Why Prototypes Collapse: Diagnosing and Preventing Partial Collapse in Prototypical Self-Supervised Learning
Authors: Gabriel Y. Arteaga
Marius Aasan
Rwiddhi Chakraborty
Martine Hjelkrem-Tan
Thalles Silva
Michael Kampffmeyer
Adín Ramírez Rivera
Venue: ICLR 2026 Poster (2026)
Keywords: Self-Supervised Learning
Representation Learning
Computer Vision
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: We trace partial prototype collapse in prototypical SSL to joint encoder–prototype optimization and propose an EM-based decoupling strategy that prevents collapse, preserving prototype diversity and improving downstream performance.

Abstract: Prototypical self-supervised learning methods consistently suffer from partial prototype collapse, where multiple prototypes converge to nearly identical representations. This undermines their central purpose—providing diverse and informative targets to guide encoders toward rich representations—and has led practitioners to over-parameterize prototype sets or add ad-hoc regularizers, which mitigate symptoms rather than address the root cause. We empirically trace the collapse to the joint optimization of encoders and prototypes, which encourages a type of shortcut learning: early in training prototypes drift toward redundant representations that minimize loss without necessarily enhancing representation diversity. To break the joint optimization, we introduce a fully decoupled training strategy that learns prototypes and encoders under separate objectives. Concretely, we model prototypes as a Gaussian mixture updated with an online EM-style procedure, independent of the encoder's loss. This simple yet principled decoupling eliminates prototype collapse without explicit regularization and yields consistently diverse prototypes, which in several settings translate to improved downstream performance.

Published as a conference paper at ICLR 2026
WHY PROTOTYPES COLLAPSE: DIAGNOSING AND PRE- VENTING PARTIAL COLLAPSE IN PROTOTYPICAL SELF- SUPERVISED LEARNING
Gabriel Y. Arteaga', Marius Aasan', Rwiddhi C Martine Hjelkrem-Tan Thalles Silva", Michael Kampffmeyer', and Adín Ramírez Rivera'
University of Osio
"UT The Aretic University of Norway Uniierrsity of Campinas
ABSTRACT
Prototypical self-supervised learning methods consistently suffer from partial pro- totype collapse, where multiple prototypes converge nearly identical representa- tions. This undermines their central purpose-providing diverse and informative targets guide encoders toward rich representations and has led practitioners wer-paaameterize prototype sets or add ad-hoc regularizers, which mitigate symp- toms rather than address the root cause. We empirically trace the collapse to the joint optimization of encoders and prototypes, which encourages type of shortcut learning: carly in training prototypes drift toward redundant representations that minimize loss without necessarily enhancing representation diversity. To break the joint optimization, we introduce a fully decoupled training strategy that learns pro- totypes and encoders under separate objectives. Concretely, model prototypes as a Gaussian mixture updated with an online EM-style procedure, independent of the encoder's loss. This simple yet principled decoupling eliminates prototype collapse without explicit regularization and yields consistently diverse prototypes, which in several settings translate improved downstream performance.
INTRODUCTION
Prototypical self-supervised learning (SSL) frameworks (Caron et al., 2021; Siméoni et al., 2025) in the image domain have come to rival the effectiveness of language-supervised alternatives in representation learning (Fan et al., 2025). In these frameworks, prototypes are learnable vectors that act cluster anchors, guiding learning so that samples organize into semantically coherent regions of the embedding space. However, recent work has demonstrated that many prototypical SSL approaches suffer from phenomenon known as partial prototype collapse (formal definition in Def. 2.1., in which multiple prototypes converge to indistinguishable representations (Govindarajan al., 2023; 2024). This phenomenon could explain why peeemarraeteiiinng the number of pro- totypes used has been a popular choice to improve performance in recent prototypical frameworks (Oquab et al., 2024; Siméoni al., 2025; Venkataramanan al., 2025).
Our experiments show that the practice of jointly optimizing the encoder and prototypes contributes this collapse. The intuition is that joint optimization drives prototypes towards redundant rep- resentations early in training by exploiting shortcuts that minimize the loss at the cost of diverse and semantically meaningful representations. This encourages the use of larger prototype sets; an expensive solution that mitigates symptoms without directly addressing the underlying issues (Oquab et al., 2024; Siméoni et al., 2025; Venkataramanan et al., 2025) while impeding model's ability to learn stronger representations and diminishing robustness imbalanced data distributions (Govin- darajan et al., 2024; Wen et al., 2024).
We find that these effects are particularly pronounced in the instance-level formulations of proto- typical SSL. In Fig. 1(a), we reaffirm previous findings (Govindarajan et al., 2024), showing how DINO's (Caron al., 2021) final prototype distribution tends to collapse one two modes, which severely limits the diversity of representations. This phenomenon also persists in more recent
Code: httpa: //th/////////////// f1
ing. Corregondence to: sobrrteya,ddiio ( guto.no

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Published as a conference paper at ICLR 2026
P2
Pl
P1
P1
P1
0.4
Density
0.3
0.2
77
0
Angle
Angle
Angle
Angle
Angle
DINO
DINO+KP
(c) DINOv2
(d) CARP
CARP+Decxuplnng
Figure 1: Uniformity of prototype representations. Prototypes are projected RR² using principal component
analysis (PCA). The resulting prototype distributions are visualized using (top) Gaussian keree density estima- tion (KDE), and (bottom) the angular distributions are estimated with a von Fiscs-Fisher KDE with x = 20.
methods such as DINOv2 (Oquab et al., 2024), cf. Fig. 1(c). While recent efforts have looked to address this issue, either via explicit regularization (Govindarajan al., 2024), cf. Fig. 1(b), or implicit mechanisms (Silva & Ramírez Rivera, 2023), ef. Fig. ((d), these models still exhibit collapse, suggesting that the underlying issue is not yet fully resolved. Motivated by these observations, we introduce a decoupling strategy designed to break the joint-optimizttonn procedure. In our approach, the encoder and prototypes are learned under separate objectives- see Fig. 2. Concretely, we model Gaussian mixture, updated via expectation maximization (EM) independently of the encoder's 's loss. This decoupled training eliminates partial prototype collapse, cf. Fig. ((e), and points joint optimization the most likely culprit driving partial prototype collapse.
the prototypes
Our main contributions are as follows: (i) we conduct systematic and quantitative analysis of a broad range of prototypical SSL frameworks, demonstrating that partial prototype collapse extends well beyond the DINO family of models; (ii) we identify the underlying mechanism driving this collapse as the joint optimization of encoders and prototypes under a shared loss, which encourages redundant prototype representations; and (iii) we introduce fully decoupled training framework that isolates prototype estimation from encoder learning, achieving consistently high prototype diversity throughout training. with downstream representation quality and robustness that improve in several prototypical SSI. settings.
UNDERSTANDING PARTIAL PROTOTYPE COLLAPSE
2.1 PRELIMINARIES
Prototypical Self-Supervised Formulation. Among recent SSL. approaches, prototypical formu- lations (where network outputs are aligned to set of learnable, class-agnostic prototypes) have achieved state-of-the-art performance on several vision benchmarks (Siméoni et al., 2025). We begin by describing the general prototypical framework used throughout this paper. Our exposition emphasizes the instance-level objective (Caron et al., 2021; Silva & Ramírez Rivera, 2022; 2023), but the same formulation readily be extended to incorporate dense objective (Zhou al., 2022) or reformulated with an explicit dense prediction objective (Darcet et al., 2025).
Given J stochastic augmentations {w))/=1 of an image v, student backbone with projection head fa and an Exponential Moving Average (EMA)-updated teacher fo map each view to latent representation hit = (w) E DRP Similarity scores with a learnable prototype set C' E :
D are computed as =/, h/ M²,Ce I and converted into prototype-assinmmett probabilities via softmax with optional temperature parameter
0 through
2
softmax
(I)
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Table 1: We evaluate the number of unique prototypes according Definition 2.1 with 0.025. *Vanilla iBOT uses the same head for both objectives; for clarity, only one is shown.
Model
Objective
Init. Protos.
Unique Protos, Dense
Unique Protos, Instance
(% of Init. protos.)
DINO CARP
Instance
60000
908
(1.5%)
Instance
65536
7052
(10.8%)
CAPI
Dense
16384
16383
(99.9%)
iBOT
Hybrid
8192
3057"
(37,3%)
iBOT KP
Hybrid
8192
7895
(96.4%)
DINOV2
Hybrid
2621
110201
2556
(43.0%)
The overall objective of prototypical frameworks is to enforce cross-view consistency between the student and teacher branches using a consistency loss Ly Lf'-see
see Fig. 2(a).
Partial Prototype Collapse. Govindarajan et al. (2024) investigated the DINO-family of methods (Assran et al., 2022: 2023b; Caron et al., 2021; Zhou et al., 2022) and demonstrated that these prototypical SSL approaches are susceptible to partial prototype collapse. This phenomenon arises when multiple prototypes converge to nearly identical representations during training. While this behavior does not amount to a complete collapse of all prototypes, it, nevertheless, reduces the diversity of representations and may hinder the effectiveness of downstream tasks. To formalize this behavior, the authors introduced the following definition of partial collapse.
Definition 2.1 (Partial prototype collapse). Consider the set C = {c* == K) of K prototype vectors, Og such that ||<||| = 1. partial prototype collapse (of degree M and distance) is said to have occurred if there exists set of M disjoint partitions of prototype vectors Vn C C, m I,..., M, and Ml representative prototype vectors Um Vn.. such that for all m -....,. M, 1 - Cn Cj < e, for all oj E Vn.. The set of M unique prototypes is defined as U {rm 1M mm=
Applying this definition, they further showed that the DINO-family of methods retained only about 2%-40% of their initially initialized prototypes as unique, thereby, revealing a substantial redundancy in the learned representations. To alleviate this issue, they proposed applying KoLeo regularization (Beirlant et al., 1997; Delattre & Fournier, 2017; Sablayrolles et al., 2019) directly to the prototypes. Specifically, they added a CoLeo-Prototyr (KP) loss term, LxP(C') = * > log(de), where de = min,4*1Ica ||c-- as an auxiliary term to encourage prototype diversity. While this helped reduce collapse, it did not fully solve the problem. Their approach also introduced a new hyperparameter AKP, which balances the KP loss with the overall objective, creating delicate trade-off: insufficient regularization limits diversity, whereas excessive regularization can impair encoder learning.
