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REVIEW 5 major objections 5 minor 41 references

Learning Fixed Points in Generative Adversarial Networks: From Image-to-Image Translation to Disease Detection and Localization

T0 review · 5 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read Fixed-Point GAN trains a generator to translate any medical image into a healthy one, so subtracting the two reveals diseased regions.

desk verdict A genuine, modestly-scoped extension of StarGAN with an honest but self-admittedly incomplete evaluation; the detection-by-removal idea is clever and worth engaging, but the 'state of the art' claim outruns the evidence. read the letter →

arxiv 1908.06965 v2 pith:CO3Q3JCJ submitted 2019-08-16 eess.IV cs.CV

classification eess.IVcs.CV
keywords fixed-pointtranslationimage-to-imagegenerativeadversarialnetworksweakly-supervisedlocalizationdiseasedetectionvirtualhealingmedicalimageanalysisdifferencemap
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

Fixed-Point GAN asks whether a generative network can remove an object or disease from an image while preserving everything else. The paper's central claim is that supervising same-domain translation with a conditional identity loss, paired with revised adversarial, domain classification, and cycle consistency losses for cross-domain translation, produces a generator that changes only the minimal set of pixels required for translation. If that holds, any medical image, diseased or healthy, can be mapped to a healthy image, and subtracting the two exposes the disease. The paper reports that this fixed-point translation improves multi-domain image-to-image translation on faces and outperforms weakly-supervised localization and anomaly-detection baselines for brain lesions and pulmonary embolism using image-level labels only.

What carries the argument

The load-bearing object is fixed-point translation learning. It adds a conditional identity loss $\mathcal{L}_{id} = \mathbb{E}_{x, c_x}[\|G(x, c_x)-x\|_1]$ that penalizes any change when the target domain is the source domain, and it revises the adversarial, domain classification, and cycle consistency losses so that same-domain translations are included; the cycle loss $\mathcal{L}_{cyc} = \mathbb{E}_{x, c_x}[\|G(G(x, c_x), c_x)-x\|_1]$ forces same-domain round trips to return the input. The generator also outputs a residual delta map that is added to the input before a $\tanh$ activation, which makes it structurally easier to leave the image unchanged. Together these components enforce that only disease- or attribute-related pixels are modified.

What would settle it

Inject a synthetic lesion of known location and size into a healthy MRI, translate the image to the healthy domain, and inspect the difference map; if noticeable differences appear outside the injected lesion, or if healthy anatomy is modified, the minimal-transformation assumption is false.

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Extended reading notes

Core claim

The discovery is a training scheme that endows a GAN with fixed-point translation: when the target domain equals the source domain, the generator is trained to behave as identity, $G(x, c_x) \approx x$, and when the domains differ, it is trained through losses that also cover same-domain pairs, so it learns minimal transformations that avoid touching unrelated content. In the 'virtual healing' application, the generator always translates toward the healthy domain, and the absolute difference between the input and the generated healthy image—the difference map—is used to detect and localize disease. This yields a weakly supervised detection and localization pipeline that needs only image-level healthy/diseased labels.

Load-bearing premise

The pipeline assumes the generator changes only disease-related pixels and preserves all other image content, so the difference between a scan and its healthy translation marks exactly the disease.

Editorial extensions

If this is right

  • Healthy images pass through the generator nearly unchanged, so their difference maps are clean and rarely trigger false positives.
  • Cross-domain translations, such as changing hair color or removing a lesion, are regularized to modify only task-relevant pixels, which improves translation quality.
  • Disease detection and localization can be carried out with only image-level labels by applying color quantization and connected-component analysis to the difference map.
  • The same fixed-point training transfers from natural images to brain MRI and CT pulmonary angiography without architectural changes.
  • Because the target domain is specified at inference and the source domain is not needed, the method works for images with unknown health status.

Reading between the lines

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

  • The authors note that large objects such as sunglasses and brain lesions are only partially removed, so the difference map is a localization signal rather than a segmentation mask; complete removal would be needed for pixel-level segmentation, which remains open.
  • A natural extension is to feed the difference maps back as pseudo-labels to train a supervised segmentation network, potentially improving boundary accuracy.
  • Since the conditional identity loss applies only when target equals source, the trained generator is source-domain-independent by construction; this suggests the 'translate to healthy' operation could be applied to any input modality without changing the inference procedure.
  • Distribution shift is a testable risk: diseases or artifacts not seen during training could make the generator either fail to remove them or hallucinate changes; a healthy-only calibration set would reveal this failure mode.
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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

5 major / 5 minor

Summary. The paper introduces Fixed-Point GAN, an extension of StarGAN that trains a single generator for both cross-domain and same-domain translations. The fixed-point training scheme adds a conditional identity loss for same-domain translation, revises the adversarial and domain-classification losses to cover both same- and cross-domain outputs, and applies cycle consistency to both. The generator is implemented with a residual/delta architecture. The authors evaluate multi-domain translation on CelebA and use the difference between an input image and its translation to the healthy domain for weakly supervised disease detection and localization on BRATS 2013 brain MRI and a pulmonary embolism CTPA dataset, comparing against StarGAN, CAM, ResNet-50-CAM, f-AnoGAN, and Alex et al. The central claim is that the proposed training yields minimal, fixed-point translations, leading to state-of-the-art image translation and superior disease detection/localization with only image-level labels.

