MAx-DNN: Multi-Level Arithmetic Approximation for Energy-Efficient DNN Hardware Accelerators

Dimitrios Soudris; Georgios Makris; Kiamal Pekmestzi; Sotirios Xydis; Vasileios Leon

REVIEW 4 major objections 6 minor 13 references

MAx-DNN: Multi-Level Arithmetic Approximation for Energy-Efficient DNN Hardware Accelerators

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Distributing approximate multipliers at filter and kernel granularity cuts DNN inference energy by up to 54% while keeping accuracy loss to 4% or less.

desk verdict Fine-grained multiplier assignment shows real Pareto gains, but the energy model is component-level and one claim is overstated. read the letter →

arxiv 2506.21371 v1 pith:TS2HCLT6 submitted 2025-06-26 cs.LG cs.AR

Vasileios Leon , Georgios Makris , Sotirios Xydis , Kiamal Pekmestzi , Dimitrios Soudris This is my paper · ORCID

classification cs.LGcs.AR

keywords ApproximatecomputingInexactmultipliersEnergy-efficienthardwareacceleratorsDeepneuralnetworksResNet-8CIFAR-10Filter-levelapproximationKernel-level

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

MAx-DNN asks where, exactly, a convolutional network can absorb arithmetic approximation: which layers, which filters, and which kernels should use which inexact multiplier. On quantized ResNet-8 trained on CIFAR-10, the paper's layer-, filter-, and kernel-level allocation schemes report up to 54% multiplication-energy savings with no more than 4% accuracy loss, and filter- and kernel-level placements beat layer-uniform approximation by roughly two times in energy with better accuracy. A layer-sensitivity study supports the placement logic: the first convolutional layers are fragile, while later layers absorb much stronger approximations. The intended consequence is a no-retraining design path from frozen quantized models to lower-power approximate hardware accelerators.

What carries the argument

The load-bearing mechanism is the ROUP approximate multiplier family, whose two tunable operations, partial-product perforation and asymmetric rounding, create a dense error-energy trade-off. For N-bit inputs the approximate product is $$\mathrm{ROUP}(A,B)=\sum_{j=P}^{N/2-1}\tilde{P}_j4^j,$$ where P is the number of least-significant partial products omitted and $\tilde{P}_j$ is a partial product whose operand is rounded to a different bit-width per column. MAx-DNN turns this library into a placement problem: an extended convolution operator lets each layer, filter group, or kernel carry its own multiplier choice, and a Pareto-optimal search selects combinations on the accuracy-energy plane. The governing energy estimate is per-layer multiplication count times average multiplier energy accumulated over the network, which is why the multiplier library dominates the comparison.

What would settle it

Build one of the reported Pareto-optimal approximate accelerators with a realistic memory hierarchy and measure total inference energy against the exact quantized accelerator; if multiplier energy is a small share of total system energy, the claimed 54% gain will not reproduce.

Watch

Extended reading notes

Core claim

The paper's central claim is that arithmetic approximation for DNN accelerators should be allocated heterogeneously at the finest practical granularity. MAx-DNN assigns a different ROUP approximate multiplier to each convolutional layer, to groups of filters, or to individual kernels, with separate channel, row, and column flavors, and in the KLMS variant skips multiplications whose kernel weights lie inside a chosen band around the layer mean. Compared with the quantized baseline, the reported best configurations save up to 54% of multiplication energy at up to 4% accuracy loss; compared with configurations that apply the same approximate multipliers uniformly per layer, the filter- and kernel-level designs report about two times lower energy and higher accuracy, and they form almost the entire accuracy-energy Pareto front. The layer-wise sensitivity experiment completes the story: the first convolutional layers are markedly less error-resilient than the final ones.

Load-bearing premise

The energy model estimates each layer's consumption as the number of multiplications times the average energy of the assigned multiplier, omitting memory access, data movement, and control logic; if multiplier energy is not the dominant cost in a real accelerator, the reported 54% savings will not become system-level savings.

Editorial extensions

If this is right

Approximation effort should be concentrated in the later convolutional layers, which tolerate stronger multipliers with almost no accuracy loss.
Several configurations lose between 0.02% and 1% accuracy while still saving multiplication energy, so fine-grained approximation can be almost lossless on a quantized model.
Filter- and kernel-level allocation dominates the reported Pareto front, so layer-uniform approximation schemes leave energy savings unrealized.
Because the flow works on frozen quantized models without retraining, it remains usable when training data are proprietary or unavailable.

