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REVIEW 4 major objections 5 minor 55 references

THOR: A Generic Energy Estimation Approach for On-Device Training

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that a DNN's on-device training energy can be estimated as the sum of per-layer Gaussian-process predictions, cutting mean absolute percentage error from about 40% to around 10% across five devices.

desk verdict A sensible engineering method for on-device training energy estimation, with a load-bearing additivity assumption that is only weakly tested; deserves a referee but needs a direct subtractivity check. read the letter →

arxiv 2501.16397 v1 pith:MCWSWXK6 submitted 2025-01-27 cs.LG

Jiaru Zhang , Zesong Wang , Hao Wang , Tao Song , Huai-an Su , Rui Chen , Yang Hua , Xiangwei Zhou
show 3 more authors
Ruhui Ma Miao Pan Haibing Guan
This is my paper · ORCID
classification cs.LG
keywords energyestimationon-devicetrainingGaussianprocesslayer-wiseadditivityDNNprofilingenergy-awarepruningmobiledevicesMAPE
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

To make on-device training energy predictable before it runs, the paper proposes treating a DNN as a sum of independent layers and fitting a Gaussian process to each layer type. The load-bearing claim is that total training energy equals the sum of per-layer energies, and that a layer's energy can be read off by subtracting the other layers' contributions from measured totals of small probe networks. On five heterogeneous devices, the summed estimates reach roughly 10% mean absolute percentage error, compared with roughly 40% for a FLOPs-based baseline. The authors then use the estimator to guide channel pruning and report cutting energy by 50% while keeping accuracy. A sympathetic reader would care because accurate, cheap energy estimates are the missing piece for job scheduling and energy budgets on battery-powered devices.

What carries the argument

The machinery is the layer-wise energy additivity and subtractivity assumption, stated in Section 3.2 and encoded in Eqs. (1) and (2), together with the Gaussian processes that fit each layer's energy as a smooth function of channel counts. A GP is a non-parametric probabilistic regressor whose predictions come with uncertainty, which the paper exploits to guide the choice of the next profiling point by maximum variance. The Matérn kernel with $\nu = 2.5$ supplies the GP's covariance, chosen to tolerate runtime optimization artifacts. The final estimator, Eq. (4), simply sums the per-layer GP predictions; profiling is a one-time cost per device and framework, and the paper reports most profiling and fitting runs finish within 20 minutes.

What would settle it

Build a two-convolutional-layer model and measure its training energy directly; then measure a one-layer model with the same first convolution and a one-layer model with the same second convolution, add them, and compare with the two-layer measurement over a range of channel counts on a device with operator fusion enabled. If the mismatch systematically exceeds the measurement noise, additivity fails and the subtractive profiling labels in Eqs. (1) and (2) are biased.

Watch

Extended reading notes

Core claim

The paper's central discovery candidate is that training energy obeys layer-wise additivity well enough to be instrumented: a model's total energy is the sum of its input, hidden, and output layer energies, and each layer's cost can be isolated by subtracting the other layers' costs from the measured total of a small variant network. Using this, THOR profiles one-, two-, and three-layer probe networks, fits a Gaussian process per layer type with the Matérn kernel, and predicts an unseen network's energy as $\hat{E}_{\mathrm{model}} = \hat{E}_{\mathrm{input}}(C_1) + \sum_{i=2}^{n-1} \hat{E}_{\mathrm{hidden}}(C_{i-1}, C_i) + \hat{E}_{\mathrm{output}}(C_{n-1})$. The paper's evaluation reports MAPE around 10% across LeNet-5, a 5-layer CNN, HAR, LSTM, Transformer, and ResNet variants on five devices, versus roughly 40% for FLOPs-based estimation. The paper acknowledges that the decomposition assumes sequential layer execution, that parallel-branch architectures such as GoogleNet and SqueezeNet fall outside the current treatment, and that estimates degrade when the framework version changes.

Load-bearing premise

The load-bearing premise is that a layer's training energy is independent of its neighbors, so the cost of any layer can be recovered by subtracting the other layers' costs from the measured total of a small probe network, and the whole model's energy is exactly the sum of these independent layer costs.

