Carbon Efficient Gain Index (CEGI)

Updated 27 October 2025

CEGI is a metric that quantifies carbon emissions per unit performance gain, normalizing results by resource dimensions like model parameters or workload mass.
It applies rigorous measurement and normalization techniques to compare diverse systems from machine learning to power grid operations.
CEGI supports sustainable decision-making by benchmarking efficiency improvements against carbon costs in domains including datacenters, networking, finance, and edge computing.

The Carbon Efficient Gain Index (CEGI) is a formalized metric designed to quantify and compare the trade-off between system efficiency (or gain) and associated carbon emissions across a diverse range of operational contexts, including machine learning model selection, datacenter workload management, networking, financial products, and power system optimization. CEGI encapsulates the concept of carbon efficiency by normalizing improvements in performance or gain against the carbon cost incurred, thus enabling a rigorous, degree-of-freedom-sensitive comparison across system configurations, temporal windows, and spatial domains.

1. Definition and Mathematical Formulation

The principal definition of CEGI centers on the normalization of carbon emissions per unit of performance gain, with additional normalization by resource dimensions (such as model parameter count or workload mass). For machine learning, as introduced in (Kumar et al., 3 Dec 2024), CEGI is defined as the carbon emission per unit percentage gain per million trainable parameters:

$\mathrm{CEGI}(G_{m,\mu,T_p}^\circ) = \frac{\sum_{Q_b, L_r} C_E \cdot |L_r|}{\left( \sum_{Q_b, L_r} G_{m,\mu}(F_T, B_M) \cdot \sum_{L_r} T_p \right)},$

where $C_E$ is the measured carbon emission, $G_{m,\mu}$ is the percentage improvement in metric $\mu$ for model $m$ for fine-tuned ( $F_T$ ) versus base ( $B_M$ ) configurations, $T_p$ is the number of trainable parameters, $Q_b$ the quantization bit-width, and $L_r$ the LoRA rank.

In networking contexts (Tabaeiaghdaei et al., 2022), the index emerges as the fractional reduction in carbon intensity of data transmission, formalized by:

$\mathrm{CEGI} = \frac{\mathrm{CIDT}_{\mathrm{BGP}} - \mathrm{CIDT}_{\mathrm{CIRo}}}{\mathrm{CIDT}_{\mathrm{BGP}}},$

where $\mathrm{CIDT}$ denotes Carbon Intensity of Data Transmission for BGP versus CIRo-selected paths.

For financial products (Kenyon et al., 2021), a plausible formulation (as Editor's term) relates the net present value (NPV) of financial gain to the absolute NPV of carbon impacts:

$\mathrm{CEGI} = \frac{\mathrm{Financial\ Gain}}{|\mathrm{NPV_{XCA}}|},$

where $\mathrm{NPV_{XCA}}$ accumulates XCA (carbon account) flows discounted over time.

In power system analysis, CEGI may incorporate metrics such as average carbon emission rate, locational marginal carbon emission, or gain in carbon reduction per operational cost or demand shift (Chen et al., 2023, Cho et al., 17 Jun 2025, Wu et al., 19 Feb 2025).

2. Methodological Foundations

The implementation of CEGI relies on rigorous measurement and attribution of both gains (performance improvements, demand response, financial returns) and carbon emissions:

Measurement of Carbon Emissions: Carbon emissions are quantified using task-dependent or system-dependent methodologies. In machine learning, energy usage during training and fine-tuning is tracked via utilities such as Eco2AI (Kumar et al., 3 Dec 2024); in networking, device-by-device power contributions are modeled in conjunction with hour-by-hour grid carbon intensity (Tabaeiaghdaei et al., 2022); in datacenters, the carbon footprint per workload shift is computed from cluster-specific utilities and grid forecasts (Radovanovic et al., 2021).
Performance Gain Quantification: Gains are captured via improvements in application-specific metrics (e.g., accuracy, BLEU, SPICE scores in ML; routing efficiency or latency in networking; financial NPV; economic cost in power systems).
Normalization Procedures: Resource normalization (e.g., per million model parameters, per gigabit, per server) and temporal normalization (day-ahead versus real-time forecasting) are employed to ensure commensurate comparison.
Aggregation and Averaging: Multiple configurations are averaged (over quantization levels, adaptation ranks, time windows, spatial zones) to produce robust CEGI scores.

3. Domain-Specific Applications

CEGI permits selection of models that maximize task performance per unit carbon emission per parameter, showing that smaller, quantized models fine-tuned with low-rank adaptation can achieve competitive performance with orders-of-magnitude lower carbon emissions than larger models. Empirically, the Qwen-VL-7B model achieved the lowest CEGI for image captioning.

By integrating day-ahead carbon intensity forecasts and risk-aware optimization to generate Virtual Capacity Curves (VCCs), datacenter schedulers minimize carbon footprint per unit compute delivered. CEGI in this context reflects both avoided emissions and peak demand cost savings attributable to dynamic workload shifting, bounded by daily compute conservation constraints.

