REVIEW 3 major objections 6 minor 26 references
Convolutional Neural Networks Do Work with Pre-Defined Filters
T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read 16 frozen edge filters match ResNet18 with 13% of the weights
desk verdict The core claim survives, but the headline 'PFNet18 beats ResNet18' rests on an uneven anti-aliasing comparison and a slightly inflated percentage. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The Pre-defined Filter Module (PFM) carries the argument. In its channel-wise part, each input channel is convolved with one kernel from a fixed pool of 16 edge filters, assigned by the index $i \bmod k$; an intermediate width parameter $f$ creates $f$ copies of the input channels so that the first layer applies every filter to every color channel. In its second part, a $1\times1$ convolution learns arbitrary linear combinations of the filter outputs, so all gradient updates affect only the combination weights. The module makes the spatial filter bank shared and fixed, isolating exactly what the network has to learn.
What would settle it
Train the same PFNet18 and ResNet18 from scratch on a dataset whose class-discriminative information is carried by high-frequency textures or periodic patterns rather than edges, and check whether PFNet18 falls far behind; a cleaner test is to vary the filter pool (random, Gabor, Fourier) on one dataset and show that no fixed pool restores ResNet-level accuracy on all datasets.
Extended reading notes
Core claim
The paper's central claim is stated in its title: convolutional neural networks do work with pre-defined filters. The authors define a Pre-defined Filter Module that performs a channel-wise convolution with frozen $1\times3\times3$ kernels drawn from a pool of 16 hand-picked edge filters, followed by a learned $1\times1$ convolution over all intermediate channels; replacing every $n\times n$ convolution in ResNet18 with this module yields PFNet18. They report that PFNet18 outperforms ResNet18 on three of six benchmarks and matches it closely on the others, despite having only 1.46 million trainable parameters. The same experiments show filter choice matters: frozen random filters perform much worse than frozen edge filters, and unfreezing the edge filters gives no improvement over freezing them.
Load-bearing premise
The load-bearing premise is that 16 hand-picked edge filters, fixed and applied in the same cyclic order in every layer, give a sufficiently rich spatial basis that no learned spatial kernel is needed on any of these datasets.
Editorial extensions
If this is right
- If spatial filters really do not need to be learned, then most of the parameters in a conventional CNN are unnecessary for image classification, and weight sharing through a small fixed filter pool can replace pruning as a compression strategy.
- Because PFNet18 uses fixed edge filters in all layers, high-level object-specific features must emerge purely from linear combinations of local edge responses, which is what the feature visualizations appear to show.
- Removing aliasing at stride-2 convolutions improves PFNet18 accuracy on Flowers102 from about 72% to 81%, so fixed-filter networks are more sensitive to spatial downsampling than standard CNNs.
- Frozen random filters still reach ResNet18-level accuracy on Flowers102, while frozen edge filters exceed it, implying the filter basis is an inductive bias that matters most on harder small-data tasks.
- The parameter reduction from 11.23M to 1.46M does not produce a comparable runtime reduction because the depthwise implementation has more graph nodes; the paper attributes this to implementation inefficiency, not to the method itself.
Reading between the lines
- The paper leaves open whether the same 16 edge filters transfer to large-scale, non-photographic, or high-frequency-texture benchmarks; a direct test would be to train PFNet18 on ImageNet or on synthetic texture datasets where edges are not the discriminating signal.
- If frozen random filters can already match ResNet18, the essential ingredient may be the learned $1\times1$ combinations rather than the edge basis; one could test whether the edge advantage grows as training data shrinks.
- The aliasing sensitivity suggests a cheap improvement: inserting an anti-aliasing blur before each stride-2 downsampling might recover most of the performance gap on datasets where PFNet18 lags, independently of any change to the filter pool.
- Since the filter order is fixed and shared across channels, the architecture is a form of structured weight sharing that could be combined with model distillation or quantization; the paper does not explore this.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces Pre-defined Filter Convolutional Neural Networks (PFCNNs), in which every spatial convolution kernel of size greater than 1 is drawn from a fixed pool of 16 hand-selected 3x3 edge filters and remains constant during training; only 1x1 convolutions are learned. The authors build PFNet18 by replacing all n>1 convolutions of ResNet18 with Pre-defined Filter Modules (PFMs), reducing the parameter count to 1.46M (13% of ResNet18). They report five-seed experiments on Caltech101, CIFAR10, CUB-200-2011, FGVC-Aircraft, Flowers102, and Stanford Cars, together with feature visualizations, an ablation on Flowers102, and an analysis of aliasing. The central empirical claim is that PFNet18 matches or outperforms ResNet18 on several datasets despite the severe restriction on learnable spatial kernels.
