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V-EfficientNets: Vector-Valued Efficiently Scaled Convolutional Neural Network Models

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Pith's one-line read Vector-valued EfficientNets claim 99.46% accuracy on leukemia images with about 70% fewer parameters.

desk verdict Useful vector-valued depthwise-convolution construction and a sensible vectorization factor, but the headline accuracy claim rests on a confounded RGB-versus-HSV comparison and needs one control experiment before it is citable. read the letter →

arxiv 2505.05659 v1 pith:4Q5NTVPT submitted 2025-05-08 eess.IV cs.CVcs.LG

Guilherme Vieira Neto , Marcos Eduardo Valle This is my paper · ORCID
classification eess.IVcs.CVcs.LG
keywords vector-valuedneuralnetworkshypercomplex-valuedEfficientNetdepthwiseconvolutionnon-associativealgebrasmedicalimageclassificationacutelymphoblasticleukemiaALL-IDB2
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

This paper tries to establish that the EfficientNet architecture, which normally operates on real-valued feature maps, can be rebuilt over a d-dimensional non-associative algebra so that each neuron processes entire vectors as single entities. The authors construct vector-valued versions of convolutional and depthwise-convolutional layers, wrap them into MBConv and Fused-MBConv blocks, and introduce a vectorization factor that controls how many real features each vector replaces. On the ALL-IDB2 leukemia image dataset, the smallest such model based on hyperbolic quaternions reports 99.46% average accuracy, compared with 98.23% for the real-valued EfficientNetV2-B0 baseline and 98.46% for the previous state of the art, while cutting trainable parameters from 5.86 million to 1.72 million. If correct, this shows that moving from scalar to vector-valued algebra is a practical way to make compact CNNs more accurate on small medical datasets.

What carries the argument

The load-bearing mechanism is the representation of vector-valued operations by real-valued tensor operations, centered on the multiplication-table tensor P whose entries define the product of basis elements in a non-associative algebra. Any vector product can be evaluated through a matrix-vector product built from P, which lets vector-valued dense, convolutional, and the newly introduced vector-valued depthwise convolutional layers be implemented with existing real-valued operations. A bank of vector-valued filters is assembled by summing Kronecker products of real filter banks with slices of P, so one vector-valued filter reuses related parameters across d channels. The architecture vectorization factor then controls whether each vector packs d real features, giving a parameter reduction by 1/d, or each real feature becomes a vector, upscaling by d, with the 1/4 setting used in the experiments. This construction is what turns the scalar EfficientNetV2-B0 into V-EfficientNet while preserving the MBConv and Fused-MBConv block structure.

What would settle it

Retrain the real-valued EfficientNetV2-B0 on HSV-encoded images with the same 50/50 split, augmentation, and 10-run protocol; if its mean accuracy reaches or exceeds the 99.46% reported for the hyperbolic-quaternion model, the vector-valued architecture's advantage is explained by color encoding rather than by the algebraic mechanism.

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Extended reading notes

Core claim

The central claim is that vector-valued EfficientNets, meaning EfficientNetV2-B0 with its scalar arithmetic replaced by multiplication in a four-dimensional hypercomplex algebra, can outperform both the real-valued baseline and prior specialized models on ALL-IDB2 while using roughly 70% fewer parameters. The winning model, based on hyperbolic quaternions and trained on HSV-encoded images, achieves 99.46% average accuracy over 10 runs, whereas the real-valued RGB baseline scores 98.23%. The paper further claims this is the highest mean accuracy reported for ALL-IDB2 to date, and presents these numbers as evidence that vector-valued networks exploit inter-channel relationships that real-valued networks must learn, with the choice of algebra acting as a meaningful design decision.

Load-bearing premise

The central claim assumes that the 1.2-point accuracy gap between the winning vector-valued model and the real baseline comes from the vector-valued algebra, not from the fact that the winning model was trained on HSV images while the baseline used RGB.

Editorial extensions

If this is right

  • Replacing real-valued depthwise and regular convolutions with vector-valued counterparts in EfficientNetV2-B0 reduces trainable parameters by approximately 70% at the 1/4 vectorization factor, while classification accuracy on ALL-IDB2 rises from 98.23% to 99.46% for the hyperbolic-quaternion model.
  • The same vectorization recipe extends to other EfficientNet variants and scales, since it only swaps the underlying arithmetic and keeps the block-level architecture intact.
  • The experiments isolate the choice of hypercomplex algebra as a performance lever: quaternions, coquaternions, tessarines, and hyperbolic quaternions deliver different accuracies on the same task, with hyperbolic quaternions performing best.
  • Vector-valued depthwise convolution, introduced here, is what allows the MBConv blocks of EfficientNet to be vectorized, so the method is not limited to dense or regular convolutional layers.

