# Aperture: Merge-Consistent Rotary States for Compressed Tokens

arXiv: https://arxiv.org/abs/2609.36781 · HTML: https://mlsanity.com/paper/2609.36781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompt and context compression, one of 12 directions in Efficient LLM inference and serving.
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Efficient LLM inference and serving / [Prompt and context compression](https://mlsanity.com/inference/prompt-and-context-compression/)

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

- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Video-MME: The First-Ever Comprehensive Evaluation Benchmark of Multi-modal LLMs in Video Analysis](https://mlsanity.com/paper/2405.21075/) (2024)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [MVBench: A Comprehensive Multi-modal Video Understanding Benchmark](https://mlsanity.com/paper/2311.17005/) (2023)
- [Token Merging: Your ViT But Faster](https://mlsanity.com/paper/2210.09461/) (2022)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Qwen2.5-Omni Technical Report](https://mlsanity.com/paper/2503.20215/) (2025)
- [NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysis](https://mlsanity.com/paper/1604.02808/) (2016)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Rescaling Egocentric Vision](https://mlsanity.com/paper/2006.13256/) (2020)
- [LLaVA-PruMerge: Adaptive Token Reduction for Efficient Large Multimodal Models](https://mlsanity.com/paper/2403.15388/) (2024)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [StreamingBench: Assessing the Gap for MLLMs to Achieve Streaming Video Understanding](https://mlsanity.com/paper/2411.03628/) (2024)
- [OVO-Bench: How Far is Your Video-LLMs from Real-World Online Video Understanding?](https://mlsanity.com/paper/2501.05510/) (2025)
- [Apollo: An Exploration of Video Understanding in Large Multimodal Models](https://mlsanity.com/paper/2412.10360/) (2024)
- [VideoRoPE: What Makes for Good Video Rotary Position Embedding?](https://mlsanity.com/paper/2502.05173/) (2025)
- [Self-attention with Functional Time Representation Learning](https://mlsanity.com/paper/1911.12864/) (2019)
- [Exact-NeRF: An Exploration of a Precise Volumetric Parameterization for Neural Radiance Fields](https://mlsanity.com/paper/2211.12285/) (2022)
- [Enhancing Multi-Scale Implicit Learning in Image Super-Resolution with Integrated Positional Encoding](https://mlsanity.com/paper/2112.05756/) (2021)
- [EchoingPixels: Aliasing-Resistant Joint Token Reduction for Audio-Visual LLMs](https://mlsanity.com/paper/2512.10324/) (2025)
- [PPE: Positional Preservation Embedding for Token Compression in Multimodal Large Language Models](https://mlsanity.com/paper/2510.22936/) (2025)
- [StreamingEval: A Unified Evaluation Protocol towards Realistic Streaming Video Understanding](https://mlsanity.com/paper/2603.21493/) (2026)
- [TIE: Time Interval Encoding for Video Generation over Events](https://mlsanity.com/paper/2605.10543/) (2026)

## Abstract (arXiv)

Token compression combines content from several positions, yet rotary position embeddings usually assign the merged token one coordinate. We ask what positional information must survive later merges. Aperture stores Fourier moments of the token's weighted support at the model's rotary frequencies. We prove that these moments have minimal real dimension among continuous states sufficient for the selected expected rotary interactions. Represented mass makes updates additive; attention normalisation remains a separate readout choice. Uniform intervals give a centre rotation times a sinc gain. We characterise when centres determine interval widths and construct matched examples where they do not. Numerical checks verify the weighted-support implementation. In trained temporal readers, compression transfer varies with gain calibration and feature placement. In a prespecified native video question-answering comparison, stored support reaches 65.63% accuracy versus 67.12% for the deployed merging rule. These results separate exact positional preservation under compression from downstream benefit.