While the work of Govindarajan al. (2024) represented important first step in identifying partial prototype collapse, their analysis did not examine its underlying mechanisms and was limited to methods within the DINO family. This opens the door to broader line of inquiry: Is partial prototype collapse restricted to the DINO family of methods, and what mechanisms drive this type of collapse?
2.2 Do ALL PROTOTYPICAL SSL FORMULATIONS EXHIBIT PARTIAL PROTOTYPE COLLAPSE?
Despite recent progress, our understanding of prototype collapse remains incomplete. The evidence so far comes exclusively from the DINO family, leaving open whether its partial collapse reflects a universal tendency of prototypical SSL or artifact of its particular architecture and training regime. To bridge this gap, we next investigate alternative prototypical frameworks, evaluating whether their learned prototypes exhibit similar degrees of redundancy-oo or if some, by design, avoid collapse altogether.
To this end, conduct straightforward analysis of the official weights of several prominent prototypical approaches. We evaluate the diversity of their learned prototypes by setting c = 0.025 following Govindarajan et al.'s (2024) setup and as defined in Definition 2.1. From the results in Table 1, we observe that CARP (Silva & Ramírez Rivera, 2023) achieves substantially higher prototype diversity than DINO. This difference may be explained by its random partitioning strategy,
'Common choices include the cross-entropy loss (Caron et al., 2021) and the cluster loss (Silva & Ramírez Rivera, 2023).
"We consider methods that have made their corresponding prototype weights publicly available.
Equiialentt to the inspected vectors having most 12.84 between them.
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Prototypes
Prototypes Manifold
Prototypes
Prototypes Manifold
Teacher
Teacher
Ce
EMA
Distribution
Distrbution
Student
Student
(b)
Figure 2: (a) Traditional joint-embedding architectures with a protolypical formulation: encoders and prototypes are optimized jointly under the same loss, which can lead to shortcut learning and prototype collapse-protayy converge to similar representations, reducing the effective representation space. (b) Our proposed solution: decouples the gradient flow to the prototypes and updates them with a separate objective, mitigating shorteut learning and preserving prototype diversity.
which closely resembles the subsampling approach proposed by Wen et al. (2024), which has been shown to enhance robustness to uncurated data. Interestingly. DINOv2's with its separate prototype heads for dense and instance-level objectives, reveal that prototype collapse can be highly objective- specific: its dense head remains relatively diverse (15.9% collapse), but the instance-level head suffers near-total collapse (98%).
To surprise, find that CAPI (Darcet et al., 2025) maintains markedly higher prototype diversity than the other methods, exhibiting near-complete uniqueness with only one collapsed prototype out of 16,384. It even manages surpass iBOT combined with the KoLeo-Proto (KP) regularization (Govindarajan et al., 2024), which explicitly encourages prototype diversity. This begs the question, what underlying mechanism in CAPI allows the prototypes to remain diverse throughout training?
A key distinction of CAPI compared to earlier prototypical joint-embedding frameworks is that it partially decouples the prototypes from the main loss. In most prototypical formulations- particularly within the DINO family-the the prototypes used to compute the teacher's 's soft assigmments are an EMA-updated version of those used for the student, keeping teacher and student prototypes tightly coupled through a joint optimization objective. However, Darcet et al. (2025) argue that, in a masked image modeling (MIM) setting such as iBOT (Zhou et al., 2022), this coupling creates a distributional mismatch: the teacher's 's prototype assignments are computed unmasked patches, whereas the student's prototype assignments are computed on masked patches. They argue that this joint optimization under distributional mismatch induces training instabilities.
CAPI addresses the instabilities driven by distributional mismatch, by introducing a partial decoupling strategy: the teacher encoder produces latent patch embeddings that assigned to prototypes learned independently within a separate clustering module, and these assignments then serve as targets for the student. The student branch, in turn, predicts these assignments using its own prototypes, which continue to be updated jointly with the encoder. Although Darcet et al. (2025) proposed this mechanism primarily for stabilizing purposes, our analysis shows that it also alleviates partial prototype collapse to an extent and, as result, improves prototype spread.
3 SOLVING PARTIAL PROTOTYPE COLLAPSE THROUGH DECOUPLING
Our analysis of CAPI reveals that decoupling the teacher's prototype updates from the main objective coincides with improved prototype diversity. This finding leads us to hypothesize that partial prototype collapse in prototypical SSL arises primarily from updating prototypes and encoders under shared loss. When prototypes are optimized jointly with the encoder, they may drift toward similar representations that minimize prediction eтror without improving the underlying features-a a form of shortcut learning.* Conversely, decoupling the teacher's prototypes from the main loss, as in CAPI (Darcet et al., 2025), should reduce this incentive, leading more stable and diverse prototype usage throughout training. This observation leads to our formal problem statement:
WWe clarify that by "mittgating shorteut learning" we do not mean shortcuts in relation to spurious correlations and group robustness (Geirhos et al., 2020), hut to the early drift of prototypes into redundant representations that artificially reduce the loss without improving the encoder's representations.
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Problem Formulation. Traditional prototypical SSL methods jointly optimize encoder fo and set of prototypes C' c= <=<c)k== k= by minimizing a consistency loss over augmented views,
min Lg (So: C)- C.C
This joint optimization often induces form of shorteut learning, where the prototypes' distribution rapidly collapse into narrow region of the representation space early in training. Such premature col- lapse undermines the very purpose of learning the prototypes C--to provide diverse and informative targets that guide fe toward representations that transfer well to downstream tasks.
If partial prototype collapse is influenced by the joint optimization of prototypes and encoders, then separating their updates may reduce the likelihood or severity of the collapse. Motivated by this intuition, and unlike CAPI (Darcet et al., 2025), which decouples only the teacher's prototypes from the main loss while keeping the student prototypes jointly optimized, we propose a fully decoupled training procedure that isolates prototype estimation from encoder learning, ef. Fig. 2(b), allowing us to directly probe the role of joint optimization in driving collapse.
Proposed Solution: Full Decoupling. Instead of jointly solving the original loss (2), over the iterations I, we alternate two separate objectives: (i) update the prototypes by solving an independent unsupervised estimation problem on the latent features, i.c.,
C² = arg min Le (C"-1,h)) CEC
and (ii) update the encoder for fixed prototypes by minimizing the consistency loss, i.e.,
g++1 arg min L C²):
where h denotes the latent representations at iteration f, and Lc is a loss that estimates prototypes directly from the latent features, independent of the encoder's loss Lj. By fully separating prototype estimation from encoder optimization, our method removes the shortcut incentive and yields stable, diverse prototypes throughout training. A theoretical motivation is provided in Appendix C.I.
3.1 DECOUPLING THE OPTIMIZATION
A central question in our framework is how to estimate prototypes once they are decoupled from the encoder. Breaking the joint optimization opens up rich design space: many unsupervised objectives could, in principle, be used for prototype estimation in Eq. (3). To be effective, however, such objectives must satisfy three key properties: (i) they should be representative and distinctive, ensuring that each prototype captures coherent and separate mode of the data; (ii) they should be learned over the evolving dataset rather than isolated mini-batches, to avoid noisy estimates and the resulting training instabilities; and (iii) they should be computationally efficient, so not to impede training time or create memory bottlenecks.
An obvious way to optimize Eq. (3) is to run K- K-Means clustering on the latent features. However, naively applying K-Means at every iteration violates two of the key properties outlined above: it bases prototype updates on the current mini-batch rather than the evolving drtaket-breaking property (ii)-and it is prohibitively expensive to run online at scale-breaking property (iii). Deep- Cluster (Caron al., 2018) and PCL (Li al., 2021) alleviated the cost by clustering only once per epoch on the full dataset, but this left prototypes outdated relative to the changing representation space. SWaV (Caron et al., 2020) addressed the issue of outdated prototypes by introducing an online, gradient-based method for prototype updates; however, this introduced the very coint-optimization dilemma we seek to avoid.
We address the optimization problem of Eq. (3), while satisfying the three outlined properties. by representing the prototypes as the means of an online Gaussian Mixture Model (GMM) (Neal & Hinton, 1998; Sato & Ishii, 2000). In contrast to naive K-Means, the online GMM incrementally updates its mixture components as new data arrive, allowing the prototypes to evolve continuously with the representation space. This procedure naturally incorporates information from the entire dataset over time rather than relying on isolated its incremental updates render it computationally feasible at scale, satisfying property (iii.. Moreover, mixture- mixture-based clustering has already been successfully applied in several deep learning contexts (Liang et al., 2022; Pu al., 2023; Zhao et al., 2023), underscoring its potential to satisfy property (i).
thereby satisfying property (ii), while
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While incorporating the GMM into our framework, developed a variant specifically designed to cope with the high-ding nigh-dimensional feature spaces and large prototype counts that naturally emerge in large-scale representation learning. Without modification, standard online updates at this scale suffer from unbalanced responsibilities and component drift. Drawing on responsihility-weighh (Celaya & Agostini, 2015) and deterministic annealing (Ueda & Nakano, 1998), we modulate both the strength of parameter updates and the sharpness of assignments, This ensures that components with fewer assignments maintain stable estimates while those with higher usage remain responsive. resulting in a more stable mixture and higher-quality prototypes at scale. We refer the reader to Appendix A for further implementation details.
forgetting
4 EXPERIMENTS
4.1 EXPERIMENTAL SETUP
To evaluate our decoupling strategy, we adopt CARP (Silva & Ramírez Rivera, 2023) as our primary point of reference. We select CARP for two main reasons. First, because it is an instance-base approach, and instance-based methods in general exhibit a higher degree of prototypical collapse (cf. Table 1), CARP provides a more challenging setting for evaluating our decoupling method, while also isolating the effect of MIM objectives prototype diversity, which we leave for future work. Second, extensive ablation experiments have demonstrated that CARP maintains robust and stable performance across wide range of hyperparameters (Silva & Ramírez Rivera, 2023), making it a suitable framework for evaluating our decoupling strategy without extensive hyperparameter tuning. In addition, we evaluate DINO (Caron et al., 2021) with our decoupling method, incorporating DINO enables broader assessment of the generality of our method and its impact on prototypical diversity.
