# CoCA: Fusing Position Embedding with Collinear Constrained Attention in Transformers for Long Context Window Extending

arXiv: https://arxiv.org/abs/2309.08646 · HTML: https://mlsanity.com/paper/2309.08646/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [Landmark Attention: Random-Access Infinite Context Length for Transformers](https://mlsanity.com/paper/2305.16300/) (2023)
- [LongNet: Scaling Transformers to 1,000,000,000 Tokens](https://mlsanity.com/paper/2307.02486/) (2023)
- [KERPLE: Kernelized Relative Positional Embedding for Length Extrapolation](https://mlsanity.com/paper/2205.09921/) (2022)

## Built on by (most cited first, 6 of 6)

- [Shifting Long-Context LLMs Research from Input to Output](https://mlsanity.com/paper/2503.04723/) (2025)
- [LADM: Long-context Training Data Selection with Attention-based Dependency Measurement for LLMs](https://mlsanity.com/paper/2503.02502/) (2025)
- [PEER: Expertizing Domain-Specific Tasks with a Multi-Agent Framework and Tuning Methods](https://mlsanity.com/paper/2407.06985/) (2024)
- [Opt-GPTQ: An Optimized GPTQ Combining Sparse Attention and Quantization Techniques](https://mlsanity.com/paper/2505.02351/) (2025)
- [Beyond Text-to-SQL: Can LLMs Really Debug Enterprise ETL SQL?](https://mlsanity.com/paper/2601.18119/) (2026)
- [KVSlimmer: Theoretical Insights and Practical Optimizations for Asymmetric KV Merging](https://mlsanity.com/paper/2603.00907/) (2026)

## Abstract (arXiv)

Self-attention and position embedding are two key modules in transformer-based Large Language Models (LLMs). However, the potential relationship between them is far from well studied, especially for long context window extending. In fact, anomalous behaviors harming long context extrapolation exist between Rotary Position Embedding (RoPE) and vanilla self-attention unveiled by our work. To address this issue, we propose a novel attention mechanism, CoCA (Collinear Constrained Attention). Specifically, we enforce a collinear constraint between Q and K to seamlessly integrate RoPE and self-attention. While only adding minimal computational and spatial complexity, this integration significantly enhances long context window extrapolation ability. We provide an optimized implementation, making it a drop-in replacement for any existing transformer-based models. Extensive experiments show that CoCA performs extraordinarily well in extending context windows. A CoCA-based GPT model, trained with a context length of 512, can seamlessly extend the context window up to 32K (60×), without any fine-tuning. Additionally, by dropping CoCA in LLaMA-7B, we achieve extrapolation up to 32K within only 2K training length. Our code is publicly available at: https://github.com/codefuse-ai/Collinear-Constrained-Attention