Energy-Aware Parameter Efficiency

Updated 1 February 2026

Energy-aware parameter efficiency is defined as the integration of energy metrics into system or model optimization, dynamically adapting parameters to balance performance and energy consumption.
It is applied across various domains such as THz communications, federated learning, hyperparameter optimization, and HPC, demonstrating energy savings of up to 40% while maintaining accuracy.
Practical frameworks leverage direct power measurement, surrogate modeling, and reinforcement learning to enable cost-effective, performance-aware energy optimization.

Energy-aware parameter efficiency refers to frameworks and methodologies in communication, machine learning, and high-performance computing that jointly optimize system or model parameters for maximal functional efficiency per unit energy. Unlike classical parameter efficiency—which investigates performance-per-parameter or performance-per-resource—energy-aware approaches explicitly measure, model, and optimize power draw and total energy consumption as first-class constraints, dynamically adapting key system parameters to the prevailing hardware, workload, or environment to attain sustainable operation and scalability.

1. Foundational Metrics: Definitions and Formalization

Conventional parameter efficiency is typically quantified as performance per parameter or per unit compute (e.g., inverse perplexity per total parameters for LLMs, or accuracy per parameter in deep vision models) (Dwyer, 10 Jan 2026). However, neglecting energy consumption in such ratios fails to capture actual operational efficiency on real platforms.

Energy-aware parameter efficiency extends these metrics by direct incorporation of power and energy. For example, in large-scale LLM training (“TinyLlama Chat”), the energy-aware efficiency metric can be expressed as:

$\mathrm{PE}_E = K \cdot \frac{\displaystyle \mathrm{invPPL} \times \mathrm{TFLOPS}_\mathrm{bench}}{\mathrm{Params}_\mathrm{M} \times \mathrm{RMS}(W)}$

where $\mathrm{invPPL}$ is the inverse perplexity, $\mathrm{Params}_\mathrm{M}$ is the parameter count in millions, and $\mathrm{RMS}(W)$ is the root-mean-square GPU power observed during training (Dwyer, 10 Jan 2026).

Experimental results indicate that, even as conventional performance may show diminishing improvement with increased compute (e.g., higher token counts), $\mathrm{PE}_E$ can degrade monotonically with increasing workload, reflecting the compounding energy penalty of scale (Dwyer, 10 Jan 2026).

2. Energy-Aware Parameter Adaptation: Techniques Across Domains

Several paradigms demonstrate how system parameters can be adaptively optimized for energy efficiency:

Information Communications (THz OOK transmission): Pulse width is dynamically adapted to channel-induced temporal broadening, minimizing inter-symbol interference and reducing unnecessary pulse transmissions. Constructively exploiting the temporal broadening effect (TBE) permits transmission of consecutive “ON” bits with one pulse, yielding up to 40% energy savings with order-of-magnitude improvements in bit error rates (Naeem et al., 1 May 2025).
Federated Learning: FedGPO employs reinforcement learning (Q-learning) to select at each round the optimal global set of training parameters (local batch size $B$ , local epochs $E$ , active participants $K$ ) based on device heterogeneity, network state, and workload type. The objective is to minimize total distributed energy consumption while meeting convergence and accuracy constraints, yielding up to 3.6x energy-efficiency improvements over fixed or less-adaptive baselines (Kim et al., 2022).
Hyperparameter Optimization: The SM² method extends successive halving by explicitly measuring the energy cost per hyperparameter configuration during an exploratory pretraining phase. Configurations with high energy cost per unit performance are eliminated early, and the trade-off between energy and performance is tunable via an explicit objective function (Geissler et al., 2024).
Activation Sparsity in Neural Training: Energy-Aware Training (EAT) introduces a differentiable $\ell_0$ -norm surrogate as an explicit sparsity regularizer, driving layer activations to zero and maximizing the energy savings achievable on zero-skipping hardware, often with negligible accuracy loss (Lazzaro et al., 2023).
HPC Region-Level Tuning: Dynamic voltage/frequency scaling (DVFS) and uncore frequency scaling (UFS) are adapted at code-region granularity, guided by neural models of performance counters and runtime behavior, to optimize per-region energy efficiency. This paradigm achieves up to 16% energy savings compared to static tuning, particularly for workloads with strong phase behavior (Chadha et al., 2021).

3. Modeling and Measurement of Energy Consumption

Accurate estimation and attribution of energy consumption are necessary for robust efficiency optimization:

Direct Power Measurement: RMS power and energy measurements are frequently obtained via utility interfaces such as NVIDIA’s System Management Interface (SMI) or advanced energy monitors (e.g., HDEEM for HPC). Real-time sampling intervals must be selected carefully (60s or 1 kSa/s) to balance granularity with logging overhead (Dwyer, 10 Jan 2026, Geissler et al., 2024, Chadha et al., 2021).
Per-Component Decomposition: In federated and distributed composites, energy is accounted for by summing per-device compute energy, communication energy, and idle energy, parameterized by hardware-specific power draw and the workload’s partitioning (Kim et al., 2022).
Surrogate Modeling: For high-frequency tuning where physical measurements are costly, surrogate neural models trained on performance monitoring counters, frequency, and voltage are employed to predict energy implications rapidly, informing per-region or per-configuration adaptation (Chadha et al., 2021).

