# Hardware-Efficient Softmax and Layer Normalization with Guaranteed Normalization for Edge Devices

arXiv: https://arxiv.org/abs/2604.23647 · HTML: https://mlsanity.com/paper/2604.23647/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 26 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Transformer in Transformer](https://mlsanity.com/paper/2103.00112/) (2021)
- [BERT: A Review of Applications in Natural Language Processing and Understanding](https://mlsanity.com/paper/2103.11943/) (2021)
- [Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers](https://mlsanity.com/paper/2103.09301/) (2021)
- [SOLE: Hardware-Software Co-design of Softmax and LayerNorm for Efficient Transformer Inference](https://mlsanity.com/paper/2510.17189/) (2025)
- [SoftmAP: Software-Hardware Co-design for Integer-Only Softmax on Associative Processors](https://mlsanity.com/paper/2411.17847/) (2024)

## Abstract (arXiv)

In Transformer models, non-GEMM (non-General Matrix Multiplication) operations -- especially Softmax and Layer Normalization (LayerNorm) -- often dominate hardware cost due to their nonlinear nature. To address this, previous approximation studies mainly target rank-oriented tasks, which is acceptable for classification. However, edge Natural Language Processing (NLP) applications and edge generative AI are largely evaluated based on score-oriented tasks, so normalization-guaranteed non-GEMM operations are essential. We propose a hardware-efficient Softmax and LayerNorm with Guaranteed Normalization for Edge devices. Our design employs hardware-efficient approximation methods while preserving the normalization (Softmax: sum p = 1, LayerNorm: σ = 1). Our architecture is described in Verilog HDL and synthesized using the Samsung 28nm CMOS process. In accuracy evaluation, we achieve high accuracy with minimal degradation: GLUE +0.07%, SQuAD -0.01%, perplexity -0.09%. Implementation results show that our architecture is small: 942,μ m2 for Softmax, 1199,μ m2 for LayerNorm. Compared to the state of the art, we achieve up to 11x and 14x reduction in area, respectively.