# Power-based Partial Attention: Bridging Linear-Complexity and Full Attention

arXiv: https://arxiv.org/abs/2601.17334 · HTML: https://mlsanity.com/paper/2601.17334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 34 references that are in the map.
- First posted on arXiv 24 Jan 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [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)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [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)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [MoBA: Mixture of Block Attention for Long-Context LLMs](https://mlsanity.com/paper/2502.13189/) (2025)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Flex Attention: A Programming Model for Generating Optimized Attention Kernels](https://mlsanity.com/paper/2412.05496/) (2024)
- [NVIDIA Nemotron Nano 2: An Accurate and Efficient Hybrid Mamba-Transformer Reasoning Model](https://mlsanity.com/paper/2508.14444/) (2025)
- [Can Mamba Learn How to Learn? A Comparative Study on In-Context Learning Tasks](https://mlsanity.com/paper/2402.04248/) (2024)
- [Nemotron-H: A Family of Accurate and Efficient Hybrid Mamba-Transformer Models](https://mlsanity.com/paper/2504.03624/) (2025)
- [The Hidden Attention of Mamba Models](https://mlsanity.com/paper/2403.01590/) (2024)
- [Log-Linear Attention](https://mlsanity.com/paper/2506.04761/) (2025)
- [PowerAttention: Exponentially Scaling of Receptive Fields for Effective Sparse Attention](https://mlsanity.com/paper/2503.03588/) (2025)
- [Optimizing Mixture of Block Attention](https://mlsanity.com/paper/2511.11571/) (2025)

## Abstract (arXiv)

It is widely accepted from transformer research that "attention is all we need", but the amount of attention required has never been systematically quantified. Is quadratic O(L2) attention necessary, or is there a sub-quadratic attention mechanism that can achieve comparable performance? To answer this question, we introduce power-based partial attention (PPA), an attention mechanism of order O(L1+p), where 0 ≤ p ≤ 1, such that p=0 corresponds to sliding window attention with linear complexity, and p=1 corresponds to full attention. With this attention construction, we can explore how transformer architecture performance varies as a function of the attention scaling behavior controlled by p. The overall trend from our experiments shows an S-curve-like behavior where the performance transitions from sliding-window (linear-complexity) attention to full attention over a narrow window of p values, and plateaus as p approaches 1. In our experiments, we show that there exists 0<p<1 such that O(L1+p) attention is sufficient to achieve similar results as O(L2) full attention.