ZEUS: Zero-shot Embeddings for Unsupervised Separation of Tabular Data

We thank the reviewer for their positive evaluation and for the insightful and constructive comments. We especially appreciate the suggestions regarding additional comparisons, architectural clarity, and stress-testing the method. In response, we have conducted new experiments and added clarifications, which we summarize below and will include in the final version of the paper.

1. Incomplete comparison. Firstly, the TabPFN repo has extensions, [..] Secondly, there are prior works on the unsupervised learning for tabular data such as Scarf or SwitchTab -- these are not zero-shot, but it would be nice to include some reference (or benchmark) to them to understand how they differ from the current work.

We appreciate the suggestion to compare ZEUS with unsupervised representation learning approaches in the context of clustering task. Accordingly, we incorporate both TabPFN-Unsupervised and SCARF into our evaluation.

For TabPFN-Unsupervised, while the linked method relies on label information from the training set to generate representations, the same repository also includes an unsupervised folder containing the TabPFNUnsupervisedModel class. We use its get_embeddings_per_column method to extract per-column representations, which we then average across columns to obtain a final row-level representation. Unfortunately, we were unable to use the get_embeddings function due to the following error:

NotImplementedError( "This method is not implemented currently. During the main TabPFN refactor this functionality was removed, [...]" )

In the case of SCARF, we follow the example.ipynb Jupyter notebook provided in the original repository. For both SCARF and TabPFN-Unsupervised, we cluster their learned representations using k-means, analogously to our approach in ZEUS. Additionally, we included IDC in our evaluation, as suggested by Reviewer 2ngo.

Based on the results in the table, one can infer that methods like SCARF or TabPFNUnsupervised are more suited for feature extraction, which can then be fine-tuned for classification tasks. Without additional regularization components during training, or specialized fine-tuning such as with DEC, we are unable to effectively separate these representations.

2. Failure cases not explained. If we take this work apart, the technical novelty lies in prior dataset generation and loss formulation. Both are formulated / generated using GMM. My complaint is that the section on the results may not accurately depict the real-world performance: [...]. In general, it would be great to see a stress test of the model to understand when it fails. Let's say there are no clusters, or if there is a severe class imbalance, or there is a mode connecting, or the geometry of clusters is very difficult.

Firstly, we acknowledge that benchmarking clustering performance in realistic failure scenarios is inherently difficult, particularly for small and medium-sized tabular datasets. To our knowledge, there is no widely accepted benchmark that provides well-defined clustering ground truth beyond class labels, which may not reflect true cluster structure.

Secondly, we are grateful to the reviewer for the insightful suggestion to examine the failure cases of our model. While such analysis requires careful consideration and time, we have taken initial steps in that direction. Specifically, we constructed four synthetic 2D scenarios:

• Cluster-Imbalance: Three clusters with 1000, 300, and 50 samples, respectively.
• Covariance-Scaled: Three equally sized clusters (500 samples each) with covariance matrices scaled by factors of 1, 6, and 36.
• Moons: Generated using make_moons from scikit-learn with 1000 samples and 0.1 noise.
• Connection: Two spherical Gaussians linked by a degenerate linear Gaussian.

ZEUS outperforms K-means across all cases and performs on par with GMM. Notably, on the Moons dataset, ZEUS is the only method that successfully separates the clusters. This suggests that these synthetic examples do not represent genuine failure cases for our approach. A more thorough analysis of datasets where ZEUS underperforms remains an important direction for future work.

Understanding loss

1. From your final objective given in (3), I have doubts about the difficulty of the optimization and the importance of good initialization. Do you keep updating $\hat{c}_k$ at each iteration?

First of all, $\hat{c}_k$​ is estimated as the average representation of the points assigned to cluster $k$. Therefore, it is indeed updated dynamically and differs across datasets.

As for initialization, it certainly plays a role in optimization process. A good initialization under a given random seed can lead to faster convergence and potentially better performance. Conversely, extremely poor initialization may result in instability or even complete collapse of pre-training. However, we did not observe this to be a significant issue during our experiments. Nonetheless, investigating the impact of initialization strategies could be a potential direction for future work.

2. What role do $\hat{\pi}$'s play? In unsupervised settings, we use EM to fit GMM, so $\hat{\pi}$'s are updated each E-step. In your case, they seem fixed, defined by the training label.