Except for the experiment reported in Section 4.2, where we rely on the officially released weights, we train all models ourselves.' This enables us to analyze the training dynamics of the different methods in greater depth (an analysis that would not be possible without access to intermediate checkpoints) and to provide more detailed assessment of how prototype diversity benefits the handling of long-tailed distributions.
4.2 UNIQUENESS OF PROTOTYPES UNDER DIFFERENT THRESHOLDS
To test our hypothesis that joint optimization is responsible for partial prototype collapse (and that decoupling prevents if) we evaluate prototype diversity by counting the number of unique prototypes under different e configurations. Setting e = imposes no restriction and therefore shows the total number of initialized prototypes. Govindarajan et al. (2024) evaluated unique prototypes using e = 0.025, which we also showease. To examine partial prototype collapse more closely and to assess the effectiveness of our decoupling approach, we additionally evaluate using stricter threshold of e = 0.5, i.c., 20 times stricter than that of Govindarajan et al.' (2024) setup, this is equivalent to the prototypes being unique only if they are separated by at least 60%.
By examining Fig. 3(a), several notable insights emerge. First, a substantial collapse is observed in DINO and DINOv2, highlighting the extent of collapse within the DINO family of methods when no preventive measures are applied. Second, CAPI preserves prototype diversity at lower thresholds of e, exhibiting only minor collapse. As the constraint increases, CAPI still retains approximately 38% of its initialized prototypes. We attribute CAPI's robustness to prototypical collapse to its partial decoupling mechanism, in which the teacher-branch prototypes are updated using loss function separate from that of the student-branch encoder.
Lastly, we observe no evidence of partial prototype collapse across all tested values of e when the prototype objective is fully decoupled from the overall loss. This stands in clear contrast to CARP, which exhibits collapse in 90% of its prototypes already decoupling. Crucially. our approach not only prevents partial prototype collapse but also improves the encoder's 's learned representations. as demonstrated in Fig. 3(b). This distinction is central to our contribution: it supports our claim that joint optimization introduces form of shortcut learning (minimizing the loss without genuinely enriching the encoder's representations) whereas decoupling avoids this pitfall and yields more informative features.
0.025 and CAPI with its partial
Details of how the baselines were trained are provided in Appendix B.

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Unique Prototypes (%)
100
Top 1 NY (INTK) [S]
72
CARP
CARP Dec.
80
70
60
40
DINO
DINOv2
CAPI
CARP
68
67.7
A
+1.8
20
DINO + Dec
CARP + Dec.
66
0.025
0.1
0.25 Epsilon threshold
0.5
(a)
(b)
Figure 3: (a) Unique prototypes versus é (Definition 2) At = 0 all initialized prototypes are counted as unique, whereas increasing enforces stricter criteria (c.g., at 0.5 only prototypes separated by least 60 are considered unique). k-NN performance INIk for CARP showcasing improvement with decoupling.
Unique prototypes over epochs
Accuracy over epochs (ImageNet)
Nr. of Unique Protetypes
65k
70
Top-1 (56
40k
40
20k
20
10
20
30
60
70
100
10
20
60
70
100
Epoch
Epoch
DINO
DINO + KP
DINO Dec.
CARL
CARP
CARP Dec.
Figure 4: (a) Number of unique prototypes epochs. Prototypical methods without explicit diversity mechanisms (c.g., DINO and CARL) exhibit substantial prototype collapse early training. Lincar evaluation accuracy on ImageNet-Ik. Higher protolype diversity generally correlates with stronger final performance, though some methods (e.g.. DINO + KP) imposes a cost of slower early convergence.
4.3 TRAINING DYNAMICS
Although previous studies have examined partial prototype collapse, they have focused almost exclusively on its manifestation at the end of training (Govindarajan et al., 2023; 2024), leaving its interaction with the training dynamics largely unexplored. To address this and gain deeper insight into the relationship between prototype collapse and training progression, in Fig. 4, we track the number of unique prototypes in use and the linear evaluation accuracy on ImageNet-1k (Deng al., 2009) over the first 100 epochs for multiple methods. Specifically, include CARL (Silva & Ramírez Rivera, 2022) and CARP (Silva & Ramírez Rivera, 2023) (CARP being an extension the CARL framework that introduces random partitioning) alongside DINO (Caron et al., 2021), DINO + KoLeoProto (KP) (Govindarajan et al., 2024), and our proposed decoupled approach.
A first observation is that partial prototype collapse emerges very early in training: after only 10 epochs, two-thirds of the prototypes have already collapsed. Introducing the KP regularizer (Govin- darajan al., 2024) proves effective maintaining prototype diversity, underscoring its role strong collapse-preventis
mechanism. While DINO+KP exhibits modest drop in accuracy during the early stages of training, this effect diminishes over time, and the final model slightly outperforms vanilla DINO. This suggests that preserving higher prototype diversity throughout training ultimately leads to stronger representations in the converged model.
Another noteworthy observation is that CARP, is far less prone to prototype collapse than the baseline CARL. By the end of training, CARL retains only about 0.2% of its initialized prototypes as unique, whereas CARP preserves 9%. This difference is also reflected in final linear evaluation performance: CARP outperforms CARL. late in training but impaired early in training. While these gains cannot be attributed solely to prototype uniqueness (training stability likely plays significant role) they nevertheless amount to a substantial margin of roughly 4 percentage points in linear accuracy by the end of training.
Finally, we find that CARP Decoupling maintains full prototype utilization while outperforming all other methods in the early and late phases of training. indicating that decoupling does not hinder its early training dynamics. By the end of training, CARP + Decoupling improves upon CARP, demonstrating that enhanced prototype diversity yields stronger representations.
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4.4 EFFECT OF PROTOTYPE DIVERSITY ACROSS HEAD, MEDIUM AND TAIL CLASSES
Prototypical SSL methods generally perform well on carefully curated datasets: however, their effectiveness deteriorates markedly when trained on uncurated data (Oquab et al., 2024; Siméoni et al., 2025), which commonly exhibit class imbalances and long-tailed distributions characteristic of real-world scenarios (Mahajan et al., 2018 8; Newman, 2005; Van Horn et al., 2018). We argue, therefore, that a desirable property of any pre-training framework is robustness to long-tailed data distributions. Such robustness would enable practitioners to improve learned representations simply by scaling the amount of training data. Nevertheless, Fan et al. (2025) report that scaling up the amount of training data for a 7B parameter version of DINOv2 yielded limited benefits: the size of the training data increased, performance across a range of benchmarks decreased. These findings on data scaling underscore a fundamental limitation of current prototypical SSL approaches.
While Govindarajan et al. (2024) and Wen et al. (2024) empirically identi- fied a link between prototype diversity and improved performance on long- tailed distributions, an important ques- tion remains: is the observed improve- ment primarily due to a better ability
Table 2: Performance comparison on the iNaturalist 2018 dataset.
Results are reported as Top-1 accuracy (%) for different class splits.
Head
Medium
Tail
Methods
All
(> 100)
(> 20 & z 100)
($ 20)
DINO
55.2
46.2
41.9
45.3
DINO KP
59.8 4.4
50.4143 4:4
41
49.0
DINO Decoupling
44.9
37.3
33.1
36.2
to model tail classes, or is it simply a byproduct of improved modeling of head-class data? To address this ques- tion, we conduct granular experiment in which we train DINO and CARP with KoLeo-Proto (KP) regularization and our proposed full decoupling mechanism on the iNaturalist- 18 dataset (Van Horn et al., 2018). This dataset contains approximately 430K images spanning 8, 1.14 classes, with naturally long-tailed class distribution, making it an ideal benchmark for assessing the robustness of different methods under realistic data conditions. Following Liu et al.'s (2019) definition of class subcategories, we define head classes as those with more than 100 training instances, tail classes as those with fewer than 20, and medium classes as those in between. This setup provides detailed view of how each method performs across the head, medium, and tail classes, and offers insights into the benefits stemming from increased prototype diversity.
CARP
56.0
46.9
42.5
45,9
CARP+ KP
55.5 1 us
46.4 4 us
41.8 07
45.3 1.00
CARP Decoupling
39.1 3.
49.3
45.9
48.9
Table 2 presents the performance of all methods across the head, medium, and tail splits of iNaturalist 2018. Consis- tent with prior observations (Govindarajan et al., 2024), increasing prototype diversity often improves robustness under long-tailed class distributions. In addition, this ex- periment shows that these gains are not confined to head classes: improvements appear across all class-frequency regimes, including the tail classes. For DINO, KP reg- ularization yields a pe---eeentage-pope accuracy. In contrast, applying our decoupling strategy directly DINO leads to a substantial performance drop regimes. We attribute this de-
Table 3: ImageNet evaluation for instance- based prototypical SSL methods.
Mathod
Barkhone
Epuclss
KNNN (S)
(S)
DINO
RN 50
400
67.5
75.3
SHW
50
65.0
74.6
DespCluass222
RN-50
75.2
CARP
RN-50
400
67.2
75.3
CARP+ Decoupling
50
08.1
75.3
DINO
VIT-5/16
72.8
76.2
CARP
VIT-916
300
73.6
76.3
CARP+ Deseupting
VIES5166
73.7
gain in overall
MSN
VIT-5116
600
76.9
DINO
VIT:5/16
8000
94.5
77.0
DINO
S/L
74.7
77.9
CARP Decoupling
VITSS/L6
800
753
76.4
across all class-frequens cline the high sensitivity of DINO excessive prototype diversity; in ImageNet-Ik, extensive hyperparameter tun- ing was required to stabilize DINO under decoupling, and these settings do not transfer effectively to the heavily imbalanced iNaturalist domain. A detailed analysis of DINOs hyperparameter sensitivity is provided in Appendix C.3.
