as raw materials, distribution, and packaging. denoted as Om: and (4) the capacity of memory Cm. Then,
model the embodied carbon of memory for large Al models follows:
Eomdde! = tm//Tmm Cm (CIm EPS/BD + am)
Here, the distribution of CIn, and EPS for memory similar that in processors. We develop the distribution based on the data we collect from Hynix 23 Figure 2 shows.
3.2.3 Embodied carbon of storage
We model the embodied carbon of large Al models caused by storage as follows: (1) the operation time of large Al models on storage L, and the storage's lifetime T.: (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 Clmi (3) the carbon released independent of electricity such raw materials, denoted as ag. aş can be found in the industry reports [24]; and (4) the capacity of storage, denoted as C.. Then, we can model the embodied carbon of storage for large Al models and omit the distribution derivation follows:
EC Eodded t./T.. C. (CIm EPG tas)
(5)
3.3 Operational carbon
The operational carbon footprint of large Al models (OCrodde) refers the carbon emissions caused by the electricity used during operation. is determined by the electricity consumed by the model (F,) and the carbon intensity of the electricity (CT,) follows:
OCmodel = E. CI.
where CI, 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, can be recorded by hardware during the model operation, or it can be estimated by the following equations:
E,
n. t2) PUE
iE HeHodwareSSet
where P. represents the peak power of hardware i; ef fr denotes the efficiency of hardware i that can be estimated by the hardware efficiency model M1 n. is the number of hardware i; and t, 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.
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., CT), 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

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Table The hardware information about XLM.
Hardware
Number
Die Size/Unit
Technology Nodes
GPU
512
8.15 cm2
12nm
CPU
64
1.47 cm2
16mm
Storage(SSD)
64
32TB
Seagate Nytro 3332
Memory(DRAM)
64
256GB
10nm ddr4
For performance evaluation, we conduct comparative analysis between PCAM and LLMCarbon, the current state-of-the-art carbon model for large AT models. The evaluation performed using published training data from four representative large Al models (XLM,, T5, GPT-3, and Switch) 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]. No-
Table 4: The comparison between LLMCarbon and
PCAM on embodied carbon accounting.
tably, to the best of our knowledge, the XLM dataset 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 pre- sented in Table is employed for XLM's training process. The training duration lasts 20.4 days, with all hardware com- ponents assumed to have standard op- erational lifetime of years (5)
Total Embodied Curbon (kg) at each Percentile 10th
Models
Median
90th
95th
Ground Truth PCAM
229.17
236.27
279.75
331.32
352.15
235.2
242.74
339.95
359.93
PCAM A
2.56%
2.67%
0.48%
2.54%
2.16%
LLMCarbon
297.71
LLMCarbonA
23.02%
20.64%
6.03%
11.29%
18.29%
CPU Embodied Carhon (kg)
each Percentile
Ground Truth
1.14
1,18
1,49
2,04
2.18
PCAM
1.16
1.19
1.48
2.01
2.12
PCAMA
1.72%
0.81%
0.52%
1.45%
2.61%
LLMCarbon
1.55
LLMCarbonA
26.50%
23.89%
4.08%
31.47%
40.25%
GPU Embodied Carbon (kg)
Percentile
Ground Truth
98.69
101.36
133.76
189.11
211.03
PCAM
96.97
99.42
132.29
187.62
209.39
The embodied carbon accounting per- formance of PCAM and LLMCarbon is compared across different hardware com- ponents and statistical percentiles, as de- tailed in Table 4 For total embodied carbon, PCAM demonstrates great align- ment with ground truth values across all percentiles, maintaining a maximum de- viation of only 2.67% at the 10th per- centile and achieving remarkable preci- sion at the median (0.48% deviation). In contrast, LLMCarbon shows substan- tially 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.
PCAMA
1.77%
1.95%
1.11%
0.79%
0.79%
MCrrbo
141.68
LLMCarbonA
66.85%
28.46%
5.59%
33.48%
48.96%
DRAM Embodied Carbon (kg) at each Percentile
Ground Truth
7.97
8.15
10.39
14.47
15.3
PCAM
7.83
8.07
10:26
14.34
15.21
PCAMA
1.79%
0.99%
1.27%
0.59%
LLMCarbon
10.85
ML
26.54%
24.88%
4.24%
33.36%
41.01%
SSD Embodied Carbon (kg)
Percentile
Ground Truth
105.99
110.23
123.62
145.17
147.74
PCAM
108.25
111.47
122.76
147.05
149.65
PCAMA
2.09%
1.11%
0.70%
1.28%
1.28%
LLMCarbon
125.64
LL
15.64%
12.27%
1.61%
15.54%
17.59%
Component-wise analysis shows that PCAM outperforms LLMCarbon at each component. For CPU carbon accounting, PCAM errors are below 2.62% versus LLMCCabon's around 4% 40% deviations. GPU calculations show PCAM's robust performance with less than 2% deviations across all percentiles, contrasted by LLMCCrbon's substantial overestimations reaching around 67% the 5th percentile. The DRAM and SSD comparison follows similar trends, with PCAM errors remaining
7

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Table 5 presents the operation carbon evaluation results of PCAM for the four large Al models, XLM, T5, GPT3, and Switch, based on their published training information [9] The training information is listed in Table 55 where "avg. power (W)" conveys the average system power per computing device Table 5: The comparison between LLMCarbon and PCAM on different large Al models for opera- tional carbon accounting.
models
Carhon Models
5th per
Openational Carbon Spacial Dimension (Inn)
10th per
Median
90th per
95h per
5th per.
