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Understanding GEMM Performance and Energy on NVIDIA Ada Lovelace: A Machine Learning-Based Analytical Approach

T0 review · 4 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that a single Random Forest multi-output model can predict GEMM runtime and power on an NVIDIA RTX 4070 from configuration features alone, reporting $R^2 = 0.98$ for runtime and $R^2 = 0.78$ for power on CUTLASS SGEMM…

desk verdict A useful profiling dataset and a plausible 16x16 tile-size result, but the headline R² numbers belong to an undefined stacking ensemble, not the Random Forest the paper describes. read the letter →

arxiv 2411.16954 v1 pith:3SZNAQKW submitted 2024-11-25 cs.DC cs.AIcs.PF

Xiaoteng (Frank) Liu , Pavly Halim (New York University) This is my paper · ORCID
classification cs.DCcs.AIcs.PF
keywords GEMMperformancepredictionGPUenergyefficiencyRandomForestmulti-outputregressionCUTLASSprofilingNVIDIAAdaLovelacetiledmatrixmultiplicationpowerconsumptionmodelingarithmeticintensity
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

The paper's central claim is that machine learning can replace hand-built analytical formulas for predicting GEMM performance and energy on a modern GPU, because interactions among matrix shape, tile size, and memory access are too complex for linear models. To support this, the authors profile 16,128 CUTLASS SGEMM operations on an RTX 4070 and train a Random Forest multi-output regression pipeline that predicts runtime, power, energy, and TFLOPS simultaneously, reporting $R^2 = 0.98$ for runtime (mean error 15.57%) and $R^2 = 0.78$ for power (median error 5.42%). A parallel hand-written tiled kernel isolates tile-size effects and leads to a $16 \times 16$ tile recommendation that the paper says improves performance up to 3.2× while cutting power by 22% versus baseline. A sympathetic reader would care because, if these accuracies hold, predicting kernel behavior no longer requires exhaustive re-profiling on every new matrix shape.

What carries the argument

The namable machinery is the stacked multi-output regression pipeline: numerical features are standardized and fed to a Random Forest regressor with 100 trees and maximum depth 6, wrapped to predict runtime, power, energy, and TFLOPS together from a single feature set. The second object is the hand-written tiled GEMM kernel, run with tile sizes 1 through 32, which isolates the shared-memory and occupancy effects that the CUTLASS sweep cannot vary independently. The features include matrix dimensions, derived arithmetic intensity, block sizes, layouts, and alpha-beta scalars, so the model sees the configuration knobs a developer can actually tune.

What would settle it

Run the same 16,128 CUTLASS SGEMM configurations on an idle, dedicated RTX 4070 with kernel-scoped power sampling (for example, NCU or an external power meter) and compare measured per-kernel power against the model's predictions; if the power $R^2$ does not stay near 0.78 or the runtime mean error exceeds the reported 15.57%, the central accuracy claim is refuted.

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Extended reading notes

Core claim

On its own terms, the paper establishes that a multi-output Random Forest regressor trained on CUTLASS profiler output can capture GEMM behavior on Ada Lovelace hardware: runtime tracks total computational volume ($r=0.98$ with $M \times N \times K$), power tracks the output matrix size more than the contraction dimension ($r=0.80$ with $M \times N$ versus $r=0.02$ with $K$), and a tile size of $16 \times 16$ gives the best shared-memory and occupancy trade-off. The measured model beats individual Random Forest and XGBoost baselines and a linear regression baseline on all targets, and the paper reports fitted relationships including $Runtime_{pred} = 0.97 \cdot Runtime_{actual} + 1.23$. The account also identifies the resource ceiling: moving from tile 16 to tile 32 drops active blocks per SM from 6 to 1 because shared-memory demand scales with tile area.

Load-bearing premise

The power labels are treated as accurate per-kernel readings even though they come from nvidia-smi on a shared machine, so activity from other users can contaminate the power measurements that the $R^2 = 0.78$ claim rests on.