Significance. If the results hold under a fair comparison, the paper makes a compelling empirical case that deep networks can achieve competitive recognition accuracy by learning only linear combinations of a small number of pre-defined spatial filters, which is a valuable contribution to the debate about what CNNs actually learn. The study is transparent: code is released, results are averaged over five seeds, and the authors include an ablation separating the effect of filter choice from the fixed-filter mechanism. The main reservation is that the headline superiority of PFNet18 is currently supported by an unequal comparison in which PFNet18 receives a Gaussian anti-aliasing blur that ResNet18 does not receive, and the reported 10% improvement exceeds the largest margin in the data; the significance is therefore conditional on correcting these issues.
major comments (3)
- [Section 5.4, Tables 4 and 7] Table 4 reports PFNet18 Flowers102 accuracy of 80.66, which Table 7 identifies as the "No aliasing, default" configuration, while the ResNet18 value of 73.40 is the default (aliasing) configuration. For Caltech101 and FGVC-Aircraft, the manuscript does not state whether the PFNet18 results use the anti-aliasing blur, and no no-aliasing ResNet18 baselines are reported for these datasets. The claimed superiority of PFNet18 on these datasets is therefore not established under equal conditions. Please either report ResNet18 no-aliasing results for all datasets in Table 4, or use the aliasing version of PFNet18 for the main comparison, and state explicitly which configuration was used for every entry.
- [Abstract and Section 7] The abstract and Section 7 state that PFNet18 outperforms ResNet18 "with an absolute increase of 10%". The largest gap in Table 4 is 8.41 percentage points (Caltech101: 65.60 vs 57.19); Flowers102 is 7.26 points and FGVC-Aircraft is 2.17 points. The claim should be reworded to report the actual margins, and it should be checked again after the aliasing treatment is aligned across models.
- [Section 5.4] The claim that "ResNet18 has a lower risk of losing image information by aliasing" and that PFNet18 relies on skip connections to compensate is supported only by a single quantitative experiment on Flowers102 plus the small illustrative example in Figure 3. If the anti-aliasing blur is intended to be part of the default PFNet18 configuration, its effect on Caltech101, FGVC-Aircraft, and the other datasets should be quantified so that the reader can separate the benefit of the fixed filters from the benefit of the blur.
minor comments (6)
- [Section 3.2] The permutation argument for f=1 is only sketched; please spell out how a permutation of kernel assignments is absorbed by the weights of the preceding and following 1x1 layers, especially in the presence of residual connections.
- [Section 4.1] The CIFAR10 paragraph states that "these adjustments apply for both, PFNet18 and ResNet18", which is ambiguous because PFNet18's first convolution is already 1x3x3; please specify the exact architectural modifications for each model.
- [Section 5.5] The filter-choice ablation is conducted only on Flowers102; the general conclusion in Section 6 that edge filters add a suitable bias would be strengthened by repeating the random-versus-edge comparison on at least one additional dataset.
- [Section 4.2] The weight decay value is reported as 1.0; please confirm this is intentional and not a typo for 1e-4, since it is an unusual setting.
- [Figure 3] Figure 3 is difficult to read at print size; please enlarge the panels and add explicit labels for the filters and the input.
- [Table 6 caption] The caption's phrase "During BP the hyperparameters described above are used" is unclear; the backward-pass time is not a function of hyperparameters, so please rephrase to indicate the exact conditions of the measurement.
Circularity Check
No circularity: the central claim is an empirical benchmark comparison of a fixed, hand-chosen filter bank against trained spatial kernels; no derivation step reduces to its own inputs.
full rationale
The paper's central claim is that freezing all n x n kernels to 16 pre-defined edge filters and learning only the 1x1 combination layer suffices to reach competitive accuracy. This is an inductive, empirical claim supported by Table 4 and the ablation in Table 7; the pre-defined filters are not fitted to the test sets, and the learned 1x1 weights are the actual subject of the experiment rather than a hidden form of the target claim. The only self-citations (refs. 1, 3, 4) appear in the introduction as background statements about CNNs and do not carry the load-bearing evidence, which is the benchmark comparison and the filter-swap ablation. The choice of edge filters is justified by an external empirical observation (refs. 9, 10) and tested by a random-filter control (Table 7), so it is not an ansatz smuggled in by self-citation. The anti-aliasing modification in Section 5.4 is a fairness and correctness concern about the ResNet18 comparison, not circularity: the Gaussian blur is itself a pre-defined, frozen operation and does not make the claim that pre-defined spatial filters suffice true by construction. The paper also states an explicit limitation that ImageNet-scale and transfer-learning behavior is left to future work, which further confirms that the claim is not presented as a necessary mathematical consequence.
Assumptions & free parameters
free parameters (3)
- Pool of 16 edge filters =
8 uneven + 8 even, zero-sum, normalized
- Kernel count k =
16
- Width factor f =
16 first PFM, 1 later PFMs
assumptions (4)
- domain assumption Edge filters provide a useful inductive bias for image classification.
