Can We Optimize the Performance-Carbon Emission Break-Even Point?: The Quest for Greener LLMs

# Can We Optimize the Performance-Carbon Emission Break-Even Point?: The Quest for Greener LLMs
Source: [https://arxiv.org/html/2608.08744](https://arxiv.org/html/2608.08744)
Sourav Das\* IIIT Kalyani sourav\_phd21@iiitkalyani\.ac\.in &Tanmay Joshi\* BITS Pilani Goa f20231102@goa\.bits\-pilani\.ac\.in &Kripabandhu Ghosh IISER Kolkata kripa\.ghosh@gmail\.com

###### Abstract

The carbon footprint of any deployed Large Language Model \(LLM\) accumulates during inference, where repeated use of the model substantially exceeds the one\-time cost of fine\-tuning\. Yet most efficiency interventions target either pre\-training scale or post\-hoc compression\. We ask whether folding a calibrated, differentiable energy surrogate into the fine\-tuning objective can produce inference behavior that gains task accuracy at zero or near\-zero carbon cost, a break\-even configuration\. We propose a joint loss mechanism with a per\-model carbon\-emission parameter, a linear surrogate over parameter norm, FLOP proxy, and memory proxy, fit from on\-hardware energy profiling\. We fine\-tune three architecturally distinct families: Gemma\-2 2B, Llama\-3\.1 8B, and Qwen\-2\.5 14B, and evaluate inference F1 and CO2emissions on three MMLU subjects: abstract algebra, philosophy, and formal logic\. We discover from several outcomes that the carbon term behaves as either harmful interference or beneficial regularization depending on the task structure\. We position calibrated carbon\-aware fine\-tuning as a lightweight, drop\-in regularizer with a non\-empty but model and task\-dependent break\-even region\.This is an ongoing work, and we will release our codebase soon\.

Can We Optimize the Performance\-Carbon Emission Break\-Even Point?: The Quest for Greener LLMs

Sourav Das\*IIIT Kalyanisourav\_phd21@iiitkalyani\.ac\.inTanmay Joshi\*BITS Pilani Goaf20231102@goa\.bits\-pilani\.ac\.inKripabandhu GhoshIISER Kolkatakripa\.ghosh@gmail\.com

††footnotetext:\*These authors contributed equally\.## 1Introduction

![Refer to caption](https://arxiv.org/html/2608.08744v1/Figure_1.png)Figure 1:The carbon–accuracy break\-even region\.Each marker is one \(model family, MMLU subject\) pair, showing inferenceΔ\\DeltaF1 and relativeΔ\\DeltaCO2of our joint\-loss model against a cross\-entropy baseline\. Points in the upper\-left quadrant are strict Pareto improvements; the dashed line marks zero carbon delta\. Five of nine pairs lie inside the break\-even region \(Δ\\DeltaF1≥0\\,\\geq\\,0andΔ\\DeltaCO≤2\+2%\{\}\_\{2\}\\,\\leq\\,\+2\\%\), including one strict Pareto improvement on Qwen\-14B / abstract algebra \(Section[3](https://arxiv.org/html/2608.08744#S3)\)\.The carbon footprint of LLMs accumulates over its operational lifetime rather than at the moment of training\. A frontier LLM is fine\-tuned a handful of times but serves significantly more forward passes when in production\. Recent measurement and accounting studies argue that inference, not training, governs the long\-run environmental cost of widely used systems\(Pattersonet al\.,[2021](https://arxiv.org/html/2608.08744#bib.bib1); Wuet al\.,[2022](https://arxiv.org/html/2608.08744#bib.bib2); Luccioniet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib3)\)\. The community’s response has nevertheless concentrated at the two ends of the lifecycle\. Training\-time work pursues better scaling laws and parameter\-efficient adaptation\(Hoffmannet al\.,[2022](https://arxiv.org/html/2608.08744#bib.bib7); Huet al\.,[2022](https://arxiv.org/html/2608.08744#bib.bib8); Dettmerset al\.,[2023](https://arxiv.org/html/2608.08744#bib.bib9)\); post\-training work targets the frozen artifact through quantization, pruning, distillation, and decoding\-time acceleration\(Frantaret al\.,[2023](https://arxiv.org/html/2608.08744#bib.bib12); Frantar and Alistarh,[2023](https://arxiv.org/html/2608.08744#bib.bib15); Xiaoet al\.,[2023](https://arxiv.org/html/2608.08744#bib.bib13); Leviathanet al\.,[2023](https://arxiv.org/html/2608.08744#bib.bib19); Sunet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib16)\)\. The fine\-tuning objective itself, the mechanism that fixes which computational pathways the deployed model will exercise for every subsequent query, has remained, in effect, carbon\-neutral terrain\.

We argue this is a missed leverage point\. The loss function chosen during fine\-tuning quietly determines the model’s inference\-time circuit usage, and a calibrated energy term inserted at this stage can steer the model toward lower\-cost pathways without modifying its architecture, its precision, or its decoding routine\. Differentiable hardware\-aware neural architecture search established this principle in the vision domain a half\-decade ago, embedding FLOP and latency proxies into the search objective and obtaining accurate, low\-energy models with no post\-hoc compression step\(Wuet al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib21); Caiet al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib22); Tanet al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib23)\)\. The corresponding move for LLMs folding a differentiable, on\-hardware energy surrogate into the fine\-tuning loss itself has not been studied, to the best of our knowledge\. Existing carbon\-aware LLM work measures and reports emissions\(Strubellet al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib5); Schwartzet al\.,[2020](https://arxiv.org/html/2608.08744#bib.bib6); Luccioniet al\.,[2023](https://arxiv.org/html/2608.08744#bib.bib4)\), but does not optimize against them at training time\.

Our paper asks a single prominent research question:*Can joint optimization of task performance and inference carbon emission reach a break\-even point?*By*break\-even*we mean an operating point at which downstream task F1 is preserved or improved while inference CO2is no higher than that of a standard cross\-entropy baseline\.We fine\-tune three architecturally distinct families: Gemma\-2\-2B\(Gemma Teamet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib24)\), Llama\-3\.1\-8B\(Grattafioriet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib25)\), and Qwen\-2\.5\-14B\(Yanget al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib26)\), and evaluate inference F1 and CO2on three MMLU subjects\(Hendryckset al\.,[2021](https://arxiv.org/html/2608.08744#bib.bib27)\): abstract algebra, philosophy, and formal logic\.