Yes, the values of $\hat{\pi}$ are defined based on the training labels and are not updated in any other way. Nonetheless, introducing $\hat{\pi}$ helped slightly improve performance, particularly on real-world datasets. This improvement may stem from the fact that incorporating information about cluster balance increases the flexibility of the learning process and provides a beneficial learning bias. The comparison between the version with a prior (ZEUS) and the one without it (ZEUS-without-prior) in the loss function is as follows:

Architecture

1. There is little that is said about the architecture in the paper. The authors mention that they re-use TabPFN backbone in Section 3.1. However, for TabPFN the training label is passed together with the features. There's also cross-attention between training and test sets. Could the authors elaborate more on the specific architectural adjustments?

Similarly to TabPFN, we employ a linear embedding layer to convert each row of the table into a 512-dimensional token. However, since we are addressing an unsupervised problem, no training label embeddings are added to these tokens. Moreover, our setting does not involve a query set, and thus we apply only self-attention within the support set. The transformer architecture matches that of TabPFN: it consists of 12 attention blocks, each with 6 attention heads and GeLU as the activation function. At its output, we obtain a representation for each data point, which is then clustered using k-means. Notably, unlike TabPFN, no additional MLP decoder is applied after the transformer.

2. Major drawback of TabPFN is the context length, which is currently limited at around 10,000 samples for TabPFN V2. Recent works such as TabFlex or Mixture of ICP have explored addressing this concern via subsampling or compressing the data. Are these approaches portable to ZEUS?

Yes, we believe that architectures of TabPFN’s successors are transferable to ZEUS. To preliminarily test this, we explore the possibility of adapting the TabICL [1] architecture pipeline to our unsupervised clustering setting, following the same methodology as in the case of TabPFN (see response above). The resulting performance is shown below:

ZEUS + TabICL performs competitively with the original ZEUS across all evaluated data collections and even surpasses it in rank on synthetic data. Nonetheless, its average ARI on real-world datasets is noticeably lower. Future work should investigate whether this is due to random seed variability, our incomplete understanding of the TabICL architecture, potential overfitting to the prior, or the need for a more expressive prior.

We are grateful for the reviewer’s thoughtful suggestions, which have led to a stronger and more complete version of the work. We hope the added comparisons (TabPFN-Unsupervised, SCARF), architectural clarifications, stress-test scenarios, and ablations help reinforce the contribution and reliability of ZEUS. We appreciate the reviewer’s positive assessment.

[1] Qu, J., Holzmüller, D., Varoquaux, G., & Le Morvan, M. (2025). TabICL: A Tabular Foundation Model for In-Context Learning on Large Data. arxiv preprint

Reviewer 3Vjr (3, conf =5) We thank the reviewer for the detailed and insightful comments. We appreciate the recognition of the potential impact of ZEUS, and agree that its claims must be supported by strong comparisons, ablations, and a deeper analysis of edge cases. Below, we respond point-by-point and provide several additional experiments (e.g., discrete-only data, impact of synthetic priors, sensitivity to noise), which will be included in the final version of the paper.

W1. Since supervised training is used, clustering performance strongly depends on the annotated datasets used for clustering.

We agree that the choice of training distributions has a strong influence on the resulting clustering behavior, and that this creates opportunities for further improvement. In our current work, we approach the problem from a generative perspective rather than by committing to a fixed clustering loss. Specifically, we adopt the widely used latent variable model (LVM) paradigm, where a discrete latent variable determines cluster membership. To make this framework applicable beyond simple Gaussian mixtures, we apply random neural transformations to the observed space, enabling a rich diversity of data distributions while preserving the underlying cluster structure. ZEUS is trained to reverse this generative process, allowing it to generalize across datasets without relying on predefined objectives like MSE. That said, we believe that incorporating more structured or domain-specific generative processes, or learning such transformations from real data, is a promising direction for future work.

W2. There are limits imposed by the input dimensionality of the transformer (dataset size, number of features)

These limitations are primarily inherent to the architecture of the vanilla TabPFN model. However, recent research, including TabPFN2 [1], TabICL [2], TabFlex [3] has shown that such restrictions can be gradually mitigated. We have conducted preliminary tests indicating that the TabICL architecture can be possibly integrated into our pre-training pipeline. The corresponding results are presented in the table below:

ZEUS + TabICL performs competitively with the original ZEUS across all evaluated dataset groups and even surpasses it in average rank on synthetic data. However, its ARI on real-world datasets is slightly lower. This may stem from seed sensitivity, architectural factors, or limitations in how the prior interacts with more heterogeneous tabular distributions. Investigating these effects and improving compatibility with TabICL-style architectures is a promising avenue for future work.

