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REVIEW 4 major objections 5 minor 31 references

Finding Optimal Kernel Size and Dimension in Convolutional Neural Networks An Architecture Optimization Approach

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Kernel size can be optimized per CNN layer, not fixed at 3x3.

desk verdict A plausible-sounding kernel-size heuristic whose own validation tables contradict the abstract and fail to isolate kernel size as the causal variable. read the letter →

arxiv 2506.14846 v1 pith:BFPNS3VM submitted 2025-06-16 cs.CV cs.AIeess.IV

Shreyas Rajeev , B Sathish Babu This is my paper
classification cs.CVcs.AIeess.IV
keywords kernelsizeoptimizationconvolutionalneuralnetworksBKSEFper-layerarchitecturesearchreceptivefieldcomputationalcostCIFAR-10ChestX-ray14
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

Kernel size in convolutional neural networks is usually treated as a fixed convention, most often uniform 3x3 kernels in every layer, but this paper argues that kernel size should be a layer-wise design variable. It introduces the Best Kernel Size Estimation Function (BKSEF), which selects, for each convolutional layer, the kernel size that maximizes a normalized combination of information gain and accuracy gain while penalizing computational cost. The paper reports that BKSEF-guided architectures improve accuracy by up to 3.1 percent and reduce FLOPs by about 42.8 percent relative to uniform 3x3 baselines across CIFAR-10, CIFAR-100, ImageNet-lite, ChestX-ray14, and GTSRB. Two case studies apply the same objective in opposite directions: larger, attention-aware kernels for chest X-ray interpretation in a cloud setting, and smaller efficient kernels for traffic sign recognition on an edge device. The paper explicitly frames this as turning kernel size from a static hyperparameter into an optimizable dimension for neural architecture search and real-time systems.

What carries the argument

The central object is the Best Kernel Size Estimation Function (BKSEF), a normalized multi-objective score for layer-wise kernel selection. The mechanism combines a receptive field recurrence $R_l(k) = R_{l-1} + (k-1)\prod_{i=1}^{l-1} s_i$, a cost model $C(k) \propto k^2 H_l W_l C_{in} C_{out}$, an information gain model $I(k) = \log(1+k)$, and an accuracy gain model $A(k) = 1 - e^{-\gamma k}$, with each term normalized to a comparable range and combined through tunable weights $\lambda_1, \lambda_2, \lambda_3$. This function carries the argument because it turns the qualitative trade-off between receptive field, computational cost, and accuracy into a single kernel choice per layer.

What would settle it

Run the same backbone with identical depth, width, activations, and attention mechanisms, varying only the kernel-size pattern between uniform 3x3 and the BKSEF-argmax pattern; the central claim stands only if the BKSEF pattern matches the reported margins. A second check is to compute BKSEF's argmax for a given layer using the paper's normalization and verify that the architectures described in the case studies actually attain that argmax.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that a computable per-layer optimum kernel size exists and is given by $k^* = \arg\max_k [\lambda_1 \tilde{I}(k) + \lambda_2 \tilde{A}(k) - \lambda_3 \tilde{C}(k)]$, where $\tilde{I}$ is normalized logarithmic information gain $\log(1+k)$, $\tilde{A}$ is normalized exponential accuracy saturation $1 - e^{-\gamma k}$, and $\tilde{C}$ is normalized quadratic FLOP cost. The paper argues that choosing kernels according to this objective yields accuracy improvements and FLOP reductions over uniform 3x3 designs, and that the same objective can justify opposite architectural choices in cloud and edge deployments. It presents BKSEF as a mathematically grounded, interpretable alternative to the heuristic default of fixed small kernels.

Load-bearing premise

The reported accuracy and FLOPs improvements are attributed to the BKSEF-selected kernel sizes even though the case studies also change first-layer kernels, attention blocks, depthwise separability, and pointwise convolutions, so the experiments never isolate kernel size as the causal variable.

Editorial extensions

If this is right

  • If BKSEF is correct, uniform 3x3 kernels are not generally optimal, and practitioners can choose kernel sizes per layer based on task and hardware constraints.
  • Because the objective is built from three cheap scalar functions, BKSEF can be inserted into neural architecture search pipelines as a layer-wise kernel selection heuristic.
  • Shifting the weights in BKSEF allows the same framework to favor accuracy in cloud deployments or efficiency in edge deployments.
  • BKSEF-guided kernel choices can reduce FLOPs by about 42.8 percent and improve accuracy by up to 3.1 percent compared with conventional fixed-kernel baselines.
  • Kernel size becomes a traceable, interpretable design decision, which the paper argues is especially relevant for high-stakes applications like medical imaging.