Figure[1](https://arxiv.org/html/2608.08744#S1.F1)represents that the break\-even region is non\-empty, though selective\. Qwen\-14B on abstract algebra delivers a strict Pareto improvement, gaining3\.53\.5F1 points while reducing inference CO2by3\.5%3\.5\\%\. Gemma\-2B on philosophy gains12\.812\.8F1 points at essentially zero carbon delta, and Llama\-8B on formal logic gains5\.35\.3F1 points for a1\.8%1\.8\\%carbon increase, a regime in which the per\-query F1 yield substantially exceeds the marginal emissions cost\. Taken together, these results suggest that carbon\-aware fine\-tuning is best understood not as a uniform efficiency intervention but as a structural regularizer whose effect is mediated by the magnitude of the target task\.To our knowledge, no prior work attempted a differentiable energy surrogate of a set of pretrained LLMs into the fine\-tuning loss to navigate the trade\-off between task accuracy and inference CO2emissions toward a break\-even configuration\.

We make four novel contributions in this work, two primary and two subsidiary:

1. 1\.We introduce*calibrated carbon\-aware fine\-tuning*for LLMs: a drop\-in joint loss that adds a differentiable energy surrogate, fitted from on\-hardware profiling of the specific model under training, directly to the task objective \(Section[2\.1](https://arxiv.org/html/2608.08744#S2.SS1), Section[2\.2](https://arxiv.org/html/2608.08744#S2.SS2)\)\.
2. 2\.Across three model families and three MMLU subjects, we identify a non\-empty break\-even region containing one strict Pareto improvement, demonstrating that the regime is reachable in practice \(Section[3\.1](https://arxiv.org/html/2608.08744#S3.SS1)\)\.
3. 3\.Through aλ\\lambda\-sensitivity study on Qwen\-14B over SQuAD and BoolQ, we show that the optimal carbon penalty is task\-structure\-conditional, reframingλ\\lambdaas a regularizer whose interpretation shifts between tasks \(Appendix[A\.2](https://arxiv.org/html/2608.08744#A1.SS2)\)\.
4. 4\.We release per\-step training histories, calibration tables, inference\-time emissions logs, and MMLU prediction files for all configurations, enabling downstream replication \(Appendix[A\.11](https://arxiv.org/html/2608.08744#A1.SS11)\)\.

## 2Method

We proposeλ\\lambdaas the Carbon regularization coefficient\. A controlledλ\\lambda\-sensitivity study on Qwen\-14B further shows that the optimal penalty is conditional on task structure:λ∗=0\\lambda^\{\*\}=0on SQuAD\(Rajpurkaret al\.,[2018](https://arxiv.org/html/2608.08744#bib.bib28)\), where the carbon term acts as harmful interference with extractive span selection, againstλ∗=0\.1\\lambda^\{\*\}=0\.1on BoolQ\(Clarket al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib29)\), where the same term operates as a beneficial regularizer for boolean reasoning\. Taken together, these results suggest that carbon\-aware fine\-tuning is best understood not as a uniform efficiency intervention but as a structural regularizer whose effect is mediated by the geometry of the target task\.

### 2\.1Joint Carbon\-Aware Objective

We fine\-tune a pretrained language model with parametersθ\\thetaunder the joint objective:

ℒjoint​\(θ\)=ℒtask​\(θ\)\+λ⋅C^​\(θ\)\+μ⋅ℒreg​\(θ\),\\mathcal\{L\}\_\{\\text\{joint\}\}\(\\theta\)\\;=\\;\\mathcal\{L\}\_\{\\text\{task\}\}\(\\theta\)\\;\+\\;\\lambda\\cdot\\hat\{C\}\(\\theta\)\\;\+\\;\\mu\\cdot\\mathcal\{L\}\_\{\\text\{reg\}\}\(\\theta\),\(1\)
whereℒtask\\mathcal\{L\}\_\{\\text\{task\}\}is the standard token\-level cross\-entropy loss on the target dataset,C^​\(θ\)\\hat\{C\}\(\\theta\)is a differentiable surrogate of per\-step inference energy,ℒreg​\(θ\)\\mathcal\{L\}\_\{\\text\{reg\}\}\(\\theta\)is a regularization loss, andλ,μ∈ℝ≥0\\lambda,\\mu\\in\\mathbb\{R\}\_\{\\geq 0\}control the strengths of the carbon and regularization terms, respectively\. Settingλ=μ=0\\lambda=\\mu=0recovers the cross\-entropy baseline; positiveλ\\lambdashifts the optimum toward parameter configurations whose forward pass the surrogate predicts to be cheaper to execute, while positiveμ\\muincreases the influence of regularization during training\. Because bothC^​\(θ\)\\hat\{C\}\(\\theta\)andℒreg​\(θ\)\\mathcal\{L\}\_\{\\text\{reg\}\}\(\\theta\)are differentiable inθ\\theta, the additional terms contribute gradients at every optimization step, and the entire objective is trained with standard first\-order methods\.

### 2\.2Surrogate Calibration

The surrogate is a per\-model linear function of three differentiable, on\-the\-fly computable features of the network state: the L2 norm of the parameters \(ϕ1=‖θ‖2\\phi\_\{1\}=\\\|\\theta\\\|\_\{2\}\), a FLOP proxy \(ϕ2\\phi\_\{2\}\) computed from the forward\-pass tensor shapes, and a memory proxy \(ϕ3\\phi\_\{3\}\) reflecting peak activation footprint\. Concretely,

C^​\(θ\)=w1​ϕ~1​\(θ\)\+w2​ϕ~2​\(θ\)\+w3​ϕ~3​\(θ\),\\hat\{C\}\(\\theta\)\\;=\\;w\_\{1\}\\tilde\{\\phi\}\_\{1\}\(\\theta\)\+w\_\{2\}\\tilde\{\\phi\}\_\{2\}\(\\theta\)\+w\_\{3\}\\tilde\{\\phi\}\_\{3\}\(\\theta\),\(2\)whereϕ~i\\tilde\{\\phi\}\_\{i\}denotes the feature normalized by its calibration\-set scale andwiw\_\{i\}are non\-negative weights fit per model\. The weights are obtained by running the pretrained model on three reference batch sizes \(B∈\{128,256,384\}B\\in\\\{128,256,384\\\}, withB∈\{128,256,512\}B\\in\\\{128,256,512\\\}for the smaller models that admit it\), measuring on\-hardware energy via CodeCarbon\(Courtyet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib30)\), and solving a non\-negative least\-squares fit of energy against the three normalized features\. The resulting weights are then frozen for the entire fine\-tuning run\.