Operational Carbon
16th per.
Median
Temporai Dimension (ten)
95th per.
95th pets.
Training Day: 20.4;
Ground Truth
4.93
25.19
56.77
62.74
33.41
34.67
39.75
45.07
46.41
LLMCuubnn
30:09
38.86
Nom, of devico:
Ave. Power: 342 kw:
PCAM
PCAM
LLMCssbon
90-46%
2.87%
2.79
83,62%
1.90%
5,13
6.11%
3.08%
29.08
88.675
0.63%
57.13
108.510 188.519
1.52%
63.71
0.54%
16.188
33.59
13,025
1.40%
34.19
2.37%
1.82%
39.07
13/09%
0.97%
45.51
0.3%%
$6.00
Num. of device: 512
Ave. Power: 310 kw:
PUE: 1.12:
Training Day: 20;
LLMCarbon
PCAM
PCAM
LLMCiabon
Ground Truth
90,45%
7.44%
2.42
83.62%
5.91%
4.74
0.668
6.32%
25.08
23.23
0.38%
51.36
51.19
626
108 108.485
0.68%
57.13
56.77
2 2.30%
16.19%
30.91
13/009
1.91%
31,95
2.91%
2,335
36.85
57.07
13.05%
1.628
40.13
16.1%
42.83
1.96%
GPT3
Nom, of device: 1OK
Ave: Powar: 130 kw:
Tarinin Day: 14.8;
PUE:L11:
LLMCabbon
LLMCarbon
PCAM
PCAM
Groun Touth
90.436
4.26%
37,75
39.36
83.505
3.138
67.53
09:71
358.21
6.32%
411,89
1.218
49
38.64%
765.12
776.22
0.94%
108.476
809.37
857.85
1.33%
16.19%
429.57
456.83
1.55%
15,00%
474.09
469599
0.67%
535.68
$43.94
2.715
559.09
1,54%
13.07%
616.31
605.95
1,71%
16.41%
634.55
626.12
1.35%
Switch
Num, of device: 1K
Ave. Power: 345 ko:
Tarinin Day: 27:
PUE:111:
LLMCarbon
LLMCwbbon
PCAM
PCAM A
Ground Truth
90.44%
6.39%
5.01
3.33
83.60%
3.69%
9.49
9.14
0.144%
52.23
52,21
55.73
6.326
88.64%
0.09%
105.04
105.13
108. 49%%
118.09
116.19
1.61%
16.19%
61.18
1.33%
61.87
13,005
1.00%
64.21
64.88
0.81%
1,54%
73.08
73.67
74.82
13.07%
0.57%
83:47
83.95
16.42%
1.01%
85.08
83.94
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. A= 1 114.36 kig) 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 conventional deterministic carbon accounting models like ILLMCarbon 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 car- bon 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
(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 202 2021-2023 years). Overall, PCAM outperforms LLMCarbon (0.09% 7.44% vs. 1.54%- 108.5 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 devia- tions of L.L.Carbon under the spatial dimension are from 90.43% (5th percentile) to 108.51 % (95th percentile), while that is from 18% to 16.43% under the temporal dimension.
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The Opreational Carbon Evaluation.
0.06-
PUT > US): 0.$166
LLMCarbon-US
LLMCarbon-DE
PII DE): 0.3306
0.05
LLMCarbon-IT
PCAM-US
Density
0.04
PCAM-DE
PCAM-IT
0.03
0.02
0.01
0.00
Opreational Carbon (t)
Figure 5: The comparison between LLMCarbon and PCAM operational carbon accounting in the US, IT, and DE.
This contrast highlights that geographical factors introduce greater uncertainty in operational carbon accounting than temporal variations.
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. 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 LLM- Carbon 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 nuanced probabilistic outcomes: there is 81.66% probability of IT's operational carbon footprint exceeding that the US and a 33.06% probability of surpassing DE's emissions. This probabilistic approach enables PCAM to provide multi-dimensional insights, em- powering AI developers to make more informed sustainability decisions.
DE, PCAM reveals
6 Related Work
The current methodologies for carbon footprint estimation of large Al models predominantly concen- trate 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-intcgrated 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) [2] 30
However, these methodologics systematically neglect the embodied carbon accounting associated with AI hardware infrastructure, which non-negligible in the carbon footprint of large Al models, power grids decarbonize and data centers increasingly adopt zero-carbon energy sources.
Regarding embodied carbon modeling, existing frameworks such as SustainableAl estimated the embodied carbon of large Al models through manufacturer-reportee emission factors for hardware components, which is an average value. I.L.Car [ adopts deterministic parametric model to estimate the embodied carbon for processors and average values for storage and memory in ESG

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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 Al models, but current large Al models' carbon models fail to capture this uncertainty.
7 Limitations and Discussions
This study examines the carbon footprint of large Al models across four life-cycle stages: (I) Hardware manufacturing, referring emissions generated during the production of core computing components; (2) Hardware transport, encompassing emissions from shipping hardware to end- users; (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 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 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/aagrregated data in various aspects (c.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 carbon emissions considerations among hardware producers drives substantial enhancements in carbon data quality. This trend leads more accurate and reliable accounting models for the carbon footprint of large Al 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 oper- ational 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, PCAM supports 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 Al development. To facilitate the decarbonization of large AI models, we are open- open-sourcing the carefully curated carbon dataset compiled 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.
