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REVIEW 4 major objections 6 minor 42 references

Can Encrypted Images Still Train Neural Networks? Investigating Image Information and Random Vortex Transformation

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Swapping any two pixels weakly reduces a distance-weighted measure of image information, and vortex encryption built on this lets neural nets train on scrambled images with under 6.5% accuracy loss.

desk verdict The vortex scramble is a real empirical trick, but the theory is a tautology and the information measure does not actually measure image content. read the letter →

arxiv 2411.16207 v2 pith:JEH3SYRW submitted 2024-11-25 cs.CR

XiaoKai Cao , WenJin Mo , ChangDong Wang , JianHuang Lai , Qiong Huang This is my paper · ORCID
classification cs.CR
keywords imageinformationcontentrandomvortextransformationencryptionneighboringpixelprivacy-preservingtrainingencrypted-datalearningResNetVisionTransformer
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

Vision systems treat images as arrays of pixels, but this paper argues that the information a network actually uses lives in the distance-weighted relationships between pixel pairs, not in isolated pixel values. It defines an image's information content as the sum, over all pixels, of a nonlinear function of how far each pixel is from every other pixel, and it proves that swapping the positions of any two pixels can only reduce or leave unchanged that total. On that basis it designs a Random Vortex Transformation, which rotates pixels along concentric circles around a random center with a bounded random twisting function, so the encrypted image looks scrambled to a human eye while nearby pixels stay nearby. Training ResNet and Vision Transformer models on the encrypted versions of MNIST, Fashion-MNIST, and CIFAR-10 costs only 0.3% to 6.5% accuracy compared with training on the originals, whereas random permutation collapses accuracy to 29% to 56%. The paper offers the positive correlation between its computed information loss and the accuracy loss as evidence that the measure tracks what learning needs.

What carries the argument

The load-bearing object is the neighbor-information pair: the distance-decay function $m_{\mathrm{neig}}(P_{ij},P_{st}) = 1 - 1/(1+e^{6-18\tilde d(P_{ij},P_{st})})$, which depends only on the normalized pixel distance $\tilde d$, and the post-transformation residual rule $m^*_{\mathrm{neig}}(P_{i'j'},P_{s't'}) = [1 - (m_{\mathrm{neig}}(P_{ij},P_{st}) - m_{\mathrm{neig}}(P_{i'j'},P_{s't'}))]\,m_{\mathrm{neig}}(P_{ij},P_{st})$. Substituting this rule into the sum over pixel pairs turns a two-pixel swap into a sum of squared differences $(\gamma_1-\gamma_2)^2$, which is what forces the total information to fall or stay flat. The Random Vortex Transformation is then the coordinate map in Eq. (17), whose bounded random twist $f$ makes large displacement of nearby pixels unlikely, so the encrypted image's neighbor-information sum stays close to the original.

What would settle it

Take a single-color image and swap any two pixel positions. The image is unchanged visually and to a classifier, but the framework's neighbor-information rule depends only on pixel coordinates, so the reported remaining-information fraction $\Upsilon$ will generally drop below 100%. A measure that reports information loss where no observable change occurs would falsify the claim that $\Upsilon$ captures image information content or predicts trainability.

Watch

Extended reading notes

Core claim

The central claim is that image information content has a well-defined, measurable form: for each pixel, sum a Z-shaped function $1 - 1/(1+e^{6-18\tilde d})$ of its normalized distance to every other pixel, and call the total the image's information content. With one additional rule for how much neighbor information survives a pixel move, the paper proves Theorem III.1, that swapping any two pixels weakly decreases the total. It then constructs the Random Vortex Transformation, $i' = d\cos(\theta+(R-d)f(d))$, $j' = d\sin(\theta+(R-d)f(d))$, with a bounded-derivative random $f$, to encrypt images while keeping each pixel near its old position. The experimental claim is that deep networks trained on such encrypted images stay within 0.3% to 6.5% of original-data accuracy, and that the computed remaining-information fractions ($\Upsilon \approx 90$--97% for vortex, $\approx 67$% for random permutation) correlate with the measured accuracy losses.

Load-bearing premise

The whole framework hinges on the untested claim that the paper's formula for 'remaining neighbor information' after a pixel move — $m^*_{\mathrm{neig}} = [1 - (m_{\mathrm{old}} - m_{\mathrm{new}})]\,m_{\mathrm{old}}$ — actually describes how much information survives; if that rule is arbitrary, the theorem and the correlation with accuracy loss collapse.