Table 1:Surrogate calibration\. Normalized weights \(w1,w2,w3w\_\{1\},w\_\{2\},w\_\{3\}\) correspond to parameter norm, FLOP proxy, and memory proxy\.R2R^\{2\}is computed on the three\-point calibration set\.Modelw1w\_\{1\}w2w\_\{2\}w3w\_\{3\}R2R^\{2\}Gemma\-2\-2B0\.0001\.0000\.0000\.974Llama\-3\.1\-8B0\.0001\.0000\.0000\.663Qwen\-2\.5\-14B0\.9880\.0000\.0121\.000Two properties of the fitted surrogates are worth noting and are visible in Table[1](https://arxiv.org/html/2608.08744#S2.T1)\. First, the weight concentration is family\-dependent: Llama and Gemma place all mass on the FLOP proxy, while Qwen places nearly all mass on the parameter norm\. This asymmetry reflects the very different parameter scales the L2 norm across architectures \(approximately10310^\{3\}for Llama and Gemma versus2×10−22\\times 10^\{\-2\}for Qwen\-2\.5\-14B\) and is absorbed by the per\-model fit rather than imposed by hand\. Second, the calibration is fit to three operating points, so the reportedR2R^\{2\}values describe a within\-sample fit and should not be read as evidence of broad generalization across batch sizes; we treat the surrogate as a locally faithful penalty rather than a global energy predictor, and we discuss this scope as a limitation in Section[A\.12](https://arxiv.org/html/2608.08744#A1.SS12)\.

### 2\.3Experimental Setup

#### Models\.

We fine\-tune three architecturally distinct pretrained checkpoints: Gemma\-2\-2B\(Gemma Teamet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib24)\), Llama\-3\.1\-8B\(Grattafioriet al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib25)\), and Qwen\-2\.5\-14B\(Yanget al\.,[2024](https://arxiv.org/html/2608.08744#bib.bib26)\)\. Each model is fine\-tuned twice: once withλ=0\\lambda=0\(the cross\-entropy baseline\), and once with the joint objective at the per\-modelλ\\lambdaselected by a small validation sweep overλ∈\{0\.01,0\.03,0\.1\}\\lambda\\in\\\{0\.01,0\.03,0\.1\\\}\(sweep results in Appendix[A\.5](https://arxiv.org/html/2608.08744#A1.SS5)\)\.

#### Tasks and evaluation\.

Downstream evaluation is on three subjects of the MMLU benchmark\(Hendryckset al\.,[2021](https://arxiv.org/html/2608.08744#bib.bib27)\):*abstract algebra*,*philosophy*, and*formal logic*, chosen to span mathematical, humanistic, and symbolic reasoning\. For each \(model, subject\) pair we report macro\-F1 and inference CO2emissions, both computed under identical decoding settings and hardware\. For theλ\\lambda\-sensitivity study in Section[A\.2](https://arxiv.org/html/2608.08744#A1.SS2)we additionally fine\-tune Qwen\-2\.5\-14B on SQuAD v2\(Rajpurkaret al\.,[2018](https://arxiv.org/html/2608.08744#bib.bib28)\)and BoolQ\(Clarket al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib29)\)across twelve values ofλ∈\[0,1\]\\lambda\\in\[0,1\]\.

#### Measurement\.

Energy and emissions are logged with CodeCarbon under a fixed grid carbon intensity of0\.369473​kg​CO2/kWh0\.369473~\\mathrm\{kg\\,CO\_\{2\}/kWh\}, the value associated with the training region; this constant cancels in all relative comparisons reported in Section[3](https://arxiv.org/html/2608.08744#S3)\. Training\-side emissions acrossλ\\lambdavalues are within measurement noise \(Section[3](https://arxiv.org/html/2608.08744#S3)\), and all carbon comparisons in the main paper therefore refer to*inference\-time*emissions on the MMLU evaluation pass\.

## 3Results

We organize the results around the research question of Section[1](https://arxiv.org/html/2608.08744#S1)\. We answer this in three stages\. Section[3\.1](https://arxiv.org/html/2608.08744#S3.SS1)reports the per\-subject MMLU comparison across the three model families and identifies the operating points that lie inside the break\-even region\. Section[3\.2](https://arxiv.org/html/2608.08744#S3.SS2)grounds the aggregate metrics with prediction\-level examples\. Section[A\.2](https://arxiv.org/html/2608.08744#A1.SS2)examines the subsidiary result of how the optimum shifts with task structure through aλ\\lambda\-sensitivity study on Qwen\-2\.5\-14B\.

Table 2:Per\-subject MMLU comparison\. CE is the cross\-entropy baseline; Joint is the carbon\-aware objective at the per\-model selectedλ\\lambda\(λ=0\.01\\lambda=0\.01for Gemma\-2B,λ=0\.1\\lambda=0\.1for Llama\-8B and Qwen\-14B\)\.Δ\\DeltaF1 is in absolute F1 points;Δ\\DeltaCO2is relative\. Bold rows indicate pairs in the break\-even region \(Δ​F1≥0\\Delta\\text\{F1\}\\geq 0andΔ​CO2≤\+2%\\Delta\\text\{CO\}\_\{2\}\\leq\+2\\%\)\. The Qwen\-14B / Abstract Algebra is a strict Pareto improvement\.ModelSubjectCE F1Joint F1Δ\\DeltaF1CE CO2\(10−310^\{\-3\}kg\)Joint CO2\(10−310^\{\-3\}kg\)Δ\\DeltaCO2Gemma\-2\-2BAbstract Algebra0\.1760\.118−0\.058\-0\.0580\.6000\.586−2\.20%\-2\.20\\%Philosophy0\.2720\.400\+0\.128\\bm\{\+0\.128\}1\.8671\.868\+0\.06%\\bm\{\+0\.06\\%\}Formal Logic0\.2990\.299\+0\.000\\bm\{\+0\.000\}0\.7650\.761−0\.56%\\bm\{\-0\.56\\%\}Llama\-3\.1\-8BAbstract Algebra0\.3650\.362−0\.003\\bm\{\-0\.003\}0\.7510\.739−1\.62%\\bm\{\-1\.62\\%\}Philosophy0\.6550\.666\+0\.011\+0\.0112\.2072\.211\+0\.16%\+0\.16\\%Formal Logic0\.3910\.444\+0\.053\\bm\{\+0\.053\}1\.0111\.029\+1\.77%\\bm\{\+1\.77\\%\}Qwen\-2\.5\-14BAbstract Algebra0\.4460\.481\+0\.035\\bm\{\+0\.035\}1\.2091\.167−3\.51%\\bm\{\-3\.51\\%\}Philosophy0\.7590\.760\+0\.001\+0\.0013\.5693\.686\+3\.27%\+3\.27\\%Formal Logic0\.5960\.604\+0\.008\+0\.0081\.6511\.622−1\.76%\-1\.76\\%### 3\.1Per\-Subject MMLU Comparison

Table[2](https://arxiv.org/html/2608.08744#S3.T2)reports inference F1 and inference CO2for each \(model, subject\) pair under the cross\-entropy baseline and the joint objective at the per\-model selectedλ\\lambda\. Five of the nine pairs fall inside the break\-even region, which we define asΔ​F1≥0\\Delta\\text\{F1\}\\geq 0together withΔ​CO2≤\+2%\\Delta\\text\{CO\}\_\{2\}\\leq\+2\\%\. One of these is a strict Pareto improvement \(Qwen\-14B on abstract algebra:\+3\.5\+3\.5F1 and−3\.5%\-3\.5\\%CO2\)\. Two further pairs gain substantial F1 at essentially zero or low carbon cost: Gemma\-2B on philosophy \(\+12\.8\+12\.8F1,\+0\.1%\+0\.1\\%CO2\) and Llama\-8B on formal logic \(\+5\.3\+5\.3F1,\+1\.8%\+1\.8\\%CO2\)\. The remaining break\-even pairs are small or null improvements with no carbon penalty \(Gemma\-2B / formal logic, Llama\-8B / abstract algebra\), and the four out\-of\-region pairs are losses that are concentrated on the smallest model \(Gemma\-2B / abstract algebra\) and on philosophy across two of the three families\. The pattern is consistent with our framing ofλ\\lambdaas a structural regularizer rather than a uniform efficiency intervention\.