Reading between the lines

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

Running the same placement search jointly with quantization-aware training or pruning of the multiplier choices could push the accuracy-energy frontier further; the paper fixes the quantized model and only varies multipliers.
The fragility of the first layers suggests error amplification through shared features and residual connections, so the sensitivity profile may shift on non-residual or deeper networks, a prediction that a repeat of the layer sweep could test.
On process nodes where data movement dominates, the likely next question is whether approximation should be restricted to compute-bound layers while memory traffic stays exact; the paper's multiplier-only energy estimate leaves that scenario open.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Let me give you the short version: this is a small but legitimate extension of ALWANN that demonstrates a real point—fine-grained assignment of approximate multipliers (per filter or kernel) gives a better energy-accuracy Pareto front than layer-level assignment. The experiments are internally consistent and the comparison to the external EvoApprox8b library is meaningful. But the headline energy numbers are computed with a simplified model that omits memory, control, and the overhead of heterogeneous multiplier placement, and the paper overstates one result: the '2x energy gains' vs ALWANN is actually about 1.3x from Table I.

What's new: the FLAM and KLAM distribution schemes, and the systematic Pareto comparison showing that finer granularity beats coarser granularity. That is a useful data point for anyone designing approximate DNN accelerators. The paper also does a reasonable job of describing the toolflow, and the ROUP multiplier library is properly characterized in prior work. No retraining is needed, which is a practical plus.

The soft spots: The energy model (Section III-F) is just #multiplications × average multiplier energy per layer. That ignores weight/activation storage, data movement, and the extra logic needed to support different multipliers in the same processing array. So the 'up to 54% energy gain vs quantized baseline' is really a multiplier-level saving, not a system-level savings. For the main comparative claim—filter/kernel beats layer—this is less of a problem because the same model is used for all approaches. More annoying: the configuration labels in Table I (e.g., 'FLAM-3clas. 2 1 1') are never explained, so a reader can't reproduce the configurations. There are no error bars on accuracy or energy. KLMS is introduced as a fourth approach but never evaluated separately; the Pareto plot merges KLAM+KLMS. And the '2x energy gains' phrase in the abstract and text is not supported: Table I shows max 54% vs 39% energy gain, about 1.3x. That should be corrected.

Bottom line: this is a credible conference-level result, modest in scope. It's worth a serious referee as a workshop/short-paper quality contribution, but the energy claims need to be positioned as component-level, and the performance statements need to match the table. If you're working on approximate DNN accelerators, it's a worthwhile read for the granularity finding.

Referee Report

4 major / 6 minor

Summary. The paper proposes MAx-DNN, an extension of the ALWANN framework that assigns approximate ROUP multipliers to DNN multiplications at three granularities: layer-level (LLAM), filter-level (FLAM), and kernel-level (KLAM, with channel/row/column variants), plus a multiplication-skip variant (KLMS). Evaluation on quantized ResNet-8 and CIFAR-10 reports up to 54% energy gain with at most 4% accuracy loss relative to the quantized baseline, and claims 2x energy efficiency compared to ALWANN with EvoApprox8b multipliers. The central contribution is the fine-grained, non-uniform distribution of approximate multipliers and the accompanying design-space exploration.

Significance. If the energy numbers are taken at face value, fine-grained multiplier approximation is a practical way to trade a few percent accuracy for substantial energy savings in DNN inference accelerators. The use of ROUP multipliers with a dense error-energy trade-off is sensible, and the controlled comparison in Fig. 4 between LLAM, FLAM, and KLAM on the same multiplier library is a useful result for the approximate-computing community. However, the headline system-level energy savings rest on a simplified energy model, and the advertised 2x advantage over the EvoApprox8b baseline is not directly supported by the data. The paper is a worthwhile proposal but needs additional validation before its claims can be considered established.

major comments (4)