DINO
VIT-R/16
400
76.1
26.2
DINO
V/T
37.4
CARP+ + Descupling
VIT-1/16
400
76.7
7K1
Roval expeeed (icddidd rdleed proeated modik
forkil ruired seigl pulllll
For CARP, the trends differ: adding KP results in slight decrease in accuracy, which we suspect is linked to the choice of KP regularization strength. Our experiments adopt the value recommended by Govindarajan et al. (2024), selected based on ablations conducted for DINO, an architecture exhibiting substantially stronger prototypical collapse than CARP, as demonstrated in Figure 3()). When applied to CARP under long-tailed conditions, using the same strength appears to hinder learning. In contrast, integrating our decoupling strategy with CARP yields consistent improvements across all frequency regimes, amounting 3.0- 2.0-percentage- point gain overall.
In summary, and in line with Govindarajan et al. (2024), increasing prototype diversity in prototypical SSL frameworks may substantially improve robustness under long-tailed data distributions. Our
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Table 4: Transfer learning results. We follow Ericsson al. (2021)
transfer learning protocol. Top performing
bold, top-2 underlined.
Method
Epochs
Airer
CTO1
Cars
Flower
Food
Pets
SUN3997
VOC2007
Avg
ResNet-50
DINO
400
59.95
90.91
65.92
95.63
78.40
89.04
66.08
84.32
78.78
CARP
400
61.03
91.66
64.21
95.82
78.88
90.25
66.10
84.51
79.06
CARP Decoupling
400
58.50
92.07
67.28
95,91
78.74
91.11
65.24
84.55
79.18
VIT-Small/16
CARP
300
59.16
93.61
64.48
96.40
77.51
93.38
65.94
85.18
79.46
CARP + KP
300
60.48
93.54
63.55
96.44
78.61
93.40
65.98
85.34
79.67
CARP + Decoupling
300
61.78
92,91
63.90
96.20
78.49
94.13
64.53
85.35
79.66
granular analysis confirms that these gains extend consistently to tail classes rather than being driven solely by improved modeling of head classes. However, for DINO, an excessively large degree of prototype diversity appears to render optimization unstable and requires extensive hyperparameter adjustment. Likewise, for KP, our experiments indicate that careful tuning of the regularization strength across frameworks is necessary when operating in long-tailed settings.
4.5 LINEAR CLASSIFICATION ON IMAGENET-IK
We obtain strong k-NN performance with our proposed decoupling approach built on top of CARP, demonstrating the benefit of increased prototype spread with 1.8-percentage-ponn poiitagg--onntttto improvement in k-NN performance (Table 3). As is well known (Caron et al., 2021), linear evaluation results are highly sensitive hyperparameter choices, particularly for methods with diverse prototypes (Darcet et al., 2025; Oquab et al., 2024). Consequently, rather than performing extensive hyperparameter tuning for linear classification, we follow light grid-search protocol" and place primary emphasis on the k-NN metric, which provides more robust, fine-tuning-free assessment of representation quality.
4.6 TRANSFER LEARNING
The transfer learning results in Table 4 show that adding decoupling to CARP does not lead to a substantial increase in transfer learning performance. Across ResNet-50 and ViT-Small/16 backbones, the decoupled variants achieve comparable accuracy to the standard CARP, with small variations across datasets. This is consistent with prior observations by Govindarajan al. (2024), who report that increasing prototype diversity does not necessarily lead to improved transfer performance.
Table 5: Peak memory reserved per GPU for CARP and CARP + Dec. across increasing global batch sizes
4.7 MEMORY USAGE AND TIME CONSUMPTION
To assess the memory implications of the proposed decou- pling strategy, we measure peak GPU memory reserved per iteration when training a ViT-S/16 model on ImageNet-
Batch Size
CARP
CARP + Dec.
128
5.4G
5.3G 10.1
Ik with 10 local crops, comparing the joint-optimized CARP baseline with our decoupled variant while varying the global batch size. All experiments
256
9.3G
9.1G 102
512
17.3G
16.8G Lo.5
conducted AMD Instinet MI250X GPUs. Table 5 reports the per-
1024
32.3G
31.5G Lo8
2048
62.4G
60.9G L1S
GPU memory reserved for each approach. At smaller batch sizes (e.g., 128), the reduction in memory footprint is minimal, as activation and optimizer-state requirements dominate overall usage in this regime. However, the batch size increases, the decoupled formulation yields progressively larger savings. This behavior follows from the mechanics of the online GMM update: because prototype parameters are updated immediately after the forward pass and independently of the encoders loss, the method avoids storing the computation graph and intermediate tensors associated with prototype optimization. contrast, jotitooptimization approaches must retain these tensors until backprop- agation, contributing to the observed increase in memory usage with larger batch sizes. Because patch-level objectives introduce substantially higher memory requirements, we expect the memory savings from decoupling to be even greater in methods such as iBOT DINOv2, which we leave as an area for future investigation.
In terms of training time, Table 6 shows that the proposed decoupling method adds only a minimal increase, just 0.2 hours, indicating that the memory savings are achieved without any significant impact runtime.
"See Appendix C.2.1 for an extended discussion of the lincar evaluation protocol and additional results.

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Published as a conference paper at ICLR 2026
5 RELATED WORK
Table 6: Training time comparison showing that introducing the online Gaussian Mixture Model for decoupling incurs only a negligi- ble increase of 0.2h.
Self-Supervised Learning leverages unlabeled data by enabling the model to generate its own supervisory sig- nals. Early approaches introduced pretext tasks such as image inpainting (Pathak et al., 2016) and solving jigsaw puzzles (Noroozi & Favaro, 2016). Since then, dominant paradigm has emerged that employs joint- embedding architectures within a contrastive framework (Chen et al., 2020; Chen & He, 2021; Chen et al., 2021; Grill et al., 2020), which was later extended by incorporating a predictor network (JEPA) (Assran et al., 2023a). Another line of work employs reconstruction-batt based objectives in- stead (Bao et al., 2022; He et al., 2022).
Metuol
Epocta
Batch
Toual
Time
CARP
100
1024
12
37.9
CARP+ Decoupiing
100
1024
12
38.1
Prototypical Supe-Supe Learning extends joint-embedding methods by introducing a dis- crete set of learnable prototypes that serve as targets for representation assignment. Such formu- lations have achieved state-of-the-ee performance among vision-only SSL approaches (Siméoni alterna- al., 2025; Venkataramanan et al., 2025), rivaling the effectiveness of language-superving tives (Fan et al., 2025; Radford et al., 2021). Early methods performed cluster assignments once per epoch (Caron al., 2018: Li et al., 2021), which could result in outdated prototypes. To mitigate this issue, online methods were introduced (Asano et al., 2020; Caron et al., 2020), enabling the joint optimization of the encoder and prototypes, a strategy that has since become the status quo for most prototypical formulations (Assran et al., 2022; 2023b; Caron et al., 2021; Oquab et al., 2024; Ruan et al., 2023; Silva & Ramírez Rivera, 2022: Siméoni et al., 2025; Zhou et al., 2022). However, this joint optimization also introduced the phenomenon of partial prototype collapse which Govindarajan et al. (2023) was first to identify, and has since been addressed to varying degrees of success both explicitly (Govindarajan et al., 2024; Wen et al., 2024) and implicitly (Darcet et al., 2025; Silva & Ramírez Rivera, 2023). Recent work departs from learning prototypes explicitly, instead us- ing fixed high-dimensional codes sampled from a Rademacher distribution (Sansone et al., 2025) or non-parametric targets built from a queue of past encoder representations that act as effective prototypes (Gidaris al., 2021; 2024; Silva et al., 2024; 2025).
Although our proposed decoupling approach alleviates prototype collapse, it introduces several limitations. The current implementation lacks mechanism ensure that prototype updates track the encoders rate of change, as updates rely solely on the forgetting factor 1, which cannot adapt to shifts in the online estimation of the mixture. The use of an online GMM also adds hyperparameters. and it assumes that incoming representations follow Gaussian distribution. While our experiments show that the method eliminates prototype collapse across all investigated thresholds, the complete removal of collapse is not universally beneficial across frameworks (cf. Appendix A.3).
Limitations:
6 CONCLUSION
This work provides, to the best of our knowledge, the first systematic investigation into the root causes of partial prototype collapse in prototypical self-supervised learning. Through an extensive empirical analysis across diverse set of frameworks, we show that prototype collapse is not confined to the DINO family but is a widespread phenomenon, drastically reducing the effective diversity of prototypes and limiting downstream transfer performance. We identify joint optimization of encoders and prototypes under a shared loss as the key mechanism driving this collapse-enccoraggnn a type of shortcut learning and redundant prototype representations early in training.
Building on this diagnosis, we introduce a fully decoupled training framework that isolates prototype estimation from encoder learning. By representing prototypes as a continuously updated Gaussian mixture and estimating them via an online EM-style procedure, our approach removes the shortcut incentive inherent to joint optimization. This design yields stable and highly diverse prototypes throughout training without ad-hoc regularization or hyperparameter trade-offs.
Across extensive experiments, including imbalanced datasets, our decoupling strategy consistently enhances prototype spread, while its impact on downstream representations and robustness to chal- lenging data distributions varies across architectures. Together, these findings highlight the benefits of breaking the joint optimization paradigm, demonstrating that decoupled prototype learning is simple, principled, and scalable strategy for preventing collapse and improving representation quality in several prototypical SSL settings.
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ACKNOWLEDGMENTS
This work was funded, in part, by RCN (the Research Council of Norway) through Visual Intelligence, Centre for Research-based Innovation (grant no. 309439), and FRIPRO (grants no. 315029 and 359216). The computations were performed, in part, on resources provided by Sigma2 the National the
Infrastructure for Bigh-Peeffrrmnce Computing and Data Storage in Norway (Project NN8 104K). We thank Shashanka Venkataramanan and Yuki M. Asano (Franca team) for providing their reproduced DINOv2 prototype weights, which broadened the scope our study.