Editorial extensions

If this is right

  • Any transformation that displaces pixels only mildly, in the sense of keeping normalized distances small, will produce encrypted images that deep classifiers can still learn, giving a design rule for encryption-then-training systems.
  • Random permutation is the negative control: it collapses accuracy to 29%--56% and $\Upsilon$ to about 67%, confirming that preserved neighbor relationships, not raw pixel values, are what carry trainable information.
  • Because RVT does not require decryption for use, it fills a gap that homomorphic encryption cannot, which is training nonlinear models such as ResNet and ViT on protected data.
  • Stacking several vortex transformations is cheap and degrades $\Upsilon$ slowly, so the scheme can be strengthened by composition without leaving the accuracy budget.

Reading between the lines

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

  • The paper's neighbor-information function never looks at pixel intensities, only at coordinates; as a result $\Upsilon$ measures rearrangement of the grid, and any claim that it captures semantic content would need independent calibration.
  • The evidence for a positive correlation between information loss and accuracy loss is limited to two transformation types per dataset; sweeping vortex strength continuously would test whether $\Upsilon$ orders transformations monotonically by learnability.
  • If $\Upsilon$ is accepted, it offers a cheap pre-training screen: compute the information-retention rate of any candidate encryption transform and predict its accuracy budget before running a single epoch.
  • The paper's security claim is human-perceptual rather than cryptographic; translating it into an adversary model (how many random vortex parameters must be guessed to undo the transform) is left open and would be needed to use RVT in real privacy settings.
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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 / 6 minor

Summary. The paper proposes a framework for measuring image information content based on pairwise pixel-neighbor information, defines a remaining-information ratio Υ, proves a "principle of verisimilitude" theorem stating that swapping any two pixels decreases or preserves total information, and introduces Random Vortex Transformation (RVT), a coordinate-based encryption method meant to preserve neighbor information while making images unrecognizable to humans. Experiments train ResNet-18 and ViT on MNIST, Fashion-MNIST, and CIFAR-10 under original, vortex-encrypted, and randomly permuted data, reporting small accuracy drops for RVT and a claimed positive correlation between information loss and accuracy loss.

Significance. If the framework were valid, it would offer a theoretical basis for training on encrypted images and a general tool for image quality and encryption evaluation. The empirical observation that models can train on vortex-transformed images with modest accuracy loss is interesting, and the authors provide code and a random-permutation baseline. However, the central theoretical result is manufactured by the definition in Eq. (6), the information measure ignores pixel values, and the claimed accuracy-information correlation is contradicted by the paper's own Table I. Because these issues affect the main claims rather than presentation, the paper's significance is not established.

major comments (4)
  1. [Section III-A, Eq. (6)] Equation (6) defines the post-transformation neighbor information as m*_neig = [1 - (m_neig(old) - m_neig(new))] * m_neig(old) without derivation from Eq. (4), from a limiting argument, or from any standard information measure. In the proof of Theorem III.1, Eqs. (9)-(11), this specific algebraic form is exactly what expands into the squared term (γ1 - γ2)^2, so the theorem's conclusion that information decreases or remains unchanged is an artifact of the definition. Since every Υ value in Table I is computed using Eq. (6), the empirical validation is circular.
  2. [Section III-A, Eqs. (4)-(5)] The function m_neig(Pij, Pst) depends only on normalized Euclidean distance between coordinates and does not depend on pixel values. Consequently, M_neig(Pij) in Eq. (5) is identical for all images of the same size. Because Section V-B2 explicitly discards the pixel-value term Mpix, the reported Υ measures only coordinate displacement, not image content. Indeed, applying Eq. (5) directly to a transformed image without the modification in Eq. (6) would yield Υ = 100% for any permutation, so the reported information loss is entirely an artifact of Eq. (6).
  3. [Table I and Section V-B2] The claimed positive correlation between information-loss rate and accuracy-loss rate is not supported by the paper's own numbers. For ResNet-18, MNIST has information loss 4.75% and accuracy loss 0.31%; Fashion-MNIST has information loss 9.96% and accuracy loss 1.27%; but CIFAR-10 has the smallest information loss (2.62%) and the largest accuracy loss (5.24%). The same inversion occurs for ViT. Thus the statement that the decrease in accuracy is "roughly proportional" to the loss of information content is contradicted by Table I.
  4. [Section III-B, Principle of Verisimilitude] The "Principle of Verisimilitude" is introduced as a requirement in Section III-A and treated as a premise rather than a proven consequence. Theorem III.1 proves only a monotonicity property of the quantity defined by Eq. (6); it does not show that the original image has maximal information content in any independent sense. The conclusion is therefore an input to the framework, not a result derived from it.
minor comments (6)
  1. [Section V-A2] The text says CIFAR-10 images are "much smaller than the images in CIFAR-10" when it appears to mean much smaller than the ImageNet images in the original ResNet-18 implementation.
  2. [Section V-B1] The bullet states that MNIST-Vortex accuracy is only "0%" lower than Origin, while Table I reports decreases of 0.31% and 0.32%; the exact values should be used.
  3. [Eqs. (20)-(22)] Equations (20)-(22) use (i′, j′) for the vortex center, but Eq. (17) defines (i′, j′) as the transformed coordinates; this notational conflict should be resolved, for example by using (i0, j0) for the center.
  4. [Eq. (17)] The paper does not specify whether the coordinate map defined by Eq. (17) is injective or bijective; if two pixels can map to the same location, the transformation is not a permutation and its relation to Theorem III.1 is unclear.
  5. [Experimental results] The reported accuracies and Υ values appear to come from single runs without error bars or multiple seeds; at least a statement of variance or repeated trials is needed to support the claimed accuracy differences.
  6. [Section V-A1] The MNIST dataset is described as handwritten digits from 1 to 10, but the standard labels are 0 to 9.