Editorial extensions

If this is right

  • On the paper's reported results, a developer on RTX 4070-class hardware can query the trained model for unseen GEMM shapes and get runtime predictions with mean error around 15.6% without running the kernel.
  • Power-aware GEMM scheduling should weight output-matrix dimensions more heavily than contraction depth, since power correlates with $M \times N$ at 0.80 and with $K$ at only 0.02.
  • A tile size of $16 \times 16$ is a practical default for SIMT SGEMM kernels on this architecture: it gives the best runtime and power balance before shared-memory occupancy collapses from 24 to 6 active blocks per SM.
  • Ensemble stacking over Random Forest and XGBoost is worth the overhead, improving runtime $R^2$ from 0.9623 (XGBoost) to 0.9808.
  • Energy predictions inherit error from both runtime and power targets, so energy-aware use of the model should not treat its 43% mean energy error as precise.

Reading between the lines

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

  • Because the dataset comes from a single RTX 4070, the model's transfer to other Ada or Hopper GPUs is untested; if the same features generalize without retraining, it would become a cheap cross-architecture predictor.
  • The power labels come from nvidia-smi on a shared machine, so the 5.42% median power error likely understates the error for kernel-only power; an isolated measurement would be a stronger test of the power claim.
  • The $16 \times 16$ tile conclusion is drawn from a SIMT SGEMM kernel and may not carry over to tensor-core or split-K GEMM variants, where shared-memory and register pressure behave differently.
  • A natural next step would be to train the same pipeline on tensor-core GEMMs and on multiple GPU generations and report per-architecture error, separating hardware-specific effects from configuration effects.
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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 / 3 minor

Summary. The paper proposes an analytical/machine-learning framework for predicting GEMM kernel runtime, power consumption, and energy efficiency on an NVIDIA RTX 4070 (Ada Lovelace). It combines a custom tiled matrix multiplication kernel, CUTLASS-based profiling of 16,128 configurations, and a multi-output Random Forest regressor. The authors report R² scores of 0.9808 for runtime and 0.7783 for power, and claim that tile size 16×16 provides the best balance, with up to 3.2× performance improvement and 22% power reduction. The paper also analyzes SM occupancy and correlation patterns between matrix dimensions and performance metrics.

Significance. The paper's practical contribution includes a large GEMM profiling dataset, an open-source implementation (GPPerf), and a systematic analysis of tile-size effects on performance and power on a modern consumer GPU. If the reported accuracy could be attributed to the described model, the result would be a useful empirical predictor for GEMM configuration selection. However, in the current manuscript, the central claim is not reproducible: the headline R² values are assigned to a stacking ensemble that is never specified, while the only described model (Random Forest, Algorithm 2) shows lower values (0.9456 runtime, 0.7234 power). The dataset split arithmetic is inconsistent, and the power measurements are acknowledged to be noisy due to shared-machine use. These problems must be resolved before the paper's findings can be considered reliable.