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Xin Wen, Bingchen Zhao, Yilun Chen, Jiangmiao Pang, and Xiaojuan Qi. What makes CLIP more robust to long-tailed pre-training data? A controlled study for transferable insights. Adv. Neural Inf. Process. Sys. (NeurIPS), 3773366677-66611, 2024. htths::::/ / /ww.odoooooooooo org 10. 52202 /079017-1153.
Bingehen Zhao, Xin Wen, and Kai Han. Learning semi-supervised gaussian mixture models for generalized category discovery. In IEEE Inter. Conf. Comput. Vis. (ICCV), pp. 16623-16633, 2023.
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Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. Image BERT pre-training with online tokenizer. In Inter. Conf. Learn. Represent. (ICLR), 2022. URL https: http:///pppeeiieeeeeee .nt/ weweeeerumiideeeeeeoeeeeee ydd
A ONLINE GAUSSIAN MIXTURE MODEL.
To decouple the joint optimization of the encoder and prototypes, we choose to represent prototypes explicitly as components of a Gaussian Mixture Model (GMM). Under this probabilistic formulation, prototypes capture the underlying structure of the data distribution independently from the encoder's training objective. By leveraging an Dnpectation-MMximiiaan et al., 1977). prototypes maximize the data likelihood of the teacher's latent embeddings, thereby, effectively disentangling their update mechanism from the encoder's s loss-driven gradient updates. This separation ensures that prototype optimization is solely governed by the statistical characteristics of the latent representations (Cc), promoting robust learning and preventing partial collapse.
(EM)-based approach (Dempster
While the classical EM algorithm provides a principled framework for prototype learning, it assumes access to a static and complete dataset. This assumption is incompatible with most SSL frameworks, where data becomes available incrementally during training. To address this limitation, we propose to adopt an online variant of the EM algorithm (Neal & Hinton, 1998; Sato & Ishii, 2000), which updates the mixture parameters incrementally using
the encoder continuously updates its representations
of data.
At each iteration f, we treat the incoming batch as sample from the evolving feature distribution and perform a two-step update: computing responsibilities for each latent vector, followed by an update of the GMM parameters using sufficient statistics.
The GMM is parameterized by ((--1) (m((1-1), (t-1), 1)-1) where n, μt, and E denote the mixture weights, means (prototypes), and diagonal covariances, respectively. For each input i, the
(t) responsibility Vik is defined
m (1-1) (-1)) (1.5) (e-1) x(((-1)) a
Vik
(A.1)
(t-1) P -e TM
(1 MK
(t-1)
_ x)(-11)
Here, 7sk denotes the soft assignment of latent vector h:00 = f (vi) from the teacher network to the k-th Gaussian component. Intuitively, it reflects how well the k-th component's 's distribution explains 1, To further enhance prototype utilization, particularly when employing a large number of components K, we introduce annealing mechanism controlled by smoothing factor / [o, 1] (Ueda & Nakano, 1998), which modulates the sharpness of the responsibilities during training.
(((()()))
Following the assignment of responsibilities, the expectation step utilizes these values to compute the intermediate sufficient statistics for the current timestep necessary to update the mixture's sufficient statistics. Specifically, each time step, the intermediate sufficient statistics for a batch B and views J are calculated as:
JB
JB
JB Σ
5(() = (500 500 200)
Σ
(4) ii
Pike
(t)
1
(
(A.2)
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These intermediate statisties are then used to update the sufficient statisties of the mixture using weighted moving average:
(())
11
+
- (1- ((t)
if > 1, otherwise.
(A.3)
Sk
where
Sk
JB K
(1) Mk SK,=
5())
5(1) k
k.
(A.4)
kRT
Here, 77 E [0, 1] is a forgetting factor, controlling the influence between new and past information. When using large number of prototypes K the mixture's components will receive sparse updates, thus, the forgetting factor 1) will tend to push the sufficient statistics towards zero. To circumvent this issue, introduce responsibility based forgetting mechanism (Celaya & Agostini, 2015) through the incorporation of the expectation of the responsibilities over the batch dimension fx- JB responsibility receive more aggressive updates, whereas those with lower responsibilities retain a larger fraction of their previous statistics, thereby, preventing the sufficient statistics to be pushed towards zero.
1 Σ. "ik- By raising the forgetting factor to the power of fn. components with higher expected
Given the updated sufficient statistics, we proceed to the maximization step of the EM algorithm, wherein the GMM parameters V are updated. This step updates the mixture weights, means, and covariances by computing their maximum likelihood estimates based on the current sufficient statistics:
$
(4) K
(
(0
K.u
(A.5)
5(0) RR R.
g
In the context of our prototypical SSL framework. the updated means μı serve as prototypes for the latent assignments, i.e., lM cą for k .,,.., K. Is important note that this maximization step is performed prior to the encoder's optimizer step, ensuring that the prototypes reflect the most recent assignment statistics before any encoder parameters are updated.
Throughout training, we use a variation of pplit-andmergy (Ueda & Nakano, 2000) for regularization. But instead of merging low-weight clusters, we instead we apply a method we call split-rexurrect. Whenever some component k exceeds a weight threshold, we identify the lightest component j. reinitialize its mean (scale-aware random initialization) and reset its variance, and then split the mass oldd For high cluster weights, we regularize the scale of the dominant of k evenly, f Ty. + T mean by
p = ue /VV ||
(1)
10 ll2
(A.6)
which avoids dominant norm clusters in the GMM.
A. ABLATION: IMPORTANCE OF THE DIFFERENT COMPONENTS
We assess the impact of the individual components in our proposed decoupling strategy - the online Gaussian mixture. Specifically, train CARP with a ViT backbone using 10 local crops ImageNet- 1 to evaluate each component. The linear accuracy is reported using PyTorchs L-BFGS solver (Liu & Nocedal, 1989; Paszke et al., 2019).
As shown in Table 1, the responsibility-foreete tini (2015) is essential given the sparse updates that occur when using large number prototypes. Without this mechanism, the forgetting factor 1) drives the sufficient statistics toward zero, ultimately leading to collapse. While the remaining modifications are less detrimental, they nonetheless yield measurable gains in the encoder's 's representational quality to varying degrees.
mechanism introduced by Celaya & Agos-
A.2 ABLATION: SENSITIVITY ANALYSIS OF THE FORGETTING-FACHE SCHEDULER
The forgetting factor r used in the online GMM update is defined through a scheduler of the form
17 0.99
(A.7)
al
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Table A.I: Ablation study of model components.
Responsibility Based Forgetting (Celaya & Agostini, 2015)
Annealing
Resurrect
Rescaling
Lin.
(Ueda & Nakano, 1998)
X
v
0.1
X
71.65
71.97 v
X
X
71.99
V
X
X
72.12
V
72.25
Table A.2: Ablation of forgetting-factor scheduler parameters ImageNet- Ik with CARP+Dec..
Method
Arch
Epoch
a
k-NN (%)
CARP Dec.
ViT-S/16
100
0.001
0.75
66.82
CARP + Dec.
ViT-S/16
100
0.001
0.95
67.41
CARP+ Dec.
VIT-S/16
100
0.0005
0.89
69.26
CARP Dec.
ViT-S/16
100
0.002
0.89
68.99
CARP Dec.
ViT-S/16
0.001
0.89
69.52
where denotes the training timestep, controls the rate at which (1)) approaches its upper bound of 0.99, and 6 0.99-6' The parameter determines the initial value the scheduler, while a governs its progression over the course of training.
In the main experiments, we set a = 0.001 and c= 0.89, which yields an initial forgetting factor of n 0.89 at the first training step. To assess the sensitivity of this choice, we evaluated alternative schedules with different values of and on ImageNet- 1k using VIT-S trained for 100 epochs with local crops, varying each parameter independently while keeping all other hyperparameters fixed.
Overall, the results indicate that performance remains stable across reasonable range of scheduler configurations. Adjusting the intercept e produces the largest effect: decreasing e 0.75 leads to a notable drop in accuracy, as the resulting schedule causes the prototypes to update too aggressively carly in training. Increasing c to 0.95 slows the early updates and yields a milder degradation, but still performs worse than the baseline. The intermediate value 0.89 provides a balanced update rate that appears most effective. contrast, modifying the convergence rate through has a more negligible influence performance, suggesting that the schedule is less sensitive to this parameter.
A.3 LIMITATIONS
Although proposed decoupling approach alleviates prototypical collapse, it comes with certain limitations. First, the current implementation lacks a mechanism to ensure that prototype updates remain aligned with the encoders rate of change. Prototype updates governed solely by the forgetting factor 7), and although a linear schedule performs reasonably well, it does not allow the method to adjust adaptively the online estimation of the Gaussian mixture. Because 7) plays role analogous to learning rate in gradicnt- based optimization, an interesting direction for future work would be incorporate momentum better regulate prototype updates.
Furthermore, incorporating an online GMM to enable our decoupling strategy introduces additional hyperparameters, such the smoothing factor and the forgetting factor 7, which required to manage the sparse update regime associated with the large prototype sets used in prototypical SSL frameworks. The online mixture model also assumes that incoming representations follow Gaussian distribution with meaningful variation in magnitude. This assumption aligns with CARP (Silva & Ramírez Rivera, 2023), which does not normalize its projection head outputs, but does not strictly hold for DINO (Caron al., 2021), where the outputs are normalized. Although our internal experiments did not reveal noticeable differences when replacing the Gaussian with a von Mises Mises-Fisher distribution, the current formulation of our decoupling method is built around Gaussian assumption.
Lastly, experiments in Section 4.2 and Section 4.3 show that the proposed decoupling method effectively eliminates prototype collapse across all our investigated thresholds e following Definition 2.1. However, the absence of prototype collapse is not universally beneficial for all frameworks, as
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Table B.1: Training hyperparameters for ViT-Small configurations for CARP & CARP Decoupling and
ViT- configurations forCARP + Decoupling.