Significance. The idea is appealing: a GAN that can 'virtually heal' an image and reveal disease by subtraction would make weakly supervised localization practical, since it requires only image-level labels. The paper includes a useful ablation (Tab. 4) separating the delta-map and fixed-point-training contributions, and the fixed-point component clearly drives most of the gain. The authors also make the implementation publicly available. However, the strongest claims ('outperforms the state of the art', 'surpasses predominant weakly-supervised localization methods') are not fully supported by the evidence as presented, because the minimal-transformation assumption is not quantitatively verified, comparisons are made at non-commensurate operating points, and no uncertainty estimates are given. With revisions that tighten these claims and add targeted analyses, the contribution would be a valuable advance.

major comments (5)
  1. [Sec. 4.2, Sec. 4.4, Eq. (4), Eq. (5)] The load-bearing minimal-transformation premise is stated but not enforced or quantitatively verified. Eq. (5) penalizes L1 only for same-domain translation, and Eq. (4) cycle consistency penalizes round-trip error; neither prevents the generator from modifying normal structures as long as the reverse map restores them. The paper's own observations—'neither StarGAN nor Fixed-Point GAN can completely remove large objects, like sunglasses or brain lesions' (Sec. 4.4) and 'our method is outperformed at the low false positive range' on real BRATS (Sec. 4.2)—show that the difference map is not guaranteed to be confined to disease. Since image-level detection uses the maximum of the difference map and localization uses connected-component analysis, any residual normal-structure change contributes to false positives. The abstract's unqualified superiority claim should be replaced with a claim conditional on the minimality of the learned transformation, and the paper should report a direct measure of preservation, e.g., the magnitude of the difference map in regions known to be healthy or the per-pixel specificity outside the lesion ground truth.
  2. [Sec. 4.2, Tab. 4, Fig. 4] The empirical support lacks uncertainty quantification and significance testing. AUC, FROC sensitivity, and IoU are reported as point estimates (e.g., mean IoU 0.2609±0.1283 vs 0.3483±0.2420, AUC 0.9668 vs 0.8832), with no confidence intervals or tests, and the test sets are small (6 real BRATS patients; 127 unique PEs). Many reported gaps, especially those with overlapping standard deviations, could easily arise from noise. Report bootstrap confidence intervals or significance tests, and show error bars on the ROC/FROC curves.
  3. [Sec. 4.2, f-AnoGAN comparison] The evaluation protocol for f-AnoGAN is selected after inspecting test performance: 'we use the average activation of difference maps as the detection score, because we find it more effective than using the maximum activation ... and also more effective than the anomaly scores proposed in the original work.' Choosing the scoring function based on the test set invalidates the comparison as a fair head-to-head. State the scoring rule before evaluation, or report all considered scores with a multiple-comparison correction, and apply the same selection procedure to all methods.
  4. [Sec. 4.2, Fig. 4b, Fig. 4d, Fig. 5b] The head-to-head claim against ResNet-50-CAM is made at different operating points: Fixed-Point GAN achieves 84.5% sensitivity at 1 false positive per image, while ResNet-50-CAM achieves 60% at 0.037 false positives per image. These numbers are not comparable. Report sensitivity for all methods at a common false-positive rate, or use a partial-area FROC measure over the same FP range; the same issue appears in the real-image FROC (Fig. 4d) and the PE FROC (Fig. 5b).
  5. [Sec. 4.1, Eq. (5), Tab. 3] The same-domain L1 comparison is partly by construction. Eq. (5) directly minimizes ||G(x,c_x)-x||_1, and Tab. 3 evaluates exactly this quantity. The fact that Fixed-Point GAN has lower same-domain L1 than StarGAN is therefore a sanity check of the loss rather than independent evidence of translation quality. The paper should present same-domain L1 as a training objective check, and use the independently trained classifier (Tab. 2) and visual inspection as the primary translation-quality evidence; ideally also report a perceptual or human-evaluation metric.
minor comments (5)
  1. [Abstract, Sec. 4.2, Sec. 4.4] The abstract should be tempered to acknowledge the low-false-positive-range underperformance on real BRATS and the partial-removal failures on large objects, both of which are disclosed in the body of the paper.
  2. [Sec. 3, Appendix Implementation Details] The main text defines the adversarial loss with the standard log form in Eq. (1), while the appendix states that the actual objective is the Wasserstein loss with gradient penalty in Eq. (8). Clarify which objective is used and keep the notation consistent throughout.
  3. [Sec. 4.3] For the PE dataset, 'localization' is defined as correct image-level classification of the candidate patch, not as lesion-level localization via connected components; the text should describe this as candidate-level detection rather than localization to avoid overstating the result.
  4. [Tab. 2] Classification accuracy on generated images is an indirect quality measure and can be biased because the classifier was trained on real images; consider reporting an additional metric, such as a classifier trained on generated images or a perceptual similarity score.
  5. [Sec. 4.3, Implementation Details] There is a duplicated word in 'sensitivity levels of of 88.9%' in Sec. 4.3, and the code URL is given as https://github.com/jlianglab/Fixed-Point-GAN in the abstract but as http://github.com/jlianglab/Fixed-Point-GAN in the implementation details; these should be unified.

