Pith. sign in

REVIEW 3 major objections 6 minor 49 references

Surprise Score Beats Per-Step Loss for Image Clustering

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · glm-5.2

2026-07-09 23:30 UTC pith:PYMT7PNX

load-bearing objection Novel ES-based self-supervised clustering framework with strong results on simple datasets, but core motivation for ES over differentiable surrogates is unproven. the 3 major comments →

arxiv 2607.06887 v1 pith:PYMT7PNX submitted 2026-07-08 cs.LG

Converge to Surprise: Evolutionary Self-supervised Image Clustering

Canlin Zhang , Xiuwen Liu This is my paper
classification cs.LG
keywords imagesurpriseclusteringmodelscoreself-superviseddeepframework
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that self-supervised image clustering does not require a per-step loss function with a defined target. Instead, it starts from the maximum-entropy null hypothesis that all pixels are independent random noise, defines a 'surprise score' measuring how unlikely the network's two-view cluster agreement would be under that null, and maximizes that score directly via an evolution-strategy outer loop with periodic gradient-descent consolidation. The central claim is that this procedure discovers semantically meaningful clusters from raw pixels without being told the number of classes, achieving state-of-the-art non-parametric clustering on MNIST, Fashion-MNIST, and USPS.

Core claim

The paper introduces a 'surprise score' S(θ) = Σ D(q̂_k || p_k²) summed over clusters where observed view-matching exceeds the null expectation, and shows that maximizing it with evolution strategy—then consolidating discovered clusters via periodic gradient descent—lets a from-scratch ResNet discover the correct number of clusters and achieve top accuracy on standard benchmarks without any per-step target or class-count prior.

What carries the argument

Complementary chessboard masking creates two pixel-disjoint views of each image. Under the i.i.d. null hypothesis these views share zero mutual information, so any statistical agreement in their cluster assignments is surprising. The surprise score sums binary KL divergences between observed and expected view-matching rates per cluster. An ES outer loop perturbs the full parameter vector and ranks mirrored pairs by this score; periodic gradient-descent inner loops use the ES-discovered surprising clusters as cross-entropy surrogate labels to consolidate and sharpen them.

Load-bearing premise

The paper's load-bearing premise is that the surprise score cannot in general be reduced to a per-step differentiable loss, which motivates the entire ES architecture. The authors state that proving this is beyond their scope. If a differentiable surrogate existed, the ES outer loop would be unnecessary and the framework's distinctive contribution would collapse to a variant of existing pseudo-label clustering.

What would settle it

A differentiable upper bound or surrogate for the surprise score that performs comparably would eliminate the need for the ES outer loop and undercut the paper's central methodological claim. Alternatively, if the binomial independence approximation across coupled cluster counts introduces systematic bias, the surprise score could reward degenerate partitioning strategies rather than genuine non-randomness.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes 'converge-to-surprise,' a self-supervised image clustering framework that does not rely on a per-step loss function. The null hypothesis H0 assumes pixels are i.i.d. noise (Principle of Maximum Entropy). The model partitions images via complementary chessboard masking into two independent views, and defines a 'surprise score' S(θ) measuring how unlikely the model's cluster co-occurrence statistics are under H0. Because the argmax operation makes S(θ) non-differentiable, the authors adopt an evolution-strategy (ES) outer loop to maximize S(θ) directly, interleaved with a periodic gradient-descent inner loop that uses the discovered 'surprising' clusters as surrogate labels. The method is evaluated on MNIST, Fashion-MNIST, and USPS in the non-parametric setting (number of classes unknown), achieving state-of-the-art or competitive results from scratch.

