# Gram-Anchored Prompt Learning for Vision-Language Models via Second-Order Statistics

arXiv: https://arxiv.org/abs/2604.03980 · HTML: https://mlsanity.com/paper/2604.03980/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompt learning and adaptation of CLIP, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Prompt learning and adaptation of CLIP](https://mlsanity.com/mllm/prompt-learning-and-adaptation-of-clip/)

## Builds on (most cited first, 24 of 24)

- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [MaPLe: Multi-modal Prompt Learning](https://mlsanity.com/paper/2210.03117/) (2022)
- [Extract Free Dense Labels from CLIP](https://mlsanity.com/paper/2112.01071/) (2021)
- [LiT: Zero-Shot Transfer with Locked-image text Tuning](https://mlsanity.com/paper/2111.07991/) (2021)
- [Visual-Language Prompt Tuning with Knowledge-guided Context Optimization](https://mlsanity.com/paper/2303.13283/) (2023)
- [Self-regulating Prompts: Foundational Model Adaptation without Forgetting](https://mlsanity.com/paper/2307.06948/) (2023)
- [DualCoOp: Fast Adaptation to Multi-Label Recognition with Limited Annotations](https://mlsanity.com/paper/2206.09541/) (2022)
- [TCP:Textual-based Class-aware Prompt tuning for Visual-Language Model](https://mlsanity.com/paper/2311.18231/) (2023)
- [Consistency-guided Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2306.01195/) (2023)
- [DePT: Decoupled Prompt Tuning](https://mlsanity.com/paper/2309.07439/) (2023)
- [MMRL: Multi-Modal Representation Learning for Vision-Language Models](https://mlsanity.com/paper/2503.08497/) (2025)
- [GalLoP: Learning Global and Local Prompts for Vision-Language Models](https://mlsanity.com/paper/2407.01400/) (2024)
- [Hierarchical Cross-modal Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2507.14976/) (2025)
- [Multi-Modal Adapter for Vision-Language Models](https://mlsanity.com/paper/2409.02958/) (2024)

## Abstract (arXiv)

Parameter-efficient prompt learning has become the de facto standard for adapting Vision-Language Models (VLMs) to downstream tasks. Existing approaches predominantly focus on aligning text prompts with first-order visual features (i.e., spatial feature maps). While effective for fine-grained semantic discrimination, we argue that relying solely on first-order information is insufficient for robust adaptation, as these spatially entangled features are highly susceptible to domain shifts and local noise. In this work, we propose Gram-Anchored Prompt Learning (GAPL) for Vision-Language Models via Second-Order Statistics, a framework that synergizes local semantic alignment with global structural consistency. Methodologically, we introduce an additional second-order statistical stream via Gram matrices that augments the standard first-order spatial interaction. By anchoring prompts to these second-order priors, our approach enables language representations to dynamically adapt to statistical distribution shifts across diverse domains. Extensive experiments indicate the effectiveness of the second-order features, and show compelling performances of GAPL on various benchmarks.