arxiv: 2604.06614 · v1 · submitted 2026-04-08 · 💻 cs.CV · cs.LG

Recognition: 2 theorem links

· Lean Theorem

Holistic Optimal Label Selection for Robust Prompt Learning under Partial Labels

Yaqi Zhao , Haoliang Sun , Yating Wang , Yongshun Gong , Yilong Yin

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:47 UTC · model grok-4.3

classification 💻 cs.CV cs.LG

keywords prompt learningpartial labelslabel selectionoptimal transportvision-language modelsweak supervisionparameter-efficient adaptation

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The pith

A dual local-and-global label selection method improves prompt learning performance when only partial labels are available.

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

The paper aims to show that partial labels can be disambiguated for prompt-based adaptation of vision-language models by selecting the most plausible ones using both local feature-space density and global batch transport costs. A local filter picks frequent labels among nearest neighbors and scores them with softmax, while an optimal transport objective assigns labels by minimizing the cost of mapping a uniform distribution to the candidates. This holistic approach addresses label ambiguity and weak supervision. If it works, it would make fine-tuning large pre-trained models feasible with far less complete annotation effort on downstream vision tasks.

Core claim

HopS selects robust labels for prompt learning under partial supervision by first applying a local density-based filter on nearest neighbors to identify plausible candidates via frequency and softmax scores, then using a global optimal transport objective to map uniform sampling to candidate label distributions across batches by minimizing expected transport cost. The two strategies together provide label assignments from complementary local and global perspectives.

What carries the argument

The holistic combination of a local density filter and an optimal transport-based global selection objective for choosing labels from partial candidate sets.

Load-bearing premise

The feature embeddings from pre-trained models preserve enough structural information about true classes to let neighbor density and transport costs reliably point to correct labels.

What would settle it

Running the method on a dataset where partial labels are randomly chosen and checking if the selected labels lead to accuracy gains over using all partial labels without selection or random choice.

Figures

Figures reproduced from arXiv: 2604.06614 by Haoliang Sun, Yaqi Zhao, Yating Wang, Yilong Yin, Yongshun Gong.

**Figure 1.** Figure 1: Illustration of the transport cost matrix and the resulting transport plan between the uniform source instance distribution (Source) and the target candidate label distribution (Target). Finally, the most plausible candidate label y local is selected as the one with the highest prediction probability in the refined candidate set, as determined by Eq. (2). 4.2 Global Optimal Transport Planner To complemen… view at source ↗

**Figure 2.** Figure 2: HopS achieves the best testing accuracy under uni-prompt (top) and clsprompts (bottom) across five rand confusion rates [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: HopS achieves the best averaged testing accuracy across three confusion rates (left). The guiding effect of LDF on GOP (right). highlights the effectiveness of our holistic label selection strategy in reducing label ambiguity and providing reliable supervision. The detailed numerical results can be found in Appendix Tabs. 7 and 8. Insd-Confusion Type. Since partial-label losses perform well under the rand… view at source ↗

**Figure 5.** Figure 5: The performance remains stable across a wide range of λ on eight datasets (directions), and λ=1 works well. GOP components in HopS. These results indicate that HopS is effective not only in synthetic settings but also in real-world scenarios with instance-dependent ambiguity, such as crowd-sourced labels or low-resource domains. The detailed per-configuration results are reported in Appendix Tabs 9 and 10.… view at source ↗

**Figure 6.** Figure 6: B close to C is recommended [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: High cosine similarity between candidate and ground-truth label distributions across batches [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 9.** Figure 9: Identifying accuracy of LDF, GOP, and HopS on the Caltech [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗

**Figure 10.** Figure 10: Identifying accuracy of LDF, GOP, and HopSon the DTD [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗

**Figure 11.** Figure 11: Identifying accuracy of LDF, GOP, and HopS on the EuroSAT [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗

**Figure 12.** Figure 12: Identifying accuracy of LDF, GOP, and HopS on the Food [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗

**Figure 13.** Figure 13: Identifying accuracy of LDF, GOP, and HopS on the FGVCAircraft [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗

**Figure 14.** Figure 14: Identifying accuracy of LDF, GOP, and HopS on the Flowers [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗

**Figure 15.** Figure 15: Identifying accuracy of LDF, GOP, and HopS on the OxfordPets [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗

**Figure 16.** Figure 16: Identifying accuracy of LDF, GOP, and HopS on the UCF [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗

**Figure 17.** Figure 17: Testing accuracy of the HopS across different B under five confusion rates [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗

**Figure 18.** Figure 18: Comparison results under 4/8-shot settings across eight datasets [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗

read the original abstract

Prompt learning has gained significant attention as a parameter-efficient approach for adapting large pre-trained vision-language models to downstream tasks. However, when only partial labels are available, its performance is often limited by label ambiguity and insufficient supervisory information. To address this issue, we propose Holistic Optimal Label Selection (HopS), leveraging the generalization ability of pre-trained feature encoders through two complementary strategies. First, we design a local density-based filter that selects the top frequent labels from the nearest neighbors' candidate sets and uses the softmax scores to identify the most plausible label, capturing structural regularities in the feature space. Second, we introduce a global selection objective based on optimal transport that maps the uniform sampling distribution to the candidate label distributions across a batch. By minimizing the expected transport cost, it can determine the most likely label assignments. These two strategies work together to provide robust label selection from both local and global perspectives. Extensive experiments on eight benchmark datasets show that HopS consistently improves performance under partial supervision and outperforms all baselines. Those results highlight the merit of holistic label selection and offer a practical solution for prompt learning in weakly supervised settings.

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.