Circularity Check

1 steps flagged · score 3.0 of 10

Same-domain L1 comparison is the trained objective itself; core detection/localization benchmarks remain externally grounded.

  1. fitted input called prediction [Sec. 4.1, Eq. (5), Table 3]
    "Lid = { 0, c =cy ; Ex,c[||G(x,c )−x||1], c =cx (5) ... Tab. 3 presents a quantitative comparison between StarGAN and Fixed-Point GAN for the task of same-domain image translation. We use the image-level L1 distance between the input and generated images as the performance metric."

    The metric reported in Table 3 is exactly the quantity minimized by the conditional identity loss in Eq. 5: for same-domain translation (c = cx), the loss is E||G(x,c)-x||_1. Fixed-Point GAN is trained to minimize this L1 distance, whereas StarGAN is not. Reporting a lower same-domain L1 distance for Fixed-Point GAN is therefore an optimization outcome, not an independent prediction of superiority. This particular comparison is forced by construction. It does not, however, make the central disease detection/localization claims circular, because those are evaluated with AUC, FROC, and IoU against external baselines such as ResNet-50-CAM and f-AnoGAN, and cross-domain translation quality is judged by an independently trained 40-attribute classifier.

full rationale

The paper's central claims are mostly self-contained and externally benchmarked: cross-domain image-to-image translation is compared against StarGAN using classification accuracy of an independently trained CelebA classifier (Table 2); brain-lesion and pulmonary-embolism detection/localization are evaluated against ResNet-50-CAM, f-AnoGAN, Alex et al., and StarGAN using ROC AUC, FROC, and IoU on BRATS 2013 and a CTPA dataset. These results do not reduce to the training losses. The one clear circular element is the same-domain translation comparison in Table 3: the image-level L1 distance there is the very objective minimized by Eq. 5, so the reported improvement over StarGAN is expected by construction rather than a discovered property. Separately, the paper's load-bearing premise that the generator performs a minimal, disease-only transformation is not guaranteed by the losses; the paper itself concedes in Sec. 4.4 that large objects such as sunglasses and brain lesions are only partially removed, and in Sec. 4.2 that on real BRATS images the method is outperformed at the low false-positive range. These are correctness risks and limitations, not circularity, but they temper the abstract's unqualified 'outperforms' and 'surpasses' wording. Overall, with one-by-construction comparison and otherwise independent benchmarks, a score of 3 is appropriate.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The method's success hinges on the generator learning a minimal transformation and on the difference map being interpretable as disease evidence. Several hyperparameters, especially the identity loss weight per dataset, are tuned empirically. No new physical entities are introduced.