### 3\.2Qualitative Examples

Table[3](https://arxiv.org/html/2608.08744#S3.T3)provides three prediction\-level examples drawn from the MMLU evaluation of Qwen\-2\.5\-14B and Llama\-3\.1\-8B, contrasting the baseline and joint models on items where they disagree\. The examples are intended to ground the aggregate metrics in Table[2](https://arxiv.org/html/2608.08744#S3.T2)and to convey what kind of items the carbon\-aware model recovers\. Additional examples are provided in Appendix[A\.10](https://arxiv.org/html/2608.08744#A1.SS10)\.

Table 3:Prediction\-level examples from MMLU where the joint model differs from the cross\-entropy baseline\. Full items, including answer options, are reproduced in Appendix[A\.10](https://arxiv.org/html/2608.08744#A1.SS10)\.Domain \(abridged\)CEJoint*Abstract algebra, Qwen\-14B*: Identify the order of the factor group\(ℤ11×ℤ15\)/⟨\(1,1\)⟩\(\\mathbb\{Z\}\_\{11\}\\times\\mathbb\{Z\}\_\{15\}\)/\\langle\(1,1\)\\rangle\.×\\times✓*Formal logic, Llama\-8B*: Select the best translation into predicate logic of*“Some kind students are eager to learn\.”*×\\times✓*Philosophy, Qwen\-14B*: According to act utilitarianism, what is the morally right action in a given situation?✓✓The two reversals in Table[3](https://arxiv.org/html/2608.08744#S3.T3)are representative of a broader pattern visible in the prediction files: items the joint model recovers are concentrated in the classes for which the per\-class AUC improves \(Appendix[A\.8](https://arxiv.org/html/2608.08744#A1.SS8)\)\. The third example, on which both models are correct, is included to make explicit that the joint model does not trade away easy items for hard ones, the break\-even improvements in Table[2](https://arxiv.org/html/2608.08744#S3.T2)are net gains, not redistributions\.

## 4Conclusion

We have asked whether joint optimization of task performance and inference carbon admits a break\-even point and have shown, on three architecturally distinct model families and three MMLU subjects, that the break\-even region is non\-empty, though selective\. The strongest operating point, a strict Pareto improvement on Qwen\-2\.5\-14B abstract algebra with\+3\.5\+3\.5F1 and−3\.5%\-3\.5\\%inference CO2, establishes that the regime is reachable in practice, and the dataset\-dependentλ\\lambdasensitivity on SQuAD v2 and BoolQ clarifies that the carbon penalty is best read as a structural regularizer\. Calibrated carbon\-aware fine\-tuning thus emerges not as a universal compression of LLM inference, but as a lightweight, drop\-in mechanism applicable when the target task admits a lower\-cost computational pathway compatible with the correct answer\. The most important future direction is characterizing*when*such pathways exist, so that the optimalλ\\lambdacan be predicted from task structure rather than discovered through per\-task sweeps\.

## Limitations

This is an ongoing work, and we have reported our first significant finding in this paper\. At this moment, we have three fundamental limitations\. First, the surrogate uses within\-sampleR2R^\{2\}\(Section[2\.2](https://arxiv.org/html/2608.08744#S2.SS2)\) calibrated on three operating points per model; it provides a locally faithful gradient signal rather than global energy predictions, necessitating future expansion of profiling points\. Second, inference\-time emission deltas are absolutely small \(single\-digit percentages of10−310^\{\-3\}kg\) and measured on fixed hardware under a single carbon intensity factor\. Thus, our claims are strictly relative, as absolute magnitudes vary with hardware and grid conditions; however, our setup in Google Colab Pro consisted of a H100 GPU with 95 GB VRAM, with 179 GB of RAM\. It is a widely popular setup for LLM fine\-tuning and inference, and hence most people will come across similar results\. Third, evaluations span only three subjects from one benchmark \(cross\-family\) and two datasets \(λ\\lambda\-sensitivity\)\. Also, the carbon penalty weightλ\\lambdais currently selected through a discrete validation sweep rather than learned end\-to\-end\. Treatingλ\\lambdaas a learnable parameter, optimized jointly withθ\\thetavia a constrained\-optimization formulation that adapts to task structure, is a direction we leave to future work\. While our regularization findings align with prior intuition, they cover a narrow NLP slice\. Primary future work will investigate whether the break\-even region remains non\-empty and if optimalλ\\lambdais predictable from task structure across instruction\-following, code generation, and open\-ended generation\.

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## Appendix AAppendix

![Refer to caption](https://arxiv.org/html/2608.08744v1/Figure_2.png)Figure 2:λ\\lambda\-sensitivity of compared models on SQuAD v2 and BoolQ\. Validation F1 is plotted against the carbon penalty weightλ\\lambda\. SQuAD attains its maximum atλ∗=0\\lambda^\{\*\}=0and degrades monotonically thereafter; BoolQ attains its maximum atλ∗=0\.1\\lambda^\{\*\}=0\.1, exceeding theλ=0\\lambda=0baseline by6\.26\.2F1 points\. The two tasks place the optimum on opposite ends of the carbon penalty axis, indicating thatλ\\lambdais best interpreted as a regularizer whose effect is conditioned on task structure\.Unfortunately, Qwen\-2\.5\-14B crashed repeatedly during the Formal Logic benchmarking\. The internal diagnosis revealed that it is designed for guided multi\-step reasoning with instruction tuning, which we did not perform explicitly to keep the benchmarking fair among all the models\.### A\.1Related Work

A growing line of work measures and reports the energy and carbon costs of training and serving language models\.\(Strubellet al\.,[2019](https://arxiv.org/html/2608.08744#bib.bib5)\)first quantified the emissions of large NLP models, and subsequent work has extended the methodology to lifecycle accounting\(Pattersonet al\.,[2021](https://arxiv.org/html/2608.08744#bib.bib1)\), datacenter\-scale inference\(Wuet al\.,[2022](https://arxiv.org/html/2608.08744#bib.bib2)\), and per\-task profiling of widely deployed checkpoints\(Luccioniet al\.,[2023](https://arxiv.org/html/2608.08744#bib.bib4),[2024](https://arxiv.org/html/2608.08744#bib.bib3)\)\.\(Schwartzet al\.,[2020](https://arxiv.org/html/2608.08744#bib.bib6)\)framed the broader*Green AI*aspect, arguing that efficiency should be reported alongside accuracy as a first\-class evaluation axis\. These efforts have produced the measurement infrastructure on which our work depends, including the CodeCarbon tooling we adopt; however, they are diagnostic rather than prescriptive\. They tell what an LLM costs, not how to train one that costs less\.

