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arxiv: 2605.01325 · v1 · submitted 2026-05-02 · 💻 cs.CV · cs.LG

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Rethinking Model Selection in VLM Through the Lens of Gromov-Wasserstein Distance

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Pith reviewed 2026-05-09 14:25 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords vision-language modelsmodel selectionGromov-Wasserstein distancevision encoderscross-modal alignmentmultimodal learningembedding similarity
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The pith

The Gromov-Wasserstein distance between vision and language embeddings predicts optimal vision encoders for VLMs better than size or accuracy.

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

Common ways to pick vision encoders for vision-language models, such as picking the biggest one or the one best at image classification, do not reliably lead to the strongest final models. The paper finds that the structural similarity between the vision encoder and the language model, measured by how well their embedding spaces can be matched using the Gromov-Wasserstein distance, is a much better guide. This distance can be calculated just from the pre-trained models without any joint training. Theory shows it relates to how easily the models can learn to map between vision and language. Tests across dozens of encoders and full training runs confirm it correlates strongly with actual VLM results.

Core claim

The learnability of cross-modality mapping in VLMs can be provably associated with the Gromov-Wasserstein distance between pre-trained vision and language embeddings, and this distance correlates more strongly with final VLM performance than traditional metrics such as model size or zero-shot accuracy.

What carries the argument

Gromov-Wasserstein distance computed between the feature spaces of pre-trained vision encoders and language models, serving as a proxy for structural similarity that aids cross-modal mapping.

If this is right

  • Vision encoders should be chosen to minimize Gromov-Wasserstein distance to the target language model rather than by scale or standalone accuracy.
  • Model selection for VLMs can be performed inference-only before any joint training occurs.
  • Structural alignment across modalities is a critical previously overlooked factor in building effective multimodal systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This selection criterion could extend to choosing encoders for other multimodal pairings such as audio-language models.
  • Vision encoder pre-training objectives might be redesigned to directly minimize this distance to common language models.

Load-bearing premise

That the structural similarity captured by Gromov-Wasserstein distance on pre-trained embeddings remains the dominant factor once the full VLM training objective and data mixture are introduced.

What would settle it

Training a VLM with an encoder that has large Gromov-Wasserstein distance yet achieves top performance, or one with small distance that underperforms after full training, would challenge the central claim.

Figures

Figures reproduced from arXiv: 2605.01325 by Bo Han, Elliot Osborne, Jianbo Ma, Muyang Li, Tongliang Liu, Yucheng Liu.

Figure 1
Figure 1. Figure 1: From left to right, we can see the correlation analysis of zero-shot classification accuracy, vision encoder size, and GW distance view at source ↗
Figure 2
Figure 2. Figure 2: A toy example to show the intuition of GW distance: view at source ↗
Figure 3
Figure 3. Figure 3: Scaling trend of runtime. how generalizable are the choice of vision encoders across different LLMs, if one have spent resources to select the op￾timal vision encoder for a specific LLM, can such informa￾tion be transferred to a different LLM without running vi￾sion encoder selection again? As shown in view at source ↗
Figure 4
Figure 4. Figure 4: Correlation of the vision encoder ranking between view at source ↗
read the original abstract

Vision-Language Models (VLMs) have enhanced traditional LLMs with visual capabilities through the integration of vision encoders. While recent works have explored various combinations of vision encoders and LLMs, there still lacks a principled understanding of what makes a vision encoder suitable for VLM alignment. In this paper, we systematically investigate this question via comprehensive experiments on a curated collection of 19 pre-trained vision encoders from diverse sources. We first demonstrate that common practices, such as choosing encoders with the largest size or highest zero-shot accuracy, consistently fail to identify optimal models. In fact, these metrics show only weak to moderate correlation with VLM performance. This intriguing finding begs a fundamental question: What factors of vision-encoders matter in VLM? Through comprehensive analysis, we identify that the structural similarity across modalities plays a crucial but previously overlooked role in vision-encoder selection, which we measure using the Gromov-Wasserstein distance as a proxy. From a theoretical perspective, we show that the learnability of cross-modality mapping can be provably associated with the Gromov-Wasserstein distance. Empirical verification on 60+ full VLM training runs shows that our proposed inference-only metric performs significantly better than alternative model selection strategies and exhibits a much stronger correlation with final VLM performance, thereby enabling efficient and effective prediction of VLM performance before full training.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The manuscript presents a study on selecting vision encoders for Vision-Language Models (VLMs) by introducing the Gromov-Wasserstein (GW) distance as a measure of structural similarity between vision and language embeddings. The authors argue that common heuristics like encoder size or zero-shot performance are poor predictors, while GW distance provides a stronger correlation with downstream VLM performance. They support this with analysis of 19 vision encoders, a theoretical argument linking GW to cross-modal mapping learnability, and empirical results from more than 60 complete VLM training runs demonstrating superior predictive power of the proposed metric.

