Pith. sign in

REVIEW 2 major objections 5 minor 74 references

Post-Training Augmentation Invariance

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that a frozen pretrained encoder can be made approximately invariant to augmentations by appending a one-hidden-layer MLP adapter trained with either of two optimal-transport losses, while leaving the original latent…

desk verdict A solid empirical paper with a genuinely useful framing: a simple anchored-MSE adapter recovers large invariance gaps on frozen features, but the near-isometry claim as written is likely in-sample and should be verified on held-out data. read the letter →

arxiv 2505.11702 v3 pith:UD2KRHFF submitted 2025-05-16 cs.LG stat.ML

Keenan Eikenberry , Lizuo Liu , Yoonsang Lee This is my paper · ORCID
classification cs.LGstat.ML MSC 68T0762H2049Q22
keywords post-trainingaugmentationinvarianceaugmentedencodersadapternetworksoptimaltransportWassersteincorrelationMarkov-Wassersteinkernelsfrozenpretrainedmodelsstructurepreservation
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

The paper sets out to prove that a pretrained encoder can be given new invariance properties after training, without changing the encoder's weights or damaging its existing feature space. The proposed mechanism is a lightweight one-hidden-layer MLP adapter appended to the frozen latent space, trained with one of two optimal-transport losses: Markov-Wasserstein (MaWa) minimization, an anchored mean-squared error, or Wasserstein correlation (WaCo) maximization. On STL10 with DINOv2 features, the MaWa-trained adapter lifts classification accuracy on arbitrarily rotated images from 71.22% to 94.74%, and on heavily noised images from 58% to 86%, while preserving pairwise distances in the original latent space almost exactly. The paper also defines augmented encoders and a formal notion of post-training augmentation invariance, and it argues that contrastive and Hilbert-Schmidt independence losses fail at this task because they corrupt the original latent geometry.

What carries the argument

The load-bearing object is the augmented encoder, a Markov-Wasserstein kernel $E_T(x)$ that returns the distribution of encoded versions of $x$ under a family of augmentations; it turns augmentation into a probabilistic encoding process. The main training mechanisms are two losses: MaWa, an anchored mean-squared error that pulls encoded augmented views toward their frozen clean embeddings while anchoring the identity on non-augmented inputs (derived as minimization of a Markov-Wasserstein metric), and WaCo, which maximizes the Wasserstein correlation of the joint distribution induced by the augmented encoder, forcing augmented views of an input to be encoded close together without needing an identity anchor. A supporting diagnostic is the aligned collision rate, which measures whether augmented features remain separable by class after a best rigid alignment; it predicts whether MaWa will succeed or face competing constraints.

What would settle it

Take a self-supervised encoder with near-zero aligned collision rate for rotations, train a MaWa adapter, and check both rotated classification accuracy and the $R^2$ of the original pairwise-distance scatter; if either fails to reproduce the paper's reported regime (accuracy near clean accuracy and $R^2$ close to 1), the central claim is contradicted. A sharper disconfirming case would be a low-collision encoder where MaWa nevertheless collapses or corrupts the clean latent space.

Watch

Extended reading notes

Core claim

The central discovery is that augmentation invariance can be cleanly separated from representation learning: instead of retraining or fine-tuning the encoder, one reshapes its latent space with a small adapter, provided the augmentation-induced displacement is globally coherent. The paper formalizes this through augmented encoders, probabilistic encoders that map each input to the distribution of its augmented and encoded views, and through the definition of $(t,\mu_X,F,V)$-invariance, which requires the composite $E_\theta \circ F$ to ignore collision-free augmentations while agreeing with $F$ up to an admissible structure-preserving map $V$. On feature spaces in which augmented views land near their clean counterparts after a global rigid alignment (low aligned collision rate), the MaWa objective achieves near-isometric behavior, with $R^2=0.96$ and NRMSD $=0.02$ for rotations, and large gains in augmented classification accuracy; the WaCo objective is competitive and can additionally reduce dimensionality. The paper reports that where that coherent-displacement condition fails, as on supervised ResNet50 features, MaWa collapses, and it flags this as a structural limitation in its Section 5.1. The paper further shows that SimCLR and HSIC objectives, two natural candidate losses, produce poor invariance and badly corrupt the original latent point cloud.

Load-bearing premise

The load-bearing premise is that a single global adapter can correct the augmentation-induced displacement of the frozen latent space: after a rigid alignment, augmented features of each class must still sit closer to their own class than to any other, so the MaWa objective faces no competing constraints; the paper's own tables show this condition fails for supervised ResNet50 features.