Circularity Check

3 steps flagged · score 8.0 of 10

Theorem III.1's decrease is manufactured by Eq. (6), an unvalidated transformation-dependent definition; the measure is content-blind, so the claimed correlation with accuracy is not independent evidence for the information framework.

  1. self definitional [Section III-A, Eq. (6) and Section III-B, Theorem III.1]
    "Principle of verisimilitude: After various transformations, an image may make the objects within it more easily recognizable. However, we still regard the original image as having the highest information content because it is the most verisimilar. ... m∗neig(Pi′j′, Ps′t′) = [1 − (mneig(Pij, Pst) − mneig(Pi′j′, Ps′t′))] ×mneig(Pij, Pst). (6)"

    The theorem's claimed decrease is produced by Eq. (6). In the proof, the post-swap terms are expanded as (1+γ1−γ2)(1−γ1)+(1+γ2−γ1)(1−γ2) = (2−γ1−γ2)−(γ1−γ2)^2, so the inequality '≤ Mneig(Pi1j1)+Mneig(Pi2j2)' is an algebraic consequence of the definition chosen in Eq. (6), not a discovered property of image information. Eq. (6) is never derived from Eq. (4) or from any standard information measure, and the 'principle of verisimilitude' it is used to prove was already assumed as a design requirement in Section III-A. The derivation therefore reduces to its own input by construction.

  2. fitted input called prediction [Section V-B2, Table I]
    "The last row of Table I displays the remaining information content Υ(·) after the image undergoes transformations. Comparing random vortex transformations and random permutations, the decrease in accuracy is roughly proportional to the loss rate of information content."

    The 'loss rate of information content' in Table I is computed with Eq. (6), the same unvalidated definition that already forces the theorem's decrease. Accuracy loss is an external experimental measurement, but the information loss is not: it is a quantity engineered so that any coordinate swap changing distance profiles yields a positive loss. Calling the observed proportionality 'further supporting the validity of the proposed image information content measurement framework' is therefore not independent confirmation; the support relation is already baked into the measure used to compute the information-loss side of the comparison.

1 more flagged steps
  1. other [Section III-A, Eqs. (4)-(7)]
    "mneig(Pij, Pst) = 1 − 1/(1 + e^{6−18 d̃(Pij,Pst)}). (4) ... Mneig(Pij) = Σ_{s,t} mneig(Pij, Pst). (5)"

    This measure depends only on pixel coordinates: d(·,·) is Euclidean distance between positions and dmax depends only on image dimensions, while pixel values never enter Eq. (4) or Eq. (5). Consequently, for images of the same size, M(P) = Σ_{i,j} Mneig(Pij) is identical before any transformation, and the only way Υ(P*) in Eq. (7) departs from 100% is through the transformation-dependent redefinition m*neig in Eq. (6). Thus the framework does not actually measure image content; the theorem and the reported correlation are properties of an arbitrary post-transform redefinition rather than of the image information.

full rationale

The paper's central theoretical result, Theorem III.1, is circular: the 'decrease or unchanged' conclusion is an algebraic identity following from Eq. (6), where the post-swap neighbor information is defined by multiplying the old value by [1 − (old − new)]. The proof then expands this into the squared difference (γ1−γ2)^2 and presents it as a discovered law. Eq. (6) is asserted without derivation from Eq. (4), from a limiting argument, or from any standard information measure; the 'Principle of Verisimilitude' that the theorem supposedly proves is already listed as a requirement before the theorem is stated. The experimental validation is similarly non-independent: the Υ values in Table I are computed with the same Eq. (6), so the claimed proportionality between information loss and accuracy loss is not an external check of the framework. Moreover, Eqs. (4)-(5) are content-blind, depending only on coordinate distances, which confirms that the measure's behavior is driven entirely by the transformation-dependent redefinition. The Random Vortex Transformation itself has real empirical content: the accuracy results on MNIST, Fashion, and CIFAR-10 are external measurements and show that vortex-encrypted images remain trainable. But the paper's information-theoretic justification for that phenomenon is circular, so the score is high but not maximal.