Reading between the lines

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

  • If the real-valued baseline were retrained on HSV input under the same augmentation and split, the reported gap might shrink: the winning model uses HSV while the baseline uses RGB, so the current comparison does not fully isolate the algebraic contribution.
  • The vector-valued depthwise convolution is a general primitive that could be dropped into other depthwise-heavy architectures, such as MobileNet-style backbones, not just EfficientNet.
  • With only 260 images and 10 runs, the separation between the best and second-best models may not be statistically significant; confidence intervals or a significance test over more seeds would settle it.
  • The algebraic structure of hyperbolic quaternions, which are non-associative and non-commutative, appears to matter for accuracy, so algebra selection could potentially be guided by geometric or group-theoretic properties of the data rather than brute force.
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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

3 major / 5 minor

Summary. The paper introduces V-EfficientNets, an adaptation of EfficientNetV2 to vector-valued non-associative algebras. The authors formalize vector-valued depthwise convolution via a real-valued implementation based on Kronecker products, introduce an architecture vectorization factor lambda in [1/d, 1], and evaluate the resulting models on the ALL-IDB2 acute lymphoblastic leukemia image classification task. They report an average accuracy of 99.46% for a hyperbolic-quaternion HSV model with about 70% fewer trainable parameters than the real-valued EfficientNetV2-B0 baseline, claiming state-of-the-art performance. The full text includes the algebraic framework, layer implementations, experimental details, and a link to source code.

Significance. If the claims are established, the paper makes a useful contribution: a general vector-valued depthwise convolution construction, a parameter-efficient vectorized EfficientNet variant, and a strong accuracy result on a medical benchmark with code provided. The algebraic derivation of the real-valued filter bank is internally consistent, and the vectorization factor is a clean design choice with no fitted constants. The reported parameter reduction is structurally plausible. However, the empirical superiority claim is not yet supported because the main comparison confounds architecture with color encoding, and the depthwise-convolution derivation is insufficiently specified.

major comments (3)
  1. [Section V, Table II] The reported advantage of the best vector-valued model over the baseline is confounded with color encoding. The real-valued EfficientNetV2-B0 baseline is reported only with RGB input (98.23 ± 1.09), while the two models that exceed it, quaternion HSV and hyperbolic quaternion HSV, both use HSV encoding. No real-valued HSV baseline is given, so the 1.23-percentage-point gap could be entirely due to HSV preprocessing rather than the vector-valued algebra. The abstract's claim that V-EfficientNets 'outperform state-of-the-art models, including the original EfficientNet' therefore needs an additional control experiment: a real-valued EfficientNetV2-B0 trained on HSV input under the same protocol.
  2. [Section V, Table II and following paragraph] No significance testing is reported for the 10 repeated runs, despite the text using the words 'significantly outperformed' and 'solid margin.' The standard deviations overlap substantially (e.g., quaternion HSV 99.23 ± 0.91, hyperbolic quaternion HSV 99.46 ± 0.60, coquaternion HSV 98.08 ± 2.07), so the observed differences may not be statistically reliable. Paired comparisons across the 10 runs (e.g., Wilcoxon signed-rank test or a paired bootstrap) should be reported for each pair of models, especially for hyperbolic quaternion HSV versus real-valued RGB and versus quaternion HSV.
  3. [Section III-B, Eqs. (9)-(12) and Figures 3-4] The conversion of the augmented real-valued depthwise output J(a) to the desired real representation J(R) is not specified precisely. The text says to sum channels 'row-wise in the Fig. 3' and then 'permutating appropriately' the channels of the resulting image, but no explicit index map or linear transformation is given. For a general non-associative algebra, a simple summation over one index followed by a permutation does not generally produce the components of the algebra product: for example, with quaternions the real component of the product requires the signed combination I0*F0 - I1*F1 - I2*F2 - I3*F3, which cannot be obtained by adding the four augmented channels that contain the positive products I1*F1, I2*F2, I3*F3. The paper should provide the explicit linear combination or permutation rule in terms of the structure constants πijk, or otherwise verify that the described operation is correct. Since the vector-valued depthwise convolution is the paper's main architectural novelty and is used in all experiments, this omission is load-bearing for the reproducibility and correctness of the method.
minor comments (5)
  1. [Section V, Table II caption and text] The table caption lists 'Color encoding' but the rows for vector models include the algebra and the encoding; consider adding a column for the algebra or a clearer separation of the two factors.
  2. [Abstract and Section V] The word 'significantly' is used to describe accuracy differences without statistical support; please reserve it for significance tests or rephrase.
  3. [Section III-B, around Eq. (10)-(12)] The notation J(a) and the tilde variant J~(R) are not formally defined before use; a short definition or a labeled equation would improve readability.
  4. [Section IV-B, lambda definition] The range of λ is stated as [1/d, 1], but the description of the two extremes (λ=1/d and λ=1) could be clarified by giving the explicit number of filters in a layer for each case; a small table or example would help.
  5. [Section V, cross-paper comparison] The comparison to previously reported accuracies (e.g., ALLNet at 98.46%) assumes that the evaluation protocols are equivalent, yet the manuscript uses a particular 50/50 split, 128×128 resizing, and augmentation. A sentence acknowledging this limitation or providing a comparison under a shared protocol would strengthen the state-of-the-art claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: derivations are algebraic and exact, accuracy is externally measured.