In path-aware architectures (SCION/CIRo), CEGI quantifies the decrease in carbon intensity when selecting greener inter-domain network paths. Simulations indicate up to 50% footprint reduction for most domains. The metric is operationalized in routing policy thresholds for admissible path selection.

The Carbon Equivalence Principle (CEP) mandates that financial products attach time-resolved carbon flows alongside monetary termsheets. CEGI can utilize this data to compute normalized financial returns per carbon impact, facilitating quantitative comparisons of product sustainability.

In transmission grid models (PGLib-CO2), CEGI may be aligned with system-wide (e.g., ACE), locational (LMCE), or marginal emission rates, as well as cost-emission trade-offs derived from carbon-aware OPF and load shifting solutions. Benchmarking different carbon-aware operational strategies is standardized via generator-level emission data.

Spatially granular workload placement exploiting mesoscale grid carbon intensity differences are optimized using CarbonEdge, where CEGI would capture emission reductions per induced latency or energy penalty. Results show that up to 78.7% emission savings are attainable in edge deployments with minimal (<10 ms) latency overhead.

4. Impact Assessment and Comparative Findings

Across domains:

Model Choice Guidance: CEGI enables practitioners to favor configurations yielding higher performance per carbon cost, especially where marginal accuracy gains are dwarfed by disproportionately higher emissions from scaling up resources (Kumar et al., 3 Dec 2024).
Operational Policy Optimization: Datacenter and networking CEGI metrics support real-time scheduling adjustments to maximize carbon efficiency in workload routing (Radovanovic et al., 2021, Tabaeiaghdaei et al., 2022).
Systematic Financial Disclosure: CEGI facilitates transparent, time-consistent assessment of sustainable financial products, moving beyond binary green labels (Kenyon et al., 2021).
Grid Planning and Auditing: In power systems, incorporating CEGI-aligned metrics (average and marginal nodal emissions) supports audit rigor, demand management, and capacity expansion studies (Chen et al., 2023, Cho et al., 17 Jun 2025).
Edge Orchestration Efficiency: CEGI structures the evaluation of geo-distributed workload placement for edge services, balancing carbon, energy, and latency constraints (Wu et al., 19 Feb 2025).

5. Technical Implementation and Practical Considerations

Data Requirements: Accurate, fine-grained carbon emission data (e.g., device-level, region-level, time-resolved) is critical. Integration with platforms such as Eco2AI for ML, Electricity Maps for grid carbon intensity, and PGLib-CO2 for grid models is recommended.
Optimization Formulations:
- Mixed-integer programming for workload placement and routing (Wu et al., 19 Feb 2025, Radovanovic et al., 2021).
- Convex/AC optimal power flow models for grid dispatch with carbon penalties (Cho et al., 17 Jun 2025).
- Statistical model selection and averaging for ML configuration assessment (Kumar et al., 3 Dec 2024).
Scalability and Resource Efficiency: Algorithms must avoid computational bottlenecks (e.g., matrix inversion in grid emissions tracing) and support real-time operation. Empirical results validate algorithmic scalability to hundreds of servers/applications with sub-second computation time (Wu et al., 19 Feb 2025).
Uncertainty and Risk-Awareness: Prediction inflation and conservative estimation techniques are incorporated to ensure reliability of SLOs and mitigate operational risk, particularly in load forecasting and scheduling (Radovanovic et al., 2021).

6. Extensions, Limitations, and Future Directions

Broader Integration: CEGI frameworks may be extended to incorporate further efficiency-enhancing techniques such as pruning, distillation, and variable carbon pricing.
Standardization Needs: Consistent methodology for cross-domain calculation and normalization of CEGI is necessary for rigorous benchmarking.
Temporal and Spatial Resolution: Increasing the granularity of emissions data (hourly, nodal, mesoscale) strengthens the precision and operational utility of CEGI-based assessments.
Potential Limitations: CEGI depends on the quality of carbon emission measurements and assumes performance gains are commensurately valued in all operational contexts; domain-specific utility metrics should be considered for comprehensive evaluation.

7. Summary Table: CEGI Application Across Domains

Domain	Gain Metric	Carbon Attribution
Machine Learning	% Score Improvement	Eco2AI emissions per million parameters
Datacenter Ops	Output Compute	Grid carbon intensity forecasts, VCC shaping
Network Routing	CIDT Reduction	Per-AS/device energy and carbon intensity
Finance	Financial NPV	Time-series of carbon flows (XCA termsheets)
Power Systems	Cost/emission trade-off	Generator-level, locational, marginal rates
Edge Computing	Service Latency/Gain	Mesoscale grid intensity, workload placement

CEGI establishes a disciplined, normalized basis for comparing the carbon efficiency of technical and financial systems, supporting objective decision-making that aligns high-performance operation with environmental sustainability. Its adoption across diverse fields demonstrates its flexibility as a sustainability metric and its potential to drive industry-wide improvements in carbon-aware design and operation.