Q1. It is not clear how the real datasets have been separated into training and testing.

We clarify that real datasets are used only for testing. The model is trained exclusively on synthetically generated data. No samples from the real datasets are seen during training, and there is no fine-tuning. This setup ensures a strict zero-shot evaluation.

Q2. In several cases, ZEUS performance is very low (much lower that k-means and GMMs). This reduces confidence in the method’s validity.

It is true that ZEUS underperforms on some individual datasets. However, no clustering method performs well across all settings, which is evident in the performance of other deep models that often fall behind k-means or GMMs on average. What sets ZEUS apart is its ability to generalize in settings where others fail. In particular, on synthetic datasets with transformed latent structures (Appendix Table 10), ZEUS outperforms all baselines by a large margin (~10 pp), showing its strength in realistic, non-Gaussian clustering scenarios with well-defined ground truth. For real-world datasets, we follow standard benchmarks where class labels are used as cluster references. While common in the literature, this is not always meaningful in practice, as classes do not necessarily align with cluster structure. Still, ZEUS ranks first on average and achieves ARI above 0.9 on datasets where many methods fail completely (ARI = 0) - for example, OpenML dataset 1462, as shown in Appendix Table 8. This demonstrates that ZEUS fills an important gap by succeeding where others collapse.

Q3. It would be interesting to compare performance on datasets with discrete features only. Discrete features cause difficulties in k-means and GMMs.

The evaluated datasets (GuptaA_2019_PA and QinN_2014_PA) are presence/absence (binary) metagenomic profiles obtained from the curatedMetagenomicData [4] collection. Each feature indicates whether a specific microbial taxon is present in a given sample. The datasets are named after the first author and year of the corresponding publication, following the convention used in the original repository. Their high dimensionality, sparsity, and purely discrete nature make them particularly challenging for clustering methods based on continuous distances, such as k-means or GMMs.

The table highlights the potential of ZEUS, which could likely be further enhanced by pre-training specifically on discrete features or by replacing one-hot encoding with alternative embedding methods.

Q4. For many real datasets the number of clusters is 2, which is quite small.

It is true that many real-world datasets in our benchmark have only 2 classes, as they originate from standard binary classification tasks. However, approximately half of the datasets contain more than two classes, and we observe that ZEUS often performs especially well in these more complex multi-cluster scenarios. For example, on datasets such as 14, 16, 22, 35, 458, 1499, 4153, and 42585, ZEUS outperforms all other baselines, which highlights its strength in capturing more nuanced latent structures. Synthetic datasets, in particular, are predominantly multi-class and further demonstrate this advantage.

Q5. It should be emphasized that k-means is applied on the transformer output in order to obtain the final cluster labels.

Thank you for pointing this out. We agree that this detail should be made explicit, and we will make sure to emphasize it clearly in the final version of the paper.

Q6. Some results on the influence of noise and outliers would add value to the experimental study.

That is a great remark, and we thank the reviewer for highlighting it. We were able to conduct some initial experiment on this matter. In addition to the standard evaluation method (referred to as ZEUS), we introduce two additional variants: ZEUS + noise: Gaussian noise with a standard deviation of 0.05 is added to each data point before the ZEUS forward pass. ZEUS + anomalies: For each dataset, we introduce a set of global anomalies corresponding to 5% of the dataset size. These anomalies are constructed by uniformly sampling numerical features from the range (−1,1) and randomly selecting categorical values. The results are as follows:

As we can see, the average performance in the perturbed variants is not significantly lower than that of the vanilla ZEUS model, highlighting a degree of stability in the method.

These additional experiments and clarifications provide a broader view of ZEUS’s strengths and limitations. We appreciate the reviewer’s thoughtful and technically grounded suggestions, which have helped improve the depth and rigor of our evaluation. We hope the extended results and stress tests address the reviewer’s concerns and support a more favorable assessment.

[1] Hollmann, N., Müller, S., Purucker, L., Krishnakumar, A., Körfer, M., Hoo, S. B., Schirrmeister, R. T., & Hutter, F. (2025). Accurate predictions on small data with a tabular foundation model. Nature.