Editorial extensions

If this is right

  • Pretrained encoders can be adapted to new augmentations using only unlabeled samples from the original distribution, with no fine-tuning and no access to the training pipeline.
  • Because the adapter is near-isometric on the clean distribution, downstream tasks built on the original features should behave essentially unchanged, while augmented inputs become usable.
  • The distinction between MaWa and WaCo gives a practical choice: use MaWa for maximal invariance and structure preservation, and WaCo when dimensionality reduction is also wanted or when collision rates are high.
  • Augmentations with near-zero aligned collision rates are essentially free wins for the adapter, whereas augmentations with high residual collision rates require the unanchored WaCo loss or a different architectural strategy.
  • Treating adversarial perturbations as augmentations may yield adversarially robust latent spaces without adversarial training, a direction the paper identifies.

Reading between the lines

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

  • The aligned collision rate could serve as a cheap pre-training diagnostic: for a new encoder and augmentation, compute it before training, and choose MaWa only when the aligned rate is near zero.
  • Because the MaWa collapse on supervised ResNet50 happens without any architectural change, the failure mode is likely inherent to anchored objectives; unanchored or class-conditional realignment may be needed for feature spaces where augmentations locally entangle classes.
  • A natural stress test is an augmentation that preserves each input's class on average but permutes local neighborhoods (e.g., rotating a subset of classes while leaving others fixed); the framework as stated would predict higher aligned collision rates and graceful degradation from MaWa to WaCo.
  • The near-isometry finding suggests that transport-based dependence measures track geometric structure that contrastive or kernel independence losses discard, which may point to principled structure-preserving objectives for other post-training modifications beyond invariance.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper formalizes the problem of post-training augmentation invariance, in which a lightweight adapter E_theta is appended to a frozen pretrained encoder F so that the composite E_theta∘F becomes approximately invariant to specified augmentations while preserving the metric structure of F's latent space. Two training objectives are proposed: Markov-Wasserstein (MaWa) minimization, an anchored MSE loss that pulls augmented features toward their clean counterparts, and Wasserstein correlation (WaCo) maximization, a transport-based dependence objective. The experiments on STL10 and TinyImageNet with DINOv2, SwAV, R-DINO, CLIP, and a supervised ResNet50 show large gains in rotation and noise robustness (for example, DINOv2 rotation accuracy rises from 71.22% to 94.74% with a nonlinear classifier), whereas SimCLR and HSIC objectives degrade the latent space. The paper also introduces collision-rate diagnostics, reports an honest failure case on supervised ResNet50, and makes code available.

Significance. The empirical findings are substantial and potentially useful: the proposed method is simple, keeps the backbone frozen, and works across several modern self-supervised feature spaces, which is a practically attractive combination. The formal definitions of augmented encoders and (t,µ_X,F,V)-invariance provide a reusable vocabulary, and the derivation of the MaWa loss from the Markov-Wasserstein metric is a nice conceptual bridge. The honest treatment of the ResNet50 failure via collision rates, the systematic comparison against SimCLR and HSIC, and the public code are strengths. The main unresolved issue is that the signature claim of near-isometric structure preservation is not yet verified on held-out data; as written, the reported R² and NRMSD values may partly restate the anchor term in the training loss when computed on training points. If the structure-preservation claim is confirmed on a proper held-out split, this would be a solid contribution to the adapter and invariance literature.

major comments (2)
  1. [4.1.2 (Eqs. 34-39, Tables 2-3)] The structure-preservation statistics are computed on pairs from supp(µ_X), but the paper never states whether supp(µ_X) is the training split, the test split, or a pooled set. This matters because the MaWa loss (Eq. 21) explicitly anchors E_θ(F(x_i)) to F(x_i) on the training batch; with roughly 3.1M parameters and only 5,000 clean training images, the adapter can memorize the identity on those points. If Tables 2-3 are computed on the training distribution, the reported R²=0.96 and NRMSD=0.02 are largely a restatement of the first term of the loss rather than evidence that the learned map is nearly isometric on new inputs. Please state the data split explicitly and recompute the structure metrics on held-out clean data (e.g., the STL10 test set) to substantiate the abstract's claim that E_theta acts 'nearly isometrically' on the latent distribution.
  2. [4.1.1 (Invariance Evaluation)] The evaluation protocol does not specify which data split is used for training the adapter, for training the classifier C, and for computing the augmented accuracy. If the classifier is trained and evaluated on the same augmented data, or if the adapter is trained and evaluated on the same clean data, the reported accuracy gains could partly reflect memorization rather than true invariance. Please describe the exact protocol (for example, adapters and classifiers trained on the STL10 train split and augmented accuracy computed on the test split) and confirm that the EC baseline follows the same split so that the comparisons in Tables 1, 6, and the appendix are interpretable as generalization results.
minor comments (5)
  1. [Section 4.2 and all tables] All tables report point estimates without seeds, confidence intervals, or error bars; given the stochasticity of MLP training, please add at least a few seeds (with means and standard deviations) for the main classification and structure-preservation tables, or explicitly state that each result is from a single run.
  2. [Eq. (21) and Eq. (25)] There are stray closing parentheses in the augmented term, which currently reads '∥(Eθ◦F)(t(ak_i,xi))−F(xi)∥2^2' with an extra ')' before the minus sign; please correct the notation.
  3. [Footnote 1 and Remark 3.6] The paper acknowledges that the experimental WaCo results use the sliced variant SWaCo and that the theoretical connection between SWC and WC maximization is left open; this caveat should be stated more prominently in the contributions section so readers do not infer that the exact WC objective is what was trained.
  4. [Section 4.2.4 (Collision Rate Analysis)] The claim that the aligned collision rate 'predicts the feasibility of MaWa minimization' is based on five models; this is an interesting observation, but it should be presented as suggestive rather than as a validated predictor, and the small sample size should be acknowledged.
  5. [Section 4.2.5 (WaCo for Dimensionality Reduction)] The MNIST dimensionality-reduction experiment is evaluated only through t-SNE visualizations; please add a quantitative metric (e.g., classification accuracy on the reduced space or a distance-preservation statistic) to support the claim that the WaCo loss performs dimensionality reduction while preserving structure.