free parameters (8)
  • lambda_id (identity loss weight) = 10 (CelebA), 0.1 (BRATS 2013), 1 (PE)
    Per-dataset tuning of the central new loss component; the value changes the strength of same-domain preservation and is not derived from any principle. Reported in Appendix Implementation Details.
  • lambda_cyc = 10
    Cycle consistency weight, inherited from StarGAN, fixed across datasets.
  • lambda_domain = 1
    Domain classification loss weight, inherited from StarGAN.
  • lambda_gp = 10
    Gradient penalty coefficient for the Wasserstein adversarial loss, fixed for all experiments.
  • learning rate = 1e-4
    Adam learning rate for both generator and discriminator, fixed across experiments.
  • training iterations = 200K (CelebA, PE), 300K (BRATS 2013)
    Chosen to 'generate good quality images', not otherwise justified.
  • connected component area threshold = 10 pixels
    Lesion candidate area threshold used for localization evaluation; chosen without sensitivity analysis.
  • delta map (residual) architecture = tanh(G(x,c) + x)
    Generator predicts a residual added to the input; this modeling choice is shared with [4] and is part of the method.
assumptions (5)
  • domain assumption A diseased image differs from its healthy counterpart by a localized, removable visual pattern such that subtracting the generated healthy image reveals the disease.
    This is the core premise of detection by removal, stated in Sec. 4.2; the difference map is the detection and localization signal.
  • domain assumption The generator can be trained to perform a minimal transformation, changing only disease-related pixels, without altering unrelated structures.
    Fixed-point translation learning (conditional identity loss and cycle consistency) is designed to enforce this, but the paper acknowledges in Sec. 4.4 that large objects are only partially removed, so the assumption holds only approximately.
  • domain assumption Image-level labels (healthy vs. diseased) are accurate and sufficient for training; the network does not require lesion-level annotations.
    The method relies on image-level labels from BRATS and PE datasets; the paper states only image-level annotations are used.
  • domain assumption Cycle consistency has a feasible inverse mapping for the translation tasks.
    The cycle consistency loss assumes the generator can translate back and forth; if the task is not invertible, the loss may not converge to a useful solution.
  • standard math Wasserstein GAN with gradient penalty provides a stable adversarial training objective.
    The paper uses the WGAN-GP loss (Appendix Implementation Details) as a standard tool; not proven here.

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Cite this review

Pith. "Pith review of Learning Fixed Points in Generative Adversarial Networks: From Image-to-Image Translation to Disease Detection and Localization." pith.science (2026). https://pith.science/paper/CO3Q3JCJ

@misc{pith2026190806965,
  author       = {Pith},
  title        = {Pith review of: Learning Fixed Points in Generative Adversarial Networks: From Image-to-Image Translation to Disease Detection and Localization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CO3Q3JCJ}},
  note         = {Machine review of arXiv:1908.06965}
}
read the original abstract

Generative adversarial networks (GANs) have ushered in a revolution in image-to-image translation. The development and proliferation of GANs raises an interesting question: can we train a GAN to remove an object, if present, from an image while otherwise preserving the image? Specifically, can a GAN "virtually heal" anyone by turning his medical image, with an unknown health status (diseased or healthy), into a healthy one, so that diseased regions could be revealed by subtracting those two images? Such a task requires a GAN to identify a minimal subset of target pixels for domain translation, an ability that we call fixed-point translation, which no GAN is equipped with yet. Therefore, we propose a new GAN, called Fixed-Point GAN, trained by (1) supervising same-domain translation through a conditional identity loss, and (2) regularizing cross-domain translation through revised adversarial, domain classification, and cycle consistency loss. Based on fixed-point translation, we further derive a novel framework for disease detection and localization using only image-level annotation. Qualitative and quantitative evaluations demonstrate that the proposed method outperforms the state of the art in multi-domain image-to-image translation and that it surpasses predominant weakly-supervised localization methods in both disease detection and localization. Implementation is available at https://github.com/jlianglab/Fixed-Point-GAN.

Figures

Figures reproduced from arXiv: 1908.06965 by the authors.

Figure 1
Figure 1. [Better viewed on-line in color and zoomed in for details] Comparing our Fixed-Point GAN with StarGAN [ [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. [Better viewed on-line in color and zoomed in for details] Comparing Fixed-Point GAN with the state-of-the-art image-to-image [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Fixed-Point GAN training scheme. Similar to StarGAN, our discriminator learns to distinguish real/fake images and classify [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Comparing Fixed-Point GAN with StarGAN, f-AnoGAN, GAN-based brain lesion detection method by Alex, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Comparing Fixed-Point GAN with StarGAN, f-AnoGAN, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Now, all humor aside, if a GAN can remove diseases [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: [Continued from Fig [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: [Continued from Fig [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: [Continued from Fig [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: [Continued from Fig [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Pulmonary Embolism (PE) detection and localization (longitudinal view). Notice the images are from the same candidates as [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Pulmonary Embolism (PE) detection and localization (cross-sectional view). Notice the images are from the same candidates as [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: [Continued from Fig [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: [Continued from Fig [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: As discussed in Sec. 4.3, f-AnoGAN [24] fails to produce good quality images for the PE dataset, resulting in noisy difference maps. Hence, performs miserably on detection and localization tasks for the PE dataset [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

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    no change

    3 Appendix Fig. 6: Now, all humor aside, if a GAN can remove diseases completely from images, it will offer an ideal method for segmenting all diseases, an ambitious goal that has yet to be achieved. Nevertheless, our method is still of great clinical significance in computer-a...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.