{"id":240522,"date":"2026-03-20T11:47:50","date_gmt":"2026-03-20T15:47:50","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=240522"},"modified":"2026-03-20T16:20:27","modified_gmt":"2026-03-20T20:20:27","slug":"cross-attention-for-cross-asset-applications","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/cross-attention-for-cross-asset-applications\/","title":{"rendered":"Cross-Attention for Cross-Asset Applications"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>The article &#8216;Cross-Attention for Cross-Asset Applications&#8221; was originally published on <a href=\"https:\/\/predictnow.ai\/cross-attention-for-cross-asset-applications\/\">PredictNow.ai<\/a> blog.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the previous&nbsp;<a href=\"https:\/\/gatambook.substack.com\/p\/applying-transformers-to-financial\">blog post<\/a>, we saw how we can apply self-attention transformers to a matrix of time series features of a&nbsp;<em>single&nbsp;<\/em>stock. The output of that transformer is a transformed feature vector r of dimension 768 \u00d7 1. 768 is the result of 12 \u00d7 64: all the lagged features are concatenated \/ flattened into one vector. 12 is the number of lagged months, and 64 is the dimension of the embedding space for the 52 features we constructed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">What if we have a portfolio of&nbsp;<em>many&nbsp;<\/em>stocks whose returns we want to predict, or whose allocations we want to optimize? That\u2019s where cross-attention transformers come in. The purpose of cross-attention is that a feature in an asset i may be relevant as a context to a feature of an asset j. Once again, we follow the development by&nbsp;<a href=\"https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=3554486\">Cong et. al. (2020)<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To recap, self-attention transformers take as input one n \u00d7 d matrix X, with n rows of features and d columns of each feature\u2019s embeddings. A cross-attention transformer takes as input 2 or more such matrices X<sub>1<\/sub>, X<sub>2,&nbsp;<\/sub>\u2026 The common application example of a cross-attention transformer is language translation. E.g. to translate from Chinese (the \u201ckey\u201d, or encoder) to English (the \u201cquery\u201d, or decoder), we would have<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X<sub>1\u00a0<\/sub>~ \u201cI am Chinese\u201d, and<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X<sub>2\u00a0<\/sub>~ \u201c\u6211\u662f\u4e2d\u56fd\u4eba\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To be exact, the rows of X<sub>1&nbsp;<\/sub>will actually be a d-dimensional vector embedding (representation) of one of the words in the English sentence, and ditto for the rows of X<sub>2&nbsp;<\/sub>for the words in the Chinese sentence. Note that while the embedding dimension d must be the same for both X<sub>1<\/sub>&nbsp;and X<sub>2<\/sub>, they obviously do not need to have the same number of words (i.e. rows).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"768\" height=\"561\" data-src=\"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2026\/03\/diagram-cross-attention.jpg\" alt=\"Cross-Attention for Cross-Asset Applications\n\" class=\"wp-image-240523 lazyload\" data-srcset=\"https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2026\/03\/diagram-cross-attention.jpg 768w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2026\/03\/diagram-cross-attention-700x511.jpg 700w, https:\/\/ibkrcampus.com\/campus\/wp-content\/uploads\/sites\/2\/2026\/03\/diagram-cross-attention-300x219.jpg 300w\" data-sizes=\"(max-width: 768px) 100vw, 768px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 768px; aspect-ratio: 768\/561;\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Source: https:\/\/sebastianraschka.com\/blog\/2023\/self-attention-from-scratch.html<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X<sub>1<\/sub>&nbsp;(query) is the English sentence. X<sub>2&nbsp;<\/sub>(key and value) is the Chinese sentence.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, we can imagine that X<sub>i<\/sub>&nbsp;(query) is asset i\u2019s context vector we called r<sub>i&nbsp;<\/sub>in the previous blog post, and X<sub>j&nbsp;<\/sub>(key and value) is asset j\u2019s context vector we called r<sub>j<\/sub>&nbsp;which provides the context for asset i\u2019s features. We can next apply the usual linear transformations W<sub>q<\/sub>, W<sub>k<\/sub>, and W<sub>v<\/sub>&nbsp;to mash up their time components to form the Q, K, and V matrices. Then we can use them to compute the cross-attention matrix A using the usual scaled dot product with the softmax function, which&nbsp;<a href=\"https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=3554486\">AlphaPortfolio<\/a>&nbsp;calls SATT(i, j) (\u201cSelf Attention function\u201d, a misnomer in our opinion). Because the Q\u2019s and K\u2019s are just 768 \u00d7 1 vectors in our case, each (i, j) element of SATT is just a scalar. So the SATT matrix is just another cross-attention matrix, and each row i represents the normalized weights given by features j=1, 2, \u2026, I, including j=i, where I is the number of assets. The context vector given an attention matrix SATT is, as usual,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(AlphaPortfolio calls this a<sup>(i)<\/sup>, an attenuation score. But we prefer to describe this as a context vector Z<sup>(i)&nbsp;<\/sup>because we are multiplying an attention matrix with an input vector v.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Voil\u00e0! Once you have the context vector, it is like a superpowered input feature vector that captures all manners of time-series and cross-sectional information about the portfolio that you can use for downstream applications. In the case of&nbsp;<a href=\"https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=3554486\">AlphaPortfolio<\/a>, the authors use Z<sup>(i)&nbsp;<\/sup>as the state variables for a deep reinforcement learning (DRL) program to find the best allocations to the stocks. It is essentially a stock selection program with a side of optimal capital allocation. In the next blog post, we will dissect one of these DRL programs.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The purpose of cross-attention is that a feature in an asset i may be relevant as a context to a feature of an asset j. <\/p>\n","protected":false},"author":591,"featured_media":181436,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":true,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,338,341],"tags":[21300,21299,21302,1688,21301,5519],"contributors-categories":[13719],"class_list":["post-240522","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-ibkr-quant-news","category-quant-development","tag-cross-asset-applications","tag-cross-attention","tag-deep-reinforcement-learning-drl","tag-portfolio-optimization","tag-self-attention","tag-time-series","contributors-categories-predictnow-ai"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v28.0) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Cross-Attention for Cross-Asset Applications | IBKR Quant<\/title>\n<meta name=\"description\" content=\"The purpose of cross-attention is that a feature in an asset i may be relevant as a context to a feature of an asset j.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.interactivebrokers.com\/campus\/wp-json\/wp\/v2\/posts\/240522\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cross-Attention for Cross-Asset Applications | IBKR Campus US\" \/>\n<meta property=\"og:description\" content=\"The purpose of cross-attention is that a feature in an asset i may be relevant as a context to a feature of an asset j.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/cross-attention-for-cross-asset-applications\/\" \/>\n<meta property=\"og:site_name\" content=\"IBKR Campus US\" \/>\n<meta property=\"article:published_time\" content=\"2026-03-20T15:47:50+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-20T20:20:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/01\/abstract-data.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1000\" \/>\n\t<meta property=\"og:image:height\" content=\"563\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Dr. Ernest P. 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