# BAPS: A Fine-Grained Low-Precision Scheme for Softmax in Attention via Block-Aware Precision reScaling

arXiv: https://arxiv.org/abs/2602.02071 · HTML: https://mlsanity.com/paper/2602.02071/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [SageAttention: Accurate 8-Bit Attention for Plug-and-play Inference Acceleration](https://mlsanity.com/paper/2410.02367/) (2024)
- [Pretraining Large Language Models with NVFP4](https://mlsanity.com/paper/2509.25149/) (2025)
- [Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers](https://mlsanity.com/paper/2103.09301/) (2021)
- [Case-Based or Rule-Based: How Do Transformers Do the Math?](https://mlsanity.com/paper/2402.17709/) (2024)
- [From Attention to Activation: Unravelling the Enigmas of Large Language Models](https://mlsanity.com/paper/2410.17174/) (2024)
- [BLASST: Dynamic BLocked Attention Sparsity via Softmax Thresholding](https://mlsanity.com/paper/2512.12087/) (2025)
- [Low-Cost FlashAttention with Fused Exponential and Multiplication Hardware Operators](https://mlsanity.com/paper/2505.14314/) (2025)

## Built on by (most cited first, 1 of 1)

- [Pretraining Transformers with Quantized Softmax in Attention](https://mlsanity.com/paper/2609.33591/) (2026)

## Abstract (arXiv)

As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data bandwidth between matrix and vector compute cores, and (2) the significant area cost of high-precision (FP32/16) exponentiation units (EXP2). To address these issues, we introduce a novel low-precision workflow that employs a specific 8-bit floating-point format (HiF8) and block-aware precision rescaling for softmax. Crucially, our algorithmic innovations make low-precision softmax feasible without the significant model accuracy loss that hampers direct low-precision approaches. Specifically, our design (i) halves the required data movement bandwidth by enabling matrix multiplication outputs constrained to 8-bit, and (ii) substantially reduces the EXP2 unit area by computing exponentiations in low (8-bit) precision. Extensive evaluation on language models and multi-modal models confirms the validity of our method. By alleviating the vector computation bottleneck, our work paves the way for doubling end-to-end inference throughput without increasing chip area, and offers a concrete co-design path for future low-precision hardware and software.