Circularity Check

0 steps flagged · score 2.0 of 10

No established circularity: the main invariance gains are measured on augmented data by classifiers trained on clean data, with only minor self-citation and an unspecified structure-evaluation split, so the paper is not substantially circular.

full rationale

Walking the claimed derivation chain, the central empirical claims do not reduce to their inputs by construction. The invariance result is evaluated in Section 4.1.1 by training a classifier C on non-augmented data and then measuring accuracy on augmented data; this is an external evaluation whose success is not baked into the MaWa or WaCo loss. The MaWa loss (Eq. 21) is explicitly presented as an anchored MSE with one term that 'enforces preservation of F' and another that enforces augmentation invariance, so the paper is transparent that structure preservation is an objective, not a discovered consequence. The one place where circularity could hide is the structure-preservation evaluation in Section 4.1.2 (Eqs. 34-38): the statistics are defined over supp(mu_X) without stating whether that support is the training set, the test set, or a held-out split. If supp(mu_X) were the same batch used in Eq. 21, the reported R2=0.96 and NRMSD=0.02 would largely restate the anchor term of the loss on that batch; however, the paper never asserts that the evaluation is in-sample, and the classification numbers are consistent with a held-out protocol. This is therefore a missing-support ambiguity rather than an exhibited reduction, and it is weighed here as a transparency gap rather than a scored circular step. The only self-reference is Eikenberry (2023), cited in Appendix A for standard measure-theoretic facts about Markov-Wasserstein kernels and for an isometric isomorphism; those facts are not the load-bearing empirical claim and the paper re-develops the main definitions itself. The WaCo, SimCLR, HSIC, and collision-rate comparisons provide independent anchors and falsifiable patterns. No circular derivation chain was established; the score of 2 reflects the minor self-citation and the unresolved evaluation-split ambiguity, not a demonstrated circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

Most of the mathematical machinery (Wasserstein spaces, disintegration, sliced distances) is standard and not counted as free. The central empirical claims rest on domain assumptions about the geometry of pretrained feature spaces and on hyperparameters chosen by hand (adapter width, augmentation sample count). No new physical entities are introduced. The sliced Wasserstein proxy is an acknowledged unproved assumption for the WaCo loss.

free parameters (4)
  • Augmentation samples per input s = 3
    Used in the MaWa and WaCo losses (Eqs. 21 and 28) and sets the anchor-to-augmentation weight ratio. Chosen by hand in Appendix B, not tuned per dataset.
  • Adapter hidden width = 4096
    One-hidden-layer MLP width for all adapters and nonlinear classifiers (Appendix B). Chosen by hand and central to the expressivity of E_theta.
  • Training schedule = batch 256, epochs 100, lr 1e-3, weight decay 1e-4, cosine minimum 4e-4
    Default hyperparameters in Table 12. The paper reports comparable results over a range but gives no ablation or seed variance.
  • WaCo reduced dimension d/4 = 384 to 96, 512 to 128, 2048 to 512
    Used for WaCo dimensionality-reduction experiments in Section 4.2.5 and Appendix B. Selected by hand, not fitted.
assumptions (5)
  • standard math Finiteness and regularity assumptions for Wasserstein spaces and existence of disintegrations (Appendix A)
    Background probability and optimal transport results used throughout Sections 2 and 3.
  • domain assumption For self-supervised feature spaces and the tested augmentations, aligned collision rates are low enough for a global adapter to succeed
    Empirically checked in Section 4.2.4, but assumed by the method; fails for ResNet50, which the paper acknowledges in Section 5.1.
  • domain assumption A one-hidden-layer MLP of width 4096 can represent the required augmentation-correction map
    Architecture is fixed in Appendix B; no capacity analysis is provided.
  • ad hoc to paper Sliced Wasserstein correlation maximization is a suitable proxy for Wasserstein correlation maximization
    Explicitly acknowledged as lacking rigorous justification in the Section 3.3.2 footnote; used for all WaCo experiments.
  • domain assumption Classifiers trained on non-augmented features transfer to augmented features after E_theta
    This is what the invariance evaluation measures in Section 4.1.1; no formal guarantee is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Post-Training Augmentation Invariance." pith.science (2026). https://pith.science/paper/UD2KRHFF