[2] Qu, J., Holzmüller, D., Varoquaux, G., & Le Morvan, M. (2025). TabICL: A Tabular Foundation Model for In-Context Learning on Large Data. arxiv preprint

[3] Zeng, Y., Dinh, T., Kang, W., & Mueller, A. C. (2025). TabFlex: Scaling Tabular Learning to Millions with Linear Attention. arxiv preprint

[4] Pasolli E, Schiffer L, Manghi P, Renson A, Obenchain V, Truong D, Beghini F, Malik F, Ramos M, Dowd J, Huttenhower C, Morgan M, Segata N, Waldron L (2017). “Accessible, curated metagenomic data through ExperimentHub.” Nat. Methods, 14(11), 1023–1024. ISSN 1548-7091, 1548-7105,

I thank the authors for clarifications and additional experimental results that strengthen the manuscript. However, I believe that weakness W1 (generalizing from synthetic annotated datasets used for training to real datasets), which is actually the main idea introduced in this work, is not adequately addressed, although there are some promising initial experimental results. The dependence on adhoc decisions - such as the datasets selected for training and the random neural transformations used - reduce the confidence on the quality of the clustering solution. Perhaps some theoretical results would make this research direction more promising.

We thank the reviewer for the thoughtful and detailed feedback. We appreciate the recognition of ZEUS’s core contribution and agree that stronger experimental comparisons and more thorough ablations are essential to supporting its claims. In response, we have expanded our evaluation with additional experiments, which we summarize below and will include in the final version of the paper.

1. The results presented in Tab. 1 & 2 and Appendix Tab. 4-7 show that, on the aggregate, ZEUS does better than the compared methods. However, it is by small margins that undermine the impact of the proposed method.

We respectfully disagree with the claim that the gains reported in Tables 1 and 2 are marginal and insufficient to support the impact of our method. Clustering is inherently an unsupervised task, and without a clearly defined target it is difficult to determine which clustering is "better." Many real-world datasets commonly used in the literature were originally constructed for classification, and their class labels often do not correspond to well-separated clusters. As a result, most methods struggle to recover them. Despite this, ZEUS achieves the highest ARI on real-world data (57.43) and the best average rank (3.60), outperforming all compared baselines.

To provide a more interpretable evaluation, we also include synthetic datasets with well-defined ground-truth clusters, based on latent variable models and mixture components. In these more structured scenarios, ZEUS shows clear and consistent advantages. We also include Gaussian mixtures as a sanity check — these are deliberately simple and yield similar results across methods, which naturally reduces visible margins.

Overall, ZEUS demonstrates strong and reliable performance across diverse clustering regimes, including both ill-posed real-world data and well-defined synthetic tasks.

2. The evaluation comparisons are lacking. Most methods compared are naive (e.g. K-Means), and more advanced methods (e.g. G-CEALS) may be at a disadvantage given the size of the models involved: my understanding is that the autoencoder used by G-CEALS is much smaller and less powerfull than the transformer architecture used by ZEUS, which means one cannot be sure how much of ZEUS' gains are related to the architecture as opposed to the method.

For all deep clustering baselines, we used the implementations provided by the authors and followed their recommended hyperparameter selection strategies. For instance, the embedding dimension was chosen from the set {5, 10, 15, 20}, as suggested in the GCEALs paper, and we adhered to this choice, as it was deemed beneficial for those baselines. ZEUS contains 25.78 million parameters because of its large-scale pretraining across millions of datasets in a zero-shot regime. Baseline methods are trained on individual datasets but still use autoencoders with over 2.5 million parameters.

As shown in the table below, increasing the size of the autoencoder from hidden layers [500,500,2000] (GCEALS-2.5M) to [500,500,2000,2000,2000] (GCEALS-10.5M) actually leads to worse performance on both real-world and synthetic Gaussian datasets. This suggests that simply scaling up the model can lead to some form of overfitting. Furthermore, if increasing the autoencoder’s size alone were beneficial, the original authors would have likely reported this. Nonetheless, exploring Transformer-based variants of DEC or GCEALs might be worthwhile, though such extensions go beyond the scope of this study.

In the case of GCEALS, the primary issue lies in its instability across different random seeds. The method exhibits high variance, which negatively affects the average performance. For illustration, the standard deviation of ARI scores on selected datasets is as follows:

In general, finding the optimal configuration for dozens of hyperparameters in an unsupervised setting is inherently challenging due to the absence of labels. Our method offers a clear advantage in this regard, as its zero-shot nature allows it to avoid such issues during inference.