(a) VIT Small Configuration
(b) VIT Base Conliguration
argument
value
conlig
value
architecture
vit_small
architecture
vit_basc
n-prototypes
65536
patch size
n. protoolspsss
65536
16
patch size
16
momentum teacher
0.996
momentum
0.992
drop-path path
0.1
drop. drop.path patt
0.1
bottleneck dim
256
bottleneck dim
256
juhhl_crrpp. scale
[0.32, 1.0]
local.crops_scale
10.05, 0.32)
goballcrops_sceee
[0.32, 1.0]
optimizer
Adam
local wwt.recrrpssceecce
[0.05, 0.32]
learning rate
7.5e
optimizer
AdamW
weight.docar
0.04
weight. cond
0.4
learning rate (Ir)
5e-4
freeze protolypes
Galse
weight.decay
0.04
min_ir
weiggh_decca_com
0.4
clip cip-grad
0.3
freeze prezeeprrtottpes
false
warmup epochs
10
min Ir clip grad warmup-epochs
lc-6
1.0
10
evidenced by the results in Section 4.4. We nonetheless view this as meaningful contribution to the community, as enables systematic evaluation of prototypical SSL methods across different degrees of collapse: whereas Govindarajan et al. (2024) reduces collapse, our approach eliminates it entirely", providing a complementary perspective for understanding its role in representation learning.
B TRAINING DETAILS
B. HYPERPARAMETERS
For our experiments in Sections 4.3 and 4.4 our baselines DINO, DINO + KP and CARP are trained using ViT-S/16 architecture while CARL is trained using a ResNet-50 backbone. Additionally, for CARL we increase the number of initialized prototypes to 65536 to enable a fairer comparison and adopt the same training improvements incorporated in CARP, which includes multi-crop augmentation and added schedulers. Besides accommodating for these architectural changes in CARL and CARP, the of the official codebase is left untouched. For the DINO model use the officially released codebase without applying any changes (Caron et al., 2021). For DINO+KP, we use the same codebase as for DINO with minor modification; we incorporate the KoLeo Proooo-e regularization proposed by Govindarajan et al. (2024), setting the regularization strength to the empirically validated value of 0.1 reported in their paper.
We report the hyperparameters used to train the vision transformer backbones (Dosovitskiy al., 2021) with CARP and CARP Decoupling in Table B.I. In addition to these hyperpa- rameters, CARP+ + Decoupling employs a weight threshold of 0.3 for the resurrect strategy, which is relatively high given the 65536 components the mixture. Furthermore, for the smoothing factor B, we use linear scheduler that increases from 0.1 at the start of training to 0.5 at its conclusion.
B. EXPERIMENT: UNIQUENESS OF PROTOTYPES UNDER DIFFERENT THRESHOLDS
In our experiment described in Section 4.2, as well as in the reported number of unique prototypes in Table 1, we use the officially released pre- pre-trained weights and reported numbers for all methods except DINOv2. At the time of writing, the prototype weights for DINOv2 were not publicly available; therefore, we rely on the re-produced weights a ViT-L/14 model from Venkataramanan et al. (2025). For DINO and CARP, we evaluate their ResNet-50 checkpoints trained for 400 epochs. For CAPI, evaluate its ViT-L/14 checkpoint pre-trained on ImageNet-Ik, lk. Since the teacher branch's 's prototypes
Under all thresholds used to define unique prototypes in our evaluations.
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unavailable, instead use the EMA-updated student branch prototypes. We evaluate the iBOT ViT-S/16 checkpoint, and the iBOT-vMF + KP unique prototype values are directly extracted from Govindarajan et al.'s (2024) paper.
B.1.2 EXPERIMENT: TRAINING DYNAMICS
We train all baselines and CARP Decoupling on ImageNet- (Deng et al., 2009) for 100 epochs using 6 local crops. For linear evaluation, we freeze the backbone and train single linear classifier us- ing a batch size of 1024 with PyTorch's LBFGS optimizer (Liu & Nocedal, 1989; Paszke al., 2019). Concretely, we minimize cross-entropy on the training set using L-BFGS with max_iter=150, tolerance.gradelXx
walerancc..cange-ll. 10-99, and history. size==00.
B.1.3 EXPERIMENT: EFFECT OF PROTOTYPE DIVERSITY ACROSS HEAD, MEDIUM AND TAIL CLASSES
We train all baselines and CARP+ Decoupling on iNaturalis20188 dataset using 10 local crops. All models use a ViT-S/16 backbone trained for 300 epochs on iNaturalist2018 The iNaturalis2011 challenge large scale species classification challenge that has long been the standard dataset for evaluating long-tailed performance. There are 8142 classes in this dataset, with 437,513 training images, and 24,426 validation images. We use the validation set for evaluation the real test is deliberately left unavailable for public use. The dataset follows a heavy long-tail, with multiple classes appearing very few times in the training set. Following Liu al. (2019), we consider all classes with more than 100 images each as head classes, between 20 to 100 images each as medium classes, and less than 20 images each to be tail classes. Using this design choice, we have 842 head classes, 3701 medium classes, and 3599 tail classes.
We adopt the linear evaluation protocol of Caron et al. (2021) to assess all methods, with results reported in Table 2.
C EXTENDED RESULTS
The preceding sections establish the empirical evidence motivating the proposed decoupled framework and its effects prototype diversity, training dynamics, and performance across distribution regimes. These findings demonstrate that joint optimization induces a form of shortcut learning, driving prototypes toward redundant representations early in training, whereas decoupled updates maintain higher prototype diversity.
C.I THEORETICAL PERSPECTIVE ON PROTOTYPE COLLAPSE
The empirical results consistently reveal a strong link between the way prototypes are optimized and the emergence of partial prototype collapse. These patterns point toward structural properties of the optimization that influence how prototypes distribute across the representation space. This section introduces theoretical perspective that explains why joint updates promote redundancy and why separating prototype estimation leads diverse set of prototypes.
C.1.1 DECOUPLING AND PROTOTYPE COLLAPSE
Consider the prototype subproblem at fixed encoder parameters 0 and soft assignments YH induced by the teacher-student logits. We can pose the subproblem as
J(C (1,7) = Σ Yak |h c+ll.. h; fo(x.))
E. Teh If distinct
whose unique minimizers are the responsibility centroids ch - 2:70
components j * & have different responsibilities Y. * 7ik. then o; * cf almost surely; hence collapsed prototypes stationary points of the prototype subproblem J.
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The decoupled optimization approximates coordinate-descent / EM scheme. For fixed 6g at step t the GMM update performs an online M-step that pushes the full set of prototypes C2 toward the centroids c (0,, 74). Morcover, for fixed Ct, we update 0 on the SSL objective (0, C,). This keeps prototypes close to block-optimal solutions of the prototype subproblem at each step, which disfavors collapse whenever components have distinct assignments.
In contrast, joint gradient updates on (0, C)) only enforce joint stationarity of Cy C.), and do not enforce optimality of J(C 0, 7). In other words, collapse with cj - c can be joint stationary points of the coupled system, even though they are suboptimal for the prototype subproblem. This is what we observe in our analysis of DINO-style modeling (Table I, Figure la, Figure 4).
We note that if student prototypes of DINO exhibit collapse, the gradients for collapsed components receive identical updates, collapsed prototypes cannot re-separate. Furthermore, any collapse in the student model will invoke collapse in the teacher, whose prototypes are EMA updates of the student. Hence, teacher asymmetry does not meaningfully help prevent collapse.
C.1.2 FORMALISATION OF DECOUPLING PROTOTYPE COLLAPSE
Lemma C.1 (Unique Centroids). For the prototype subproblem
J(C (0,7) Ju(ck) J&(ck)
Σ Yik [1 cx11?
(C.1)
each Jg is strictly convex quadratic in og with unique minimizer
(0,7))
Σ racs,
m. =
Σ Vik-
(C.2)
m&
Proof. The gradient and Hessian of Jr. are given by
V Je(c)) --2
-25
"Innah Tach + 2mpck
V2 Ju(cx) 2m
(C.3)
As ml > the Hessian positive definite, so Ja strictly convex with unique minimizer
1
V Jo(c))
Σ rahh
(C.4)
we wanted to show.
Proposition C.2 (Non-collapse for decoupled prototype subproblem). Assume features h; E Rd are drawn from a distribution that absolutely continuous w.r.t. Lebesgue measure. Fix responsibilities 2 0 and masses my Σ; Vik > 0.
Then for any pair j + k with 7i # Yuk we have that Pr(c; ct) 0. i.c. ot # oj almost surely. Equivalently, collapsed centroids occur on subset of measure zero.
Proof. By Lemma the centroids are
my Σ Light &
mi Σ Eishh
These are convex combinations of the features with normalized weight distributions (1y//m,) and Pra/mm)ii
Since Yij + Tik these weight distributions differ: there exists at least one index such that J # 7/mk/mg-
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Collapse of cj occurs if and only if
Σ Vij h4
Vike hi my
Σ wyh, = 0,
my
where w, = "Ky/mm Yoke mg.
Since the weight distributions differ, w * 0 (i.e., not all w, 0). The collapse condition Σ, wih 0 therefore imposes a non-trivial linear constraint on the features.
Geometrically, this defines a hyperplane in Rn the set {(h),...,, hnn) E, wyhe = 0} is (nd - dimeensiio affine subspace of the ambient nd-dimensional space. Since each h, drawn independently from a distribution absolutely continuous with respect to Lebesgue measure, the joint distribution of (h.....,h, is absolutely continuous on paxd and assigns measure zero any proper affine subspace.
Therefore, P(c ( = 0.
Corollary C.3 (No Prototype Collapse at Decoupled Fixed Points). Let (0", C') be decoupled fixed point, such that
C* is local minimizer of the prototype subproblem
C
arg min [C ;");,,)
0 is a stationary point of the SSL objective
(0 = 0.
Then given the conditions of Proposition 1, for any pair of distinct components j * & with nig o 7:kt we have
P(c = = 0.