full rationale

The paper's derivation chain is self-contained: vector multiplication is fixed by a multiplication table (Table I), and the vector-valued dense, convolutional, and depthwise convolutional layers are implemented through exact linear-algebra identities (Eqs. 7 and 12) plus explicit channel permutations (Figs 2-4). No fitted constants or parameters are back-solved from the reported accuracy values. The parameter reduction follows from the explicitly defined vectorization factor λ=1/4, so the roughly 70% parameter decrease is a constructional arithmetic consequence, not an empirical prediction; it is a design specification rather than a derived physical law. The accuracy numbers in Table II are measured on a fixed 50/50 split over 10 runs, and the claimed 99.46% is compared against external published results, making the central performance claim an independently measurable empirical benchmark. Although the paper cites the authors' prior works for motivation and experimental protocol (refs 9, 28, 35), the load-bearing derivation of the vector-valued depthwise convolution is performed in-place, and the empirical claims do not reduce to those citations. No circular step exhibiting Eq. X = Eq. Y by construction, or a fitted parameter renamed as a prediction, was found.

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

The central construction rests on standard non-associative algebra multiplication and on the equivalence between algebra products and real matrix/depthwise operations. The vectorization factor is a hand-chosen design value. No new physical entities are introduced.

free parameters (1)
  • architecture vectorization factor lambda = 1/4
    Chosen as the smallest allowed value (1/d with d=4). It controls the claimed parameter reduction and is not tuned on the test set, but no other values were explored, so the efficiency claim is conditional on this choice.
assumptions (3)
  • standard math A non-associative algebra product is fully determined by the structure constants pi_ijk and can be computed as a matrix-vector product using ML(x) in Eq. (6).
    Standard linear algebra result used throughout Sections II and III.
  • domain assumption Real-valued depthwise convolution with a Kronecker-built filter bank F^(R) in Eq. (12) correctly emulates the vector-valued depthwise convolution defined in Eq. (9).
    The paper provides a derivation and figures but no machine-checked proof; correctness depends on the alignment of library semantics with Eq. (8).
  • domain assumption Vector-valued neural networks generalize better on small datasets because they assume inter-channel correlations and reuse parameters.
    This is the motivational premise from Refs [11], [28], [35]; the paper does not isolate this factor from color encoding or other experimental differences.

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Cite this review

Pith. "Pith review of V-EfficientNets: Vector-Valued Efficiently Scaled Convolutional Neural Network Models." pith.science (2026). https://pith.science/paper/4Q5NTVPT

@misc{pith2026250505659,
  author       = {Pith},
  title        = {Pith review of: V-EfficientNets: Vector-Valued Efficiently Scaled Convolutional Neural Network Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4Q5NTVPT}},
  note         = {Machine review of arXiv:2505.05659}
}
read the original abstract

EfficientNet models are convolutional neural networks optimized for parameter allocation by jointly balancing network width, depth, and resolution. Renowned for their exceptional accuracy, these models have become a standard for image classification tasks across diverse computer vision benchmarks. While traditional neural networks learn correlations between feature channels during training, vector-valued neural networks inherently treat multidimensional data as coherent entities, taking for granted the inter-channel relationships. This paper introduces vector-valued EfficientNets (V-EfficientNets), a novel extension of EfficientNet designed to process arbitrary vector-valued data. The proposed models are evaluated on a medical image classification task, achieving an average accuracy of 99.46% on the ALL-IDB2 dataset for detecting acute lymphoblastic leukemia. V-EfficientNets demonstrate remarkable efficiency, significantly reducing parameters while outperforming state-of-the-art models, including the original EfficientNet. The source code is available at https://github.com/mevalle/v-nets.

Figures

Figures reproduced from arXiv: 2505.05659 by the authors.

Figure 2
Figure 2. Computation of F (R) by (12). output J (V) = I (V) ∗DW F (V) ∈ V H′×W′×(KC) from the vector-valued depthwise convolution operation is defined as J (V) i,j,(k+cK) = X m,n I (V) (i−1)sH+m,(j−1)sW +n,c × F (V) m,n,c,k, (9) where sH and sW denote the vertical and horizontal strides, respectively [25]. We would like to remark that while the pixel indices are included, (9) is analogous to (8), differing only in that vecto… view at source ↗
Figure 3
Figure 3. Augmented image J (a) = I (R) ∗DW F (R) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Building blocks of the EfficientNet models. Here, BN indicates batch [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

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