Finally, it is unclear to me why methods such as DEPICT and IDC are not included in the comparisons.

Indeed, you are right, that IDC should have been included in our evaluation. According to the tables in the GCEALS paper, DEPICT is among the weaker methods and is also 4 to 5 times slower than GCEALS or DEC. Therefore, unfortunately, due to limited time and computational resources, we decided to exclude it from our experiments. However, in addition to our baseline methods, we also include TabPFN-Unsupervised and SCARF, as suggested by Reviewer gk7v. Similar to ZEUS, we cluster their learned representations using k-means. The clustering quality results are presented below:

For IDC, we adhere to the setup and guidelines outlined in the official repository's Jupyter notebooks.

3. The ablations should be more thorough. Most importantly, I found no study of the impact of using different synthetic data (Gaussian/Categorical/NN transformed) in the training mix, despite that being a key contribution/component of the paper.

Indeed, such an analysis would significantly strengthen our paper. Therefore, we conduct an experiment using the setup described in Section 3.1 to evaluate the clustering quality under four configurations of the data-generating prior:

• Gaussian + Categorical,
• NN-transformed + Categorical,
• Gaussian + NN-transformed,
• Gaussian + NN-transformed + Categorical (our standard ZEUS model from Section 3.2).

As expected, the “Gaussian + Categorical” model achieves top performance on the Synthetic Gaussian datasets, while the” NN-transformed + Categorical” method excels on Synthetic Transformed data collections. Notably, the latter also performs well on Gaussian sets, as its prior is built upon transformed Gaussian mixtures. In contrast, the “Gaussian + NN-transformed” model yields relatively poor average ARI scores across both synthetic benchmarks. This drop is primarily caused by a significant decline in ARI performance on categorical datasets. Nonetheless, its average rank remains consistently competitive. For the OpenML datasets, the best performance is achieved when pre-training includes all three types of priors, underscoring the complementary importance of each prior in the training process.

These additions clarify the role of individual components in ZEUS and help isolate the sources of its performance. We believe they provide a more complete and transparent evaluation of the method. We appreciate the reviewer’s feedback, which helped us improve the clarity and depth of the empirical study, and we hope these extended experiments support a more favorable assessment.

We thank the reviewer for the thoughtful and detailed feedback, as well as for recognizing the core idea and potential of ZEUS — particularly its ability to generalize to real-world clustering tasks without downstream supervision. We appreciate the acknowledgement of the zero-shot setting and the novel use of synthetic generative processes as a meaningful contribution.

We address your main concerns below:

At many instances the paper refers to appendices for more details, which are, however, not present in the paper. An evaluation of these crucial aspects is thus not possible in the presented version, which hinders several aspects of understanding and reproducibility.

The appendix to our publication is available in the “Supplementary Material” section on the Openreview website, under the abstract.

It is not really clear how the pre-training exactly affects the model performance. It seems that ZEUS is the only model that is trained on data other than the downstream task, even though similar pre-training may also be conceivable for some of the baseline models. A comment or even additional experiments on that end may be beneficial.

We acknowledge the reviewer’s suggestion to analyze the impact of pretraining. However, none of the baseline methods are designed to support pretraining or cross-dataset transfer. We followed the official repositories and authors’ recommendations, which do not include such procedures. Extending these methods beyond their intended scope is outside the remit of this paper. The performance of ZEUS variants, pre-trained under the same settings as in Section 3.1 of the main paper, except for the use of different combinations of data-generating prior (Gaussian, Categorical, and NN-transformed) is presented in the following table. We evaluate four configurations:

• Gaussian + Categorical,
• NN-transformed + Categorical,
• Gaussian + NN-transformed,
• Gaussian + NN-transformed + Categorical (our standard ZEUS model from Section 3.2).

Details of these data-generating probabilistic models are provided in Appendix B.

Furthermore, it would be interesting to see how pre-training on real datasets would affect the ZEUS representations. It also doesn't really become clear how many samples or epochs the model has been trained on. The paper could clearly benefit from additional details and discussion of the data selection.

ZEUS, like in-context learning methods, requires hundreds of thousands or even millions of datasets during pre-training in order to generalize effectively and perform well on entirely new downstream tasks. Unfortunately, it is not feasible to obtain such a large number of real-world datasets with well-defined and consistently labeled clusters. Pre-training on only a handful of real datasets is insufficient, and under such conditions, ZEUS would perform poorly. To address this limitation, we rely on pre-training with synthetically generated datasets.