@misc{pith2026250511702,
  author       = {Pith},
  title        = {Pith review of: Post-Training Augmentation Invariance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UD2KRHFF}},
  note         = {Machine review of arXiv:2505.11702}
}
abstract

This work develops a framework for post-training augmentation invariance, in which our goal is to add invariance properties to a pretrained network without altering its behavior on the original, non-augmented input distribution. We define this notion precisely and additionally introduce augmented encoders, which are probabilistic encoders that formalize augmentation-based encoding processes and that serve as our fundamental object of study. We introduce two losses for augmented encoders, namely, Markov-Wasserstein minimization and Wasserstein correlation maximization, and we demonstrate empirically that both losses can be used to train lightweight, one-hidden-layer MLP adapter networks $E_{\theta}$ that, when appended to the latent space of a pretrained network $F$, do indeed lead to (approximate) post-training augmentation invariance. For example, on STL10 with $F=\text{DINO}$ features, the composite network $C\circ E_{\theta}\circ F$, where $C$ is a linear classifier and where $E_{\theta}$ is one of our proposed adapter networks, achieves 94% classification accuracy on arbitrarily rotated images, whereas a network of the form $C\circ F$ without the adapter $E_{\theta}$ drops to 71% accuracy. Similarly, we can boost noise-invariant classification results from 58% up to 86%. Significantly, we obtain these results with no fine-tuning (the weights of $F$ remain frozen throughout), and our methods introduce little corruption to the original features, since $E_{\theta}$ acts nearly isometrically on the non-augmented latent distribution. In contrast, we show that adapter networks trained with alternative candidate losses, specifically SimCLR and HSIC maximization, produce uncompetitive classification results and fundamentally corrupt the original latent space. Code available at https://github.com/keenan-eikenberry/augmentation_invariance

Figures

Figures reproduced from arXiv: 2505.11702 by the authors.

Figure 1
Figure 1. Structure preservation for MaWa rotation-invariant encoder on DINOv2 features. [PITH_FULL_IMAGE:figures/full_fig_p023_1.png] view at source ↗
Figure 2
Figure 2. Structure preservation for WaCo rotation-invariant encoder on DINOv2 features. [PITH_FULL_IMAGE:figures/full_fig_p025_2.png] view at source ↗
Figure 3
Figure 3. Structure preservation for SimCLR rotation-invariant encoder on DINOv2 fea [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Structure preservation for HSIC rotation-invariant encoder on DINOv2 features. [PITH_FULL_IMAGE:figures/full_fig_p028_4.png]
Figure 5
Figure 5. Figure 5: t-sne visualizations of the original STL10 DINOv2 latent distribution F♯µX compared to (Eθ ◦ F)♯µX for encoders trained for noise invariance with one of the four losses. 64 [PITH_FULL_IMAGE:figures/full_fig_p064_5.png]
Figure 6
Figure 6. Figure 6: t-sne visualizations of MNIST plus 90-degree rotated digits for Eθ with final dimension d = 64 trained on the WaCo loss with T = {idX}, which does dimensionality reduction (Dim) only, versus the case of T = {idX, t}, which does Dim plus invariance (Inv) to t, where t h…

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

74 extracted references · 40 canonical work pages

  1. [1]

    Gradient flows: in metric spaces and in the space of probability measures

    Luigi Ambrosio, Nicola Gigli, and Giuseppe Savar \'e . Gradient flows: in metric spaces and in the space of probability measures. Springer Science & Business Media, 2008

    2008

  2. [2]

    Wasserstein generative adversarial networks

    Martin Arjovsky, Soumith Chintala, and L \'e on Bottou. Wasserstein generative adversarial networks. In International conference on machine learning, pp.\ 214--223. PMLR, 2017

    2017

  3. [3]

    Learning representations by maximizing mutual information across views

    Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. Advances in neural information processing systems, 32, 2019

    2019

  4. [4]