The fine\-tuning objective itself remains, in effect, carbon\-neutral terrain for LLMs\. To our knowledge, no prior work fits a differentiable energy surrogate from on\-hardware profiling of a specific pretrained LLM and inserts that surrogate into the fine\-tuning loss to steer inference\-time pathway selection\. Our paper offers either accounting without optimization \(Section[2\.3](https://arxiv.org/html/2608.08744#S2.SS3)\), or optimization that leaves the loss intact \(Section[3\.1](https://arxiv.org/html/2608.08744#S3.SS1)\) and efficiency \(Figure[2](https://arxiv.org/html/2608.08744#A1.F2)\), or hardware\-aware objectives that operate at the wrong granularity for adapting deployed LLMs\. Our work targets exactly this gap, and the empirical question: whether the resulting joint objective can preserve task accuracy while reducing inference emissions is what Sections[2](https://arxiv.org/html/2608.08744#S2)and[3](https://arxiv.org/html/2608.08744#S3)take up\.

### A\.2Dataset\-Dependentλ\\lambdaon Qwen\-2\.5\-14B

The cross\-family results above use a small per\-modelλ\\lambdasweep over\{0\.01,0\.03,0\.1\}\\\{0\.01,0\.03,0\.1\\\}\. A natural question is whether the optimum ofλ\\lambdais a model property or a task property\. Figure[2](https://arxiv.org/html/2608.08744#A1.F2)answers this with a finer\-grained sweep on Qwen\-2\.5\-14B over twelve values ofλ\\lambdaacross SQuAD v2 and BoolQ, the two non\-MMLU datasets for which we performed an extended sweep\.

The two datasets place the optimum on opposite ends of the sweep\. SQuAD v2, an extractive question answering task in which the model must select an exact answer span \(or abstain\), attains its peak validation F1 of0\.8080\.808atλ∗=0\\lambda^\{\*\}=0and degrades to0\.1730\.173atλ=1\.0\\lambda=1\.0, with the steepest drop occurring betweenλ=0\.003\\lambda=0\.003andλ=0\.01\\lambda=0\.01\. The carbon term in this regime acts as harmful interference: span selection is brittle to objective perturbation, and any nonzero penalty pulls the model away from the cross\-entropy optimum\. BoolQ exhibits the inverse behavior\. Its baseline atλ=0\\lambda=0is0\.3600\.360, its peak is0\.4220\.422atλ∗=0\.1\\lambda^\{\*\}=0\.1, and it remains above the baseline for a wide band ofλ\\lambdavalues up to1\.01\.0\. The carbon term in this regime acts as a beneficial regularizer for boolean reasoning\. We read this contrast as evidence that the effect ofλ\\lambdaon F1 is mediated by the geometry of the target task, extractive tasks penalize any objective perturbation, while binary classification benefits from a mild implicit\-complexity prior, and that no singleλ\\lambdavalue should be expected to be optimal across tasks\.

### A\.3Full Seven\-Model MMLU Comparison

The main paper restricts the cross\-family comparison to three architecturally distinct families that exhibit the cleanest break\-even behavior: Gemma\-2\-2B, Llama\-3\.1\-8B, and Qwen\-2\.5\-14B\. Table[4](https://arxiv.org/html/2608.08744#A1.T4)reports the equivalent measurements for all seven models in our experimental matrix, including the four models omitted from the main text \(Llama\-3\.2\-1B, Qwen\-2\.5\-1\.5B, Mistral\-Small\-3\.1\-3B, and Mistral\-7B\-v0\.1\)\. The broader picture is consistent with the main paper’s interpretation\. Five of seven models reduce inference energy on at least one MMLU subject under the joint objective, and joint F1 improvements appear across all three subjects and across both the smaller and larger size tiers\. The two cases that weaken the headline narrative are Mistral\-7B on formal logic, which incurs a20\.3%20\.3\\%inference carbon overhead despite a modest F1 gain, and Qwen\-1\.5B on philosophy and formal logic, which records carbon increases of6\.4%6\.4\\%and21\.2%21\.2\\%respectively\. These cases motivated the selection of the three families in the main paper and are themselves worth examining in future work as instances where the surrogate gradient direction and the empirical inference cost diverge\.

Table 4:Per\-subject MMLU comparison across all seven models in the experimental matrix\. CE is the cross\-entropy baseline; Joint is the carbon\-aware objective at the per\-model selectedλ\\lambda\. Models above the rule are reported in the main paper \(Section[3\.1](https://arxiv.org/html/2608.08744#S3.SS1)\); models below are reported here only\.ModelSubjectCE F1Joint F1Δ\\DeltaF1CE CO2\(10−310^\{\-3\}kg\)Joint CO2\(10−310^\{\-3\}kg\)Δ\\DeltaCO2Gemma\-2\-2BAbstract Algebra0\.1760\.118−0\.058\-0\.0580\.6000\.586−2\.20%\-2\.20\\%Philosophy0\.2720\.400\+0\.128\+0\.1281\.8671\.868\+0\.06%\+0\.06\\%Formal Logic0\.2990\.299\+0\.000\+0\.0000\.7650\.761−0\.56%\-0\.56\\%Llama\-3\.1\-8BAbstract Algebra0\.3650\.362−0\.003\-0\.0030\.7510\.739−1\.62%\-1\.62\\%Philosophy0\.6550\.666\+0\.011\+0\.0112\.2072\.211\+0\.16%\+0\.16\\%Formal Logic0\.3910\.444\+0\.053\+0\.0531\.0111\.029\+1\.77%\+1\.77\\%Qwen\-2\.5\-14BAbstract Algebra0\.4460\.481\+0\.035\+0\.0351\.2091\.167−3\.51%\-3\.51\\%Philosophy0\.7590\.760\+0\.001\+0\.0013\.5693\.686\+3\.27%\+3\.27\\%Formal Logic0\.5960\.604\+0\.008\+0\.0081\.6511\.622−1\.76%\-1\.76\\%Llama\-3\.2\-1BAbstract Algebra0\.1370\.163\+0\.026\+0\.0260\.6000\.586−2\.20%\-2\.20\\%Philosophy0\.1360\.126−0\.010\-0\.0101\.8671\.868\+0\.06%\+0\.06\\%Formal Logic0\.2070\.155−0\.052\-0\.0520\.7650\.761−0\.56%\-0\.56\\%Qwen\-2\.5\-1\.5BAbstract Algebra0\.1720\.163−0\.009\-0\.0090\.8150\.764−6\.30%\-6\.30\\%Philosophy0\.3420\.326−0\.016\-0\.0162\.1782\.317\+6\.36%\+6\.36\\%Formal Logic0\.3730\.419\+0\.046\+0\.0460\.9061\.098\+21\.16%\+21\.16\\%Mistral\-3BAbstract Algebra0\.0870\.080−0\.007\-0\.0070\.3700\.355−3\.99%\-3\.99\\%Philosophy0\.0780\.087\+0\.009\+0\.0091\.0351\.036\+0\.16%\+0\.16\\%Formal Logic0\.1440\.186\+0\.042\+0\.0420\.4850\.484−0\.16%\-0\.16\\%Mistral\-7BAbstract Algebra0\.3000\.290−0\.010\-0\.0100\.7000\.674−3\.71%\-3\.71\\%Philosophy0\.5500\.565\+0\.015\+0\.0152\.0302\.034\+0\.20%\+0\.20\\%Formal Logic0\.3700\.400\+0\.030\+0\.0300\.9461\.138\+20\.30%\+20\.30\\%
### A\.4Surrogate Calibration: Full Data