Editorial extensions

If this is right

  • Energy-aware job schedulers can treat the per-layer GP sum as a cheap, differentiable budget oracle for on-device training.
  • Energy-constrained pruning can use THOR as the objective: the case study hits a 50% energy budget while the FLOPs-based baseline misses it.
  • One-time profiling per device and framework yields reusable layer models, so unseen architectures built from profiled layer types can be estimated without new measurements.
  • Because the estimator tracks nonlinear layer behavior (plateaus and ridges) that FLOPs misses, it can detect slow spots or energy cliffs missed by compute-based proxies.
  • The method's scope is sequential execution; the paper explicitly leaves parallel-branch models and framework-version drift as limitations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If additivity holds beyond the tested models, the same subtractive recipe could produce per-layer estimates for other resources, such as latency, memory bandwidth, or thermal load, extending the profiling idea beyond energy.
  • The GP's predictive variance is a natural input for scheduling under probabilistic energy budgets, a use the paper hints at but does not develop.
  • A direct stress test would be to profile GoogleNet or SqueezeNet-style multi-branch blocks; until that is done, the additivity claim is effectively established only for sequential architectures.
  • The framework-version sensitivity reported (MAPE rising from 8% to 11% after an upgrade) suggests that a lightweight re-calibration rule could be derived from the GP's posterior variance, an extension the paper leaves implicit.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes THOR, a per-layer Gaussian Process (GP) based energy estimator for on-device DNN training. The method assumes layer-wise energy additivity and subtractivity, profiles one-, two-, and three-layer probe networks to obtain per-layer energy labels, fits GP models to those labels, and then predicts total training energy as the sum of per-layer GP predictions (Eq. 4). The evaluation compares THOR against a FLOPs-based linear baseline on five devices (OPPO, iPhone, Xavier, TX2, Server) and several model families (LeNet-5, a 5-layer CNN, HAR, LSTM, Transformer, ResNet), reporting an average MAPE around 10% versus roughly 40% for the baseline, and a pruning case study on Xavier that claims a 50% energy reduction.

Significance. If the layer-wise additivity premise holds, THOR is a practically attractive approach: it is device-agnostic, uses active-learning-style GP profiling with uncertainty-based termination, and its per-layer decomposition could enable energy-aware scheduling and pruning. The breadth of the empirical study across heterogeneous devices and model types is a real strength, as is the use of a nonparametric model that does not require hardware-specific analytical simulators. However, the central additivity/subtractivity assumption is validated only qualitatively, the per-layer labels are derived by subtracting GP estimates rather than by direct measurement, and the main MAPE figures lack error bars. These issues currently limit confidence in the central claim and in the pruning case study.

major comments (4)
  1. [Sec. 3.2, Fig. 2, Eqs. (1)-(2)] The layer-wise energy additivity/subtractivity premise is load-bearing but is validated only visually on a CNN with identical stacked Conv2d layers. The paper's own Sec. 2.3 states that frameworks fuse operations such as Conv-BN-ReLU into a single kernel, making execution 'more like a black box'; under such fusion, per-layer energy is not independently measurable, so subtracting estimated energies of other layers from measured totals can produce biased hidden-layer labels. Please provide a direct validation of subtractivity on architectures that include BatchNorm fusion, residual connections, attention blocks, and recurrent cells, or otherwise demonstrate that the per-layer decomposition in Eqs. (1), (2), and (4) does not inherit a systematic bias from cross-layer coupling.
  2. [Eqs. (1)-(2), Sec. 4.2] The hidden- and input-layer labels are formed by subtracting GP-based estimates (\hat E_output and \hat E_input) from measured totals. Any systematic error in those GPs enters the training labels for the remaining GPs and propagates into the final sum in Eq. (4). The reported end-to-end MAPE can be accurate even when per-layer estimates are badly biased, because over- and under-estimates from different layers may cancel in the sum. The paper should report per-layer estimation errors (e.g., quantified MAPE/RMSE for the surfaces in Figs. 11-12), provide an error-propagation analysis, or compare the subtraction-derived labels against a direct per-layer measurement on at least one device.
  3. [Sec. 4.1, Fig. 8, Appendix A5.1] The main quantitative claim (MAPE around 10% versus roughly 40% for the FLOPs baseline) is presented as bar charts without error bars or confidence intervals, even though Appendix A5.1 states that each experiment was repeated three times and that the mean and standard error are reported. Without these values, the reader cannot judge whether the observed improvements are statistically significant, particularly for models with higher error such as HAR or LSTM on smartphones. Please add error bars to Figs. 8-10 and include a table with per-device, per-model means and standard errors.
  4. [Sec. 4.3, Fig. 13] The pruning case study claims that THOR reduces energy consumption by 50% while preserving accuracy, but it is unclear whether the reported 49.2% figure is a measured energy value or a THOR prediction. The claim also depends on per-layer GP gradients whose accuracy is not independently established. Please report the actually measured energy of the pruned model, specify the measurement procedure, and include multiple devices or models with variance across runs to support the generality of the claim.
minor comments (5)
  1. [Sec. 3.2] There is a typo in the sentence 'Based on the presented layer-wise energy additivity pf DNN'; it should read 'of DNN'. Similarly, Sec. 3.3 contains 'we use the the upper and lower bounds', which should be 'the upper and lower bounds'.
  2. [Fig. 2 caption] The caption says 'Energy consumption from NeuralPower estimation and from observation for a CNN', but the surrounding text describes an adapted training-phase profiling method. Please clarify exactly what is plotted, how NeuralPower was adapted to training, and how the linear trend supports additivity rather than merely showing a correlation.
  3. [Fig. 11] The subcaptions are garbled and repeated: the six panels are labeled '(a) H=W=42, N=10 (b) ... (a) Xavier, H=W=42 ...' in an overlapping way. Please relabel the panels uniquely by device and spatial size so the reader can map each surface to the correct setting.
  4. [References] The bibliography appears to contain a duplicated and largely unrelated block of references (e.g., Abelson et al. 1985, Baumgartner et al. 2001, Brachman and Schmolze 1985, Gottlob 1992, Levesque 1984, Nebel 2000) that are not cited in the text. Please remove this block and ensure every reference is cited and every citation appears in the reference list.
  5. [Abstract and Sec. 1] The phrase 'reduced the Mean Absolute Percentage Error (MAPE) by up to 30%' is ambiguous because MAPE is already a percentage. Since the reported improvement is from about 40% to about 10%, please state the change as an absolute percentage-point reduction or as a relative reduction to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: THOR is an empirical GP regression against external device measurements; the subtractive label construction is a decomposition assumption, not a self-fulfilling prediction.