    Wasserstein distributional robustness of neural networks

    Xingjian Bai, Guangyi He, Yifan Jiang, and Jan Obloj. Wasserstein distributional robustness of neural networks. Advances in Neural Information Processing Systems, 36: 0 26322--26347, 2023

    work page 2023

  5. [5]

    Mutual information neural estimation

    Mohamed Ishmael Belghazi, Aristide Baratin, Sai Rajeshwar, Sherjil Ozair, Yoshua Bengio, Aaron Courville, and Devon Hjelm. Mutual information neural estimation. In International conference on machine learning, pp.\ 531--540. PMLR, 2018

    2018

  6. [6]

    Lower bounds on adversarial robustness from optimal transport

    Arjun Nitin Bhagoji, Daniel Cullina, and Prateek Mittal. Lower bounds on adversarial robustness from optimal transport. Advances in Neural Information Processing Systems, 32, 2019

    work page 2019

  7. [7]

    Measure theory, volume 1

    Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007

    2007

  8. [8]

    Sliced and radon wasserstein barycenters of measures

    Nicolas Bonneel, Julien Rabin, Gabriel Peyr \'e , and Hanspeter Pfister. Sliced and radon wasserstein barycenters of measures. Journal of Mathematical Imaging and Vision, 51: 0 22--45, 2015

    2015

Show all 74 references
  1. [9]

    Unidimensional and evolution methods for optimal transportation

    Nicolas Bonnotte. Unidimensional and evolution methods for optimal transportation. PhD thesis, Universit \'e Paris Sud-Paris XI; Scuola normale superiore (Pise, Italie), 2013

    2013

  2. [10]

    From optimal transport to generative modeling: the vegan cookbook

    Olivier Bousquet, Sylvain Gelly, Ilya Tolstikhin, Carl-Johann Simon-Gabriel, and Bernhard Schoelkopf. From optimal transport to generative modeling: the vegan cookbook. arXiv preprint arXiv:1705.07642, 2017

    2017 arXiv

  3. [11]

    Unsupervised learning of visual features by contrasting cluster assignments

    Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning of visual features by contrasting cluster assignments. Advances in neural information processing systems, 33: 0 9912--9924, 2020

    2020

  4. [12]

    Emerging properties in self-supervised vision transformers

    Mathilde Caron, Hugo Touvron, Ishan Misra, Herv \'e J \'e gou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pp.\ 9650--9660, 2021

    2021

  5. [13]

    A simple framework for contrastive learning of visual representations

    Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International conference on machine learning, pp.\ 1597--1607. PmLR, 2020

    2020

  6. [14]

    Disintegration and bayesian inversion via string diagrams

    Kenta Cho and Bart Jacobs. Disintegration and bayesian inversion via string diagrams. Mathematical Structures in Computer Science, 29 0 (7): 0 938--971, 2019

    2019

  7. [15]

    Pointless learning

    Florence Clerc, Vincent Danos, Fredrik Dahlqvist, and Ilias Garnier. Pointless learning. In Foundations of Software Science and Computation Structures: 20th International Conference, FOSSACS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Softwar...

    2017

  8. [16]

    Optimal transport for domain adaptation

    Nicolas Courty, R \'e mi Flamary, Devis Tuia, and Alain Rakotomamonjy. Optimal transport for domain adaptation. IEEE transactions on pattern analysis and machine intelligence, 39 0 (9): 0 1853--1865, 2016

    2016

  9. [17]

    Joint distribution optimal transportation for domain adaptation

    Nicolas Courty, R \'e mi Flamary, Amaury Habrard, and Alain Rakotomamonjy. Joint distribution optimal transportation for domain adaptation. Advances in neural information processing systems, 30, 2017

    2017

  10. [18]

    A categorical foundation for bayesian probability

    Jared Culbertson and Kirk Sturtz. A categorical foundation for bayesian probability. Applied Categorical Structures, 22: 0 647--662, 2014

    2014

  11. [19]

    Sinkhorn distances: Lightspeed computation of optimal transport

    Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. Advances in neural information processing systems, 26, 2013

    2013

  12. [20]

    An image is worth 16x16 words: Transformers for image recognition at scale

    Alexey Dosovitskiy. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020

    2010 arXiv

  13. [21]

    Your representations are in the network: composable and parallel adaptation for large scale models

    Yonatan Dukler, Alessandro Achille, Hao Yang, Varsha Vivek, Luca Zancato, Benjamin Bowman, Avinash Ravichandran, Charless Fowlkes, Ashwin Swaminathan, and Stefano Soatto. Your representations are in the network: composable and parallel adaptation for large scale models. Advanc...