Significance. The paper presents a genuinely novel perspective on self-supervised clustering by framing representation discovery as rejection of a maximum-entropy null hypothesis, and by using ES to optimize a non-differentiable objective without reducing it to a per-step loss. The experimental results are strong, particularly on USPS (94.9% ACC vs. 89% for DeepDPM) and MNIST (98.3% ACC), and the model is trained from scratch without pre-trained features, which is a notable advantage over baselines. The code is publicly available, enhancing reproducibility. The conceptual framework in Appendix A (learning as iterative rejection of the null hypothesis; orderliness as building order out of chaos) is thought-provoking and adds intellectual depth. However, the significance is tempered by the limited scope of benchmarks (only simple digit/fashion datasets) and the unaddressed question of whether the non-differentiability is truly fundamental or merely a design choice.

major comments (3)
  1. §3.2, Eq. (4)–(12): The paper's central architectural choice—using ES instead of gradient descent—rests on the claim that 'a surprise score cannot, in general, be reduced to a per-step loss function.' The sole source of non-differentiability is the argmax in Eq. (4). However, S(θ) is a function of cluster co-occurrence counts, which are expectations over categorical distributions. Standard relaxation techniques such as the Straight-Through Estimator (Bengio et al., 2013) or the Gumbel-Softmax reparameterization (Jang et al., 2017) could provide differentiable surrogates with per-step gradients. The paper does not discuss or rule out these approaches. If a differentiable surrogate exists and converges to similar solutions, the claim that surprise scores 'cannot in general be reduced to a per-step loss' is overstated, and the ES outer loop becomes a computational choice rather than a 'fund
  2. §3.2, Eq. (7): The surprise score derivation treats each cluster count t_k as an independent Binomial(N, q_k) random variable, which the authors acknowledge is a simplification since the K output dimensions are coupled (each view maps to exactly one cluster). This approximation is load-bearing for the Chernoff bound in Eq. (9) and hence for the surprise score S(θ) in Eq. (12). The paper does not provide any bound on the error introduced by this independence approximation, nor does it discuss regimes under which it might fail (e.g., when K is small or when a few clusters dominate). A sensitivity analysis or at least a more rigorous justification of when the approximation is valid would strengthen the theoretical foundation.
  3. §4.1, Table 1: The experimental evaluation is limited to three relatively simple benchmarks (MNIST, Fashion-MNIST, USPS), all of which are small-resolution grayscale digit/fashion datasets. The central claim of achieving 'state-of-the-art results in non-parametric self-supervised image clustering' would be substantially strengthened by evaluation on at least one more challenging dataset (e.g., CIFAR-10, CIFAR-100, or STL-10). Without this, it is unclear whether the framework scales to natural images with higher complexity, color channels, and more diverse class structure. The authors should either add such experiments or explicitly scope their claims to simple datasets.
minor comments (6)
  1. §3.2, Eq. (6): The notation p_k = (n_k^(i) + n_k^(j)) / (2N) conflates the marginal probability across both views. It would be clearer to explicitly state that under H0, the marginal distributions of seq^(i) and seq^(j) are identical, so pooling is valid.
  2. §3.3, Algorithm 1, line 10: The condition 'e % T_{1,b} = 0' for triggering gradient-descent training is somewhat opaque. A brief comment explaining the modular arithmetic schedule would improve readability.
  3. Table 4 (Appendix B): The augmentation parameters are listed but the rationale for specific values (e.g., rotation range ±20° for MNIST vs. ±10° for USPS) is only partially explained. A brief justification would help reproducibility.
  4. Appendix A.2, Eq. (24): The orderliness measure Ω = H*_Π + λ / Ĥ_Π + λ uses a small constant λ to avoid division by zero, but the choice of λ is not specified. The sensitivity of Ω to this parameter should be briefly discussed.
  5. Figure 2: The pipeline diagram is somewhat dense. Labeling the arrows with the corresponding equation numbers (e.g., Eq. 4 for argmax, Eq. 12 for surprise score) would improve clarity.
  6. §4.1: The batch size N=3000 for MNIST/Fashion-MNIST and N=3650 for USPS is stated, but the interaction between batch size and the reliability of the surprise score statistics (which depend on binomial tail probabilities) is not discussed. A brief note on why these batch sizes are sufficient would be helpful.