Acknowledgements
Dan Wang's 's work is supported in part by RGC GRF 15200321, 15201322, 15230624, 15239925, ITC ITF-ITS/056/22XX ITS/052/23MX, and PolyU I-CDKK, G-SAC8, K-ZYAP.
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19

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Table 6: The comparison between PCAM and STEC on the embodied carbon accounting of XLM.
Total Embodied Carbon (kg) at each Percentile
Models
5th
10th
Median
90th
95th
Ground Truth
229.17
236.27
279.75
331.32
352.15
PCAM
235.20
242.74
281.09
339.95
359.93
PCAMA
2.56%
2.67%
0.48%.
2.54%
2.16%
STEC
283.01
286.00
294.90
303.02
305.01
STECA
23.49%
21.05%
5.42%
8.55%
13.39%
LLMCarbon
297.71
LLMCarbonA
23.02%
20.64%
6.03%
11.29%
18.29%
Appendix
We provide additional experiments compare PCAM with STEC [3]. which is embodied carbon accounting model for computer systems. STEC incorporates spatiotemporal variability in the carbon intensity of electricity used during hardware manufacturing. However, 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 direct quantitative comparison with PCAM at the Al model level, we extended the STEC methodology by scaling its bardware-level carbon accounting using the foundational equation (Eq. 2 from the main text) and generating 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 shows.
20


Reviews:
[{"review_id": "Ag80J4DbzL", "reviewer": "Reviewer_ETm3", "summary": "This 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.", "questions": "In 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.", "limitations": "Yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**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.", "was_revised": true, "final_justification": "The authors addressed majority of my questions/concerns. This is a high‑quality paper tackling an important and timely problem in carbon accounting, using AI as a primary use-case. Given the prior precedence of similar papers appearing in top ML venue, I would increase my score to accept.", "rebuttal": "We sincerely appreciate the reviewer's insightful comments. We are glad that the reviewer found our work solved an important problem and made a Novel contribution both in approach and dataset. Below, we respond to each of your points individually.\n\n**W(1):Lack of component attribution analysis: While the paper models distributions over multiple factors, it does not perform an attribution analysis to assess which parameter contributes most to overall variance...**\n\nWe have now conducted a Sobol sensitivity analysis for embodied carbon of XLM model for each hardware component. Below, we summarize key results.\n\n(1)Hardware Contribution Analysis:\nWe first analyze the relative contribution of hardware components to total embodied carbon as the following table shows. We find that GPUs (50%) and SSDs (46%) dominate the embodied carbon footprint of the AI model, collectively accounting for 96% of emissions. CPUs (1%) and DRAM (4%) play minor roles comparatively. This confirms GPUs and SSDs as primary optimization targets.\n\n| Hardware | CPU | GPU | SSD | DRAM |\n|-|-|-|-|-|\n| EC (%)   |  1% | 50% | 46% |   4% |\n\n\n(2)Parameter Sensitivity Attribution:\nThe blow table shows the component attribution analysis for each hardware using the Sobol approach. We find that: \n\nGPU: All parameters significantly impact variance, with Yield (Y, 0.97) and Carbon Intensity (CI, 0.99) being the strongest drivers; \n\nCPU: CI (0.99) and EPS (0.98) dominate over Yield (0.85). This is mainly because, compared to a GPU, a CPU uses a more mature process (a more stable yield).\n\nSSD: Carbon Intensity (CI, 1.0) is the exclusive determinant of variance; \nDRAM: Both CI (0.98) and EPS (0.97) contribute near-equally to uncertainty; \n\n| Sobol Indices | Y     | CI   | EPS  |\n|-|-|-|-|\n| CPU           | 0.85  | 0.99 | 0.98 | \n| GPU           |  0.97 | 0.99 | 0.95 |\n| SSD           | /     |    1 | /    |\n| DRAM          | /     | 0.98 | 0.97 |\n\nKey Insight from Analysis:\n\n(1)Shift Focus to Storage Optimization: \n\nStorage contributes 46% of embodied carbon—nearly equal to GPUs (50%)—yet remains overlooked in sustainability efforts. Beyond GPU-centric strategies, AI developers can prioritize:\n(a)Reducing storage footprint (e.g., via data-efficient training, model pruning).\n(b)Adopting low-capacity/high-durability SSDs to minimize replacement cycles.\n\n(2)Procurement Options: \n\nWhile NVIDIA’s market dominance limits sustainable options for GPUs (e.g., fab location), for storage, a diverse range of suppliers (Seagate, Samsung, Western Digital) supports green sourcing to reduce the embodied carbon of AI deployments (e.g., prioritizing SSDs from regions and time periods with lower CI).\n\n\n**W(2) and Q(1): 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?\nIt is not clear how’s the ground truth embodied carbon data is calculated in Table 5?**\n\nWe apologize for the unclear description. The “ground truth” is based on the published LLM training information (e.g., training duration, hardware set), the hardware manufacturing data set we collected (see Table 3). We further clarify as follows.\n\nThe published LLM training information used for the embodied carbon accounting in Table 5 contains (1) training duration of the AI model $t$ (i.g., 20.4 days for XLM in Table 5); (2) the hardware set used to train the model, e.g., GPU(12nm), CPU (16nm), Storage (64*32TB), Memory(64*256gb), as shown in Table 4. \n\nWe clarify that the carbon intensity of the manufacturing process used in the calculation of embodied carbon uses the following data:\n(1)GPU: NVIDIA has a monopoly, so production is located in Taiwan, but the manufacturing period is uncertain. Therefore, we use recent carbon intensity data (2021-2023) from Taiwan.\n(2)CPU (16nm), Storage (64*32TB), and Memory (64*256GB) have multiple manufacturers to choose from. We aggregate the carbon intensity of the manufacturing process based on the wafer fabrication capacity of each global region at the corresponding technology node (Table 2). \n\nWe can get the distribution of Yield and EPS for each hardware according to its technology node, e.g., 16nm CPU, 12nm GPU, 10nm DDR4 DRAM (see Figures 3 and 4), from the hardware manufacturing data set we collected (see Table 3).