# Approximating Softmax in Pretrained LLMs: Model Sensitivity and Kernel Acceleration

arXiv: https://arxiv.org/abs/2609.33586 · HTML: https://mlsanity.com/paper/2609.33586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 30 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [SageAttention: Accurate 8-Bit Attention for Plug-and-play Inference Acceleration](https://mlsanity.com/paper/2410.02367/) (2024)
- [FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2111.13824/) (2021)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [SageAttention2: Efficient Attention with Thorough Outlier Smoothing and Per-thread INT4 Quantization](https://mlsanity.com/paper/2411.10958/) (2024)
- [I-ViT: Integer-only Quantization for Efficient Vision Transformer Inference](https://mlsanity.com/paper/2207.01405/) (2022)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [SageAttention3: Microscaling FP4 Attention for Inference and An Exploration of 8-Bit Training](https://mlsanity.com/paper/2505.11594/) (2025)
- [FlashAttention-4: Algorithm and Kernel Pipelining Co-Design for Asymmetric Hardware Scaling](https://mlsanity.com/paper/2603.05451/) (2026)
- [Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers](https://mlsanity.com/paper/2103.09301/) (2021)
- [PTQ4SAM: Post-Training Quantization for Segment Anything](https://mlsanity.com/paper/2405.03144/) (2024)
- [Efficient Attention Mechanisms for Large Language Models: A Survey](https://mlsanity.com/paper/2507.19595/) (2025)
- [ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameters](https://mlsanity.com/paper/2402.10930/) (2024)
- [ITA: An Energy-Efficient Attention and Softmax Accelerator for Quantized Transformers](https://mlsanity.com/paper/2307.03493/) (2023)
- [INT-FlashAttention: Enabling Flash Attention for INT8 Quantization](https://mlsanity.com/paper/2409.16997/) (2024)
- [LRP-QViT: Mixed-Precision Vision Transformer Quantization via Layer-wise Relevance Propagation](https://mlsanity.com/paper/2401.11243/) (2024)
- [EXAQ: Exponent Aware Quantization For LLMs Acceleration](https://mlsanity.com/paper/2410.03185/) (2024)
- [IntAttention: A Fully Integer Attention Pipeline for Efficient Edge Inference](https://mlsanity.com/paper/2511.21513/) (2025)
- [VFA: Relieving Vector Operations in Flash Attention with Global Maximum Pre-computation](https://mlsanity.com/paper/2604.12798/) (2026)
- [MXAttention: Data-Free Optimal Scaling and Pre-Normalization Quantization for MXFP4 Attention](https://mlsanity.com/paper/2607.24377/) (2026)

## Abstract (arXiv)

On NVIDIA Blackwell B200, tensor-core throughput outpaces special-function exponential throughput by more than two orders of magnitude, exposing exponential evaluation in fused attention kernels. A pretrained Transformer, however, may not need it evaluated accurately at every element. We characterize what a pretrained model does need by approximating softmax at inference in ten frozen decoder-only models (0.5B-72B). The number of positions the softmax map assigns probability to and within-row resolution can be cut substantially, yet uniform weighting of the same positions is damaging. Where a fixed resolution budget is placed matters as much as its size, with resolution near the row maximum consistently favored. Perturbations matched on scalar distortion produce model-dependent responses of opposite sign. These findings motivate Rowmax-PoT, a coarse logarithmic weight representation anchored at each row maximum, and Rowmax-H15, its hardware specialization in FlashAttention-4. On B200, the patched FP8 attention forward is 12.4% faster at causal 8K and 25.8% faster at non-causal 8K in host-side call-latency measurements; board energy per forward falls by 8.4% at causal 16K. Measured separately on the BF16 kernel path at 2K, Rowmax-H15 increases perplexity by 0.091-0.492% across five models from three families.