Sustainability of TSFM Deployment and Pretraining: From Carbon Footprint Analysis to Mitigation via Pruning

Cécile Luc; Nathanaël Lemonnier; Ievgen Redko

cs.LGOct 23, 2026

Sustainability of TSFM Deployment and Pretraining: From Carbon Footprint Analysis to Mitigation via Pruning

Authors: Cécile Luc, Nathanaël Lemonnier, Ievgen Redko

Organizations: Strategy & Innovation, AI Hub, Schneider Electric, Rueil-Malmaison, France · Strategy & Innovation, AI Hub, Schneider Electric, Grenoble, France

Abstract

Time Series Foundation Models (TSFMs) offer strong zero-shot forecasting capabilities, but their high pretraining cost raises a practical sustainability question: does this upfront investment pay off over a full deployment lifecycle, compared to supervised standalone models that must be periodically retrained? We model the cumulative carbon cost of different approaches across a realistic industrial scenario: Chronos-2 amortizes its pretraining cost within months for large or frequently queried deployments, but a classical model remains cheaper indefinitely for small or rarely queried ones. For cases where reducing the TSFM's own cost matters, we show that removing a single encoder block (7.9% of parameters) via a gradient-free pruning criterion yields a consistent 6 to 9% reduction in FLOPs, CO2 emissions, and latency, at essentially no cost to zero-shot forecasting performance across a 25-task benchmark.

Figures & tables

Model	Operation	Carbon (gCO 2 )	FLOPs
LightGBM	Training	$7.2\times 10^{-3}$	$5.3\times 10^{10}$
LightGBM	Inference	$6.8\times 10^{-6}$	$2{,}973$
PatchTST	Training	$1.08$	$5.5\times 10^{14}$
PatchTST	Inference	$6.6\times 10^{-6}$	$7.6\times 10^{8}$
Chronos-2	Pretraining (1 step)	$3.3\times 10^{-4}$	$1.5\times 10^{12}$
Chronos-2	Inference	$6.1\times 10^{-5}$	$1.5\times 10^{9}$

Table 1: Carbon cost and FLOPs per approach (LightGBM: CPU; others: GPU). Full measurements and details in Appendix B .

Figure 1: Cumulative carbon cost for all five approaches, baseline scenario, versus time at $N_{a}=1000$ (left) and versus number of assets at $t=60$ months (right).

Panel of Figure 2 — Figure 2: Cost ratio of Chronos-2 ZeroShot (left) and full fine-tuning (right) over LightGBM, at $N_{a}=1{,}000$ , under four retraining/fine-tuning scenarios.

Figure 3: Cost ratio of Chronos-2 ZeroShot over LightGBM, at $N_{a}=1{,}000$ , under three inference frequency scenarios.

Panel of Figure 4 — Figure 4: (a) Mean cosine similarity score per Chronos-2 encoder block, averaged across the 6 calibration tasks (error bars: std across tasks). (b) Aggregated MASE skill score vs number of blocks removed on the same tasks; the dotted line marks the full model baseline, and the retained configuration (1 block) is highlighted.

Metric	Full	Pruned	$\Delta$
MASE skill score (%)	22.99	21.87	$-1.12$
WQL skill score (%)	41.24	41.53	$+0.29$
MASE win rate (%)	–		40.0
WQL win rate (%)	–		52.0

Table 2: Aggregated performance comparison between the full and pruned Chronos-2 models on the 25-task evaluation set. Skill scores are computed relative to a Seasonal Naive baseline (higher is better). Win rate is the share of tasks on which the pruned model beats the full model.

Metric	Full	Pruned	Reduction
Parameters	119.48M	110.04M	7.90%
FLOPs	59.52 G	54.67 G	8.15%
CO2 emissions (g CO2eq)	$1.221\pm 0.037$	$1.114\pm 0.002$	8.72%
Latency (ms)	$19.43\pm 1.02$	$18.27\pm 1.00$	5.97%

Table 3: Compute cost comparison between the full and pruned Chronos-2 models.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Unit	Description
$t$	months	Time elapsed since deployment.
$N_{a}$	–	Number of assets.
$n_{\text{inf}}$	inf./month	Number of 24h forecasts requested per month, per asset.
$W_{i}$	windows	Size of the training set used at the $i$ -th retraining.
$a,b$	windows	Bounds of $W_{i}\sim\mathcal{U}[a,b]$ .
$\alpha$	gCO 2 /window	Carbon cost of training LightGBM on a single window.

Appendix

Table 4: Notation used in the cost equations.