\n\nNow, we have all the distributions in Eqs. 3, 4, and 5. Then we can get the embodied carbon of the AI model using Eq.2. We label this result as “ ground truth” in the evaluation. In the evaluation, the output of PCAM is the accounting result using resampled data based on the probability distribution curve generated by PCAM via KDE.\n\n\n**W(3) and Q(2): 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?\nSection 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\nWe apologize for this unclear description. The electricity consumption is calculated based on published training information from [8][1].“avg. system power (W)” conveys the average system power per computing device, including TPU/GPU, host CPU, DRAM, and network interface. It is measured data. The electricity consumption is calculated by Training time * Ave. Power *Num. of device *PUE.\n\n\n**W(4) and Q(3): Geographic granularity concerns: ...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. ...What’s the geographic granularity used for operational carbon analysis in the US? ...In Figure 5, is the variability only caused by temporal differences?**\n\nWe sincerely thank the reviewer for raising this important point about geographic granularity in US operational carbon analysis. You are correct that aggregating carbon intensity at the country level obscures significant intra-country variance in large, diverse regions like the US, and that Balancing Authority (BA)-level data (e.g., from ElectricityMaps) offers finer resolution. In our initial analysis (Fig 5), operational carbon for the US was indeed calculated using national average grid carbon intensity. We acknowledge this likely suppressed observable variance. We have performed a new experiment using hourly carbon intensity data for California (CAISO) from ElectricityMaps, representing BA-level granularity. Results comparing CAISO to the US national average are summarized below:\n\n| Operational   Carbon (t) | 5th per. | 10th per. | Median | 90th per. | 95th per. |  Var.  |\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|          US          |   33.4   |   34.7    |  39.8  |   45.1    |   46.4    | 15.8  |\n|         CAISO        |   12.9   |   14.6    |  26.1  |   33.8    |   35.4    | 49.8  |\n\n\n\n\nKey Observations:\n\nThe significantly higher variance (49.8 vs 15.8) and wider spread (e.g., 5th percentile: 12.9 vs 33.4) in CAISO confirm that country-level averaging masks critical regional variability in the US.\n\n\n**W(5): 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\nPCAM is the first framework to quantify uncertainty in AI’s carbon footprint, focusing on the uncertainty caused by spatiotemporal characteristics in manufacturing. While PCAM incorporates hardware lifespan (T) in its probabilistic model, T is currently treated as deterministic (fixed at 5 years). We plan to add a sensitivity analysis to assess how variations in T affect embodied carbon uncertainty. Preliminary results indicate that reducing T to 4 years increases amortized carbon by up to 25%, whereas extending T to 6 years decreases it by approximately 17%.\n\nWe clarify the system boundary of PCAM encompasses four LCA stages: hardware manufacturing, hardware transport, operational use (software electricity consumption), and end-of-life processing (hardware recycling). Operational use corresponds to operational carbon, while the other stages pertain to embodied carbon of AI models.\n\nHardware manufacturing and operational use dominate emissions (e.g., >97% for Dell R740), while transport and end-of-life contribute minimally (<3%). We omit transport and end-of-life. Within hardware manufacturing, we focus on computer hardware emissions in manufacturing process (e.g., materials, energy, chemicals), omitting ancillary components like buildings, cooling, labor, **environmental factors **. We acknowledge that these are also important for embodied carbon. Quantifying the uncertainties of these requires interdisciplinary collaboration and will be our future work. The main difficulty lies in collecting relevant data. In the absence of data, using a normal distribution is a potential option for quantifying the uncertainty.​\n\n**W(6):Typos and presentation issues...**\n\nWe sincerely thank the reviewer for their meticulous reading of our manuscript. We have undertaken a thorough, line-by-line proofreading of the entire manuscript. \n\n**W(7): The scope of this paper.**\n\nOur work addresses the urgent issue of large AI models’ carbon footprint at a time when environmental sustainability in AI is a major concern across academia, industry, and policy. By examining uncertainties in both operational and embodied carbon emissions, our work offers a comprehensive perspective on AI’s environmental impact, supporting recent demands for greater transparency and accountability in AI development."}, {"review_id": "Q4G0qDAQFP", "reviewer": "Reviewer_ug1P", "summary": "The 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.", "questions": "•\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.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\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”.", "was_revised": true, "final_justification": "The authors replied carefully and thoroughly to my comments. They have responded to the three specific issues I raised as needing attention in order to accept for publication. The discussion with other reviewers has also helped clarify that the scope of this paper is a good fit for the venue, which has resolved my concerns in that area. As I result I am changing my rating to accept.", "rebuttal": "We sincerely appreciate your valuable time and constructive comments.\n\n**W1 and Recommend changes (R)1: Specification of the system boundary and the “life stages” are included/excluded and a discussion of the reasons.