full rationale

THOR's derivation chain is an empirical measurement pipeline. The claimed result, Eq. (4), sums GP models fitted to energy labels obtained by physically training 1-, 2-, and 3-layer probe networks on real devices (Sec. 3.2, Eqs. (1)-(2)); the ground-truth totals in the evaluation are external power measurements, not outputs of the model. The subtractive construction of hidden-layer labels (E_hidden = E_model - E_input_hat - E_output_hat) is a decomposition assumption, and it does create indirect coupling among the fitted GPs. However, that is a model-identification/robustness threat, not a circular reduction: the paper does not present the training profiles as predictions, and the reported MAPE is computed on randomly sampled, unseen channel configurations (Sec. 4.1) against independently measured totals, so the end-to-end estimate is not equal to its training labels by construction. The pruning case study similarly validates against a measured 20,000J baseline and a measured final energy of 49.2%. Self-citations in the paper (e.g., [Li et al., 2021], which shares co-author Miao Pan) are used only to contextualize prior energy assumptions and are not load-bearing for THOR's method. No uniqueness theorem, ansatz, or fitted parameter is imported from self-citation as a substitute for evidence, and no result in the paper is renamed from a known empirical pattern. Therefore the derivation chain is self-contained with respect to circularity, and the appropriate finding is no significant circularity (score 0).

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on three domain assumptions: layer-wise additivity, channel-only parametrization of layer energy, and sequential execution. These are plausible for simple feed-forward models but are not quantitatively established. No invented entities. The main free parameters are the GP hyperparameters (fit to data) and hand-chosen thresholds for profiling stop conditions and measurement intervals.

free parameters (5)
  • Matérn kernel hyperparameters (length scale, signal variance, noise) = not reported; learned from profiling data
    The GP predictions for layer energy depend on these fitted hyperparameters; no values or ranges are given.
  • Matérn smoothness parameter nu = 2.5
    Chosen by hand in Sec. 3.3, requiring only twice-differentiable functions.
  • Profiling stopping thresholds (max points, variance threshold) = variance threshold 5%; max points not specified
    Chosen in Sec. 3.3 as end conditions; they trade profiling cost against GP accuracy.
  • Profiling iteration count = 500 batches
    Selected in Appendix A5.2 based on Fig. A16 to balance stability and cost; affects the measured energy labels.
  • Energy sampling interval = 100 ms on phones/Jetson; 50 Hz nvidia-smi on server
    Chosen in Appendix A5.2 after testing; interval affects the accuracy of the E = P-bar times T approximation.
assumptions (6)
  • domain assumption Total training energy is the sum of independent per-layer energies (additivity), and a layer's energy equals total minus the other layers' energies (subtractivity).
    Introduced in Sec. 3.2, used in Eqs. (1), (2), and (4); if framework fusion or memory reuse violates it, the method's labels and predictions are biased.
  • domain assumption Layer energy depends only on channel counts and layer type for a fixed device, framework, input shape, and batch size, so a GP over channels can generalize to unseen widths.
    Layer parsing in Sec. 3.2 encodes layers by channels; Fig. 11 suggests energy also varies with input height and width, which is not explicit in Eq. (4).
  • domain assumption Layers execute sequentially with negligible inter-layer effects.
    Stated in Sec. 3.2 and acknowledged in Appendix A4 to be violated by parallel architectures like GoogLeNet and SqueezeNet.
  • domain assumption Training time is positively correlated with training energy, so time uncertainty can be used as a surrogate for energy uncertainty during guided profiling.
    Sec. 3.3, Fig. 6; used when real-time energy acquisition is not available on smartphones.
  • domain assumption Energy measured with the E = P-bar times T approximation at 100 ms sampling adequately represents true training energy.
    Appendix A5.2, Eq. (6); short kernels may be missed at 100 ms sampling, though 500 iterations are averaged.
  • standard math Gaussian Process regression with the Matérn kernel is a valid model for layer-wise energy functions.
    Standard GP theory from Rasmussen and Williams, cited in Sec. 3.3; not specific to this paper.