Figure 5: Break-even usage duration $T^{*}$ between Chronos-2 ZeroShot and LightGBM versus a multiplier on $C_{\text{pr}}$ , at $N_{a}=1000$ (baseline scenario). Beyond $60\times$ , no crossover is found within our 100-year search horizon.

Model	Parameter	Value
LightGBM	Estimators	300
	Num. leaves	31
	Max bin	255
	Learning rate	0.05
	Feature/bagging fraction	0.8
	Bagging frequency	5

Appendix

Table 5: Hyperparameters used for the models in Section 3.1 .

Model	Operation	Carbon (gCO 2 )	FLOPs	Latency (ms)
LightGBM	Training, CPU	$0.00722\pm 0.00070$	$5.32\times 10^{10}$	$2{,}903.6\pm 163.7$
LightGBM	Training, GPU	$0.01769\pm 0.00078$	$5.32\times 10^{10}$	$5{,}698.1\pm 222.5$
	Inference, CPU	$(6.81\pm 0.39)\times 10^{-6}$	$2{,}972.5$	$2.17\pm 0.57$
	Inference, GPU	$(6.99\pm 1.42)\times 10^{-6}$	$2{,}972.5$	$2.33\pm 1.04$
PatchTST	Training, GPU	$1.0800\pm 0.0087$	$5.48\times 10^{14}$	$185{,}478.9\pm 784.9$
	Inference, CPU	$(3.26\pm 0.15)\times 10^{-5}$	$7.61\times 10^{8}$	$8.70\pm 13.87$

Appendix

Table 6: Raw measures: carbon cost, FLOPs, and latency for one full training run and one inference call, per approach (mean

\pm

std). Chronos-2’s training row is a single pretraining step, not a full run.

Parameter	Value
$\alpha$ (gCO 2 /window)	$5.51\times 10^{-7}$
$C_{\text{inf}}^{\text{C}}$ (gCO 2 )	$6.44\times 10^{-6}$
$\alpha_{\text{ptst}}$ (gCO 2 /window)	$9.01\times 10^{-5}$
$C_{\text{inf}}^{\text{ptst}}$ (gCO 2 )	$7.43\times 10^{-6}$
$C_{\text{pr}}$ (gCO 2 )	$65.17$
$C_{\text{inf}}^{\text{T}}$ (gCO 2 )	$6.44\times 10^{-5}$

Appendix

Table 7: Cost model parameters (Section 3.1 ).

Figure 6: Break-even usage duration $T^{*}$ (months) as a function of the number of assets $N_{a}$ , at which Chronos-2 ZeroShot becomes cheaper than LightGBM under the baseline scenario.

Removed block	Cosine score	MASE skill (%)	WQL skill (%)
None (full model)	–	9.57	26.89
Block 6 (retained)	0.963	10.24	28.65
Block 5	0.954	9.16	28.40
Block 11	0.576	$-$ 47.30	$-$ 63.09

Appendix

Table 8: Aggregated MASE and WQL skill scores on the 6 calibration tasks, removing a single block at a time.

Block	Cosine score
6	0.963
4	0.960
2	0.957
3	0.955
5	0.954
1	0.946

Appendix

Table 9: Mean cosine score per encoder block, averaged across the 6 calibration tasks (median within task, equal weight across tasks). Lower scores indicate less redundant blocks.

Dataset	Domain	Freq.	# Series	Series length			$H$
				min	avg	max
Australian Electricity	energy	30min	5	230736	231052	232272	48
CIF 2016	banking	1M	72	28	98	120	12
Car Parts	retail	1M	2674	51	51	51	12
Covid Deaths	healthcare	1D	266	212	212	212	30
Dominick	retail	1D	100014	201	296	399	8

Appendix

Table 10: Task-level statistics for the 27 tasks of Chronos Benchmark II, reproduced from Ansari et al. [2024] (Table 3). ETT (15 Min.) and ETT (Hourly) are excluded from our evaluation due to a data loading incompatibility; our study covers the remaining 25 tasks.

Task	MASE		WQL
	Full	Pruned	Full	Pruned
dominick	0.809	0.796	0.324	0.321
ercot	0.832	0.822	0.026	0.026
exchange_rate	1.852	1.807	0.012	0.011
m4_quarterly	1.201	1.186	0.076	0.075
m4_yearly	3.378	3.427	0.117	0.118

Appendix

Table 11: Per-task comparison between the full and pruned Chronos-2 models on the 25 tasks of Chronos Benchmark II. Lower MASE and WQL indicate better performance. Bold values mark the better-performing configuration on each task, based on full-precision values even where rounded figures appear equal.

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Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

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