**\n\nWe analyze the carbon footprint across four life stages:\nHardware manufacturing: emissions from producing core computer components;\nHardware transport: emissions from shipping hardware to users;\nOperational use: emissions from running software (electricity consumption) ;\nEnd-of-life processing: emissions from hardware recycling;\nThe third stage is related to the operation carbon of AI models. Other stages are related to the embodied carbon of AI models. \n\nHardware manufacturing and operational use dominate emissions (e.g., >97% for Dell R740), while transport and end-of-life contribute minimally. We omit transport and end-of-life. Within hardware manufacturing, we focus on computer hardware emissions (e.g., materials, energy, chemicals), omitting ancillary components like buildings, cooling, labor. We acknowledge that these are also important for embodied carbon. Quantifying the uncertainties of these requires interdisciplinary collaboration and will be our future work.\n\n**W2, R2 and Q[L247]: How published training data were used to develop a distribution of embodied carbon emission estimates (as “ground truth”), and a clear discussion about how this applies to the inference phase. How do you determine the geographic region where training occurred? How do you determine the emissions associated with manufacturing for hardware used in training?**\n\nWe develop the distribution for hardware and then derive the distribution for AI models based on training duration. To develop the distribution of hardware, we need hardware specs (Tab 4) and hardware manufacturing data (Tab 3). NVIDIA dominates GPU production; thus, we use Taiwan's carbon intensity for GPUs. For multi-sourced components (CPU, SSD, DRAM), the fabrication region is modeled as a discrete random variable. Probabilities are proportional to regional production capacity (e.g., DRAM: US 3%, CN 18%, TW 20%, KR 52%, JP 7%). A mixture CI distribution for each component is constructed by aggregating region-specific CI distributions (via KDE). Similarly, Yield (LINE 174) and EPS (LINE 189) distributions are obtained. Embodied carbon distributions for GPU/CPU (Eq.3), memory(Eq.4), and storage (Eq.5) are then calculated. Other parameters in Eq.3-5 are constants and from the collected hardware dataset (Tab. 3). \n\nThe geographic region of training affects operational but not embodied carbon accounting. To reveal the uncertainty, we fix time and vary training regions (90 global locations) for spatial analysis, and fix location (e.g., DE) while varying training times (e.g., throughout 2023) for temporal analysis.\n\nPCAM's probabilistic framework can inherently apply to both training and inference, as it accounts for both based on hardware utilization time and hardware set specifications. \n\nWe conducted new experiments on embodied carbon during inference. Specifically, we account for the embodied carbon of ChatGPT-3 inference based on the published inference data from [1]. The published inference data contains average computation per request (i.g, 2.07 GPU-seconds /request) and the corresponding hardware set (i.g, NDasrA100_v4 sizes series). \n\nDue to the word limit of the rebuttal, we list a simplified version of the experimental results table below (the complete one will be in the revised manuscript). Overall, our conclusion does not change. PCAM still outperforms LLMCarbon, demonstrating great alignment with ground truth values across all percentiles, maintaining a maximum deviation of only 2.7% at the 10th percentile. In contrast, LLMCarbon shows substantially larger deviations up to 41%. \n\n|Error|Toatal|CPU|GPU|DRAM|SSD|\n|-|-|-|-|-|-|\n|PCAM|<2.7%|<2.3%|<2.2%|<1.8%|<2.6%|\n|LLMCarbon|<33%|<31%|<41%|<36%|<24%|\n\n**W3,R3: discussion about what insights could actually provide to decision-makers developing LLMs, and which of these are practically feasible** \n\nPCAM can generate practical value in the following aspects.\n\n(1)Risk-Aware Decision Making & Budgeting: \nPCAM can help an AI company estimate the probability of exceeding specific carbon thresholds or budgets, which is crucial for realistic sustainability targets and mitigating the risk of policy violations (e.g., carbon tax, carbon credit).\n\n(2)Sensitivity Analysis: Identifying which parameters (e.g., operational location/time, hardware components) contribute most to uncertainty. This guides prioritization (e.g., focus on operational scheduling vs. advocating for low-carbon hardware).\n\n(3)Practical Operational Choices: A Cloud computing developer can choose when and where to run models to reduce operational carbon based on the carbon intensity of grids, since PCAM models these differences over time and place.\n\n(4)Multi-source Hardware Choice: Developers can compare the distribution of embodied carbon for different hardware (e.g., SDD by Samsung vs. SK Hynix) to guide green risk-aware procurement and deployment, balancing performance and environmental impact.\n\n(5)Broader Value & Feasibility:\nWhile supply-chain factors (like yield) require industry engagement, quantifying their impact motivates advocacy for transparent reporting and sustainable practices.\n\nProbabilistic reporting (confidence intervals) enhances credibility for compliance and stakeholder communication.\n\nPCAM aligns with growing industry trends (e.g., Google's Carbon-Intelligent Computing) by providing the essential confidence bounds needed for robust auditing, reporting, and long-term planning.\n\n**Q[L63] Comments on significant figures**\n\nWe sincerely appreciate your comments. We will revise that in our revised manuscript.\n\n**Q[L97] 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\nThey are from ref[2]. The factors are used as model inputs. Our published code allows users to easily replace them with more precise regional or technology-specific factors if available. \n\n**Q[L141] Uncertainties about the F-gas and the raw material**\n\nWe acknowledge these uncertainties were not quantified in the discussion. We use the average values from industrial reports [30][31]. Quantifying their uncertainty relies on data disclosed by manufacturers. We do not find relevant data in manufacturers' ESG reports. In the absence of historical data, using a normal distribution is a potential option for quantifying uncertainty.