Circularity Check

0 steps flagged

No circularity: the surprise score is defined from an externally grounded null hypothesis, and the optimization target is not constructed from the result it claims to produce

full rationale

The paper's derivation chain is self-contained and does not reduce to its own inputs by construction. The null hypothesis H0 (pixels are i.i.d. random noise, from the Principle of Maximum Entropy) is an externally defined prior, not a quantity fitted to the model's output. The surprise score S(θ) = Σ D(q̂_k || q_k) is derived from the binomial tail probability under H0 (Eqs. 7–12): the null probability q_k = p_k² is computed from the model's marginal cluster frequencies, while the observed matching probability q̂_k = t_k/N is computed from the model's actual co-occurrence counts. These are two distinct statistics of the model's output — one marginal, one joint — and their divergence measures whether the joint behavior rejects the i.i.d. null. This is not a self-definitional loop: the score is not defined in terms of the clustering result it claims to produce, but rather in terms of a statistical hypothesis test against an externally specified null. The inner-loop gradient-descent training (Eq. 15) uses clusters discovered by ES as surrogate labels, which is a self-referential bootstrapping step, but this is standard practice in deep clustering (cf. DeepCluster, IIC) and does not constitute circularity in the derivation sense — the surrogate labels are intermediate training signals, not the final claimed output. The paper's fundamental assumption that 'a surprise score cannot, in general, be reduced to a per-step loss' (§3.2) is an unproven conjecture that the authors acknowledge is beyond their scope, but an unproven conjecture is a correctness risk, not a circularity. No self-citation chain is load-bearing for the central result: the ES algorithm (Salimans et al., 2017) is an external method, and the experimental benchmarks (MNIST, Fashion-MNIST, USPS) are standard external datasets. The results are externally falsifiable. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

8 free parameters · 4 axioms · 2 invented entities

The method relies on several empirically chosen hyperparameters and an unproven fundamental assumption about the non-reducibility of surprise scores to per-step losses. The surprise score and optimization scheme are novel constructs validated empirically.

free parameters (8)
  • K (output dimension) = 64
    Set as an upper bound on the number of clusters; chosen by hand, not learned.
  • m (ES population size) = 32
    Standard ES hyperparameter chosen empirically.
  • σ (ES noise variance) = Not explicitly stated
    Used in the ES update rule; its value is not specified in the main text.
  • η (learning rate) = Not explicitly stated
    Used in the ES update rule; its value is not specified in the main text.
  • λ (weight decay) = Not explicitly stated
    Used in the ES update rule; its value is not specified in the main text.
  • τ (surprise threshold) = 0.005
    Pre-defined threshold for identifying contributing clusters; chosen empirically.
  • T0, T1,a, T1,b (schedule params) = 2000, 4, 25 (MNIST/FMNIST)
    Training schedule lengths chosen empirically per dataset.
  • N (batch size for surprise score) = 3000 (MNIST/FMNIST), 3650 (USPS)
    Chosen based on dataset size and statistical reliability.
axioms (4)
  • domain assumption Principle of Maximum Entropy implies pixels are i.i.d. random noise under the null hypothesis H0.
    Stated in §3.1; this is the foundational assumption for the surprise score.
  • ad hoc to paper A surprise score cannot, in general, be reduced to a per-step loss function.
    Stated in §3.2 as a 'fundamental assumption'; unproven but motivates the use of ES.
  • domain assumption The binomial distribution is a valid approximation for the coupled multinomial counts of cluster matches.
    Used in Eq. 7; the authors note the coupling has a 'very weak effect' but this is unproven.
  • domain assumption Nearby pixels in an original image have almost identical distributions.
    Stated in §3.2 to justify that complementary masked views have identical distributions under H0.
invented entities (2)
  • Surprise score S(θ) no independent evidence
    purpose: Measures how unlikely the model's output representation is under the null hypothesis H0.
    A novel objective function defined in Eq. 12; its effectiveness is tested empirically but it is not derived from an external physical principle.
  • Converge-to-surprise optimization scheme no independent evidence
    purpose: Hybrid ES outer loop and gradient-descent inner loop to maximize the non-differentiable surprise score.
    A novel optimization algorithm; its performance is validated on benchmarks but it is an invented procedure.