Reading between the lines

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

  • A reader should not attribute the reported gains to kernel size alone: the two case studies change several architectural components at once, so the causal role of the BKSEF-selected kernels is not isolated.
  • The functional forms $\log(1+k)$ and $1 - e^{-\gamma k}$ are chosen as analytic proxies; replacing them with measured mutual information and empirical accuracy curves could produce different kernel recommendations.
  • BKSEF's argmax over odd kernel sizes can be computed exactly for a layer with fixed weights, which suggests a direct test of whether the architectures reported in the paper actually attain the stated optimum.
  • The approach is limited to 2D convolutions and small-to-medium datasets, so extending it to 3D convolution, video, or large-scale benchmarks would clarify how broadly the objective generalizes.
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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 the Best Kernel Size Estimation Function (BKSEF), a per-layer objective k* = argmax_k [λ1·Ĩ(k) + λ2·Ã(k) − λ3·C̃(k)] meant to select CNN kernel sizes by balancing normalized information gain, accuracy gain, and computational cost. The authors present two case studies—chest X-ray classification (Case 1) and traffic sign recognition (Case 2)—and claim broader benchmarks (CIFAR-10, CIFAR-100, ImageNet-lite) with improvements up to +3.1% accuracy and ~42.8% FLOPs reduction over uniform 3×3 baselines. The manuscript concludes with heuristics and suggestions for NAS integration.

Significance. If properly validated, a simple analytic kernel-size selection rule would be a useful complement to neural architecture search, and the emphasis on interpretability in medical imaging is a worthwhile direction. The paper is clearly written in parts and honestly lists several limitations. However, the central empirical claim is unsupported: the BKSEF objective contains unspecified free parameters, the case studies confound kernel size with other architectural changes, and the headline benchmark results claimed in the abstract and conclusion do not appear anywhere in the manuscript. As presented, the paper does not provide evidence that BKSEF can predict optimal kernel sizes or that its guidance improves accuracy or efficiency beyond the specific hand-designed architectures shown.

major comments (4)
  1. [Section IV, Eq. (1)-(4)] The BKSEF objective depends on four free parameters (λ1, λ2, λ3, and γ) that are never fixed, fitted, or given a selection protocol. As written, k* cannot be computed from the formula for any layer, so the objective has no predictive content. The manuscript must either specify default parameter values, a fitting procedure, or a sensitivity analysis, and then show the resulting argmax for each layer in the case studies.
  2. [Section V, Table 5.1 (Case Study 1)] The 'BKSEF-guided' model changes multiple architectural components beyond kernel size: the first layer becomes 7×7, middle layers alternate 3×3 and 5×5, and a final 7×7 layer adds an SE-block. The SE-block is not part of the BKSEF objective, so the +1.8% accuracy gain cannot be attributed to kernel size selection. The table also reports a 16% increase in FLOPs, which contradicts the abstract's claim of a 42.8% FLOPs reduction. No calculation is shown connecting the selected kernel pattern to the argmax of Eq. (4).
  3. [Section V, Table 5.2 (Case Study 2)] The optimized model replaces standard 5×5 convolutions with 3×3 depthwise separable convolutions plus 1×1 pointwise convolutions. This changes the convolution type and layer composition, not merely the kernel size, so the reported 30.6% FLOPs reduction and latency improvement are largely explained by depthwise separable convolutions. Again, no BKSEF argmax computation is provided, and the accuracy decreases by 0.4%, so the positive efficiency claims do not validate the kernel-size selection function.
  4. [Abstract and Section VI] The abstract and conclusion claim benchmarking on CIFAR-10, CIFAR-100, and ImageNet-lite with up to +3.1% accuracy and ~42.8% FLOPs reduction, but no such experiments or results appear in the manuscript. The only quantitative comparisons are the two case-study tables, which report +1.8%/-0.4% accuracy and +16%/-30.6% FLOPs. The headline figures are therefore unsupported and internally inconsistent with the reported tables.
minor comments (5)
  1. [Section V, opening paragraph] The paragraph about a confusion matrix for 'spoof' and 'bonafide' samples is unrelated to the two case studies that follow and should be removed or integrated into a relevant section.
  2. [Introduction, literature review statistics] The claim of a 'review of 92 CNN architecture papers' with percentages for kernel-size usage has no citation or methodology. Please provide the source or remove the claim.
  3. [References] Several references are listed as 'Anonymous' (e.g., [4], [5], [7], [9]) even though the venues suggest known authors; this should be corrected.
  4. [Section IV, normalization] The min-max normalization of I(k), A(k), and C(k) does not specify the range of k over which the minima and maxima are taken; clarify whether this is over {1,3,5,7,9} or another set.
  5. [Section III, receptive field formula] The receptive field formula R_l(k) is defined but never used in the BKSEF derivation or in any experiment; either connect it to the objective or remove it to avoid an unused definition.