[Section III-F] The energy estimate in Section III-F is defined as #mult × avg multiplier energy per layer, with no contribution from memory access, data movement, control logic, or the overhead of instantiating heterogeneous multiplier types within a processing array. Since the paper's central claim is energy reduction, this model is load-bearing; if multiplier datapath energy is not dominant in a real accelerator, the reported 46–54% gains will be diluted. The paper should either report a more complete energy model including memory and control, or present measured results from a synthesized accelerator implementing the heterogeneous assignments, or explicitly caveat the headline as an upper bound.
[Table I, Section IV] The claim of '2× energy gains versus the state-of-the-art DNN approximations' is not supported by Table I. The maximum proposed energy gain is 54%, while the best EvoApprox8b configuration (Evo mul8u ZFB) has a 39% gain, a ratio of roughly 1.4×. Moreover, the comparison is confounded: the proposed configurations use ROUP multipliers with fine-grained assignment, while the baseline uses EvoApprox8b multipliers with layer-wise assignment, so any improvement could stem from the multiplier library rather than from the fine-grained level. The controlled comparison in Fig. 4 (all ROUP) supports the fine-grained benefit, but the abstract and conclusion should not attribute the 2× claim to the approximation level without a same-library comparison.
[Section III-D, Fig. 4] KLMS (kernel-level multiplication skip) is defined as a proposed approach, but it is never evaluated separately. Fig. 4 groups 'KLAM+KLMS' and Table I lists only KLAM configurations, so the contribution of the skip mechanism is unquantified. The reader cannot determine whether KLMS improves the Pareto front or whether it is an independent design choice.
[Table I, Section IV] The configuration labels in Table I (e.g., 'FLAM-3clas. 2 1 1', 'KLAM-chan. 1 0 1') are not explained, and the ROUP L/M/H multipliers used in the sensitivity study are not mapped to their (P, r) parameters. Without this information, the reported Pareto-optimal configurations cannot be reproduced or compared across papers, which undercuts the empirical contribution.

minor comments (6)

[Abstract] The word 'defacto' should be 'de facto', and 'state-of-the-art' should be hyphenated consistently.
[Figure 3] The baseline label is 'm=0' in part (a) but 'Layer=0' in the caption; use a single convention throughout.
[Table I] The caption states that 'Accuracy Loss' is compared to the full accurate model, but the text refers to 4% loss relative to the quantized baseline. Please define the reference point in the caption and in the text to avoid confusion.
[Section III-F] The energy model is described only in prose; include an explicit equation and state the assumptions about input statistics and switching activity used for the power measurements.
[Section IV] The sentence 'the average loss of the EvoApprox8b configurations is ∼23%' should specify that this is relative to the full accurate model, otherwise it appears inconsistent with the 4% claim in the abstract.
[Throughout] The framework name ALWANN is typeset as 'ALW ANN' with a space in several places (e.g., Section II and Fig. 1); use 'ALWANN' consistently.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the fine-grained ROUP placement results are benchmarked against the external EvoApprox8b and ALWANN baselines; the only self-citation, the ROUP multiplier library, is prior work that is not derived from the present claims.

full rationale

The paper's derivation chain is self-contained. Accuracy is obtained by running ResNet-8 on CIFAR-10 with quantized weights, and energy is computed from Synopsys synthesis of the approximate multipliers on TSMC 45-nm, using the formula #mult × avg multiplier energy (Section III-F). This energy model is a simplification that ignores memory and control overhead, but it is an architectural assumption, not a quantity defined in terms of the target result. The ROUP multipliers are cited from prior work by the same authors, but the paper's central contribution is the layer-, filter-, and kernel-level placement of those multipliers, and the reported gains are established by comparison with the external EvoApprox8b library and the ALWANN framework, not by fitting parameters to force the outcome. The Pareto configurations are found by NSGA-II search over the proposed approximation space, so no fitted input is renamed as a prediction. The claimed '2x energy gains versus EvoApprox8b' is not supported by Table I, where the best proposed gain is 54% versus the best Evo gain of 39%, i.e., roughly 1.33x; however, that is a numerical consistency issue, not circularity. No equation reduces to its own input, and no load-bearing step is justified solely by a self-citation.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new theoretical entities. It depends on the ROUP multiplier library (prior work), the ALWANN framework, and a simplified energy model. The key free choice is the assignment of ROUP configurations across the network, which is explored but not fully disclosed.

free parameters (1)

ROUP multiplier configuration (perforation P, rounding bits r) per layer/filter/kernel = Not reported; selected via NSGA-II Pareto search
The central results depend on which approximate multiplier strengths are assigned at each granularity. The exact choices are not given, so the dependency is a free design choice.

assumptions (3)

domain assumption Energy of each DNN layer is estimated as number of multiplications times average multiplier energy.
Section III-F states the energy model; it ignores the energy of memory accesses, data movement, and other datapath logic, which can dominate in real accelerators.
domain assumption The accuracy impact can be evaluated on a frozen, quantized model without retraining or weight tuning.
The paper adopts the ALWANN approach of no retraining; if weight tuning or retraining were used, the accuracy losses could be different.
domain assumption The ROUP multiplier library provides a representative set of error/energy trade-offs.
The results depend on the properties of ROUP multipliers from the authors' DAC 2019 paper; using a different library could change the Pareto front.