\n\n**Q[L155] ...You are using data from 2021 and 2023 to estimate the carbon intensity of electricity consumption. How can your approach be efficiently kept up-to-date with changing grid generation mixes?**\n\nSince hardware typically has a 5-year lifespan, much of it in use is not newly manufactured. Additionally, our model takes carbon intensity as an input, and our public code allows users to easily input the latest grid carbon intensity data or specify values based on the model’s training or hardware manufacturing time.\n\n**Q[L203] 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\nThe energy efficiency data is from TSMC’s ESG reports [20]. It improves every year, but as the mass production time increases, the improvement rate will become smaller. For example, the normalized energy efficiency of 16nm improves annually as (1.3, 1.7, 2.8, 3.2, 3.3).\n\n**Q[L267] 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\nLLMCarbon intrinsically considers a hardware class (e.g., 28nm CPU) to have the same embodied carbon. Yet a hardware instance in this class can be manufactured from diverse regions and in diverse time periods with different embodied carbon, e.g., in the 2021 winter in Ireland or in the 2022 summer in Taiwan with different CI, Y, and EPS. LLMCarbon uses the average data of the hardware class. PCAM models the distribution of the hardware class. The average of PCAM output should be close to the output of LLMCarbon. \n\n**Q[L295] The feasibility of companies choosing different manufacturing schedules and geographies for their GPUs.**\n\nWe agree that GPU production is geographically constrained due to NVIDIA’s technical monopoly. However, memory/storage components have lower technical barriers and multiple suppliers (e.g., Samsung, SK Hynix, Seagate). Their embodied carbon rivals GPUs. While currently challenging commercially, evolving carbon policies (carbon taxes, trading systems) will increasingly equate emissions with cost when carbon carries direct financial weight; some options that were not feasible before will become feasible.\n\n**W4: The scope of this paper**\n\nOur work addresses the urgent issue of large AI models’ carbon footprint at a time when environmental sustainability in AI is a major concern across academia, industry, and policy. By examining uncertainties in both operational and embodied carbon emissions, our work offers a comprehensive perspective on AI’s environmental impact, supporting recent demands for greater transparency and accountability in AI development.\n\n**Formatting Concern[L212]:**\n\nWe have carefully reviewed and revised the formatting throughout the manuscript.\n\nRef:\n\n[1]Chien, Andrew A., et al. \"Reducing the Carbon Impact of Generative AI Inference (today and in 2035).\" HOTCARBON. 2023.\n\n[2]Maji, Diptyaroop., et al. \"CarbonCast: multi-day forecasting of grid carbon intensity.\" ACM Buildsys. 2022."}, {"review_id": "J5cHGrP6L9", "reviewer": "Reviewer_Xggk", "summary": "The 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.", "questions": "1) 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?", "limitations": "The limitation were addressed adequately; however, they can also argue in their discussion about the hidden carbon emissions that is often neglected like labor.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\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", "was_revised": true, "final_justification": "My questions were answered properly by the authors and I keep my ratings the same.", "rebuttal": "We sincerely thank the reviewer for the insightful comments and recognition of the novelty and impact of our work. Below are our responses to the weaknesses and questions.\n\n**Weakness (1) and Question (1): 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. 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.**\n\nWe apologize for not making our description clear enough. In the evaluation of the operational part, we would like to show the uncertainty/distribution of the carbon footprint of an AI model when the AI model can be trained anywhere/any time. This distribution can provide AI deployers with macroscopic information about the carbon footprint of the model operation. Of course, if the training location or time is specified, this uncertainty will be reduced. As you say, if users want to know the embodied carbon if the training is limited from 12 pm to 2 pm in California, the corresponding carbon intensity data (not using the CI distribution) should be used for the accounting. In fact, our model supports this operation as the carbon intensity is just the input for our model. In our publicly available model code, users can easily change the carbon intensity input according to their needs. \n\n**Weakness (2) and Question(2): Other factors like cooling infrastructure in data centers are neglected which plays a pivotal role in carbon accounting. Can the cooling infrastructure's embodied and operational carbon accounting be modeled with PCAM?**\n\n\nWe thank the reviewer for highlighting cooling infrastructure. Its operational carbon is indeed captured via PUE in our model (Eq.7, Table 6). PUE is the ratio of the total amount of energy consumed by the entire data center facility to the energy delivered to the IT equipment.