Circularity Check

3 steps flagged · score 8.0 of 10

Case-study 'successes' are post-hoc labels: free parameters make BKSEF vacuous, and the tested architectures are known heuristics, not formula-derived designs.

  1. renaming known result [Section V, Case Study 1, paragraph 'BKSEF-Guided Optimized Model' and 'Empirical Results']
    "Using BKSEF principles, the architecture was restructured as follows: First Layer: 7×7 kernel (to quickly expand receptive field) • Mid Layers: Alternating 3×3 and 5×5 kernels • Final Layer: 7×7 kernel with an SE-block (Squeeze-and-Excitation) to enhance attention and suppress noise. This design captures both global anatomical context (important for detecting diffused pneumonia) and fine-grained abnormalities such as local opacity or lesions."

    The case-study architecture is labeled 'BKSEF-guided' without any computation of k* from the BKSEF objective. The equation k*=argmax[λ1Ĩ(k)+λ2Ã(k)-λ3C̃(k)] contains no SE-block term, no layer-type term, and no receptive-field-schedule term; λ1, λ2, λ3 and γ are never assigned values in the paper. The chosen design (7×7 first layer, alternating 3×3/5×5, SE block) is a known heuristic ensemble, not the result of the stated optimization. The subsequent claim that this model 'outperformed the baseline with a +1.8% increase in accuracy' is therefore a post-hoc attribution: the architecture is called BKSEF-optimized by assertion, so the measured improvement is presented as validating BKSEF while BKSEF played no generative role.

  2. self definitional [Section IV, paragraph 'Interpretations']
    "By adjusting the weights λ1, λ2, λ3, BKSEF can be tailored to prioritize efficiency (e.g., mobile devices), accuracy (e.g., classification tasks), or feature richness (e.g., segmentation or detection)."

    Because λ1, λ2, λ3 and γ are entirely free and never fixed, the objective function has no decision-theoretic content: for any candidate kernel size there exists a choice of weights that makes it the argmax. The paper claims that BKSEF determines 'optimal, layer-wise kernel size determination,' but the only way to connect the formula to the reported 7×7 or 3×3 choices is to select the free parameters after observing the architecture. This is a fitted input called a prediction: the 'prediction' (kernel size) is retrofitted through unstated weights, and the same cases are then used as empirical validation.

1 more flagged steps
  1. renaming known result [Section V, Case Study 2, paragraph 'BKSEF-Guided Optimized Model']
    "Following BKSEF: • All 5×5 kernels were replaced with 3×3 depthwise separable convolutions • 1×1 pointwise convolutions were added for channel mixing • The model depth and width were preserved to ensure fair comparison. This structure aligns with the core BKSEF principle: reduce kernel width in low-resolution or latency-critical applications."

    This changes the convolution type (standard to depthwise separable) and adds a 1×1 pointwise layer, which are architectural changes outside the kernel-size objective. The FLOPs reduction from 124M to 86M (≈30.6%) is due to depthwise separable convolutions, not to a BKSEF-selected kernel size. Naming this MobileNet-style modification 'BKSEF-guided' renames a known efficiency technique as the proposed framework's output, and the measured gains (latency, model size, FLOPs) are then claimed as evidence for BKSEF, even though the kernel-size choice itself was not produced by the formula.