In other words, decoupled fixed points do not admit prototype collapse almost surely whenever the induced responsibilities are non-identical and non- non-degenerate.
Proof. Since C* minimizes J(. (00,"") each centroid must be the cesponsibility-weighhe mean:
of
m
By Proposition if n/ # vi and mj, m > 0, then
P(e = cf) = 0.
Note that this result does not necessarily hold for coupled optimization such as with DINO, which can yield cases where a joint optima over the SSL loss function admits cj = Ck.
C.2 LINEAR CLASSIFICATION
C.2.1 IMAGENET-IK
In Table C.I, we report extended linear classification results obtained using our proposed decoupling approach built on top of CARP and compare them with other prototypical methods, including those with added dense objectives. For these linear results we train all our models using 10 local crops. For our k-NN evaluation we adopt Caron et al.'s (2021) evaluation protocol. We find that linear classification performance is highly sensitive to hyperparameter choices, consistent with observations by Caron et al. (2021). When directly applying DINO's 's (Caron et al., 2021) linear evaluation protocol, results hypothesize that this protocol's 's hyperparameters are tuned for methods exhibiting strong prototypical collapse. This interpretation is supported by the fact that DINO and iBOT (Zhou al., 2022)
substantially lower than suggested by k-NN evaluations. We
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Table C.I: ImageNet evaluation results for various prototypical SSL methods and architectures.
Method
Backbone
Epochs
K-NN (%)
Linear (%)
DINO
RN-50
400
67.5
75.3
SWAV
RN-50
400
65.0
74.6
CARP
RN-50
400
67.7
75.3
CARP + Decoupling
RN-50
400
69.1
73.3
DINO
ViT-S/16
300
72.8
76.2
IBOT
VIT-S/16
300
74.6
77,4
CARP
ViT-S/16
300
73.6
76.3
CARP KP
VIT-S/16
300
73.7
76.1
CARP + Decoupling
ViT-S/16
300
74.1
76.2
MSN
VIT-S/16
600
76.9
IBOT
ViT-S/16
800
75.2
77.9
DINO
ViT-S/16
800
74.5
77.0
DINO-vMF
VIT-S/16
800
74.7
77.0
iBOT-vMF
ViT-S/16
800
75.3
77.9
iBOT-vMF+ KP
VIT-S/16
800
75,3
77.9
CARP + Decoupling
ViT-S/16
800
76.4
DINO
ViT-B/16
400
76.1
78.2
DINO-vMF
VIT-B/16
400
77.4
78.8
iBOT
ViT-B/16
400
77.1
79.5
iBOT~MMF
ViT-B/16
400
78.7
80.3
iBOT-vMF + KP
ViT-B/16
400
78.8
80.5
CARP + Decoupling
ViT-B/16
400
76.7
78.1
Table C.2: iNat-2011 2018 classification accuracics with full data.
'Results retrieved from Govindarajan et al. (2024).
Method
Unique Protos.
Linear (%)
Fine-tuned (%)
ViT-Small/16
DINO-vMFt
1380
(2.1%)
49.7
68.5
iBOT-vMF*
1804
(22.0%)
50.1
69.4
iBOT-vMF (kd)
1843
(22.5%)
50.5
69.1
iBOT-vMF (kp)
7895
(96.4%)
51.1
69.3
MSN (A = 1)'
3363
(41.3%)
53.8
63.5
PMSN 5)
3005
(36.9%)
41.8
64.2
CARP Decoupling
65536
(100%)
49.1
71.7
ViT-Base/16
iBOT-vMF (kd)²
1634
(19.9%)
50.4
73.3
iBOT-vMF (kp)
7573
(92.4%)
51.4
74.0
CARP Decoupling
65536
(100%)
48.3
71.8
use these hyperparameters successfully, whereas methods with greater prototype diversity (Darcet al., 2025; Oquab et al., 2024) typically perform much broader hyperparameter searches for linear evaluation ranging from 30 configurations (Darcet et al., 2025) to over one hundred (Oquab al., 2024). Accordingly, we adopt the lighter grid-search protocol of CAPI (Darcet et al., 2025) while retaining DINO's choice of which outputs train the classifier on: the concatenation of the last four ViT layers for ViT-Small and the last VIT layer with averaged patch tokens for ViT-Base. While we believe further hyperparameter tuning could improve the linear results, we intentionally refrain from doing so and instead recommend interpreting our representations primarily through the N-NN metric, which offers more reliable, tin-ttuningfff free measure of representation quality.
C.2.2 INATURALIST2018
In Table C.2, report the linear and fine-tuned classification accuracies iNaturalist2018 for CARP + Decoupling trained with 10 local crops over 300 epochs. Baseline results are taken from Govindarajan et al. (2024).
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Table C.3: Sensitivity analysis of DINO under different configurations of hyyperparaeeeers.
Method
Dec.
Cent.
SK
# Prototypes
Teacher temperature
k-NN (%)
DINO
65536
0.04 - 0.07
68.91
DINO
65536
0.04 + 0.07
27.8,
DINO
65536
0.04 - 0.07
62.2. 6.7
DINO
65536
0.05 0.025
67.7u 1.2
DINO
1024
0.05 + 0.025
68.0, 0.9
DINO
2048
0.05 0.025
68.7, 0.2
Our produced DINO backbone using 6 local urups and mixed precision training.
C.3 SENSITIVITY OF DINO WITH FULL DECOUPLING
While the proposed decoupling method mitigates prototypical collapse in both CARP (Silva & Ramírez Rivera, 2023) and DINO (Caron et al., 2021), it also introduces training instabilities in DINO. To examine DINOs sensitivity to increased prototype diversity, we reproduce a baseline DINO model using the official codebase with two slight modifications. First, we adapt the dataset loader to meet the constraints of our High-Performance Computing (HPC) environment, which prevents us from reusing the exact same data-loading seed. Second, to reduce training time and computational cost, we employ mixed-precision training instead of float32.
The resulting k-NN performance is reported in Table C.3. While the original DINO paper reports k-NN accuracy of 69.7, our reproduced model exhibits modest performance drop of 0.8 percentage points. We attribute this difference primarily (a) the altered data ordering introduced by our changed dataloader and (b) the reduced numerical precision during training. All other baselines are produced under the same conditions, ensuring that the results in the table remain directly comparable. All models are trained on ImageNet- 1k for 100 epochs using six local crops.
Building on these observations, we next investigate how DINO behaves when its prototype optimiza- tion is replaced by the decoupled online GMM update. As shown in Table C.3, replacing the prototype update mechanism from gradient descent to an online GMM, while keeping all other hyperparameters fixed, results in performance reduction of 41.1 percentage points. This suggests that the centering operation in the standard DINO formulation is insufficient to promote sufficiently diverse assign- ments when prototype diversity increases. To address this limitation, we employ Sinkhorn-Knn Knopp normalization (Cuturi, 2013), which substantially improves assignment uniformity and reduces the performance gap with vanilla DINO to 6.7 percentage points. This effect improving uniformity accross assignments was first identified by Ruan et al. (2023) and later adopted by Oquab et al. (2024) in the DINOv2 framework.
Next, we follow the recommendations of Ruan et al. (2023) and adopt their teacher-temperatur scheduling strategy, which progressively increases the sharpening of the teachers assignment distri- bution and thus provides a stronger learning signal. We observe that this modification substantially benefits DINO under increased prototype diversity: the additional sharpening yields further im- provement of 5.5 percentage points, narrowing the remaining gap to the vanilla DINO baseline even more effectively.
Finally, we investigate whether adjusting the number of prototypes can further stabilize training under the decoupled formulation. We find that substantially reducing the prototype count 1k yields a small additional improvement, leaving remaining gap of 0.9 percentage points to the baseline. Exploring this further, we identify an intermediate setting with 2k prototypes as the most effective configuration: this choice closes the gap almost entirely, reducing the difference to only 0.2 percentage points.
We use these selected configurations for all DINO + Decoupling experiments Section 4.3 and Section 4.2. For the long-tailed setting in Section 4.4, retain the same hyperparameters but increase the number of prototypes to 8192 to match the 8142 classes in iNaturalist- 18. Applying the settings tuned ImageNet-Il 1 to iNaturalist-15 18 leads to substantial performance drop, reported in Table 2. Although further tuning tailored to the long-tailed distribution could likely mitigate this behavior, such investigation falls outside the scope of this work.
Ultimately, we find the pronounced sensitivity of DINO to prototype diversity to be an interesting empirical observation. Although CARP is architecturally similar to DINO, it differs in four key
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Published as a conference paper at ICLR 2026
components: random partitioning to stabilize training, unnormalized projection-head outputs, entropy regularization in place of centering the teacher logits, and loss formulation that favors more one- hot-like predictions. Any of these design choices, some combination thereof, may underlic CARPs ability to remain stable and benefit from increased prototype diversity. Determining which components responsible for this robustness, and how they interact, represents compelling direction for future research.
D DECLARATION OF USE OF LARGE LANGUAGE MODELS
During the preparation of this work, the author(s) used Large Language Models (LLMs) for grammar and spelling checks, paraphrasing and rewording, code writing, writing assistance and reviewing, as well as for identifying and summarizing related work. After using these services, the author(s) reviewed and edited all generated content as needed and take(s) full responsibility for the publication's content.