Table[5](https://arxiv.org/html/2608.08744#A1.T5)reports the raw calibration profiling data collected for all seven models in our study\. For each model we profile three batch sizes and measure the parameter L2 norm, FLOP proxy, memory proxy, and on\-hardware energy via CodeCarbon\. The non\-negative least\-squares fit over these three points produces the per\-model surrogate weights used in Equation[2](https://arxiv.org/html/2608.08744#S2.E2)of the main paper\. The within\-sampleR2R^\{2\}values for the seven models range from0\.6630\.663\(Llama\-8B\) to1\.0001\.000\(Qwen\-14B\)\. We reiterate the scope statement from Section[2\.2](https://arxiv.org/html/2608.08744#S2.SS2): the surrogate is treated as a locally faithful gradient signal for fine\-tuning, not as a globally calibrated energy predictor, and the small calibration set is one of the limitations named in Section[A\.12](https://arxiv.org/html/2608.08744#A1.SS12)\.

Table 5:Surrogate calibration data for all seven models\. “Param Norm” is the L2 norm of the parameter vector; “FLOP Proxy” is computed from the forward\-pass tensor shapes; “Mem Proxy” reflects peak activation footprint; “Energy” is measured on\-hardware via CodeCarbon at the indicated batch size\.ModelBParam NormFLOP ProxyMem ProxyEnergy \(kWh\)Llama\-1B128582\.3514978\.840\.9080\.000271256582\.8617806\.391\.0780\.000327512583\.1118096\.661\.0950\.000364Qwen\-1\.5B1280\.03762127\.800\.6620\.0003692560\.03760305\.101\.0210\.0004333840\.03763370\.041\.1090\.000444Gemma\-2B128946\.8031790\.462\.1590\.000447256947\.0237507\.662\.5450\.000617512946\.4138106\.612\.5850\.000675Mistral\-3B128506\.1450293\.001\.7460\.000827256506\.2662565\.052\.1700\.001185512507\.1564367\.202\.2320\.001390Mistral\-7B1281155\.4285790\.052\.9790\.0006652561149\.19106827\.653\.7050\.0009533841161\.83109841\.653\.8090\.001105Llama\-8B1281143\.3278399\.982\.7230\.0011762561149\.9093141\.163\.2330\.0015943841151\.1394661\.513\.2850\.001856Qwen\-14B1280\.02006535\.372\.8060\.0010442560\.020051318\.304\.3790\.0015213840\.020061575\.724\.7410\.001645The per\-model surrogate weights derived from this calibration data are summarized in Table[6](https://arxiv.org/html/2608.08744#A1.T6)\. Two patterns are visible\. First, the FLOP proxy receives nearly all weight for the Llama, Gemma, and Mistral families, whose parameter L2 norms are in the range5×1025\\times 10^\{2\}to1\.2×1031\.2\\times 10^\{3\}\. Second, the parameter norm receives nearly all weight for the Qwen family, whose parameter L2 norms are in the range2×10−22\\times 10^\{\-2\}to4×10−24\\times 10^\{\-2\}\. The asymmetry is absorbed by the per\-model fit and reflects the parameter normalization conventions of the respective architectures rather than a property of the surrogate\.

Table 6:Per\-model surrogate weights \(normalized\) and within\-sampleR2R^\{2\}\.Modelw1w\_\{1\}\(Param\)w2w\_\{2\}\(FLOP\)w3w\_\{3\}\(Mem\)R2R^\{2\}Llama\-1B0\.0001\.0000\.0000\.974Qwen\-1\.5B0\.9710\.0000\.0290\.998Gemma\-2B0\.0001\.0000\.0000\.974Mistral\-3B0\.0001\.0000\.0000\.989Mistral\-7B0\.0001\.0000\.0000\.872Llama\-8B0\.0001\.0000\.0000\.663Qwen\-14B0\.9880\.0000\.0121\.000
### A\.5Lambda Sweep: Full Results

Table[7](https://arxiv.org/html/2608.08744#A1.T7)reports the full validation sweep overλ∈\{0\.01,0\.03,0\.1\}\\lambda\\in\\\{0\.01,0\.03,0\.1\\\}for all seven models in our experimental matrix\. The per\-model selectedλ\\lambdavalues \(bolded\) are the ones used to fine\-tune the joint models reported in Table[4](https://arxiv.org/html/2608.08744#A1.T4)\. For four models \(Llama\-1B, Qwen\-1\.5B, Llama\-8B, Qwen\-14B\), the highest penaltyλ=0\.1\\lambda=0\.1achieves the best validation F1\. For the remaining three models \(Gemma\-2B, Mistral\-3B, Mistral\-7B\), all three values produce identical or near\-identical validation F1, and we select the smallest penaltyλ=0\.01\\lambda=0\.01on the principle of minimizing the perturbation to the cross\-entropy objective when the carbon term provides no F1 advantage\.

