# Learning Neural Networks with Sparse Activations

arXiv: https://arxiv.org/abs/2406.17989 · HTML: https://mlsanity.com/paper/2406.17989/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 26 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [PaLI: A Jointly-Scaled Multilingual Language-Image Model](https://mlsanity.com/paper/2209.06794/) (2022)
- [Large scale distributed neural network training through online distillation](https://mlsanity.com/paper/1804.03235/) (2018)
- [Large Memory Layers with Product Keys](https://mlsanity.com/paper/1907.05242/) (2019)
- [The Lazy Neuron Phenomenon: On Emergence of Activation Sparsity in Transformers](https://mlsanity.com/paper/2210.06313/) (2022)
- [ReLU Strikes Back: Exploiting Activation Sparsity in Large Language Models](https://mlsanity.com/paper/2310.04564/) (2023)
- [Augmenting Self-attention with Persistent Memory](https://mlsanity.com/paper/1907.01470/) (2019)
- [A Study on ReLU and Softmax in Transformer](https://mlsanity.com/paper/2302.06461/) (2023)
- [Statistical-Query Lower Bounds via Functional Gradients](https://mlsanity.com/paper/2006.15812/) (2020)
- [Hardness of Noise-Free Learning for Two-Hidden-Layer Neural Networks](https://mlsanity.com/paper/2202.05258/) (2022)
- [Approximating Two-Layer Feedforward Networks for Efficient Transformers](https://mlsanity.com/paper/2310.10837/) (2023)
- [Supervision Complexity and its Role in Knowledge Distillation](https://mlsanity.com/paper/2301.12245/) (2023)
- [Accelerating Deep Neural Networks via Semi-Structured Activation Sparsity](https://mlsanity.com/paper/2309.06626/) (2023)
- [A Theoretical Explanation of Activation Sparsity through Flat Minima and Adversarial Robustness](https://mlsanity.com/paper/2309.03004/) (2023)

## Built on by (most cited first, 6 of 6)

- [Mixture of Experts Made Intrinsically Interpretable](https://mlsanity.com/paper/2503.07639/) (2025)
- [Universal Properties of Activation Sparsity in Modern Large Language Models](https://mlsanity.com/paper/2509.00454/) (2025)
- [Spark Transformer: Reactivating Sparsity in FFN and Attention](https://mlsanity.com/paper/2506.06644/) (2025)
- [How Controlling the Variance can Improve Training Stability of Sparsely Activated DNNs and CNNs](https://mlsanity.com/paper/2602.05779/) (2026)
- [COUNTDOWN: Contextually Sparse Activation Filtering Out Unnecessary Weights in Down Projection](https://mlsanity.com/paper/2505.17701/) (2025)
- [Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks](https://mlsanity.com/paper/2609.09130/) (2026)

## Abstract (arXiv)

A core component present in many successful neural network architectures, is an MLP block of two fully connected layers with a non-linear activation in between. An intriguing phenomenon observed empirically, including in transformer architectures, is that, after training, the activations in the hidden layer of this MLP block tend to be extremely sparse on any given input. Unlike traditional forms of sparsity, where there are neurons/weights which can be deleted from the network, this form of em dynamic activation sparsity appears to be harder to exploit to get more efficient networks. Motivated by this we initiate a formal study of PAC learnability of MLP layers that exhibit activation sparsity. We present a variety of results showing that such classes of functions do lead to provable computational and statistical advantages over their non-sparse counterparts. Our hope is that a better theoretical understanding of em sparsely activated networks would lead to methods that can exploit activation sparsity in practice.