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Reviews:
[{"review_id": "tbpW5jge4h", "reviewer": "Reviewer_Lrqz", "summary": "This work explores the pervasiveness of a type of shortcut learning in self-supervised methods called partial protytype collapse. The authors show not all methods exhibit equal susceptibility to partial protytpe collapse, noting that methods that have decoupled training objectives for prototypes suffer much less from this shortcut. Motivated by this finding the authors proposes learning prototypes using an EM approach that's separate from the main self-supervisd training objective.", "questions": "see above", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- findings in Section 2 that not all methods suffer from partial prototype collapse is novel and nicely motivates the decoupled training method proposed.\n- the authors connect this collapse to recent findings regarding the muted effect of data scaling in SSL methods (lines 388). This is a fundamental open question that is carefully studied here through the lens of prototypes. \n- examining training dynamics of the prototype collapse in Section 4.3 is an insightful approach that goes beyond simply examining the final representation. This section offers several nice insights such as the fact that the collapse emerges early on in training. \n- authors include a nice comparison for KNN and linear probing for both iNaturalist and ImageNet, showing decoupling outperforms baselines. \n- authors include hyperparameters and training details in the appendix", "weaknesses": "- define prototype in the introduction, and provide a clear accessible explanation of the partial prototype collapse you're aiming to solve.\n- as described in section 2.1 the setting you're working with is focused on image domain, make sure this is clearly defined early on in the paper so readers have the right expectation of the setting you're exploring. \n- similarly, technial terms such as KP regularization also require even a brief explanation to make this work accessible to broader audience. The authors assume too much prior knoweldge in my opinion. \n- what limitations does using a Gaussian Mixture Model impose on the learned algorithm? A discussion and exploration of the limitations this imposes is missing.\n- the authors discuss the merits of CARP w/ Decoupling in Section 4.4 with respect to head and tail classes, but offer a discussion or explanation of why CARP w/ decoupling underperforms DINO + KP for medium tailed classes as shown in Table 2. \n- I'd be curious to see scaling trends for CARP w/ decoupling given the discussion of scale in Section 4.4. Have the authors experimented with this?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VTxQXmF4Fa", "reviewer": "Reviewer_7bAf", "summary": "Prototypical self-supervised representation learning (SSL) methods such as DINO suffer from a partial prototype collapse issue, which heavily limits the diversity of the learned prototypes. This paper argues that this issue is caused by the joint optimization of the encoders and the prototypes. Inspired by partially decoupled training in CAPI [1], this paper proposes a fully decoupled training method. Through empirical experiments on the CARP [2] SSL method, the paper shows that this eliminates prototype collapse. By using diverse prototypes, they claim to learn improved representations, as reflected in improved downstream performance.", "questions": "- How much time and memory overhead does the online GMM add, including all the proposed techniques in Table A.1?\n- Is the online GMM setup (techniques and related hyperparameters) the same for both ImageNet and iNeturalist2018 pre-training? Is it necessary to adapt them to different pre-training datasets?\n- In Table 2, what is the backbone used for all the models?\n- The kNN performance reported in Figure 3b does not match with the results reported in Table 3. Can the authors clarify if the results in Figure 3b are after 100 epochs (corresponding to Fugure 4) and what backbone model is used here?\n- CARP uses prototypes that are divided into P blocks of size N_B each. The paper specifies the total number of prototypes. But how many partitions are used? Just to clarify, is the online GMM applied to each block separately or is it applied to the complete set of prototypes?", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Prototypical SSL methods such as DINO have grown to become widely used and better understanding the partial prototype collapse issue sheds light on the inner workings of these methods and provides insights on how to further improve them.\n- The development of the fully decoupled training methodology by using an online Gaussian Mixture Model to update the prototypes is interesting. This is a valuable contribution as this involves specific choice of techniques such as responsibility based forgetting to avoid collapse and other techniques to further improve performance.\n- Decoupled training of the encoders and the clustering model/prototypes offers an interesting pathway to simplify and improve prototypical SSL pre-training like DINO.", "weaknesses": "**Major:**\n- The partial prototype collapse occurs in many prototypical learning methods. The decoupled training is presented as a more general contribution, but the paper only experiments with CARP. So, it is unclear if the proposed method is indeed general.\n- In Table 3, there is a direct comparison between CARP and CARP+Decoupling only for the Resnet-50 model. Can the authors produce similar results for the other backbones (ViT-S, ViT-B)? Otherwise, it is hard to identify the impact of the proposed decoupled training method.\n- One prior approach to prevent partial prototype collapse is the KoLeo-Proto (KP) regularization [3]. But the paper does not directly compare against this. For example, this can be clarified in Table 2 by adding the results for DINO+Decoupling and CARP+KP. That can show both the generality of the decoupling approach and comparison with KP regularization, at least in the long-tail context.\n- Since the paper mainly experiments with the CARP method, it is also worth comparing CARP+Decoupling with CARP+KP in some of the ImageNet experiments in Table 3.\n- The best possible linear probing accuracy achievable using the learned representations is a useful indicator of the representation quality. The hyperparameter choice is indeed important but running this is trivial and not expensive.  See section B.3 in DINOv2 [4]. The forward pass through the model is done once and several linear classifiers with different hyperparameters are trained simultaneously. For a publicly available implementation, I refer the authors to the iBOT repo (https://github.com/bytedance/ibot/).\n- The paper shows improved prototype diversity but does not sufficiently demonstrate how this translates to better representations. An important aspect of SSL is the transferability of learned representations. Currently, no transfer learning experiments are included. [3] found that the transfer learning performance was similar or worse when pre-training on ImageNet with KP regularization. Is this also the case with Decoupling? In that sense, it is especially important to evaluate this (for say, CARP vs CARP+Decoupling and if possible CARP+KP).\n- The motivation for choosing CARP in section 4.1 is not clear. It is stated that CARP exhibits a higher degree of collapse and hence, a bigger challenge. But in section 2.2 (line 153) it is stated that \"CARP achieves substantially higher prototype diversity than DINO\" and in section 4.3 (line 368) it is stated that \"CARP is far less prone to prototype collapse than the baseline CARL\". These statements are conflicting. Wouldn't it make sense to experiment with DINO instead if the idea is to choose the method that exhibits the highest amount of collapse/challenge (see Table 1)?\n\n**Minor:**\n- On one hand, this simplifies some complexities in training prototypical SSL methods by not requiring centering, sharpening. But this introduces other techniques and hyperparameter choices in the online GMM step. Since the responsibility based forgetting is important to prevent collapse, how sensitive is the training to the choice of the forgetting factor $\\eta$? An ablation experiment on this choice can be useful. Also, what is the value of $\\eta$ in the paper?\n\n[1] Darcet et al. “Cluster and Predict Latent Patches for Improved Masked Image Modeling.” TMLR 2025.\n\n[2] Silva et al. “Representation learning via consistent assignment of views over random partitions.” *NeurIPS 2023*.\n\n[3] Govindarajan et al. “On partial prototype collapse in the dino family of self-supervised methods.” BMVC 2024.\n\n[4] Oquab et al. “Dinov2: Learning robust visual features without supervision.” TMLR 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Uu3jXq1y5n", "reviewer": "Reviewer_qYSn", "summary": "The article is on the prototype collapse problem for prototypical self-supervised learning algorithms. In such algorithms, representations are organized around certain prototype points, where the prototype points are also trained. A major issue is that during training, these prototypes can merge or collapse into a smaller set. The article offers an empirically evidenced hypothesis for the cause of this problem as the joint estimation of the encoder parameters and prototype points based on the same loss. Then it proposes a solution where different loss functions are defined for the encoder and prototype points, with the prototype loss based on Gaussian mixture models. The article presents various numerical experiments to support its analytical hypothesis and the proposed solution.", "questions": "- Line 96: Provide the full form for EMA-updated (Exponential Moving Average).\n\n- Line 99: Not a proper matrix multiplication (is the transpose of C necessary?).\n\n- Definition 2.1: Is there a constraint $\\|v_m\\|=1$?\n\n- Is this a logical necessity: “If partial prototype collapse truly stems from the joint optimization of prototypes and encoders, then separating their updates should prevent the collapse”?\n\n- Is it possible to provide some analytical guarantee that the use of separate losses avoids prototype collapse?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The article offers a practically valuable observation about the potential cause of the prototype collapse problem in relation to the joint optimization of encoder parameters and prototype points.\n\n- It also provides a loss separation approach (for encoder and prototype points) that is demonstrated to be successful in avoiding the collapse problem.\n\n- A clear measure of collapse is also introduced in the article.", "weaknesses": "The main weakness of the article is that it is entirely based on an empirical approach, lacking a satisfactory analytical foundation for both the cause and the proposed solution of the prototype collapse problem. Although the article is useful in terms of practical implementations, a stronger theoretical grounding is needed to make its arguments more convincing and provide deeper insights for a potential ICLR submission.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "7LQbYK6hZW", "reviewer": "Reviewer_k3fq", "summary": "This paper studies partial prototype collapse in prototypical self-supervised learning (SSL), where many prototypes become almost the same. The authors show that this happens because encoders and prototypes are trained together under the same loss, which encourages shortcut learning. To fix this, they propose a fully decoupled training strategy: prototypes are learned as Gaussian mixture components using an online EM update, separated from encoder optimization. The method removes prototype collapse and improves prototype diversity, k-NN accuracy, and robustness to long-tailed datasets.", "questions": "This paper reminds me of non-parametric or memory-based approaches in contrastive learning—such as MoCo, which keeps a memory queue of past embeddings, or OBoW and SwAV, which use fixed or slowly updated codebooks as pseudo-prototypes.\n\nCould the authors clarify whether their decoupled update is conceptually related to these methods?\nAnd is the proposed online EM procedure similar to maintaining a dynamic memory bank of cluster centers?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- The paper explains well why prototype collapse matters and gives strong evidence that this issue is general across many SSL methods, not only DINO.\n- The proposed decoupling is easy to understand, no need new hyperparameters, and is supported by strong experiments.\n- The authors test several popular baselines (DINO, CARP, iBOT, CAPI) and evaluate both balanced and long-tailed datasets. The analysis of prototype uniqueness and training dynamics is very complete.\n- The paper is well structured and the figures help a lot to understand the argument.", "weaknesses": "The reviewer is happy with the paper overall. Here is a few area that could be improved:\n- The paper mostly gives empirical evidence, but not a full theoretical explanation of why joint optimization causes collapse. IMO, a simple gradient or convergence analysis would make the argument stronger.\n- The improvements in accuracy are clear but not very large (around +1–2%). The contribution is more diagnostic than algorithmic. \n- The method is mainly tested on CARP. It would be good to see results on other recent large-scale SSL frameworks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)