Table 7:Lambda sweep validation F1, exact match, energy, and emissions per model\. Bold rows mark the per\-model selectedλ\\lambdaused in the main paper\.Modelλ\\lambdaVal F1Val EMEnergy \(kWh\)CO2\(kg\)Llama\-1B0\.010\.53910\.53910\.01210\.004480\.030\.54760\.54690\.01210\.004480\.100\.54760\.54690\.01210\.00446Qwen\-1\.5B0\.010\.53910\.53910\.01700\.006270\.030\.53130\.53130\.01730\.006400\.100\.55080\.54690\.01730\.00638Gemma\-2B0\.010\.54690\.54690\.02700\.009970\.030\.54690\.54690\.02710\.010010\.100\.54690\.54690\.02710\.01003Mistral\-3B0\.010\.53910\.53910\.05870\.021690\.030\.53910\.53910\.06000\.022180\.100\.53910\.53910\.05870\.02169Mistral\-7B0\.010\.56770\.56250\.04770\.017620\.030\.56770\.56250\.04820\.017810\.100\.56770\.56250\.04800\.01775Llama\-8B0\.010\.55110\.54690\.08050\.029740\.030\.55040\.54690\.05850\.021620\.100\.55120\.54690\.04430\.01636Qwen\-14B0\.010\.57070\.56250\.07890\.029150\.030\.57070\.56250\.07950\.029370\.100\.57850\.57030\.07930\.02929

The training\-side CO2values within any single model are within measurement noise acrossλ\\lambda\. The Llama\-8B row is the one apparent exception, where training\-time emissions appear to decrease withλ\\lambdafrom0\.0300\.030kg to0\.0160\.016kg; this is an artifact of run\-to\-run variation in step count and checkpointing overhead rather than an effect of the carbon term, as discussed in Section[3](https://arxiv.org/html/2608.08744#S3)and visible in the per\-step emission traces of Table[7](https://arxiv.org/html/2608.08744#A1.T7)\.

### A\.6Extended Lambda\-Sensitivity on Qwen\-14B

The main paper reports theλ\\lambda\-sensitivity of Qwen\-14B on SQuAD v2 and BoolQ across twelve values ofλ\\lambda\. The full numerical results, including the GSM8K math reasoning dataset that was omitted from the main paper is reported in Table[8](https://arxiv.org/html/2608.08744#A1.T8)\. We omit GSM8K from the main paper’s analysis because the absolute F1 on this benchmark falls in the range\[0\.005,0\.013\]\[0\.005,0\.013\]across allλ\\lambdavalues, which is well within the noise floor of the evaluator under our current pipeline\. Reliable conclusions aboutλ\\lambda\-sensitivity on math reasoning will require a revised evaluation protocol with partial\-credit scoring or a chain\-of\-thought decoding setting, both of which lie outside the scope of this paper\.

Table 8:Extendedλ\\lambda\-sweep validation F1 on Qwen\-14B across SQuAD v2, BoolQ, and GSM8K\. Per\-dataset optima are in bold\.λ\\lambdaSQuAD F1BoolQ F1GSM8K F10\.0000\.80850\.35970\.00630\.0010\.79350\.05340\.00740\.0030\.80160\.14610\.00650\.0100\.43170\.07100\.00590\.0300\.33540\.10680\.00530\.0700\.39260\.17330\.00700\.1000\.24250\.42180\.01040\.2000\.26450\.19050\.01300\.3500\.37460\.09960\.01320\.5000\.18630\.20010\.01180\.7500\.30370\.29600\.01071\.0000\.17260\.20760\.0092
### A\.7μ\\mu\-Sensitivity Study

In addition to the carbon\-penalty weightλ\\lambda, the training objective admits an entropy\-regularization term with weightμ\\muthat we held fixed in the main paper for exposition\. Figures[3](https://arxiv.org/html/2608.08744#A1.F3),[4](https://arxiv.org/html/2608.08744#A1.F4), and[5](https://arxiv.org/html/2608.08744#A1.F5)report the validation F1, emissions, and validation loss for Qwen\-14B across twelve values ofμ\\muon the three sweep datasets at fixedλ=0\.003\\lambda=0\.003\. The F1 surface is essentially flat acrossμ\\mufor all three datasets, with variation within±0\.025\\pm 0\.025F1 around the mean; the emissions and loss surfaces are similarly flat\. We include these data for completeness and as evidence that theμ\\muterm does not interact meaningfully with the carbon penalty within the range studied\.

![Refer to caption](https://arxiv.org/html/2608.08744v1/Figure_3.png)Figure 3:Validation F1 across varyingμ\\muvalues for Qwen\-14B atλ=0\.003\\lambda=0\.003\.![Refer to caption](https://arxiv.org/html/2608.08744v1/Figure_4.png)Figure 4:Training emissions \(kgCO2eq\) across varyingμ\\muvalues for Qwen\-14B atλ=0\.003\\lambda=0\.003\.![Refer to caption](https://arxiv.org/html/2608.08744v1/Figure_5.png)Figure 5:Validation loss across varyingμ\\muvalues for Qwen\-14B atλ=0\.003\\lambda=0\.003\.
### A\.8Per\-Class AUC Analysis

The aggregate F1 numbers reported in Tables[2](https://arxiv.org/html/2608.08744#S3.T2)and[4](https://arxiv.org/html/2608.08744#A1.T4)can mask redistribution of accuracy across answer classes\. To examine whether the joint model’s gains are uniformly distributed, we report per\-class AUC\-PR and AUC\-ROC for the four MMLU answer options \(A, B, C, D\) on the three main\-paper models in Table[9](https://arxiv.org/html/2608.08744#A1.T9)\. The reversals visible in Table[3](https://arxiv.org/html/2608.08744#S3.T3)of the main paper concentrate in the classes for which AUC improves most under the joint objective, supporting the interpretation that the carbon term is recovering specific decision boundaries rather than diffusely shifting confidence across all classes\.

Table 9:Per\-class AUC\-PR for Qwen\-14B on the three MMLU subjects, comparing CE baseline and joint \(λ=0\.1\\lambda=0\.1\)\. Largest per\-row gain are in bold\.SubjectConfigABCDAbs\. AlgebraCE0\.5610\.6910\.6010\.489Joint0\.5910\.6960\.6280\.552PhilosophyCE0\.7930\.8750\.9180\.823Joint0\.7990\.8700\.9260\.814Formal LogicCE0\.7120\.7470\.5760\.792Joint0\.7450\.7580\.6180\.806
### A\.9Loss Curves

Figure[6](https://arxiv.org/html/2608.08744#A1.F6)reports the training\-loss curves for the three models reported in the main paper, comparing the cross\-entropy baseline and the joint objective at the per\-model selectedλ\\lambda\. The curves are visually similar in shape and converge to similar terminal values, consistent with the claim that the joint loss perturbs the optimum without destabilizing the optimization itself\.

