Memorization Capacity of Multi-Head Attention in Transformers

2023/06/03 by Sadegh Mahdavi, Mahdavi, Sadegh, Renjie Liao +3 · 8 citations
Computer Science · Engineering · #Advanced Memory and Neural Computing #Advanced Neural Network Applications #FOS: Computer and information sciences #Ferroelectric and Negative Capacitance Devices #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2306.02010

openalex publication_date 2023/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with H heads, dimension d, and context size n < d, featuring Θ(Hd²) parameters, can memorize Ω(Hn) examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator's saturation property. We validate our findings through experiments on synthetic data.

Cited by

• Analyzing the Power of Chain of Thought through Memorization Capabilities
• The Effect of Attention Head Count on Transformer Approximation
• Memory Limitations of Prompt Tuning in Transformers
• Towards Theoretical Understanding of Transformer Test-Time Computing: Investigation on In-Context Linear Regression
• Understanding Transformers through the Lens of Pavlovian Conditioning
• Systematic Evaluation of Optimization Techniques for Long-Context Language Models
• Capacity Matters: a Proof-of-Concept for Transformer Memorization on Real-World Data
• Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective

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