# Post-Boundary Bridge: Must Local Attention Go Global Between Global Layers?

arXiv: https://arxiv.org/abs/2606.02680 · HTML: https://mlsanity.com/paper/2606.02680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 30 of 36)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [BLiMP: The Benchmark of Linguistic Minimal Pairs for English](https://mlsanity.com/paper/1912.00582/) (2019)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Model Tells You What to Discard: Adaptive KV Cache Compression for LLMs](https://mlsanity.com/paper/2310.01801/) (2023)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [MInference 1.0: Accelerating Pre-filling for Long-Context LLMs via Dynamic Sparse Attention](https://mlsanity.com/paper/2407.02490/) (2024)
- [DuoAttention: Efficient Long-Context LLM Inference with Retrieval and Streaming Heads](https://mlsanity.com/paper/2410.10819/) (2024)
- [LongLoRA: Efficient Fine-tuning of Long-Context Large Language Models](https://mlsanity.com/paper/2309.12307/) (2023)
- [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)

## Abstract (arXiv)

Hybrid Transformers reduce the cost of long-context modeling by combining local attention with periodic full-attention layers. When global communication is already available, however, the best use of local computation remains unclear. We introduce Post-Boundary Bridge (PBB), which preserves causal attention within blocks and adds direct connections across their boundaries. Rather than extending the range of information relayed through successive local layers, PBB prioritizes within-block modeling and nearby exchange, leaving long-range communication to full-attention layers. Across dense and mixture-of-experts models with 205 million to 2.07 billion stored parameters, PBB hybrids retain near-Full perplexity and competitive performance on standard downstream benchmarks while improving controlled source retrieval. At 205 million parameters, PBB also matches a hybrid using sliding-window attention (SWA) in perplexity and achieves higher source-retrieval accuracy. The same boundary-aligned structure enables Flash-PBB, an exact decoding implementation that updates its key-value cache without relocating retained entries. Compared with Flash-SWA, Flash-PBB delivers 1.82x decode attention-core throughput with half the allocated local key-value cache. These results show that targeted boundary exchange can preserve model quality while enabling faster, more memory-efficient local attention between global layers.