# ReLU2 Wins: Discovering Efficient Activation Functions for Sparse LLMs

arXiv: https://arxiv.org/abs/2402.03804 · HTML: https://mlsanity.com/paper/2402.03804/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 76 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 30 of 63)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)

## Built on by (most cited first, 30 of 67)

- [Don't be lazy: CompleteP enables compute-efficient deep transformers](https://mlsanity.com/paper/2505.01618/) (2025)
- [Training-Free Activation Sparsity in Large Language Models](https://mlsanity.com/paper/2408.14690/) (2024)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [ProSparse: Introducing and Enhancing Intrinsic Activation Sparsity within Large Language Models](https://mlsanity.com/paper/2402.13516/) (2024)
- [CATS: Contextually-Aware Thresholding for Sparsity in Large Language Models](https://mlsanity.com/paper/2404.08763/) (2024)
- [Turbo Sparse: Achieving LLM SOTA Performance with Minimal Activated Parameters](https://mlsanity.com/paper/2406.05955/) (2024)
- [Physics of Language Models: Part 4.1, Architecture Design and the Magic of Canon Layers](https://mlsanity.com/paper/2512.17351/) (2025)
- [Beyond Matryoshka: Revisiting Sparse Coding for Adaptive Representation](https://mlsanity.com/paper/2503.01776/) (2025)
- [Mixture of Experts Made Intrinsically Interpretable](https://mlsanity.com/paper/2503.07639/) (2025)
- [A Unified View of Attention and Residual Sinks: Outlier-Driven Rescaling is Essential for Transformer Training](https://mlsanity.com/paper/2601.22966/) (2026)
- [Configurable Foundation Models: Building LLMs from a Modular Perspective](https://mlsanity.com/paper/2409.02877/) (2024)
- [Sparsing Law: Towards Large Language Models with Greater Activation Sparsity](https://mlsanity.com/paper/2411.02335/) (2024)
- [R-Sparse: Rank-Aware Activation Sparsity for Efficient LLM Inference](https://mlsanity.com/paper/2504.19449/) (2025)
- [Monet: Mixture of Monosemantic Experts for Transformers](https://mlsanity.com/paper/2412.04139/) (2024)
- [Yi-Lightning Technical Report](https://mlsanity.com/paper/2412.01253/) (2024)
- [Accelerating Transformer Inference and Training with 2:4 Activation Sparsity](https://mlsanity.com/paper/2503.16672/) (2025)
- [FloE: On-the-Fly MoE Inference on Memory-constrained GPU](https://mlsanity.com/paper/2505.05950/) (2025)
- [SparseLoRA: Accelerating LLM Fine-Tuning with Contextual Sparsity](https://mlsanity.com/paper/2506.16500/) (2025)
- [Activation Approximations Can Incur Safety Vulnerabilities Even in Aligned LLMs: Comprehensive Analysis and Defense](https://mlsanity.com/paper/2502.00840/) (2025)
- [Universal Properties of Activation Sparsity in Modern Large Language Models](https://mlsanity.com/paper/2509.00454/) (2025)
- [Composing Global Solutions to Reasoning Tasks via Algebraic Objects in Neural Nets](https://mlsanity.com/paper/2410.01779/) (2024)
- [DuoGPT: Training-free Dual Sparsity through Activation-aware Pruning in LLMs](https://mlsanity.com/paper/2506.20194/) (2025)
- [La RoSA: Enhancing LLM Efficiency via Layerwise Rotated Sparse Activation](https://mlsanity.com/paper/2507.01299/) (2025)
- [BlockFFN: Towards End-Side Acceleration-Friendly Mixture-of-Experts with Chunk-Level Activation Sparsity](https://mlsanity.com/paper/2507.08771/) (2025)
- [Simply Stabilizing the Loop via Fully Looped Transformer](https://mlsanity.com/paper/2605.18797/) (2026)
- [Exploring the Benefit of Activation Sparsity in Pre-training](https://mlsanity.com/paper/2410.03440/) (2024)
- [Neuralink: Fast LLM Inference on Smartphones with Neuron Co-Activation Linking](https://mlsanity.com/paper/2410.19274/) (2024)
- [Spark Transformer: Reactivating Sparsity in FFN and Attention](https://mlsanity.com/paper/2506.06644/) (2025)
- [SmallThinker: A Family of Efficient Large Language Models Natively Trained for Local Deployment](https://mlsanity.com/paper/2507.20984/) (2025)
- [iFairy: the First 2-bit Complex LLM with All Parameters in ±1, ± i](https://mlsanity.com/paper/2508.05571/) (2025)

## Abstract (arXiv)

Sparse computation offers a compelling solution for the inference of Large Language Models (LLMs) in low-resource scenarios by dynamically skipping the computation of inactive neurons. While traditional approaches focus on ReLU-based LLMs, leveraging zeros in activation values, we broaden the scope of sparse LLMs beyond zero activation values. We introduce a general method that defines neuron activation through neuron output magnitudes and a tailored magnitude threshold, demonstrating that non-ReLU LLMs also exhibit sparse activation. To find the most efficient activation function for sparse computation, we propose a systematic framework to examine the sparsity of LLMs from three aspects: the trade-off between sparsity and performance, the predictivity of sparsity, and the hardware affinity. We conduct thorough experiments on LLMs utilizing different activation functions, including ReLU, SwiGLU, ReGLU, and ReLU2. The results indicate that models employing ReLU2 excel across all three evaluation aspects, highlighting its potential as an efficient activation function for sparse LLMs. We will release the code to facilitate future research.