\n\nWe analyze the carbon footprint of AI mdoels across four life stages:\nHardware manufacturing: Emissions from producing core computer components;\nHardware transport: Emissions from shipping hardware to users;\nOperational use: Emissions from running software (electricity consumption) ;\nEnd-of-life processing: Emissions from hardware recycling;\nThe third stage is related to the operational carbon of AI models. Other stages are related to the embodied carbon of AI models. \n\nHardware manufacturing and operational use dominate emissions (e.g., >97% for Dell R740), while transport and end-of-life contribute minimally (<3%). We omit transport and end-of-life. Within hardware manufacturing, we focus on computer hardware emissions (e.g., materials, energy, chemicals), omitting ancillary components like buildings, **cooling**, labor. We acknowledge that these are also important for embodied carbon. Quantifying the uncertainties of these requires interdisciplinary collaboration and will be our future work. The main difficulty lies in collecting relevant data. If the related data is available, PCAM's probabilistic framework can be extended to cooling infrastructure using the same distributional modeling approach (e.g., develop the distribution of embodied carbon according to the carbon intensity of electricity used in cooling infrastructure manufacturing). In the absence of data, using a normal distribution is a potential option for quantifying the uncertainty.\n \n\n**Question(3): 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\n\nPCAM can generate practical value in the following aspects:\n\n(1) Risk-Aware Decision Making & Budgeting: \nPCAM can help an AI company estimate the probability of exceeding specific carbon thresholds or budgets, crucial for realistic sustainability targets and mitigating the risk of policy violations.\n\n(2) Sensitivity Analysis: Identifying which parameters (e.g., operational location/time, hardware components) contribute most to uncertainty. This guides prioritization (e.g., focus on operational scheduling vs. advocating for low-carbon hardware). PCAM can also help hardware manufacturers optimize green production, e.g., factory site selection, capacity scheduling, and carbon-centric process optimization.\n\n(3) Practical Operational Choices: A Cloud computing developer can choose when and where to run models based on the carbon intensity of the electricity grid, since PCAM models these differences over time and place. \n\n(4) Multi-source Hardware Choice: Developers can compare the distribution of embodied carbon for different hardware (e.g., SDD by Samsung vs. SK Hynix) to guide procurement and deployment, balancing performance and environmental impact.\n\n(5) Broader Value & Feasibility:\nWhile supply-chain factors (like yield) require industry engagement, quantifying their impact motivates advocacy for transparent reporting and sustainable practices;\n\nProbabilistic reporting (confidence intervals) enhances credibility for compliance and stakeholder communication;\n\nPCAM aligns with growing industry trends (e.g., Google's Carbon-Intelligent Computing) by providing the essential confidence bounds needed for robust auditing, reporting, and long-term planning."}, {"review_id": "mYrqMfwGuK", "reviewer": "Reviewer_rNJZ", "summary": "This 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%.", "questions": "1. 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.", "limitations": "yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "## 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.", "was_revised": true, "final_justification": "Although I think the authors should perform a more comprehensive comparison aginst [12], from my side, there are no major concerns preventing the acceptance of this paper.", "rebuttal": "We thank the reviewer for the insightful feedback. We appreciate your recognition of our paper's contribution to addressing environmental sustainability in large-scale AI. The only concern is the inclusion of an additional baseline. We have added the new baseline in the experiments as requested by the reviewer.\n\n**Weakness[1] and Questions[1]: No comparison against a highly-related prior work. 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). ...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\n\nThank you for suggesting the inclusion of the STEC model [12] as an additional baseline. We have conducted new experiments comparing PCAM against STEC and add the new experimental results to Table 5 as follows. Overall, the conclusion does change. PCAM still demonstrates a significant advantage in accuracy. \n\nSTEC only incorporates spatiotemporal electricity carbon intensity in manufacturing but remains fundamentally deterministic. It fails to probabilistically model the Geotemporal manufacturing variability (regional production capacity + temporal carbon intensity fluctuations) and dynamic manufacturing evolution (yield/fabrication efficiency improvements). To enable the comparison of STEC with PCAM, we extend STEC by scaling its hardware-level accounting to AI models carbon accounting (using Eq.2) and generating the distributions of embodied carbon based on regional electricity carbon intensity frequency data. \n\nThe following table compares STEC with PCAM. Specifically, PCAM outperforms STEC consistently across all percentiles, with ≤2.7% error vs. STEC’s ≤23.5% error. Component-wise analysis shows that PCAM outperforms STEC at each component. For CPU carbon accounting, PCAM errors are below 2.6% versus STEC's ≤22.8%. GPU calculations show PCAM’s robust performance with less than 2% deviations across all percentiles, contrasted by STEC’s substantial overestimations reaching 32.3% at the 5th percentile. The DRAM comparison follows similar trends, with PCAM errors remaining below 1.8% in DRAM versus STEC ≤22.2%. \nWe omit the comparison of SSD as the extended STEC by us and PCAM use the same approach to model storage. We will add these comparisons to the evaluation section and discuss STEC’s limitations in our revised manuscripts.