    2023

  14. [22]

    Bayesian Inference for Markov Kernels Valued in Wasserstein Spaces

    Keenan Eikenberry. Bayesian Inference for Markov Kernels Valued in Wasserstein Spaces. PhD thesis, Arizona State University, 2023

    2023

  15. [23]

    A synthetic approach to markov kernels, conditional independence and theorems on sufficient statistics

    Tobias Fritz. A synthetic approach to markov kernels, conditional independence and theorems on sufficient statistics. Advances in Mathematics, 370: 0 107239, 2020

    2020

  16. [24]

    Finetune like you pretrain: Improved finetuning of zero-shot vision models

    Sachin Goyal, Ananya Kumar, Sankalp Garg, Zico Kolter, and Aditi Raghunathan. Finetune like you pretrain: Improved finetuning of zero-shot vision models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.\ 19338--19347, 2023

    2023

  17. [25]

    Measuring statistical dependence with hilbert-schmidt norms

    Arthur Gretton, Olivier Bousquet, Alex Smola, and Bernhard Sch \"o lkopf. Measuring statistical dependence with hilbert-schmidt norms. In International conference on algorithmic learning theory, pp.\ 63--77. Springer, 2005

    2005

  18. [26]

    Bootstrap your own latent-a new approach to self-supervised learning

    Jean-Bastien Grill, Florian Strub, Florent Altch \'e , Corentin Tallec, Pierre Richemond, Elena Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar, et al. Bootstrap your own latent-a new approach to self-supervised learning. Advances in neur...

    2020

  19. [27]

    Momentum contrast for unsupervised visual representation learning

    Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.\ 9729--9738, 2020

    2020

  20. [28]

    Masked autoencoders are scalable vision learners

    Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Doll \'a r, and Ross Girshick. Masked autoencoders are scalable vision learners. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.\ 16000--16009, 2022

    2022

  21. [29]

    R. D. Hjelm, A. Fedorov, S. Lavoie-Marchildon, K. Grewal, P. Bachman, A. Trischler, and Y. Bengio. Learning deep representations by mutual information estimation and maximization. arXiv preprint arXiv:1808.06670, 2018

    2018 arXiv

  22. [30]

    Learning discrete representations via information maximizing self-augmented training

    Weihua Hu, Takeru Miyato, Seiya Tokui, Eiichi Matsumoto, and Masashi Sugiyama. Learning discrete representations via information maximizing self-augmented training. In International conference on machine learning, pp.\ 1558--1567. PMLR, 2017

    2017

  23. [31]

    Customizing domain adapters for domain generalization

    Yuyang Ji, Zeyi Huang, Haohan Wang, and Yong Jae Lee. Customizing domain adapters for domain generalization. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp.\ 934--944, 2025

    2025

  24. [32]

    Foundations of Modern Probability

    Olav Kallenberg. Foundations of Modern Probability. Springer Nature, Switzerland AG, 3rd edition, 2021

    2021

  25. [33]

    Selfreg: Self-supervised contrastive regularization for domain generalization

    Daehee Kim, Youngjun Yoo, Seunghyun Park, Jinkyu Kim, and Jaekoo Lee. Selfreg: Self-supervised contrastive regularization for domain generalization. In Proceedings of the IEEE/CVF international conference on computer vision, pp.\ 9619--9628, 2021

    2021

  26. [34]

    Sliced wasserstein auto-encoders

    Soheil Kolouri, Phillip E Pope, Charles E Martin, and Gustavo K Rohde. Sliced wasserstein auto-encoders. In ICLR (Poster), 2019

    2019

  27. [35]

    Fine-tuning can distort pretrained features and underperform out-of-distribution

    Ananya Kumar, Aditi Raghunathan, Robbie Jones, Tengyu Ma, and Percy Liang. Fine-tuning can distort pretrained features and underperform out-of-distribution. arXiv preprint arXiv:2202.10054, 2022

    2022 arXiv

  28. [36]

    Kunkel and M

    L. Kunkel and M. Trabs. A wasserstein perspective of vanilla gans. arXiv preprint arXiv:2403.15312, 2024

    2024 arXiv

  29. [37]

    Sliced wasserstein discrepancy for unsupervised domain adaptation

    Chen-Yu Lee, Tanmay Batra, Mohammad Haris Baig, and Daniel Ulbricht. Sliced wasserstein discrepancy for unsupervised domain adaptation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.\ 10285--10295, 2019

    2019

  30. [38]

    Wasserstein smoothing: Certified robustness against wasserstein adversarial attacks

    Alexander Levine and Soheil Feizi. Wasserstein smoothing: Certified robustness against wasserstein adversarial attacks. In International conference on artificial intelligence and statistics, pp.\ 3938--3947. PMLR, 2020

    2020

  31. [39]

    T. Li, J. Yu, and C. Meng. Scalable model-free feature screening via sliced-wasserstein dependency. Journal of Computational and Graphical Statistics, 32 0 (4): 0 1501--1511, 2023