pith-pipeline@v1.1.0-glm · 23659 in / 2309 out tokens · 285826 ms · 2026-07-09T23:30:49.649388+00:00 · methodology

0 comments
read the original abstract

Most self-supervised image clustering models, actually almost all deep learning approaches, are based on gradient descent: In order to calculate the loss, every optimization step requires a clearly defined target, whether a contrastive split, a masked patch or entity, an EMA-teacher output, a pseudo-label, or a differentiable information-theoretic functional. We propose a self-supervised framework that drops this requirement for image clustering. Without any prior knowledge, we have to assume that each pixel is i.i.d. according to the Principle of Maximum Entropy. Taking this as our null hypothesis H0, we define a "surprise score" that measures how unlikely the model's output representation would be under H0. Maximizing the surprise score forces the deep learning model to reject H0 - equivalently, to discover non-random feature from data. Also, here is our fundamental assumption: a surprise score cannot, in general, be reduced to a per-step loss. Hence, we propose the "converge-to-surprise" scheme to optimize our model: an evolution-strategy (ES) outer loop, which directly maximizes the surprise score without needing its gradient, paired with a periodic gradient-descent inner loop, which uses the surprising clusters already discovered by ES as surrogate targets. On standard image benchmarks, our framework achieves new state-of-the-art results in non-parametric self-supervised image clustering - the strictest deep-clustering setting, in which the number of ground-truth classes is not given to the model.

Figures

Figures reproduced from arXiv: 2607.06887 by Canlin Zhang, Xiuwen Liu.

Figure 1
Figure 1. Figure 1: Chessboard masking: i-side can only view pixels in white chessboard positions; j-side can only view pixels in black chessboard positions. The two views share no pixel in common. Here, I(· ; ·) denotes the mutual-information functional. If formula 3 is rejected, then the null hypothesis H0 can￾not be true. This will be our approach to reject H0. 3.2. Cluster co-occurrence as a surprise score Again, given an… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of our pipeline. The deep network is implemented on complementary masked and independently augmented views. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: MNIST test-set clustering. Each panel shows nine random images of a single ground-truth class assigned to a given cluster. The [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: USPS test-set clustering for a run that inferred [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Fashion-MNIST test-set clustering. Beyond coarse categories, the network separates finer attributes: clusters [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Number of discovered (surprising) clusters vs. train [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Number of discovered (surprising) clusters vs. training [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages · 9 internal anchors

  1. [1]

    A review on deep convolutional neural networks

    Neena Aloysius and M Geetha. A review on deep convolutional neural networks. In2017 international conference on communication and signal processing (ICCSP), pages 0588–0592. IEEE, 2017. 6

    work page 2017

  2. [2]

    Self-supervised learn- ing from images with a joint-embedding predictive architecture

    Mahmoud Assran, Quentin Duval, Ishan Misra, Piotr Bojanowski, Pascal Vincent, Michael Rabbat, Yann LeCun, and Nicolas Ballas. Self-supervised learn- ing from images with a joint-embedding predictive architecture. InProceedings of the IEEE/CVF con- ference on computer vision and pattern recognition, pages 15619–15629, 2023. 1, 2

    work page 2023

  3. [3]

    VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning

    Adrien Bardes, Jean Ponce, and Yann LeCun. Vicreg: Variance-invariance-covariance regulariza- tion for self-supervised learning.arXiv preprint arXiv:2105.04906, 2021. 1, 2

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  4. [4]

    Batina, B

    L. Batina, B. Gierlichs, E. Prouff, M. Rivain, F.-X. Standaert, and Veyrat-Charvillon N. Web text corpus for natural language processing.Journal of Cryptol- ogy, 24(2):269–291, 2011. 3

    work page 2011

  5. [5]

    An intuitive proof of the data processing inequality

    Normand J Beaudry and Renato Renner. An intuitive proof of the data processing inequality.arXiv preprint arXiv:1107.0740, 2011. 3