- domain assumption A frozen depthwise 3x3 filter followed by a learned 1x1 convolution can express the spatial operations needed in a residual network.
- standard math The permutation-invariance argument for f=k and f=1 holds (Section 3.2).
- domain assumption The same training hyperparameters (300 epochs, Lamb, lr=0.003, weight decay=1) are appropriate for all datasets and both architectures.
Cite this review
Pith. "Pith review of Convolutional Neural Networks Do Work with Pre-Defined Filters." pith.science (2026). https://pith.science/paper/UJE2KAGY
@misc{pith2026241118388,
author = {Pith},
title = {Pith review of: Convolutional Neural Networks Do Work with Pre-Defined Filters},
year = {2026},
howpublished = {\url{https://pith.science/paper/UJE2KAGY}},
note = {Machine review of arXiv:2411.18388}
}
read the original abstract
We present a novel class of Convolutional Neural Networks called Pre-defined Filter Convolutional Neural Networks (PFCNNs), where all nxn convolution kernels with n>1 are pre-defined and constant during training. It involves a special form of depthwise convolution operation called a Pre-defined Filter Module (PFM). In the channel-wise convolution part, the 1xnxn kernels are drawn from a fixed pool of only a few (16) different pre-defined kernels. In the 1x1 convolution part linear combinations of the pre-defined filter outputs are learned. Despite this harsh restriction, complex and discriminative features are learned. These findings provide a novel perspective on the way how information is processed within deep CNNs. We discuss various properties of PFCNNs and prove their effectiveness using the popular datasets Caltech101, CIFAR10, CUB-200-2011, FGVC-Aircraft, Flowers102, and Stanford Cars. Our implementation of PFCNNs is provided on Github https://github.com/Criscraft/PredefinedFilterNetworks
Figures
Reference graph
Works this paper leans on
-
[1]
Large neural networks learning from scratch with very few data and without regularization,
C. Linse and T. Martinetz, “Large neural networks learning from scratch with very few data and without regularization,” 2022
work page 2022
-
[2]
Deep Residual Learning for Image Recognition,
K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) . Las Vegas, NV , USA: IEEE, Jun. 2016, pp. 770–778
work page 2016
-
[3]
Handcrafted versus CNN Features for Ear Recognition,
H. Alshazly, C. Linse, E. Barth, and T. Martinetz, “Handcrafted versus CNN Features for Ear Recognition,” Symmetry, vol. 11, no. 12, p. 1493, Dec. 2019
work page 2019
-
[4]
Deep Convolutional Neural Networks as Generic Feature Extractors
L. Hertel, E. Barth, T. Käster, and T. Martinetz, “Deep Convolutional Neural Networks as Generic Feature Extractors,” arXiv:1710.02286 [cs], Oct. 2017, arXiv: 1710.02286
work page Pith review arXiv 2017
-
[5]
Reconciling modern machine-learning practice and the classical bias–variance trade-off,
M. Belkin, D. Hsu, S. Ma, and S. Mandal, “Reconciling modern machine-learning practice and the classical bias–variance trade-off,” Proceedings of the National Academy of Sciences , vol. 116, no. 32, pp. 15 849–15 854, Aug. 2019
work page 2019
-
[6]
K. Fukushima, “Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position,” Biological Cybernetics, vol. 36, no. 4, pp. 193–202, Apr. 1980
work page 1980
-
[7]
PCFNet: Deep neural network with predefined convolutional filters,
Y . Ma, Y . Luo, and Z. Yang, “PCFNet: Deep neural network with predefined convolutional filters,”Neurocomput- ing, vol. 382, pp. 32–39, Mar. 2020
work page 2020
-
[8]
Rethinking 1x1 Convolutions: Can we train CNNs with Frozen Random Filters?