    2023

  32. [40]

    Self-supervised learning with kernel dependence maximization

    Yazhe Li, Roman Pogodin, Danica J Sutherland, and Arthur Gretton. Self-supervised learning with kernel dependence maximization. Advances in Neural Information Processing Systems, 34: 0 15543--15556, 2021

    2021

  33. [41]

    Self-organization in a perceptual network

    Ralph Linsker. Self-organization in a perceptual network. Computer, 21 0 (3): 0 105--117, 1988

    1988

  34. [42]

    Entropy regularized optimal transport independence criterion

    Lang Liu, Soumik Pal, and Zaid Harchaoui. Entropy regularized optimal transport independence criterion. In International Conference on Artificial Intelligence and Statistics, pp.\ 11247--11279. PMLR, 2022

    2022

  35. [43]

    Sliced-wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions

    Antoine Liutkus, Umut Simsekli, Szymon Majewski, Alain Durmus, and Fabian-Robert St \"o ter. Sliced-wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions. In International Conference on machine learning, pp.\ 4104--4113. PMLR, 2019

    2019

  36. [44]

    Decoupled weight decay regularization

    Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017

    2017 arXiv

  37. [45]

    Formal limitations on the measurement of mutual information

    David McAllester and Karl Stratos. Formal limitations on the measurement of mutual information. In International Conference on Artificial Intelligence and Statistics, pp.\ 875--884. PMLR, 2020

    2020

  38. [46]

    Measuring dependence between random vectors via optimal transport

    Gilles Mordant and Johan Segers. Measuring dependence between random vectors via optimal transport. Journal of Multivariate Analysis, 189: 0 104912, 2022

    2022

  39. [47]

    The earth mover's correlation

    Tam \'a s F M \'o ri and G \'a bor J Sz \'e kely. The earth mover's correlation. arXiv preprint arXiv:2009.04313, 2020

    2009 arXiv

  40. [48]

    Asymptotic guarantees for learning generative models with the sliced-wasserstein distance

    Kimia Nadjahi, Alain Durmus, Umut Simsekli, and Roland Badeau. Asymptotic guarantees for learning generative models with the sliced-wasserstein distance. Advances in Neural Information Processing Systems, 32, 2019

    2019

  41. [49]

    Hierarchical sliced wasserstein distance

    Khai Nguyen, Tongzheng Ren, Huy Nguyen, Litu Rout, Tan Nguyen, and Nhat Ho. Hierarchical sliced wasserstein distance. arXiv preprint arXiv:2209.13570, 2022

    2022 arXiv

  42. [50]

    Optimal transport model distributional robustness

    Van-Anh Nguyen, Trung Le, Anh Bui, Thanh-Toan Do, and Dinh Phung. Optimal transport model distributional robustness. Advances in Neural Information Processing Systems, 36: 0 24074--24087, 2023

    2023

  43. [51]

    Transport dependency: Optimal transport based dependency measures

    Thomas Giacomo Nies, Thomas Staudt, and Axel Munk. Transport dependency: Optimal transport based dependency measures. arXiv preprint arXiv:2105.02073, 2021

    2021 arXiv

  44. [52]

    Representation learning with contrastive predictive coding

    Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748, 2018

    2018 arXiv

  45. [53]

    Dinov2: Learning robust visual features without supervision

    Maxime Oquab, Timoth \'e e Darcet, Th \'e o Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, et al. Dinov2: Learning robust visual features without supervision. arXiv preprint arXiv:2304.07193, 2023

    2023 arXiv

  46. [54]

    Wasserstein dependency measure for representation learning

    Sherjil Ozair, Corey Lynch, Yoshua Bengio, Aaron Van den Oord, Sergey Levine, and Pierre Sermanet. Wasserstein dependency measure for representation learning. Advances in Neural Information Processing Systems, 32, 2019

    2019

  47. [55]

    Hausdorff and wasserstein metrics on graphs and other structured data

    Evan Patterson. Hausdorff and wasserstein metrics on graphs and other structured data. Information and Inference: A Journal of the IMA, 10 0 (4): 0 1209--1249, 2021

    2021

  48. [56]

    On variational bounds of mutual information

    Ben Poole, Sherjil Ozair, Aaron Van Den Oord, Alex Alemi, and George Tucker. On variational bounds of mutual information. In International Conference on Machine Learning, pp.\ 5171--5180. PMLR, 2019

    2019

  49. [57]

    Mass Transportation Problems: Volume 1: Theory

    Svetlozar T Rachev and Ludger R \"u schendorf. Mass Transportation Problems: Volume 1: Theory. Springer Science & Business Media, 2006

    2006

  50. [58]

    Learning transferable visual models from natural language supervision

    Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pp...