Desk Editor's Note private letter to a colleague

HopS combines local density filtering with batch optimal transport for partial-label selection in prompt tuning, but the gains rest on pre-trained features already separating the classes.

read the letter

The paper's core move is to clean partial labels for prompt learning by first running a local density filter on nearest-neighbor candidate sets in the fixed encoder space, then solving a batch-level optimal transport problem that assigns labels to minimize transport cost from uniform to the per-sample distributions. That pairing is the actual novelty; each piece exists elsewhere, but the joint use for this setting is new on the evidence given in the abstract.

Referee Report

1 major / 2 minor

Summary. The paper proposes Holistic Optimal Label Selection (HopS) for prompt learning with partial labels. It combines a local density-based filter that selects plausible labels from nearest neighbors' candidate sets in the pre-trained feature space (using frequency and softmax scores) with a global batch-wise optimal transport objective that minimizes expected transport cost from a uniform distribution to per-sample candidate label distributions. The authors claim that this holistic approach yields consistent performance gains on eight benchmark datasets over existing baselines in weakly supervised prompt tuning.

Significance. If the results hold, the work offers a practical, parameter-efficient technique for disambiguating partial labels by exploiting both local structural regularities and global assignment consistency in pre-trained vision-language encoders. The combination of density filtering and optimal transport is a reasonable and novel integration for this setting, with potential impact on adapting large models under incomplete supervision. Credit is due for grounding the method in standard OT and nearest-neighbor operations without introducing new free parameters beyond standard choices.

major comments (1)

[Experiments] Experiments section: The abstract asserts that 'extensive experiments on eight benchmark datasets show that HopS consistently improves performance under partial supervision and outperforms all baselines,' yet no ablation studies, encoder controls, or sensitivity analyses are described that would test the load-bearing assumption that the fixed pre-trained encoder's feature space already encodes task-specific nearest-neighbor structure sufficient for correct label recovery from partial candidates. Without such controls (e.g., swapping in weaker features or non-random partial-label generation), the reported gains cannot be confidently attributed to HopS rather than the assumption holding on standard benchmarks.

minor comments (2)

[Method] Method section: The local density filter description would be clearer with an explicit algorithm box or pseudocode showing how 'top frequent labels' are chosen from neighbor candidate sets and how softmax weighting is normalized.
[Experiments] The paper would benefit from a table summarizing the partial-label ratios and dataset statistics used in the eight benchmarks.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting the need for stronger experimental controls. We address the major comment below and will revise the manuscript to incorporate additional analyses.

read point-by-point responses

Referee: [Experiments] Experiments section: The abstract asserts that 'extensive experiments on eight benchmark datasets show that HopS consistently improves performance under partial supervision and outperforms all baselines,' yet no ablation studies, encoder controls, or sensitivity analyses are described that would test the load-bearing assumption that the fixed pre-trained encoder's feature space already encodes task-specific nearest-neighbor structure sufficient for correct label recovery from partial candidates. Without such controls (e.g., swapping in weaker features or non-random partial-label generation), the reported gains cannot be confidently attributed to HopS rather than the assumption holding on standard benchmarks.

Authors: We agree that the current manuscript does not include explicit ablations testing the reliance on the pre-trained encoder's feature space or controlled variations in partial-label generation. To address this, the revised version will add: (1) experiments replacing the default CLIP encoder with weaker alternatives (e.g., ImageNet-pretrained ResNet without language alignment) to verify that HopS gains diminish when nearest-neighbor structure is degraded; (2) non-random partial-label generation protocols (e.g., biased or adversarial candidate sets) to confirm robustness beyond standard random masking; and (3) sensitivity plots on the number of neighbors k and density threshold. These controls will isolate HopS's contribution from the base encoder quality while preserving the core claim that the method exploits existing structure in standard VL encoders. revision: yes

Circularity Check

0 steps flagged

No circularity: method introduces external-encoder-based filters and standard OT without self-referential derivation

full rationale

The paper defines HopS via a local density filter on nearest-neighbor candidate sets from a fixed pre-trained encoder plus a batch-wise optimal transport objective minimizing transport cost to candidate distributions. Neither component is defined in terms of the other or of the final performance claim; both are standard techniques applied to external features. Experiments on eight benchmarks serve as independent validation rather than tautological confirmation. No equations reduce a prediction to a fitted input by construction, and no load-bearing premise rests solely on self-citation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review is based solely on the abstract; full text details on any fitted parameters, thresholds, or additional assumptions are unavailable.

axioms (1)

domain assumption Pre-trained vision-language feature encoders capture structural regularities in feature space usable for label disambiguation.
Stated as the basis for the local density-based filter.

pith-pipeline@v0.9.0 · 5503 in / 1105 out tokens · 38073 ms · 2026-05-10T18:47:32.074280+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

we design a local density-based filter that selects the top frequent labels from the nearest neighbors' candidate sets and uses the softmax scores to identify the most plausible label... global selection objective based on optimal transport that maps the uniform sampling distribution to the candidate label distributions across a batch
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

min_P ⟨P, M_cost⟩ − ε H(P) s.t. P 1_C = r, P^T 1_B = c ... Sinkhorn-Knopp algorithm

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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A.2 Implementation Details

most similar labels—excluding the ground-truth—are selected, contributing to more challenging and informative candidate label sets with visually similar confusing labels. A.2 Implementation Details. A16-shottraining set is randomly sampled from each dataset in a class- balanced manner, with a fixed random seed to ensure experimental reproducibil- ity. The...
[53]

Theweighting coefficientfor the two loss components is set toλ = 1.0. Regarding computational resources, all experiments are conducted on a Linux- based system equipped with eight NVIDIA RTX 4090 GPUs, with each model requiring approximately 18–30 minutes for training and peaking at 6696 MiB of memory usage. The software environment includes Python 3.8, P...

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