As evidence, we conduct an experiment where we split a set of real/OpenML datasets into two groups, each containing 17 datasets. The first group is used for pre-training, while the second one serves as the evaluation set. The results are presented below:

Regarding the pretraining duration, ZEUS was trained for 500 epochs, each comprising 1,000 batches of single dataset sample, whereas details on the synthetic data generation process are discussed in Appendix B.

The role of the underlying transformer model is not very clear and how its importance measures against that of the data basis. The paper would benefit from additional experiments in this regard.

The transformer backbone is used in ZEUS because it enables processing the entire dataset jointly — a requirement of our formulation. This design follows similar precedents in NLP and tabular learning (e.g., TabPFN). At the time of writing, transformers are the de facto state-of-the-art architecture for such use cases, and alternative architectures are either not suitable or not competitive.

What dimensional output does Zeus have and what role does the dimensionality play?

The output dimensionality of ZEUS is 512. The table below summarizes our model’s clustering performance (ARI) for different output sizes: 32, 128, 512, and 768.

For synthetic data, increasing the dimensionality leads to a consistent improvement in performance, whereas for OpenML datasets, there is a drop between dimensions 512 and 768, which may be caused by overfitting to the prior.

How exactly does the nature of zero-shot learning come into play here and how does it differ from more general transfer learning through feature extraction settings? The reference experiments seem to employ the pre-trained ZEUS network to transform features from the raw data domain to a different embedding space, in which the clustering can be performed, which seems to be a common technique under the umbrella term of transfer learning.

We respectfully disagree. While both zero-shot learning and transfer learning involve reusing knowledge from a source domain, they are conceptually distinct. Transfer learning assumes access to the target dataset and typically involves fine-tuning the model on the downstream task — using labeled data (in supervised settings) or task-specific objectives (in unsupervised ones). In contrast, zero-shot learning requires the model to generalize to new tasks without any access to the target task during training or fine-tuning, and offers much faster inference. This is the regime we operate in. In our case, the ZEUS model is trained only on synthetic data generated from known probabilistic models. It never sees the downstream datasets during training and is applied to them as-is. We do not define or optimize any task-specific loss on the downstream clustering tasks. We explored fine-tuning using objectives inspired by DEC, but preliminary results were inconsistent and unstable - further motivating a pure zero-shot approach. In this sense, ZEUS learns a general mapping from data distributions to clustering structure, which can be applied without any adaptation - distinguishing it from conventional transfer learning pipelines.

As ZEUS effectively only transforms the features, why weren't other approaches than k-means employed for the clustering to allow a better understanding of how valuable the transformed ZEUS representations are?

ZEUS is inherently designed to form spherical clusters, so in theory, k-means (ZEUS-KM) should be a sufficient method for separating the learned representation. Its primary advantage lies in its speed, which is a crucial factor for us during inference. Moreover, as demonstrated in the tables below, its clustering quality (measured by ARI) is comparable to the more computationally intensive Gaussian Mixture Model (ZEUS-GMM). For reference, we also include results from a simplified variant of GMM with fixed identity covariance matrices (ZEUS-SGMM), as employed in Section 3.3 of the main paper. All experiments were performed using the same checkpoint and datasets as in Section 3.2. To enhance clarity, the second table presents an extended version of the comparison across 5 arbitrarily selected datasets per group.

Analysis of the average ARI scores indicates that ZEUS's output is well-suited to evaluated approaches, as there are no significant differences in their results. Deep clustering techniques such as DEC or IDEC could also potentialy be employed. Nevertheless, their reliance on intensive, dataset-specific training contradicts ZEUS’s objective of delivering efficient, zero-shot representations.

We hope that our responses have addressed the reviewer’s concerns. In particular, we have added:

• a detailed ablation on the impact of different pretraining distributions,
• a new experiment comparing synthetic vs. real-data pretraining (Table: ZEUS - OpenML),
• dimensionality sensitivity analysis (ZEUS-32 to ZEUS-768),
• and a comparison of downstream clustering heads (k-means, SGMM, GMM) using identical checkpoints.

These additions, which we will include in the final version of the paper, further clarify the design choices and robustness of ZEUS. We believe they strengthen the overall contribution and hope they support a more favorable evaluation.