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  6. [6]

    Mirrored sampling and sequential selection for evolution strategies

    Dimo Brockhoff, Anne Auger, Nikolaus Hansen, Dirk V Arnold, and Tim Hohm. Mirrored sampling and sequential selection for evolution strategies. In International conference on parallel problem solving from nature, pages 11–21. Springer, 2010. 5

    work page 2010

  7. [7]

    Deep clustering for unsupervised learning of visual features

    Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep clustering for unsupervised learning of visual features. InProceedings of the Eu- ropean conference on computer vision (ECCV), pages 132–149, 2018. 1, 2

    work page 2018

  8. [8]

    Un- supervised learning of visual features by contrasting cluster assignments.Advances in neural information processing systems, 33:9912–9924, 2020

    Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Un- supervised learning of visual features by contrasting cluster assignments.Advances in neural information processing systems, 33:9912–9924, 2020. 1, 2

    work page 2020

  9. [9]

    Emerging properties in self-supervised vision transformers

    Mathilde Caron, Hugo Touvron, Ishan Misra, Herv ´e J´egou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. InProceedings of the IEEE/CVF inter- national conference on computer vision, pages 9650– 9660, 2021. 1, 2

    work page 2021

  10. [10]

    Deep adaptive image clustering

    Jianlong Chang, Lingfeng Wang, Gaofeng Meng, Shiming Xiang, and Chunhong Pan. Deep adaptive image clustering. InProceedings of the IEEE inter- national conference on computer vision, pages 5879– 5887, 2017. 2

    work page 2017

  11. [11]

    A simple framework for con- trastive learning of visual representations

    Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for con- trastive learning of visual representations. InInterna- tional conference on machine learning, pages 1597–

    work page

  12. [12]

    John Wiley & Sons, 1999

    Thomas M Cover.Elements of information theory. John Wiley & Sons, 1999. 4

    work page 1999

  13. [13]

    L. Deng. The mnist database of handwritten digit im- ages for machine learning research [best of the web]. IEEE Signal Processing Magazine, pages 141–142,

    work page

  14. [14]

    Unsupervised visual representation learning by con- text prediction

    Carl Doersch, Abhinav Gupta, and Alexei A Efros. Unsupervised visual representation learning by con- text prediction. InProceedings of the IEEE interna- tional conference on computer vision, pages 1422– 1430, 2015. 1

    work page 2015

  15. [15]

    An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

    Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale.arXiv preprint arXiv:2010.11929, 2020. 5

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  16. [16]

    A density-based algorithm for dis- covering clusters in large spatial databases with noise

    Martin Ester, Hans-Peter Kriegel, J ¨org Sander, Xi- aowei Xu, et al. A density-based algorithm for dis- covering clusters in large spatial databases with noise. Inkdd, pages 226–231, 1996. 3, 7

    work page 1996

  17. [17]

    Deep k-means: Jointly clustering with k- means and learning representations.Pattern Recogni- tion Letters, 138:185–192, 2020

    Maziar Moradi Fard, Thibaut Thonet, and Eric Gaussier. Deep k-means: Jointly clustering with k- means and learning representations.Pattern Recogni- tion Letters, 138:185–192, 2020. 2, 7

    work page 2020

  18. [18]

    An introduction to probability theory and its applications.Third edition

    W Feller. An introduction to probability theory and its applications.Third edition. New York: Wiley. Theorem is in section VI.3, 1968. 4

    work page 1968

  19. [19]

    John Wiley & Sons,

    William Feller.An introduction to probability theory and its applications, Volume 2. John Wiley & Sons,

    work page

  20. [20]

    Unsupervised Representation Learning by Predicting Image Rotations

    Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by predicting image rotations.arXiv preprint arXiv:1803.07728,

    work page internal anchor Pith review Pith/arXiv arXiv

  21. [21]

    Bootstrap your own latent-a new approach to self- supervised learning.Advances in neural information processing systems, 33:21271–21284, 2020

    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 neural information processing systems, 33:21271–21284, 2020. 1, 2

    work page 2020

  22. [22]