    2021

  51. [59]

    Learning multiple visual domains with residual adapters

    Sylvestre-Alvise Rebuffi, Hakan Bilen, and Andrea Vedaldi. Learning multiple visual domains with residual adapters. Advances in neural information processing systems, 30, 2017

    2017

  52. [60]

    Learning representations by maximizing mutual information in variational autoencoders

    Ali Lotfi Rezaabad and Sriram Vishwanath. Learning representations by maximizing mutual information in variational autoencoders. In 2020 IEEE International Symposium on Information Theory (ISIT), pp.\ 2729--2734. IEEE, 2020

    2020

  53. [61]

    Kornia: an open source differentiable computer vision library for pytorch

    Edgar Riba, Dmytro Mishkin, Daniel Ponsa, Ethan Rublee, and Gary Bradski. Kornia: an open source differentiable computer vision library for pytorch. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp.\ 3674--3683, 2020

    2020

  54. [62]

    Wasserstein distance guided representation learning for domain adaptation

    Jian Shen, Yanru Qu, Weinan Zhang, and Yong Yu. Wasserstein distance guided representation learning for domain adaptation. In Proceedings of the AAAI conference on artificial intelligence, volume 32, 2018

    2018

  55. [63]

    Wasserstein auto-encoders

    Ilya Tolstikhin, Olivier Bousquet, Sylvain Gelly, and Bernhard Schoelkopf. Wasserstein auto-encoders. arXiv preprint arXiv:1711.01558, 2017

    2017 arXiv

  56. [64]

    Tschannen, J

    M. Tschannen, J. Djolonga, P. K. Rubenstein, S. Gelly, and M. Lucic. On mutual information maximization for representation learning. arXiv preprint arXiv:1907.13625, 2019

    1907 arXiv

  57. [65]

    Topics in Optimal Transportation

    C \'e dric Villani. Topics in Optimal Transportation. Number 58. American Mathematical Soc., 2003

    2003

  58. [66]

    J. C. Wiesel. Measuring association with wasserstein distances. Bernoulli, 28 0 (4): 0 2816--2832, 2022

    2022

  59. [67]

    Wasserstein adversarial examples via projected sinkhorn iterations

    Eric Wong, Frank Schmidt, and Zico Kolter. Wasserstein adversarial examples via projected sinkhorn iterations. In International conference on machine learning, pp.\ 6808--6817. PMLR, 2019

    2019

  60. [68]

    Robust fine-tuning of zero-shot models

    Mitchell Wortsman, Gabriel Ilharco, Jong Wook Kim, Mike Li, Simon Kornblith, Rebecca Roelofs, Raphael Gontijo Lopes, Hannaneh Hajishirzi, Ali Farhadi, Hongseok Namkoong, et al. Robust fine-tuning of zero-shot models. In Proceedings of the IEEE/CVF conference on computer vision...

    2022

  61. [69]

    Sliced wasserstein generative models

    Jiqing Wu, Zhiwu Huang, Dinesh Acharya, Wen Li, Janine Thoma, Danda Pani Paudel, and Luc Van Gool. Sliced wasserstein generative models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.\ 3713--3722, 2019

    2019

  62. [70]

    Stronger and faster wasserstein adversarial attacks

    Kaiwen Wu, Allen Wang, and Yaoliang Yu. Stronger and faster wasserstein adversarial attacks. In International conference on machine learning, pp.\ 10377--10387. PMLR, 2020

    2020

  63. [71]

    Disentangled representation learning with wasserstein total correlation

    Yijun Xiao and William Yang Wang. Disentangled representation learning with wasserstein total correlation. arXiv preprint arXiv:1912.12818, 2019

    1912 arXiv

  64. [72]

    Parameter-efficient fine-tuning for pre-trained vision models: A survey

    Yi Xin, Siqi Luo, Haodi Zhou, Junlong Du, Xiaohong Liu, Yue Fan, Qing Li, and Yuntao Du. Parameter-efficient fine-tuning for pre-trained vision models: A survey. arXiv e-prints, pp.\ arXiv--2402, 2024

    2024

  65. [73]

    Side adapter network for open-vocabulary semantic segmentation

    Mengde Xu, Zheng Zhang, Fangyun Wei, Han Hu, and Xiang Bai. Side adapter network for open-vocabulary semantic segmentation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.\ 2945--2954, 2023

    2023

  66. [74]

    Infovae: Balancing learning and inference in variational autoencoders

    Shengjia Zhao, Jiaming Song, and Stefano Ermon. Infovae: Balancing learning and inference in variational autoencoders. In Proceedings of the aaai conference on artificial intelligence, volume 33, pp.\ 5885--5892, 2019

    2019

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.