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Cite this review

Pith. "Pith review of MAx-DNN: Multi-Level Arithmetic Approximation for Energy-Efficient DNN Hardware Accelerators." pith.science (2026). https://pith.science/paper/TS2HCLT6

@misc{pith2026250621371,
  author       = {Pith},
  title        = {Pith review of: MAx-DNN: Multi-Level Arithmetic Approximation for Energy-Efficient DNN Hardware Accelerators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TS2HCLT6}},
  note         = {Machine review of arXiv:2506.21371}
}

read the original abstract

Nowadays, the rapid growth of Deep Neural Network (DNN) architectures has established them as the defacto approach for providing advanced Machine Learning tasks with excellent accuracy. Targeting low-power DNN computing, this paper examines the interplay of fine-grained error resilience of DNN workloads in collaboration with hardware approximation techniques, to achieve higher levels of energy efficiency. Utilizing the state-of-the-art ROUP approximate multipliers, we systematically explore their fine-grained distribution across the network according to our layer-, filter-, and kernel-level approaches, and examine their impact on accuracy and energy. We use the ResNet-8 model on the CIFAR-10 dataset to evaluate our approximations. The proposed solution delivers up to 54% energy gains in exchange for up to 4% accuracy loss, compared to the baseline quantized model, while it provides 2x energy gains with better accuracy versus the state-of-the-art DNN approximations.

Figures

Figures reproduced from arXiv: 2506.21371 by the authors.

**Figure 2.** The proposed non-uniform approximation approaches at different levels: (a) layer-level, (b) filter-level & (c) kernel-level approximate multiplication, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** The energy consumption and accuracy loss of the approximate ResNet [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

A Survey of Techniques for Approximate Computing,

S. Mittal, “A Survey of Techniques for Approximate Computing,” ACM Computing Surveys, vol. 48, no. 4, Mar. 2016

work page 2016
[2]

Cooperative Arithmetic-Aware Approximation Tech- niques for Energy-Efficient Multipliers,

V . Leon et al. , “Cooperative Arithmetic-Aware Approximation Tech- niques for Energy-Efficient Multipliers,” in Design Automation Confer- ence (DAC), 2019, pp. 1–6

work page 2019
[3]

AUGER: A Tool for Generating Approximate Arithmetic Circuits,

D. Hernandez-Araya et al., “AUGER: A Tool for Generating Approximate Arithmetic Circuits,” in IEEE Latin American Symposium on Circuits Systems (LASCAS), 2020, pp. 1–4

work page 2020
[4]

Approximate Hybrid High Radix Encoding for Energy- Efficient Inexact Multipliers,

V . Leon et al. , “Approximate Hybrid High Radix Encoding for Energy- Efficient Inexact Multipliers,” IEEE Transactions on V ery Large Scale Integration (VLSI) Systems, vol. 26, no. 3, pp. 421–430, Mar. 2018

work page 2018
[5]

EvoApprox8b: Library of Approximate Adders and Multipliers for Circuit Design and Benchmarking of Approximation Meth- ods,

V . Mrazek et al. , “EvoApprox8b: Library of Approximate Adders and Multipliers for Circuit Design and Benchmarking of Approximation Meth- ods,” in Design, Automation and Test in Europe Conference (DATE), 2017, pp. 258–261

work page 2017
[6]

Exploiting the Potential of Approximate Arithmetic in DSP & AI Hardware Accelerators,

V . Leon et al., “Exploiting the Potential of Approximate Arithmetic in DSP & AI Hardware Accelerators,” inInt’l. Conference on Field Programmable Logic and Applications (FPL) , 2021, pp. 1–2

work page 2021
[7]

ALW ANN: Automatic Layer-Wise Approximation of Deep Neural Network Accelerators without Retraining,

V . Mrazek et al. , “ALW ANN: Automatic Layer-Wise Approximation of Deep Neural Network Accelerators without Retraining,” in Int’l. Confer- ence on Computer-Aided Design (ICCAD) , 2019, pp. 1–8

work page 2019
[8]