4. Algorithmic Frameworks for Energy-Aware Parameter Optimization

Energy-aware parameter efficiency is pursued by formulating multi-objective or constrained optimization problems, coupling traditional accuracy or convergence objectives with direct penalties or regularization terms for measured or modeled energy:

Regularized Loss Functions: In EAT, objective functions augment standard loss with a smooth sparsity regularizer scaled by a coefficient $\lambda$ , balancing activation sparsity (energy reduction) with classification accuracy (Lazzaro et al., 2023).
RL-Driven Adaptive Scheduling: FedGPO’s Q-learning formalism encodes per-round system state, device heterogeneity, and recent test accuracy into a state-action-reward loop; the reward jointly penalizes energy draw and penalizes non-improving accuracy, tightly coupling energy cost and convergence speed (Kim et al., 2022).
Pruning-Based HPO: In SM², an explicit multi-objective scoring function—linearly weighting normalized performance, inverted energy, and learning-rate stability—prunes half the search space per rung based on user-selected trade-off coefficients ( $\alpha$ , $\beta$ ), breaking away from performance-only search (Geissler et al., 2024).
Region-Based Dynamic Tuning: In HPC workloads, code regions are categorized by runtime and behavioral metrics, and parameter candidates (thread count, DVFS, UFS) are evaluated per-region via neural proxy models and direct measurement; scenarios with identical optima are merged for runtime efficiency (Chadha et al., 2021).

5. Empirical Results and System-Level Impact

Energy-aware parameter efficiency has demonstrated substantial impact in real-system and simulation-based studies:

Domain	Method	Relative Energy Reduction	Key Performance Impact	Reference
THz Comm	Pulse-width adapt.	Up to 40% (β_br=4)	BER reduction orders-of-magnitude; no Rx overhead	(Naeem et al., 1 May 2025)
FL/Edge	FedGPO (Q-Learning)	3.6× over best static	2.4× faster to target accuracy; accuracy preserved	(Kim et al., 2022)
HPO	SM² (SHA+Energy)	8–47% vs energy-ignoring	Maintains or improves test accuracy; tunable α	(Geissler et al., 2024)
NN Training	EAT (ℓ₀-reg.)	8–28% per Table 1	Accuracy maintained within 3%; ↑ sparsity	(Lazzaro et al., 2023)
HPC	Region-level tuning	16.1% (dynamic tuning)	3–10% performance drop tolerated	(Chadha et al., 2021)

Such outcomes highlight that substantial fractions of energy can be saved even in legacy workflows by tuning or adapting key parameters, provided energy is elevated as an explicit optimization goal.

6. Practical Guidelines and Adaptation Strategies

Effective deployment of energy-aware parameter efficiency frameworks requires:

Simultaneously tuning multiple parameters; do not fix global values a priori. Adaptive or RL-driven scheduling outperforms static choices, particularly in heterogeneous or non-stationary environments (Kim et al., 2022, Geissler et al., 2024).
Incorporating real-time power measurement into evaluation pipelines; for hyperparameter optimization and large-model training, monitor RMS power or total energy and prefer configurations that minimize energy per performance gain (Dwyer, 10 Jan 2026, Geissler et al., 2024).
Adjusting algorithmic penalty weights ( $\lambda$ , $\alpha$ ) to balance desired trade-offs between accuracy and energy; in SM², $\alpha=0.75$ yielded good energy-performance compromise (Geissler et al., 2024).
Exploiting code phase behavior in HPC: instrument region boundaries, select significant regions (e.g., >100 ms), and apply per-region tuning models to maximize energy savings (Chadha et al., 2021).
For zero-skipping hardware, prioritize activation sparsity in training and consider differentiable sparsity objectives for maximal energy reduction (Lazzaro et al., 2023).

7. Limitations, Open Questions, and Future Directions

Despite empirical success, notable limitations remain:

Most studies focus on single hardware instances or model architectures; the generality of efficiency trends across architectures, larger model scales, and hardware backends warrants further systematic study, as underscored in recent LLM training experiments (Dwyer, 10 Jan 2026).
Many optimization frameworks assume perfect “zero-skipping” or perfectly linear energy scaling with sparsity—real hardware may have overheads or nonlinearities not captured in simulation (Lazzaro et al., 2023).
Dynamic parameter adaptation can incur modest runtime or measurement overhead (often <1%), but real-time energy measurement with high granularity remains a challenge for large clusters or multi-GPU systems (Geissler et al., 2024, Chadha et al., 2021).
Incorporating additional energy domains (CPU, memory, PSU, cooling) beyond GPU or core metrics will yield more holistic measurement (Geissler et al., 2024).

A plausible implication is that as power costs become primary constraints in large-scale AI and exascale HPC, explicit energy-aware parameter efficiency optimization will increasingly shape the design and operation of future systems, necessitating tight integration between adaptive software algorithms and energy-aware system monitors throughout the ML and HPC stack.