major comments (4)
  1. [Abstract / §III-C / §IV-C4 / Table VI / Algorithm 2] The paper's headline accuracy numbers (R²=0.98 for runtime, 0.78 for power) are attributed in Table VI to a 'Stacking Ensemble,' but the only model construction described (Algorithm 2) is a MultiOutputRegressor wrapping RandomForestRegressor. Section IV-C4 mentions a 'stacked model approach' but provides no base learners, meta-learner, or weights, and it is not reconciled with Algorithm 2. As a result, the abstract's central claim is not traceable to the model specified in the paper, and the reported results cannot be reproduced or even attributed. The authors must either describe the stacking ensemble in full (including algorithms, hyperparameters, and code) or revise the abstract and tables to report the Random Forest results actually supported by the methodology.
  2. [§V-B] Section V-B states that the dataset comprised 16,128 samples, split into 2,076 training samples and 519 test samples. Since 2,076 + 519 = 2,595, these numbers are inconsistent. The discrepancy is load-bearing because the evaluation set is undefined; the R² values in Table IV cannot be interpreted without knowing the exact split and whether the 16,128 figure includes pre-processing steps such as outlier removal.
  3. [§V-A2] The power measurements used to train and evaluate the model were collected via nvidia-smi on a shared machine, and Section V-A2 states that power usage is 'more stable to noise like other users using the same device.' This admission indicates that the power labels may include contributions from other processes, which directly affects the validity of the R²=0.7783 power prediction claim. The authors should either isolate the GPU or clearly quantify the noise contribution and report error bars on the power predictions.
  4. [§III-C and §V-B3] Equations (1)-(3) present the relationships as Runtime_pred = α·Runtime_actual + β + ε, Power_pred = f(...) ± ε_power, and Energy_pred = Runtime_pred · Power_pred · γ, but these are not analytical models derived from first principles; they are empirical fits to the collected data. The abstract and Section III-C call the framework 'analytical' and present the coefficients α, β, and γ as if they were derived, when in fact they are fitted parameters of a regression. This framing overstates the theoretical contribution. Please revise the terminology to accurately describe the method as a machine-learning-based empirical model.
minor comments (3)
  1. [§V-B3(a) and §V-B3(b)] In Section V-B3(a), the runtime prediction plot is referred to as 'Figure 6' but the actual figure is Figure 7; similarly, in Section V-B3(b), the power prediction graph is called 'Figure 7' but it is Figure 8. Please correct the cross-references.
  2. [§V-A1] In Section V-A1, the phrase 'after tile size researches 16' should be 'reaches 16.'
  3. [§V-B3(c)] In Equation (3), the energy prediction is written as Energy_pred = Runtime_pred · Power_pred · γ, but if the units are compatible, multiplying runtime and power already gives energy; the role of γ as an empirical correction factor should be explained.

Circularity Check

1 steps flagged · score 2.0 of 10

No load-bearing circularity: the headline runtime/power numbers are out-of-sample ML evaluations, not derivations; only the energy 'prediction' equation is a fitted rescaling of the product of the other two predictions.

  1. fitted input called prediction [Section V-B3c, Eq. (3); contrast with Section IV-C3]
    "Energy pred = Runtimepred · Powerpred · γ + ϵenergy (3) where γ represents the energy efficiency coefficient."

    Section IV-C3 defines Energy as Power × Runtime. Hence Eq. (3) is not an independent energy prediction: it is the product of the runtime and power predictions multiplied by an unexplained free constant γ (and an error term), so any reported energy R² is inherited from the two fitted targets rather than derived. This is a minor framing issue; the headline runtime/power claims are test-set evaluations of a fitted regression and are not circular.

full rationale

The central claim is empirical: a multi-output regression model is trained on GEMM configurations and evaluated on a held-out test split (Section IV-C4). That is the standard non-circular meaning of prediction, so the runtime R²=0.98 and power R²=0.78 values do not reduce to their inputs by construction. The paper's 'analytical' language and coefficient tables are interpretations of fits, not first-principles derivations. The only definitional circularity is the energy equation (Eq. 3), since energy is already defined as power × runtime and the equation just rescales the product of two predictions by an unexplained coefficient. Separate correctness concerns exist — the abstract's R² values match Table VI's 'Stacking Ensemble' row while Algorithm 2 describes a Random Forest, and the stated train/test counts (2,076 + 519) do not sum to the 16,128-sample dataset — but these are reproducibility and attribution problems, not circularity. The power measurements are acknowledged to be noisy due to shared-machine usage, which affects measurement validity, not circularity.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central prediction is empirical: the only 'parameters' are the learned model coefficients and hyperparameters. No first-principles derivation is offered. The paper's analytical framing is largely descriptive.