    Guiasu and A

    S. Guiasu and A. Shenitzer. The principle of maximum entropy.The Mathematical Intelligencer. doi.org/10.1007/BF03023004, 7:42–48, 1985. 1, 3

    work page doi:10.1007/bf03023004 1985

  23. [23]

    Deep residual learning for image recognition

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016. 6 9

    work page 2016

  24. [24]

    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. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9729–9738, 2020. 1, 2

    work page 2020

  25. [25]

    Masked autoencoders are scalable vision learners

    Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Doll´ar, and Ross Girshick. Masked autoencoders are scalable vision learners. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 16000–16009, 2022. 1, 2

    work page 2022

  26. [26]

    Learning deep representations by mutual information estimation and maximization

    R Devon Hjelm, Alex Fedorov, Samuel Lavoie- Marchildon, Karan Grewal, Phil Bachman, Adam Trischler, and Yoshua Bengio. Learning deep repre- sentations by mutual information estimation and max- imization.arXiv preprint arXiv:1808.06670, 2018. 1, 2

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [27]

    Memoized on- line variational inference for dirichlet process mixture models.Advances in neural information processing systems, 26, 2013

    Michael C Hughes and Erik Sudderth. Memoized on- line variational inference for dirichlet process mixture models.Advances in neural information processing systems, 26, 2013. 2, 7

    work page 2013

  28. [28]

    Jonathan J. Hull. A database for handwritten text recognition research.IEEE Transactions on pattern analysis and machine intelligence, 16(5):550–554,

    work page

  29. [29]

    In- variant information clustering for unsupervised image classification and segmentation

    Xu Ji, Joao F Henriques, and Andrea Vedaldi. In- variant information clustering for unsupervised image classification and segmentation. InProceedings of the IEEE/CVF international conference on computer vi- sion, pages 9865–9874, 2019. 1, 2, 4

    work page 2019

  30. [30]

    The hungarian method for the as- signment problem.Naval research logistics quarterly, 2(1-2):83–97, 1955

    Harold W Kuhn. The hungarian method for the as- signment problem.Naval research logistics quarterly, 2(1-2):83–97, 1955. 2

    work page 1955

  31. [31]

    Dying clusters is all you need-deep clustering with an unknown number of clusters

    Collin Leiber, Niklas Strauß, Matthias Schubert, and Thomas Seidl. Dying clusters is all you need-deep clustering with an unknown number of clusters. In 2024 IEEE International Conference on Data Mining Workshops (ICDMW), pages 726–733. IEEE, 2024. 2, 6, 7

    work page 2024

  32. [32]

    Deep dirichlet process mixture models

    Naiqi Li, Wenjie Li, Yong Jiang, and Shu-Tao Xia. Deep dirichlet process mixture models. InUncertainty in Artificial Intelligence, pages 1138–1147. PMLR,

    work page

  33. [33]

    Introduction to gaussian pro- cesses.NATO ASI series F computer and systems sci- ences, 168:133–166, 1998

    David JC MacKay et al. Introduction to gaussian pro- cesses.NATO ASI series F computer and systems sci- ences, 168:133–166, 1998. 5

    work page 1998

  34. [34]

    Cross- entropy loss functions: Theoretical analysis and ap- plications

    Anqi Mao, Mehryar Mohri, and Yutao Zhong. Cross- entropy loss functions: Theoretical analysis and ap- plications. InInternational conference on Machine learning, pages 23803–23828. pmlr, 2023. 5

    work page 2023

  35. [35]

    Indicator functions for adaptive image processing.Journal of the Optical So- ciety of America A, 8(1):141–156, 1991

    GF McLean and ME Jernigan. Indicator functions for adaptive image processing.Journal of the Optical So- ciety of America A, 8(1):141–156, 1991. 3

    work page 1991

  36. [36]

    K-nearest neighbor classification

    Antonio Mucherino, Petraq J Papajorgji, and Panos M Pardalos. K-nearest neighbor classification. InData mining in agriculture, pages 83–106. Springer, 2009. 2

    work page 2009

  37. [37]