![Refer to caption](https://arxiv.org/html/2608.08744v1/Figure_6.png)Figure 6:Training\-loss curves for Gemma\-2B, Llama\-8B, and Qwen\-14B, comparing the cross\-entropy baseline and the joint objective at the per\-model selectedλ\\lambda\.
### A\.10Extended Qualitative Examples

Table[10](https://arxiv.org/html/2608.08744#A1.T10)extends the qualitative examples of Table[3](https://arxiv.org/html/2608.08744#S3.T3)in the main paper to include the full item text, answer options, gold answer, baseline prediction, and joint prediction for each example\. We provide additional examples from each of the three models and three MMLU subjects to allow inspection of the kinds of items the joint model recovers\.

Table 10:Extended qualitative examples\. Each row is an item on which the cross\-entropy baseline produced an incorrect answer and the joint model atλ=0\.1\\lambda=0\.1produced the correct one\. Probabilities are the per\-option scores returned by the model on the four answer choices\.SubjectQuestionOptions \(A / B / C / D\)GoldCE→\\toJoint→\\toAbstractAlgebraCompute the product in the given ring\.\(20\)​\(−8\)\(20\)\(\-8\)inℤ26\\mathbb\{Z\}\_\{26\}\.A\. 0 B\. 1 C\. 11 D\. 22DA \(p=0\.38p\{=\}0\.38\)D \(p=0\.43p\{=\}0\.43\)AbstractAlgebraStatement 1: Every permutation is a cycle\. Statement 2: Every cycle is a permutation\.A\. True, True B\. False, False C\. True, False D\. False, TrueDA \(p=0\.48p\{=\}0\.48\)D \(p=0\.73p\{=\}0\.73\)Formal LogicIdentify the antecedent of the conditional:*“The Bees win their first game only if either the Aardvarks or the Chipmunks do not win their first games\.”*A\. The Aardvarks do not win\. B\. The Bees win their first game\. C\. The Chipmunks do not win\. D\. Either the Aardvarks or the Chipmunks do not win\.BD \(p=0\.52p\{=\}0\.52\)B \(p=0\.52p\{=\}0\.52\)Formal LogicConstruct a complete truth table for the argument∼C⊃D\\sim\\\!C\\supset D;D⊃C/CD\\supset C\\,/\\,C\. Then, using the truth table, determine whether the argument is valid or invalid\.A\. Valid\. B\. Invalid\. Counterexample whenCCandDDare true\. C\. Invalid\. Counterexample whenCCis true andDDis false\. D\. Invalid\. Counterexample whenDDis true andCCis false\.AB \(p=0\.31p\{=\}0\.31\)A \(p=0\.32p\{=\}0\.32\)PhilosophyAccording to Kant, the supreme principle of morality is:A\. analytic and a priori\. B\. analytic and a posteriori\. C\. synthetic and a priori\. D\. synthetic and a posteriori\.CA \(p=0\.49p\{=\}0\.49\)C \(p=0\.57p\{=\}0\.57\)PhilosophyAristotle says that what makes things be what they are — their essence — does not exist apart from individuals that exist in the world\. If all the members of a species were destroyed, their essence or form:A\. would likewise be destroyed\. B\. would be destroyed only if no one remembers the species\. C\. would continue existing in some other realm of being\. D\. would not be destroyed because there was no essence originally\.AD \(p=0\.59p\{=\}0\.59\)A \(p=0\.67p\{=\}0\.67\)
### A\.11Reproducibility Details

All fine\-tuning runs use AdamW with a constant learning rate, batch sizes matched to each model’s calibration set, and a fixed number of optimization steps per \(model, configuration\) pair\. The fixed grid carbon intensity is0\.369473​kg​CO2/kWh0\.369473~\\mathrm\{kg\\,CO\_\{2\}/kWh\}, corresponding to the training region; all relative CO2comparisons in the paper are invariant to this constant\. Energy is logged with CodeCarbon at per\-step granularity\. We release the per\-step training histories, calibration tables, inference\-time emission logs, MMLU prediction files for all configurations, and the surrogate\-weight JSON files referenced in Tables[1](https://arxiv.org/html/2608.08744#S2.T1)and[6](https://arxiv.org/html/2608.08744#A1.T6)\. The release supports independent recomputation of every numerical claim in the main paper and in the Appendix\.

### A\.12Discussion

#### The non\-empty but selective break\-even region\.

Our central empirical finding is that joint optimization of task performance and inference carbon admits operating points at which F1 is preserved or improved while inference CO2is held at or below the cross\-entropy baseline\. The strongest of these operating points, Qwen\-2\.5\-14B on abstract algebra, with a3\.53\.5\-point F1 gain and a3\.5%3\.5\\%CO2reduction, is a strict Pareto improvement, and two further pairs \(Gemma\-2\-2B on philosophy and Llama\-3\.1\-8B on formal logic\) deliver substantial F1 gains at essentially zero or low carbon cost\. The result we do*not*report is equally important: the break\-even region is not universal\. Four of nine \(model, subject\) pairs in Table[2](https://arxiv.org/html/2608.08744#S3.T2)fall outside it, and theλ\\lambda\-sensitivity study in Figure[2](https://arxiv.org/html/2608.08744#A1.F2)shows that SQuAD v2 strictly degrades under any nonzeroλ\\lambda\. We read these two facts together as supporting a specific interpretation:λ\\lambdaacts as a structural regularizer whose sign of effect is determined by the geometry of the target task, not as a uniform efficiency intervention\. Tasks that admit a lower\-cost computational pathway compatible with the correct answer \(boolean reasoning, multi\-step symbolic manipulation\) benefit from a mild implicit\-complexity prior; tasks that require exact span selection \(extractive QA\) are brittle to any objective perturbation\. Practitioners should expect the optimalλ\\lambdato be calibrated per task rather than transferred across them\.

#### Concentrated effect at inference time\.

Training\-side emissions acrossλ\\lambdavalues are within measurement noise \(Table[7](https://arxiv.org/html/2608.08744#A1.T7)\), which might at first appear to undercut the framing of a “carbon\-aware” objective\. We argue the opposite: it clarifies where the mechanism actually operates\. The joint loss does not reduce the cost of producing the model\. Fine\-tuning a fixed\-architecture LLM for a fixed number of steps incurs approximately the same energy regardless of which scalar penalty is added to the cross\-entropy term\. What the joint loss does instead is shift the optimum to which fine\-tuning converges, selecting parameter configurations whose forward pass the surrogate predicts to be cheaper to execute\. The carbon\-aware character of the resulting model is therefore a property of the deployed checkpoint rather than of the fine\-tuning run that produced it, and the empirical signature of the mechanism appears on the inference\-time emission columns of Table[2](https://arxiv.org/html/2608.08744#S3.T2)rather than on the training\-time columns\. This positioning aligns the contribution with the lifecycle observation that motivated the paper: that the operational carbon of a widely deployed LLM is dominated by its serving footprint rather than its training footprint\(Pattersonet al\.,[2021](https://arxiv.org/html/2608.08744#bib.bib1); Wuet al\.,[2022](https://arxiv.org/html/2608.08744#bib.bib2)\)\.