P. Gavrikov and J. Keuper, “Rethinking 1x1 Convolutions: Can we train CNNs with Frozen Random Filters?” Jan. 2023, arXiv:2301.11360 [cs]
arXiv 2023
Show all 26 references
-
[9]
ImageNet Classification with Deep Convolutional Neural Networks,
A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet Classification with Deep Convolutional Neural Networks,” in Advances in Neural Information Processing Systems , F. Pereira, C. J. Burges, L. Bottou, and K. Q. Weinberger, Eds., vol. 25. Curran Associates, Inc., 2012
2012
-
[10]
CNN Filter DB: An Empirical Investigation of Trained Convolutional Filters,
P. Gavrikov and J. Keuper, “CNN Filter DB: An Empirical Investigation of Trained Convolutional Filters,” in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) . New Orleans, LA, USA: IEEE, Jun. 2022, pp. 19 044–19 054
2022
-
[11]
Learning Generative Visual Models from Few Training Examples: An Incremental Bayesian Approach Tested on 101 Object Categories,
Li Fei-Fei, R. Fergus, and P. Perona, “Learning Generative Visual Models from Few Training Examples: An Incremental Bayesian Approach Tested on 101 Object Categories,” in2004 Conference on Computer Vision and Pattern Recognition Workshop. Washington, DC, USA: IEEE, 2004, pp. 178–178
2004
-
[12]
The Caltech-UCSD Birds-200-2011 Dataset,
C. Wah, S. Branson, P. Welinder, P. Perona, and S. Belongie, “The Caltech-UCSD Birds-200-2011 Dataset,” California Institute of Technology, Tech. Rep. CNS-TR-2011-001, 2011
2011
-
[13]
Caltech-UCSD Birds 200,
P. Welinder, S. Branson, T. Mita, C. Wah, F. Schroff, S. Belongie, and P. Perona, “Caltech-UCSD Birds 200,” California Institute of Technology, Tech. Rep. CNS-TR-2010-001, 2010
2010
-
[14]
Fine-Grained Visual Classification of Aircraft,
S. Maji, E. Rahtu, J. Kannala, M. Blaschko, and A. Vedaldi, “Fine-Grained Visual Classification of Aircraft,” arXiv:1306.5151 [cs], Jun. 2013, arXiv: 1306.5151
2013 arXiv
-
[15]
Automated Flower Classification over a Large Number of Classes,
M.-E. Nilsback and A. Zisserman, “Automated Flower Classification over a Large Number of Classes,” in2008 Sixth Indian Conference on Computer Vision, Graphics & Image Processing . Bhubaneswar, India: IEEE, Dec. 2008, pp. 722–729
2008
-
[16]
3D Object Representations for Fine-Grained Categorization,
J. Krause, M. Stark, J. Deng, and L. Fei-Fei, “3D Object Representations for Fine-Grained Categorization,” in 2013 IEEE International Conference on Computer Vision Workshops . Sydney, Australia: IEEE, Dec. 2013, pp. 554–561
2013
-
[17]
Learning multiple layers of features from tiny images,
A. Krizhevsky, “Learning multiple layers of features from tiny images,” 2009
2009
-
[18]
Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification,
K. He, X. Zhang, S. Ren, and J. Sun, “Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification,” in 2015 IEEE International Conference on Computer Vision (ICCV) . Santiago, Chile: IEEE, Dec. 2015, pp. 1026–1034
2015
-
[19]
Large batch optimization for deep learning: Training BERT in 76 minutes,
Y . You, J. Li, S. Reddi, J. Hseu, S. Kumar, S. Bhojanapalli, X. Song, J. Demmel, and C.-J. Hsieh, “Large batch optimization for deep learning: Training BERT in 76 minutes,” in International Conference on Learning Representations, 2020
2020
-
[20]
PyTorch: An Imperative Style, High-Performance Deep Learning Library,
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, “PyTorch: An Imperative Style, High-Pe...
2019
-
[21]
Visualizing higher-layer features of a deep network,
D. Erhan, Y . Bengio, A. Courville, and P. Vincent, “Visualizing higher-layer features of a deep network,”University of Montreal, vol. 1341, no. 3, pp. 1–13, 2009
2009
-
[22]
Understanding deep image representations by inverting them,
A. Mahendran and A. Vedaldi, “Understanding deep image representations by inverting them,” in 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) . Boston, MA, USA: IEEE, Jun. 2015, pp. 5188–5196
2015
-
[23]
Understanding Neural Networks Through Deep Visualization,
J. Yosinski, J. Clune, A. Nguyen, T. Fuchs, and H. Lipson, “Understanding Neural Networks Through Deep Visualization,” Jun. 2015, number: arXiv:1506.06579 arXiv:1506.06579 [cs]
2015 arXiv
-
[24]
Inceptionism: Going deeper into neural networks,
A. Mordvintsev, C. Olah, and M. Tyka, “Inceptionism: Going deeper into neural networks,” 2015
2015
-
[25]
Deep neural networks are easily fooled: High confidence predictions for unrecognizable images,
A. Nguyen, J. Yosinski, and J. Clune, “Deep neural networks are easily fooled: High confidence predictions for unrecognizable images,” in 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) . Boston, MA, USA: IEEE, Jun. 2015, pp. 427–436
2015
-
[26]
ImageNet Large Scale Visual Recognition Challenge,
O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, and L. Fei-Fei, “ImageNet Large Scale Visual Recognition Challenge,” International Journal of Computer Vision, vol. 115, no. 3, pp. 211–252, Dec. 2015. 13
2015
Reviewed August 12, 2026 · model on record in the stance chip above.
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