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

The central derivation rests on an invented post-transform information function (Eq. 6) that encodes the intended result, plus a hand-chosen logistic kernel (Eq. 4) that ignores pixel values. The empirical correlation is then compared against this same self-defined loss, so the framework is not independently anchored.

free parameters (3)
  • logistic kernel shift 6 = 6
    Hand-chosen constant in Eq. (4) to position the Z-shaped decay; no criterion or data used to set it.
  • logistic kernel steepness 18 = 18
    Hand-chosen constant in Eq. (4) controlling how fast neighbor information decays with normalized distance.
  • number of superposed vortex transforms = 4 or 5
    Experimental choices in Section V-A that affect accuracy and remaining information; not derived from theory.
assumptions (5)
  • domain assumption An image's information content is the sum of independent pixel information and pairwise neighbor information (Eqs. 1-2).
    Additivity of information across pixels is asserted, not proven.
  • ad hoc to paper mneig(Pij,Pst) = 1 - 1/(1+exp(6-18 d_tilde)) measures information between two pixels.
    The logistic form and constants are chosen by hand; it depends only on coordinates, not pixel values.
  • ad hoc to paper Post-transform information is given by Eq. (6), m* = [1-(mneig_old - mneig_new)] * mneig_old.
    This definition is the source of the theorem's decrease and is never independently justified.
  • ad hoc to paper Principle of verisimilitude: the original image always has maximal information content.
    Assumed in Section III-A and then 'proven' from Eq. (6); it is a choice about what information means.
  • domain assumption Preserving neighbor information (as defined by this kernel) is sufficient for neural networks to recognize objects.
    Used to connect information retention to classification accuracy; not proven.

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Cite this review

Pith. "Pith review of Can Encrypted Images Still Train Neural Networks? Investigating Image Information and Random Vortex Transformation." pith.science (2026). https://pith.science/paper/JEH3SYRW

@misc{pith2026241116207,
  author       = {Pith},
  title        = {Pith review of: Can Encrypted Images Still Train Neural Networks? Investigating Image Information and Random Vortex Transformation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JEH3SYRW}},
  note         = {Machine review of arXiv:2411.16207}
}
read the original abstract

Vision is one of the essential sources through which humans acquire information. In this paper, we establish a novel framework for measuring image information content to evaluate the variation in information content during image transformations. Within this framework, we design a nonlinear function to calculate the neighboring information content of pixels at different distances, and then use this information to measure the overall information content of the image. Hence, we define a function to represent the variation in information content during image transformations. Additionally, we utilize this framework to prove the conclusion that swapping the positions of any two pixels reduces the image's information content. Furthermore, based on the aforementioned framework, we propose a novel image encryption algorithm called Random Vortex Transformation. This algorithm encrypts the image using random functions while preserving the neighboring information of the pixels. The encrypted images are difficult for the human eye to distinguish, yet they allow for direct training of the encrypted images using machine learning methods. Experimental verification demonstrates that training on the encrypted dataset using ResNet and Vision Transformers only results in a decrease in accuracy ranging from 0.3\% to 6.5\% compared to the original data, while ensuring the security of the data. Furthermore, there is a positive correlation between the rate of information loss in the images and the rate of accuracy loss, further supporting the validity of the proposed image information content measurement framework.

Figures

Figures reproduced from arXiv: 2411.16207 by the authors.

Figure 1
Figure 1. Researching and analyzing the application scenarios of image information. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Cartesian coordinate system. A. Definition In order to accurately quantify the information content of an image, we establish the following requirements: • The term “information content of an image” does not have a strict definition. In this paper, we consider it to be composed of the pixel values and the neighboring relationships between pixel points. • The neighboring information of each pixel point depends on its … view at source ↗
Figure 4
Figure 4. The neighboring information of each pixel is not solely determined by [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Design objectives of the encryption scheme. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 7
Figure 7. Figure 7: In each subplot, the left image represents the original image from [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Example of permuting pixel positions. 0 0.2 0.4 0.6 0.8 1 −30 −20 −10 0 10 20 30 d f(d) [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: A graph of a randomly generated function. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 11
Figure 11. Figure 11: The image presentation of three datasets is shown. The first and second rows are from MNIST, the third and fourth rows are from Fashion, and the [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: The curve of testing error variation. 0 5 10 15 20 Transform Times 60 65 70 75 80 85 90 95 100 Remaining Information Content(%) Information Content on MNIST Vortex Random 0 2 4 6 8 10 12 14 16 Transform Times 60 65 70 75 80 85 90 95 100 Remaining Information Content(%…
Figure 13
Figure 13. Figure 13: The curve represents the variation in information content after the image undergoes transformations. The horizontal axis represents the number [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.