full rationale

The paper's central validation loop is closed only by post-hoc labeling, not by deriving the tested architectures from BKSEF. The formula k* = argmax[λ1Ĩ(k)+λ2Ã(k)-λ3C̃(k)] has parameters λ1, λ2, λ3, γ that are never assigned values, so it cannot emit a concrete kernel-size prediction without an explicit fitting protocol. The two case-study architectures are described as 'BKSEF-guided' but no computation of the argmax is shown for any layer; moreover, the designs include elements that are not terms in the objective (SE-block, alternating schedules, depthwise-separable convolutions, 1x1 pointwise layers). Thus the reported accuracy and FLOPs improvements are fully explained by concurrent architectural changes, not by the kernel-size rationale. In effect, the paper renames familiar architectural heuristics as 'BKSEF' and then treats the resulting measurements as empirical support for BKSEF. This is a circular justification of the framework's validity, though it is not a self-citation chain and the formula itself is an explicit, if underdetermined, ansatz. Hence the score is 8 rather than 10: the result is forced by the free-parameter definition and by labeling, not by a chain of self-citations.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central derivation rests on four assumptions: two ad hoc functional forms (log information gain, exponential accuracy gain), a per-layer independence assumption, and a standard FLOPs complexity model. The first three are not derived or validated; the free parameters λ1-λ3 and γ are never fixed, so the 'optimal kernel size' is underdetermined.

free parameters (4)
  • λ1 (weight on information gain)
    Tunable hyperparameter in the BKSEF objective; never assigned in the paper. The optimal kernel size depends critically on it.
  • λ2 (weight on accuracy gain)
    Tunable hyperparameter; never assigned. Controls the balance toward accuracy in the argmax.
  • λ3 (weight on computational cost)
    Tunable hyperparameter; never assigned. Penalizes FLOPs; must be set to make the trade-off.
  • γ (accuracy saturation rate)
    Shape parameter in A(k)=1-e^{-γk}; never specified. The exponential accuracy model is assumed without support.
assumptions (4)
  • ad hoc to paper Information gain from a kernel of size k scales as I(k)=log(1+k)
    Chosen to reflect diminishing returns but not derived from information theory; the paper provides no entropy calculation.
  • ad hoc to paper Accuracy gain from larger kernels follows A(k)=1-e^{-γk}
    Inspired by learning curves but no empirical or theoretical derivation; γ is a free parameter.
  • domain assumption Kernel size can be optimized independently for each layer via a single argmax
    The objective is evaluated per layer; cross-layer interactions (e.g., downstream receptive fields, channel dependencies) are ignored.
  • standard math FLOPs of a convolution scale as k^2·H·W·C_in·C_out
    This is the standard FLOPs formula for a 2D convolution layer; reasonable but simplified (ignores memory access, stride effects).

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Cite this review

Pith. "Pith review of Finding Optimal Kernel Size and Dimension in Convolutional Neural Networks An Architecture Optimization Approach." pith.science (2026). https://pith.science/paper/BFPNS3VM

@misc{pith2026250614846,
  author       = {Pith},
  title        = {Pith review of: Finding Optimal Kernel Size and Dimension in Convolutional Neural Networks An Architecture Optimization Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BFPNS3VM}},
  note         = {Machine review of arXiv:2506.14846}
}
read the original abstract

Kernel size selection in Convolutional Neural Networks (CNNs) is a critical but often overlooked design decision that affects receptive field, feature extraction, computational cost, and model accuracy. This paper proposes the Best Kernel Size Estimation Function (BKSEF), a mathematically grounded and empirically validated framework for optimal, layer-wise kernel size determination. BKSEF balances information gain, computational efficiency, and accuracy improvements by integrating principles from information theory, signal processing, and learning theory. Extensive experiments on CIFAR-10, CIFAR-100, ImageNet-lite, ChestX-ray14, and GTSRB datasets demonstrate that BKSEF-guided architectures achieve up to 3.1 percent accuracy improvement and 42.8 percent reduction in FLOPs compared to traditional models using uniform 3x3 kernels. Two real-world case studies further validate the approach: one for medical image classification in a cloud-based setup, and another for traffic sign recognition on edge devices. The former achieved enhanced interpretability and accuracy, while the latter reduced latency and model size significantly, with minimal accuracy trade-off. These results show that kernel size can be an active, optimizable parameter rather than a fixed heuristic. BKSEF provides practical heuristics and theoretical support for researchers and developers seeking efficient and application-aware CNN designs. It is suitable for integration into neural architecture search pipelines and real-time systems, offering a new perspective on CNN optimization.

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Reviewed August 7, 2026 · model on record in the stance chip above.