Combining Arithmetic Approximation Techniques for Improved CNN Circuit Design,

G. Lentaris et al. , “Combining Arithmetic Approximation Techniques for Improved CNN Circuit Design,” in Int’l. Conference on Electronics, Circuits and Systems (ICECS), 2020, pp. 1–4

work page 2020

Show all 13 references

[9]

Efficient AI System Design With Cross-Layer Approximate Computing,

S. Venkataramani et al. , “Efficient AI System Design With Cross-Layer Approximate Computing,” Proceedings of the IEEE , vol. 108, no. 12, pp. 2232–2250, Dec. 2020

2020
[10]

ApproxQAM: High-Order QAM Demodulation Circuits with Approximate Arithmetic,

V . Leon et al. , “ApproxQAM: High-Order QAM Demodulation Circuits with Approximate Arithmetic,” in Int’l. Conference on Modern Circuits and Systems Technologies (MOCAST), 2021, pp. 1–5

2021
[11]

Flexpoint: An Adaptive Numerical Format for Efficient Training of Deep Neural Networks,

U. K ¨oster et al., “Flexpoint: An Adaptive Numerical Format for Efficient Training of Deep Neural Networks,” in Int’l. Conference on Neural Infor- mation Processing Systems (NIPS), 2017, pp. 1740–1750

2017
[12]

Quantized Convolutional Neural Networks for Mobile De- vices,

J. Wu et al., “Quantized Convolutional Neural Networks for Mobile De- vices,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016, pp. 4820–4828

2016
[13]

Structured Pruning of Deep Convolutional Neural Net- works,

S. Anwar et al., “Structured Pruning of Deep Convolutional Neural Net- works,” ACM Journal on Emerging Technologies in Computing Systems (JETC), vol. 13, no. 3, Feb. 2017

2017

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

A Survey of Techniques for Approximate Computing,

S. Mittal, “A Survey of Techniques for Approximate Computing,” ACM Computing Surveys, vol. 48, no. 4, Mar. 2016

work page 2016

[2] [2]

Cooperative Arithmetic-Aware Approximation Tech- niques for Energy-Efficient Multipliers,

V . Leon et al. , “Cooperative Arithmetic-Aware Approximation Tech- niques for Energy-Efficient Multipliers,” in Design Automation Confer- ence (DAC), 2019, pp. 1–6

work page 2019

[3] [3]

AUGER: A Tool for Generating Approximate Arithmetic Circuits,

D. Hernandez-Araya et al., “AUGER: A Tool for Generating Approximate Arithmetic Circuits,” in IEEE Latin American Symposium on Circuits Systems (LASCAS), 2020, pp. 1–4

work page 2020

[4] [4]

Approximate Hybrid High Radix Encoding for Energy- Efficient Inexact Multipliers,

V . Leon et al. , “Approximate Hybrid High Radix Encoding for Energy- Efficient Inexact Multipliers,” IEEE Transactions on V ery Large Scale Integration (VLSI) Systems, vol. 26, no. 3, pp. 421–430, Mar. 2018

work page 2018

[5] [5]

EvoApprox8b: Library of Approximate Adders and Multipliers for Circuit Design and Benchmarking of Approximation Meth- ods,

V . Mrazek et al. , “EvoApprox8b: Library of Approximate Adders and Multipliers for Circuit Design and Benchmarking of Approximation Meth- ods,” in Design, Automation and Test in Europe Conference (DATE), 2017, pp. 258–261

work page 2017

[6] [6]

Exploiting the Potential of Approximate Arithmetic in DSP & AI Hardware Accelerators,

V . Leon et al., “Exploiting the Potential of Approximate Arithmetic in DSP & AI Hardware Accelerators,” inInt’l. Conference on Field Programmable Logic and Applications (FPL) , 2021, pp. 1–2

work page 2021

[7] [7]

ALW ANN: Automatic Layer-Wise Approximation of Deep Neural Network Accelerators without Retraining,

V . Mrazek et al. , “ALW ANN: Automatic Layer-Wise Approximation of Deep Neural Network Accelerators without Retraining,” in Int’l. Confer- ence on Computer-Aided Design (ICCAD) , 2019, pp. 1–8

work page 2019

[8] [8]

Combining Arithmetic Approximation Techniques for Improved CNN Circuit Design,

G. Lentaris et al. , “Combining Arithmetic Approximation Techniques for Improved CNN Circuit Design,” in Int’l. Conference on Electronics, Circuits and Systems (ICECS), 2020, pp. 1–4

work page 2020