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Cite this review

Pith. "Pith review of THOR: A Generic Energy Estimation Approach for On-Device Training." pith.science (2026). https://pith.science/paper/MCWSWXK6

@misc{pith2026250116397,
  author       = {Pith},
  title        = {Pith review of: THOR: A Generic Energy Estimation Approach for On-Device Training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MCWSWXK6}},
  note         = {Machine review of arXiv:2501.16397}
}
read the original abstract

Battery-powered mobile devices (e.g., smartphones, AR/VR glasses, and various IoT devices) are increasingly being used for AI training due to their growing computational power and easy access to valuable, diverse, and real-time data. On-device training is highly energy-intensive, making accurate energy consumption estimation crucial for effective job scheduling and sustainable AI. However, the heterogeneity of devices and the complexity of models challenge the accuracy and generalizability of existing estimation methods. This paper proposes THOR, a generic approach for energy consumption estimation in deep neural network (DNN) training. First, we examine the layer-wise energy additivity property of DNNs and strategically partition the entire model into layers for fine-grained energy consumption profiling. Then, we fit Gaussian Process (GP) models to learn from layer-wise energy consumption measurements and estimate a DNN's overall energy consumption based on its layer-wise energy additivity property. We conduct extensive experiments with various types of models across different real-world platforms. The results demonstrate that THOR has effectively reduced the Mean Absolute Percentage Error (MAPE) by up to 30%. Moreover, THOR is applied in guiding energy-aware pruning, successfully reducing energy consumption by 50%, thereby further demonstrating its generality and potential.

Figures

Figures reproduced from arXiv: 2501.16397 by the authors.

Figure 1
Figure 1. Illustration of the energy estimation process on [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Energy consumption from NeuralPower estima [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. illustrates an overview of THOR. It broadly contains three processes listed below, where the profiling and the fit￾ting processes are carried out in an iterative manner. Profiling: In THOR, all layers are parsed into input layer, hidden layer, and output layer. To estimate the energy con￾sumption of these layers, THOR generates 1-layer, 2-layer, and 3-layer variant NNs with different parameters, respec￾tively. Initi… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: GP after 4 and 5 steps for FC layer on OPPO taking 500 batches of (10, input channel, 28, 28) input. 0e6 2e6 4e6 6e6 FLOPs Groundtruth Profiled Estimation FLOPs Energy (J) 0 2 4 6 8 10 12 Input Channel 0 10 20 30 40 50 60 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Energy consumption of a Fully Connected (FC) [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 7
Figure 7. Figure 7: Estimation results of FLOPs-based method and [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 8
Figure 8. Figure 8: End-to-end energy estimation for five devices. [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: Energy estimation of Transformer. Probability 0 0.2 0.4 0.6 0.8 1.0 MAPE 0 0.5 Energy of Server ResNet-20 ResNet-56 ResNet-110 Probability 0 0.2 0.4 0.6 0.8 1.0 MAPE 0 0.5 Energy of Xavier THOR FLOPs-based [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]
Figure 10
Figure 10. Figure 10: ResNet evaluation on Server and Xavier. More Results on Transformers. To further demon￾strate the superiority of THOR, we present the energy es￾timation results for the Transformer architecture using both THOR and FLOPs-based methods in [PITH_FULL_IMAGE:figures/full_…
Figure 11
Figure 11. Figure 11: Profiled v.s. estimated energy for Xavier and Server (The [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]
Figure 12
Figure 12. Figure 12: Differences of energy estimation and observa [PITH_FULL_IMAGE:figures/full_fig_p007_12.png]

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Pith tools

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