# GRAMformer: Any-Order Modality Interactions via Volumetric Multimodal Cross-Attention

arXiv: https://arxiv.org/abs/2606.06249 · HTML: https://mlsanity.com/paper/2606.06249/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Video-LLaMA: An Instruction-tuned Audio-Visual Language Model for Video Understanding](https://mlsanity.com/paper/2306.02858/) (2023)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [VideoBERT: A Joint Model for Video and Language Representation Learning](https://mlsanity.com/paper/1904.01766/) (2019)
- [CLIP4Clip: An Empirical Study of CLIP for End to End Video Clip Retrieval](https://mlsanity.com/paper/2104.08860/) (2021)
- [Multimodal Transformer for Unaligned Multimodal Language Sequences](https://mlsanity.com/paper/1906.00295/) (2019)
- [Language Is Not All You Need: Aligning Perception with Language Models](https://mlsanity.com/paper/2302.14045/) (2023)
- [Tensor Fusion Network for Multimodal Sentiment Analysis](https://mlsanity.com/paper/1707.07250/) (2017)
- [LanguageBind: Extending Video-Language Pretraining to N-modality by Language-based Semantic Alignment](https://mlsanity.com/paper/2310.01852/) (2023)
- [mPLUG-Owl3: Towards Long Image-Sequence Understanding in Multi-Modal Large Language Models](https://mlsanity.com/paper/2408.04840/) (2024)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [Efficient Low-rank Multimodal Fusion with Modality-Specific Factors](https://mlsanity.com/paper/1806.00064/) (2018)
- [MISA: Modality-Invariant and -Specific Representations for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2005.03545/) (2020)
- [Learning Modality-Specific Representations with Self-Supervised Multi-Task Learning for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2102.04830/) (2021)
- [MultiBench: Multiscale Benchmarks for Multimodal Representation Learning](https://mlsanity.com/paper/2107.07502/) (2021)
- [Gramian Multimodal Representation Learning and Alignment](https://mlsanity.com/paper/2412.11959/) (2024)
- [What to align in multimodal contrastive learning?](https://mlsanity.com/paper/2409.07402/) (2024)
- [Multimodal Multi-loss Fusion Network for Sentiment Analysis](https://mlsanity.com/paper/2308.00264/) (2023)
- [Flowing from Words to Pixels: A Noise-Free Framework for Cross-Modality Evolution](https://mlsanity.com/paper/2412.15213/) (2024)
- [Enriching Multimodal Sentiment Analysis through Textual Emotional Descriptions of Visual-Audio Content](https://mlsanity.com/paper/2412.10460/) (2024)
- [Unveiling the Power of Audio-Visual Early Fusion Transformers with Dense Interactions through Masked Modeling](https://mlsanity.com/paper/2312.01017/) (2023)
- [Contrasting with Symile: Simple Model-Agnostic Representation Learning for Unlimited Modalities](https://mlsanity.com/paper/2411.01053/) (2024)
- [M-SENA: An Integrated Platform for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2203.12441/) (2022)
- [Rethinking Cross-Modal Interaction in Multimodal Diffusion Transformers](https://mlsanity.com/paper/2506.07986/) (2025)

## Abstract (arXiv)

Transformer-based multimodal models rely on attention mechanisms to integrate information across heterogeneous modalities. Despite their success, existing multimodal attention formulations compute their scores through collections of pairwise dot-product interactions or by concatenating all the modalities into the keys, even when multiple modalities should be jointly involved. As a consequence, current approaches either incur quadratic complexity in the number of modalities or fail to explicitly model interactions that depend on the joint configuration of multiple representations. In this work, we introduce the Volumetric Multimodal cross-Attention (VMA), a novel cross-attention mechanism in which attention scores are defined as a function of the joint geometry of a query and multiple modality-specific keys. VMA computes the volume spanned by query and key vectors across multiple modalities, capturing joint multimodal dependencies beyond pairwise similarity, enabling native modeling of any-order modality interactions. We integrate VMA into our novel multimodal transformer architecture, named GRAMformer, explicitly designed to integrate any number of modalities. We evaluate the proposed model on multimodal learning tasks, demonstrating improved effectiveness and efficiency.