\n\n\n\n|    Models    | Total Embodied Carbon (kg) at each Percentile |        |         |        |        |\n|:------------:|:---------------------------------------------:|:------:|:-------:|:------:|:------:|\n|              |                      5th                      |  10th  |  Median |  90th  |  95th  |\n| Ground Truth |                     229.2                     | 236.3  |  279.8  | 331.3  | 352.2  |\n| PCAM         |                     235.2                     | 242.7  |  281.1  | 340.0  | 359.9  |\n| PCAM#        |                      2.6%                     |  2.7%  |   0.5%  |  2.5%  |  2.2%  |\n| STEC         |                     283.0                     | 286.0  |  294.9  | 303.0  | 305.0  |\n| STEC#        |                     23.5%                     |  21.0% |   5.4%  |  8.5%  |  13.4% |\n| LLMCarbon    |                     297.7                     |        |         |        |        |\n| LLMCarbon#   |                     23.0%                     |  20.6% |   6.0%  |  11.3% |  18.3% |\n|              |  CPU Embodied Carbon (kg) at each Percentile  |        |         |        |        |\n| Ground Truth |                      1.1                      |  1.2   |   1.5   |  2.0   |  2.2   |\n| PCAM         |                      1.2                      |  1.2   |   1.5   |  2.0   |  2.1   |\n| PCAM#        |                      1.7%                     |  0.8%  |   0.5%  |  1.4%  |  2.6%  |\n| STEC         |                      1.4                      |  1.4   |   1.4   |  1.6   |  1.7   |\n| STEC#        |                     18.4%                     |  16.1% |   4.1%  |  22.0% |  22.8% |\n| LLMCarbon    |                      1.6                      |        |         |        |        |\n| LLMCarbon#   |                     26.5%                     |  23.9% |   4.1%  |  31.5% |  40.3% |\n|              |  GPU Embodied Carbon (kg) at each Percentile  |        |         |        |        |\n| Ground Truth |                     98.7                      | 101.4  |  133.8  | 189.1  | 211.1  |\n| PCAM         |                     97.0                      |  99.4  |  132.3  | 187.6  | 209.4  |\n| PCAM#        |                      1.8%                     |  2.0%  |   1.1%  |  0.8%  |  0.8%  |\n| STEC         |                     130.5                     | 132.7  |  138.8  | 144.8  | 145.9  |\n| STEC#        |                     32.3%                     |  30.9% |   3.8%  |  23.5% |  30.9% |\n| LLMCarbon    |                     141.7                     |        |         |        |        |\n| LLMCarbon#   |                     66.9%                     |  28.5% |   5.6%  |  33.5% |  49.0% |\n|              |  DRAM Embodied Carbon (kg) at each Percentile |        |         |        |        |\n| Ground Truth |                      8.0                      |  8.2   |  10.4   |  14.5  |  15.3  |\n| PCAM         |                      7.8                      |  8.1   |  10.3   |  14.3  |  15.2  |\n| PCAM#        |                      1.8%                     |  1.0%  |   1.3%  |  0.9%  |  0.6%  |\n| STEC         |                      9.7                      |  10.0  |  10.6   |  12.2  |  12.4  |\n| STEC#        |                     22.1%                     |  22.2% |   2.1%  |  15.6% |  18.8% |\n| LLMCarbon    |                     10.9                      |        |         |        |        |\n| LLMCarbon#   |                     26.5%                     |  24.9% |   4.2%  |  33.4% |  41.0% |\n|              |  SSD Embodied Carbon (kg) at each Percentile  |        |         |        |        |\n| Ground Truth |                     106.0                     | 110.2  |  123.6  | 145.2  | 147.7  |\n| PCAM/STEC    |                     108.3                     | 111.5  |  122.8  | 147.1  | 149.7  |\n| PCAM/STEC#   |                      2.1%                     |  1.1%  |   0.7%  |  1.3%  |  1.3%  |\n| LLMCarbon    |                     125.6                     |        |         |        |        |\n| LLMCarbon#   |                     15.6%                     |  12.3% |   1.6%  |  15.5% |  17.6% |\n\nTable: The evaluation results on embodied carbon accounting."}]

Author rebuttal:

Meta-review: This paper presents a Probabilistic Carbon Accounting Model (PCAM) providing a carbon footprint distribution for large AI models. In PCAM, the footprint is broken down in several contributions and uncertainties pertaining to 1) geotemporal manufacturing variability, 2) dynamic manufacturing evolution, and 3) dynamic operating context are propagated. The model relies on a curated hardware and electricity dataset constructed 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, as detailed in Table 3), that the authors promised to open-source when the paper is published. From this data set, Kernel Density Estimators are derived, and random variable can be propagated though the equations underlying PCAM.   The paper was refereed by four reviewers with gradings ranging from weak accept to accept (one weak accept, three accept gradings). The paper was found to be well written and of practical relevance, yet several questions and concerns were raised in the reviews and discussion. Overall, the referees acknowledged post discussion to be satisfied with the answers and/or that their concerns were addressed.I too found the paper to be of interest and prone to generate valuable discussions in a conference such as NeurIPS, yet I was puzzled (in line with ETm3) by the employed notion of ground truth. While I conceive that it might not be feasible to get some real carbon footprint measurements for validation purposes, it is not entirely clear to me to what extent the model used to generate the said ground truth parallels the PCAM model and more precisely whether one is comparing here a marginal distribution with a conditional one (e.g., with NVIDIA being produced in Taiwan). I find this to call for further clarifications in the paper regarding what the ground truth distributions precisely stand for (whether the ground truth terminology is kept or not). On a different note, I found the idea of using PCAM in a sensitivity analysis context very interesting. This might require some care though about potential independence assumptions between the “parameters”, in case classical versions of variance-based global sensitivity analysis are used, and special procedures dealing with dependent factors, else. I hope this is useful towards finalizing this paper.
Decision: Accept (poster)