free parameters (5)
  • Random Forest hyperparameters (n_estimators, max_depth) = n_estimators=100, max_depth=6
    Chosen without stated tuning procedure; affect prediction quality.
  • Stacking ensemble weights w_i = not reported
    Equation 9 defines ensemble prediction with weights w_i but the paper reports no values or fitting procedure.
  • Runtime regression coefficients α, β = α=0.97, β=1.23
    Equation 1 fitted to data; described as a relation between predicted and actual runtime.
  • Energy efficiency coefficient γ = not reported
    Equation 3 introduces γ as an energy efficiency coefficient; no value or fitting procedure is given.
  • Tiled-kernel linear regression coefficients (M,N,K,tile_size) = -0.672907, 1.222868, 8.127956, -2588.457605 for runtime; 0.001255, 0.001584, 0.002479, -0.769036 for power
    Linear fits reported in Table II and III are fitted to the custom kernel datasets.
assumptions (3)
  • domain assumption nvidia-smi power readings represent kernel power consumption on a shared machine
    Used for all power/energy labels; Section V-A2 admits noise from other users.
  • domain assumption The profiled CUTLASS configurations are representative of the GEMM workloads being predicted
    The model is trained only on the chosen M,N,K, block, layout, and alpha-beta combinations; generalization beyond them is assumed.
  • domain assumption Roofline ridge point of 59 FLOPs/Byte from a vendor spec webpage
    Used in the introduction to frame performance regimes; not derived or measured.

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Cite this review

Pith. "Pith review of Understanding GEMM Performance and Energy on NVIDIA Ada Lovelace: A Machine Learning-Based Analytical Approach." pith.science (2026). https://pith.science/paper/3SZNAQKW

@misc{pith2026241116954,
  author       = {Pith},
  title        = {Pith review of: Understanding GEMM Performance and Energy on NVIDIA Ada Lovelace: A Machine Learning-Based Analytical Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3SZNAQKW}},
  note         = {Machine review of arXiv:2411.16954}
}
read the original abstract

Analytical framework for predicting General Matrix Multiplication (GEMM) performance on modern GPUs, focusing on runtime, power consumption, and energy efficiency. Our study employs two approaches: a custom-implemented tiled matrix multiplication kernel for fundamental analysis, and NVIDIA's CUTLASS library for comprehensive performance data collection across advanced configurations. Using the NVIDIA RTX 4070 as our experimental platform, we developed a Random Forest-based prediction model with multi-output regression capability. Through analysis of both naive tiled matrix multiplication with varying tile sizes (1 to 32) and 16,128 CUTLASS GEMM operations across diverse configurations, we identified critical performance patterns related to matrix dimensions, thread block configurations, and memory access patterns. Our framework achieved exceptional accuracy with an R^2 score of 0.98 for runtime prediction (mean error 15.57%) and 0.78 for power prediction (median error 5.42%). The system successfully predicts performance across matrix sizes, demonstrating robust scaling behavior. Our results show that optimal tile size selection can improve performance by up to 3.2x while reducing power consumption by 22% compared to baseline configurations. Analysis of shared memory utilization and SM occupancy reveals that tile sizes of 16x16 achieve the best balance between parallelism and resource usage. The implementation of our framework, including prediction models and analysis tools, is available as an open-source project at GPPerf [https://github.com/pavlyhalim/GPPerf].

Figures

Figures reproduced from arXiv: 2411.16954 by the authors.

Figure 1
Figure 1. Roofline Performance Model for the Ada Architecture showing [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 4
Figure 4. The runtime of tiled matrix multiplication for different matrix sizes [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. The runtime of tiled matrix multiplication for different matrix sizes [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: The power usage of matrix multiplication for different matrix sizes [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Correlation matrix between matrix dimensions & performance metrics [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Runtime prediction accuracy across different matrix configurations [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Power consumption prediction accuracy c) Energy Efficiency: The energy consumption plot (Fig￾ure 8) combines the effects seen in both runtime and power predictions. The strong correlation (R² = 0.8572) demonstrates our model’s ability to capture the multiplicative rela…

Discussion (0). Continue with ORCID to comment.

Forward citations

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