# Outlier-Efficient Hopfield Layers for Large Transformer-Based Models

arXiv: https://arxiv.org/abs/2404.03828 · HTML: https://mlsanity.com/paper/2404.03828/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 74 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books](https://mlsanity.com/paper/1506.06724/) (2015)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Revealing the Dark Secrets of BERT](https://mlsanity.com/paper/1908.08593/) (2019)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Inductive Biases and Variable Creation in Self-Attention Mechanisms](https://mlsanity.com/paper/2110.10090/) (2021)
- [DNABERT-2: Efficient Foundation Model and Benchmark For Multi-Species Genome](https://mlsanity.com/paper/2306.15006/) (2023)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)
- [Fast Attention Requires Bounded Entries](https://mlsanity.com/paper/2302.13214/) (2023)
- [CLOOB: Modern Hopfield Networks with InfoLOOB Outperform CLIP](https://mlsanity.com/paper/2110.11316/) (2021)
- [Energy Transformer](https://mlsanity.com/paper/2302.07253/) (2023)
- [Robust Quantization: One Model to Rule Them All](https://mlsanity.com/paper/2002.07686/) (2020)
- [Efficient 8-Bit Quantization of Transformer Neural Machine Language Translation Model](https://mlsanity.com/paper/1906.00532/) (2019)
- [Modern Hopfield Networks and Attention for Immune Repertoire Classification](https://mlsanity.com/paper/2007.13505/) (2020)
- [How to Capture Higher-order Correlations? Generalizing Matrix Softmax Attention to Kronecker Computation](https://mlsanity.com/paper/2310.04064/) (2023)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [On Sparse Modern Hopfield Model](https://mlsanity.com/paper/2309.12673/) (2023)

## Built on by (most cited first, 30 of 38)

- [Active-Dormant Attention Heads: Mechanistically Demystifying Extreme-Token Phenomena in LLMs](https://mlsanity.com/paper/2410.13835/) (2024)
- [Computational Limits of Low-Rank Adaptation (LoRA) Fine-Tuning for Transformer Models](https://mlsanity.com/paper/2406.03136/) (2024)
- [Mind the Inconspicuous: Revealing the Hidden Weakness in Aligned LLMs' Refusal Boundaries](https://mlsanity.com/paper/2405.20653/) (2024)
- [Multi-Layer Transformers Gradient Can be Approximated in Almost Linear Time](https://mlsanity.com/paper/2408.13233/) (2024)
- [Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent](https://mlsanity.com/paper/2410.11268/) (2024)
- [Conv-CoA: Improving Open-domain Question Answering in Large Language Models via Conversational Chain-of-Action](https://mlsanity.com/paper/2405.17822/) (2024)
- [A Tighter Complexity Analysis of SparseGPT](https://mlsanity.com/paper/2408.12151/) (2024)
- [HSR-Enhanced Sparse Attention Acceleration](https://mlsanity.com/paper/2410.10165/) (2024)
- [Provably Optimal Memory Capacity for Modern Hopfield Models: Transformer-Compatible Dense Associative Memories as Spherical Codes](https://mlsanity.com/paper/2410.23126/) (2024)
- [Empirical Guidelines for Deploying LLMs onto Resource-constrained Edge Devices](https://mlsanity.com/paper/2406.03777/) (2024)
- [Nonparametric Modern Hopfield Models](https://mlsanity.com/paper/2404.03900/) (2024)
- [Attention Sinks: A 'Catch, Tag, Release' Mechanism for Embeddings](https://mlsanity.com/paper/2502.00919/) (2025)
- [Do LLMs dream of elephants (when told not to)? Latent concept association and associative memory in transformers](https://mlsanity.com/paper/2406.18400/) (2024)
- [Provable Differentially Private Computation of the Cross-Attention Mechanism](https://mlsanity.com/paper/2407.14717/) (2024)
- [Beyond Scaling Laws: Understanding Transformer Performance with Associative Memory](https://mlsanity.com/paper/2405.08707/) (2024)
- [Video Latent Flow Matching: Optimal Polynomial Projections for Video Interpolation and Extrapolation](https://mlsanity.com/paper/2502.00500/) (2025)
- [Decoupled Alignment for Robust Plug-and-Play Adaptation](https://mlsanity.com/paper/2406.01514/) (2024)
- [Advanced AI Framework for Enhanced Detection and Assessment of Abdominal Trauma: Integrating 3D Segmentation with 2D CNN and RNN Models](https://mlsanity.com/paper/2407.16165/) (2024)
- [Modern Hopfield Networks Require Chain-of-Thought to Solve mathsfNC1-Hard Problems](https://mlsanity.com/paper/2412.05562/) (2024)
- [Fast and Low-Cost Genomic Foundation Models via Outlier Removal](https://mlsanity.com/paper/2505.00598/) (2025)
- [Value-State Gated Attention for Mitigating Extreme-Token Phenomena in Transformers](https://mlsanity.com/paper/2510.09017/) (2025)
- [FROST: Filtering Reasoning Outliers with Attention for Efficient Reasoning](https://mlsanity.com/paper/2601.19001/) (2026)
- [Unlocking the Theory Behind Scaling 1-Bit Neural Networks](https://mlsanity.com/paper/2411.01663/) (2024)
- [Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers](https://mlsanity.com/paper/2501.10688/) (2025)
- [AERO: Entropy-Guided Framework for Private LLM Inference](https://mlsanity.com/paper/2410.13060/) (2024)
- [Advancements in Natural Language Processing: Exploring Transformer-Based Architectures for Text Understanding](https://mlsanity.com/paper/2503.20227/) (2025)
- [GenoArmory: A Unified Evaluation Framework for Adversarial Attacks on Genomic Foundation Models](https://mlsanity.com/paper/2505.10983/) (2025)
- [Attention Sinks and Outliers in Attention Residuals](https://mlsanity.com/paper/2605.17887/) (2026)
- [On the Relationship Between Activation Outliers and Feature Death in Sparse Autoencoders](https://mlsanity.com/paper/2605.31518/) (2026)
- [On the Role of Hidden States of Modern Hopfield Network in Transformer](https://mlsanity.com/paper/2511.20698/) (2025)

## Abstract (arXiv)

We introduce an Outlier-Efficient Modern Hopfield Model (termed OutEffHop) and use it to address the outlier inefficiency problem of training gigantic transformer-based models. Our main contribution is a novel associative memory model facilitating textitoutlier-efficient associative memory retrievals. Interestingly, this memory model manifests a model-based interpretation of an outlier-efficient attention mechanism (rm Softmax1): it is an approximation of the memory retrieval process of OutEffHop. Methodologically, this allows us to introduce novel outlier-efficient Hopfield layers as powerful alternatives to traditional attention mechanisms, with superior post-quantization performance. Theoretically, the Outlier-Efficient Modern Hopfield Model retains and improves the desirable properties of standard modern Hopfield models, including fixed point convergence and exponential storage capacity. Empirically, we demonstrate the efficacy of the proposed model across large-scale transformer-based and Hopfield-based models (including BERT, OPT, ViT, and STanHop-Net), benchmarking against state-of-the-art methods like mathttClippedSoftmax and mathttGatedAttention. Notably, OutEffHop achieves an average reduction of 22+% in average kurtosis and 26+% in the maximum infinity norm of model outputs across four models. Code is available at hrefhttps://github.com/MAGICS-LAB/OutEffHopGitHub; models are on hrefhttps://huggingface.co/collections/magicslabnu/outeffhop-6610fcede8d2cda23009a98fHugging Face Hub; future updates are on hrefhttps://arxiv.org/abs/2404.03828arXiv.