{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/memorization-capacity-of-multi-head-attention","title":"Memorization Capacity of Multi-Head Attention in Transformers","arxiv_id":"2306.02010","date":"2023-06-03","proceeding":null,"authors":["Sadegh Mahdavi","Renjie Liao","Christos Thrampoulidis"],"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 $\\Theta(Hd^2)$ parameters, can memorize $\\Omega(Hn)$ 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.","url_abs":"https://arxiv.org/abs/2306.02010v3","url_pdf":"https://arxiv.org/pdf/2306.02010v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"memorization-capacity-of-multi-head-attention","repo_url":"https://github.com/smahdavi4/attention-memorization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"memorization","task_name":"Memorization"},{"task_slug":null,"task_name":"Position"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"},{"method_slug":"vision-transformer","method_name":"Vision Transformer"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2306.02010","atlas_url":"https://app.syntology.ai/?focus=2306.02010","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}