Significance. If the central claims hold, this paper makes a significant contribution by offering a principled, training-free method for vision encoder selection in VLMs, which could substantially reduce computational costs in multimodal model development. The empirical validation across a large number of full training runs (60+) is a notable strength, providing concrete evidence beyond small-scale ablations. Additionally, the attempt to ground the metric in a theoretical association with learnability adds depth, though its rigor needs confirmation. This approach could shift practices in the field toward more informed model selection strategies.

major comments (3)
  1. Theoretical Analysis section: The abstract claims that learnability of cross-modality mapping 'can be provably associated' with the Gromov-Wasserstein distance, yet the provided text lacks the full derivation or key proof steps. This makes it impossible to verify whether the association is rigorous or relies on unstated assumptions about the mapping objective.
  2. Experimental Results (60+ VLM runs): The central empirical claim rests on pre-computed GW distance predicting final performance, but the manuscript does not specify whether vision encoders remain frozen or are updated during VLM training. If encoders are fine-tuned (common in joint cross-modal objectives), the initial structural similarity may become transient, directly challenging the claim that pre-training GW remains the dominant factor (see skeptic note on joint optimization).
  3. Comparison to baselines: The paper states that GW outperforms alternatives like size or zero-shot accuracy with 'much stronger correlation,' but without reporting exact coefficients (e.g., Pearson r or R^{2} values) in a dedicated table or the precise implementation of the 60+ runs (data mixture, VLM architecture, training hyperparameters), the superiority cannot be fully assessed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions where appropriate to strengthen the paper.

read point-by-point responses
  1. Referee: Theoretical Analysis section: The abstract claims that learnability of cross-modality mapping 'can be provably associated' with the Gromov-Wasserstein distance, yet the provided text lacks the full derivation or key proof steps. This makes it impossible to verify whether the association is rigorous or relies on unstated assumptions about the mapping objective.

    Authors: We appreciate the referee pointing out the need for greater rigor in the theoretical section. The manuscript outlines the association by showing that the Gromov-Wasserstein distance bounds the optimal transport cost between vision and language embedding spaces, which directly relates to the sample complexity required for learning a cross-modal mapping under standard assumptions on the alignment objective. However, we agree that the current presentation would benefit from explicit key proof steps and a clearer statement of assumptions. In the revised manuscript, we will expand the Theoretical Analysis section with the full derivation and include a complete proof in the appendix. revision: yes

  2. Referee: Experimental Results (60+ VLM runs): The central empirical claim rests on pre-computed GW distance predicting final performance, but the manuscript does not specify whether vision encoders remain frozen or are updated during VLM training. If encoders are fine-tuned (common in joint cross-modal objectives), the initial structural similarity may become transient, directly challenging the claim that pre-training GW remains the dominant factor (see skeptic note on joint optimization).

    Authors: This is a valid concern regarding experimental clarity. In all 60+ VLM training runs described in the paper, the vision encoders are kept entirely frozen, and only the cross-modal alignment module (projector) is trained. This setup is consistent with standard VLM training protocols that aim to leverage pre-trained visual representations without altering them. As a result, the pre-computed GW distance remains a stable predictor. We will explicitly document this design choice, including the training protocol details, in the revised Experimental Results section to eliminate any ambiguity. revision: yes

  3. Referee: Comparison to baselines: The paper states that GW outperforms alternatives like size or zero-shot accuracy with 'much stronger correlation,' but without reporting exact coefficients (e.g., Pearson r or R^{2} values) in a dedicated table or the precise implementation of the 60+ runs (data mixture, VLM architecture, training hyperparameters), the superiority cannot be fully assessed.

    Authors: We agree that quantitative precision and reproducibility details are essential for evaluating the claimed superiority. In the revision, we will add a dedicated table that reports the exact Pearson correlation coefficients (r) and R² values comparing GW distance to VLM performance, alongside the same metrics for baselines such as encoder size and zero-shot accuracy. We will also expand the experimental setup subsection to fully specify the VLM architecture, data mixture, training hyperparameters, and other implementation details for the 60+ runs. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper computes the Gromov-Wasserstein distance directly as an inference-only metric on frozen pre-trained vision encoder embeddings, without any fitting or optimization against VLM performance targets. The theoretical claim of a provable association between GW distance and cross-modality learnability is presented as an independent derivation rather than a post-hoc fit. Empirical validation relies on 60+ separate full VLM training runs to measure correlation, providing external evidence. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citation chains appear in the provided derivation steps. The central result remains self-contained against the stated benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that Gromov-Wasserstein distance on frozen embeddings faithfully reflects the learnability of the cross-modal mapping under standard VLM objectives; no new entities are introduced and no parameters are fitted to the target VLM performance.

axioms (1)
  • standard math Gromov-Wasserstein distance quantifies structural dissimilarity between two metric spaces in a way that is invariant to isometries.
    Invoked when the paper treats GW distance as a proxy for modality alignment.

pith-pipeline@v0.9.0 · 5554 in / 1273 out tokens · 25173 ms · 2026-05-09T14:25:21.531418+00:00 · methodology

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