    Unsupervised learning of visual representations by solving jigsaw puzzles

    Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw puzzles. InEuropean conference on computer vision, pages 69–84. Springer, 2016. 1

    work page 2016

  38. [38]

    The Effectiveness of Data Augmentation in Image Classification using Deep Learning

    Luis Perez and Jason Wang. The effectiveness of data augmentation in image classification using deep learn- ing.arXiv preprint arXiv:1712.04621, 2017. 3

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  39. [39]

    Mul- tilayer perceptron and neural networks.WSEAS trans- actions on circuits and systems, 8(7):579–588, 2009

    Marius-Constantin Popescu, Valentina E Balas, Lil- iana Perescu-Popescu, and Nikos Mastorakis. Mul- tilayer perceptron and neural networks.WSEAS trans- actions on circuits and systems, 8(7):579–588, 2009. 2

    work page 2009

  40. [40]

    Deepdpm: Deep clustering with an unknown number of clusters

    Meitar Ronen, Shahaf E Finder, and Oren Freifeld. Deepdpm: Deep clustering with an unknown number of clusters. InProceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition, pages 9861–9870, 2022. 2, 6, 7

    work page 2022

  41. [41]

    D. E. Rumelhart, G. E. Hinton, and R. J. Williams. Learning internal representations by back-propagating errors.Nature, 323:533–536, 1986. 1

    work page 1986

  42. [42]

    Evolution Strategies as a Scalable Alternative to Reinforcement Learning

    Tim Salimans, Jonathan Ho, Xi Chen, Szymon Sidor, and Ilya Sutskever. Evolution strategies as a scalable alternative to reinforcement learning.arXiv preprint arXiv:1703.03864, 2017. 2, 5

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  43. [43]

    A mathematical theory of communication.The Bell system technical journal, 27 (3):379–423, 1948

    Claude Elwood Shannon. A mathematical theory of communication.The Bell system technical journal, 27 (3):379–423, 1948. 4

    work page 1948

  44. [44]

    Notes on Kullback-Leibler Divergence and Likelihood

    Jonathon Shlens. Notes on kullback-leibler divergence and likelihood.arXiv preprint arXiv:1404.2000, 2014. 4

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  45. [45]

    Natural evolution strategies.The Journal of Machine Learn- ing Research, 15(1):949–980, 2014

    Daan Wierstra, Tom Schaul, Tobias Glasmachers, Yi Sun, Jan Peters, and J ¨urgen Schmidhuber. Natural evolution strategies.The Journal of Machine Learn- ing Research, 15(1):949–980, 2014. 5

    work page 2014

  46. [46]

    Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms

    Han Xiao, Kashif Rasul, and Roland V ollgraf. Fashion-mnist: a novel image dataset for benchmark- ing machine learning algorithms.arXiv preprint arXiv:1708.07747, 2017. 6, 13

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  47. [47]

    Unsu- pervised deep embedding for clustering analysis

    Junyuan Xie, Ross Girshick, and Ali Farhadi. Unsu- pervised deep embedding for clustering analysis. In International conference on machine learning, pages 478–487. PMLR, 2016. 2, 7

    work page 2016

  48. [48]

    Towards k-means-friendly spaces: Si- multaneous deep learning and clustering

    Bo Yang, Xiao Fu, Nicholas D Sidiropoulos, and Mingyi Hong. Towards k-means-friendly spaces: Si- multaneous deep learning and clustering. Ininterna- tional conference on machine learning, pages 3861–

    work page

  49. [49]

    Clusterk, digitp

    Jure Zbontar, Li Jing, Ishan Misra, Yann LeCun, and St´ephane Deny. Barlow twins: Self-supervised learn- 10 ing via redundancy reduction. InInternational con- ference on machine learning, pages 12310–12320. PMLR, 2021. 1, 2 A. Discussions The main paper presents converge-to-surprise as a novel self-supervised learning framework. Here, we step back and dis...

    work page 2021