Upload 2 files

Browse files

Files changed (3) hide show

.gitattributes +1 -0
Untwisting RoPE： Frequency Control for Shared Attention in DiTs.html +3 -0
[2602.05013] Untwisting RoPE： Frequency Control for Shared Attention in DiTs.html +362 -0

.gitattributes CHANGED Viewed

@@ -34,3 +34,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 *.zst filter=lfs diff=lfs merge=lfs -text
 *tfevents* filter=lfs diff=lfs merge=lfs -text
 vid.mp4 filter=lfs diff=lfs merge=lfs -text

 *.zst filter=lfs diff=lfs merge=lfs -text
 *tfevents* filter=lfs diff=lfs merge=lfs -text
 vid.mp4 filter=lfs diff=lfs merge=lfs -text
+Untwisting[[:space:]]RoPE：[[:space:]]Frequency[[:space:]]Control[[:space:]]for[[:space:]]Shared[[:space:]]Attention[[:space:]]in[[:space:]]DiTs.html filter=lfs diff=lfs merge=lfs -text

Untwisting RoPE： Frequency Control for Shared Attention in DiTs.html ADDED Viewed

	@@ -0,0 +1,3 @@

+version https://git-lfs.github.com/spec/v1
+oid sha256:f9274483d8119bb2d73a55671d6c7ce144fdefe82d0d7e0977ea9a0c5c4a295f
+size 100155414

[2602.05013] Untwisting RoPE： Frequency Control for Shared Attention in DiTs.html ADDED Viewed

	@@ -0,0 +1,362 @@

+<!DOCTYPE html> <html lang=en style><!--
+ Page saved with SingleFile
+ url: https://arxiv.org/abs/2602.05013
+ saved date: Fri Jun 05 2026 08:36:15 GMT+0530 (India Standard Time)
+--><meta charset=utf-8>
+<title>[2602.05013] Untwisting RoPE: Frequency Control for Shared Attention in DiTs</title>
+<meta name=viewport content="width=device-width, initial-scale=1">
+<meta name=msapplication-TileColor content=#da532c>
+<meta name=theme-color content=#ffffff>
+<style media=screen>body{margin:0;padding:0;background-color:#fff;color:#000;font-family:"Lucida Grande",helvetica,arial,verdana,sans-serif}a:link,a:visited,a:active{text-decoration:none;font-weight:normal}a:hover{text-decoration:underline}img{border:0}em{font-weight:bold;font-style:normal}.primary-subject{font-weight:bold}#cu-identity{font-family:verdana,arial,helvetica,sans-serif;font-size:63.125%;color:#fff;background-color:#222;width:100%;display:flex;justify-content:space-between}#support-ack-url a:hover{color:#1e8bc3}#support-ack .btn-header-donate:hover{background-color:#fb595a;color:black}#header{background-color:#b31b1b;color:#fff;margin:0;padding:10px 0 10px 0;border-bottom:2px solid #ccc;position:relative;overflow:auto}#header a:visited{color:#fff;text-decoration:none}#header a:hover{text-decoration:underline}main{flex-grow:1}.flex-wrap-footer{display:flex;min-height:100vh;flex-direction:column}footer ul li{display:flex;align-items:center;font-size:14px}footer ul li a{font-size:13.5px}#footer a:visited{text-decoration:none}#footer a:hover{text-decoration:underline}footer{background-color:hsl(0,0%,95%);color:#000;padding:1em 2em;font-size:0.9rem;-webkit-font-smoothing:antialiased;margin-top:6rem}footer a,footer a:visited{color:#000;text-decoration:none;border-bottom:1px solid transparent;line-height:1.75em}footer a:hover,footer a:active{color:#005e9d;border-bottom:1px dotted #005e9d;text-decoration:none}footer ul{padding:0;margin:0}footer .sorry-app-links .help{font-size:0.75rem;margin-bottom:0;line-height:1.75em}footer .sorry-app-links .help a,footer .sorry-app-links .help a:visited{border-bottom:1px dotted #000}footer .sorry-app-links .help a:hover,footer .sorry-app-links .help a:active{border-bottom:1px dotted #005e9d}footer .sorry-app-links svg.icon{margin-bottom:-2px!important}footer .sorry-app-links .icon.filter-black:hover,footer .sorry-app-links .icon.filter-black:active,footer .sorry-app-links a:hover .icon.filter-black,footer .sorry-app-links a:hover .icon.filter-black{fill:#005e9d!important}footer .sorry-app-links .a11y-main-link{font-size:110%;border-bottom:1px solid transparent!important;padding:0;margin:0}@media screen and (max-width:768px){footer .sorry-app-links.column{padding:0}}.endorsers .help{position:relative;top:4rem}@media screen and (min-width:990px){.endorsers .help{top:5rem}}@media screen and (min-width:769px){.columns{display:flex;flex-direction:row}}.icon{width:.9rem;margin-right:.45em;margin-top:-.15rem}.help{font-family:"Lucida Grande","Helvetica Neue",Helvetica,Arial,sans-serif;display:block;font-size:0.75rem;margin-top:0.25rem}#content,#content-inner{margin:.7em;font-size:90%}.button-fancy:hover{border-bottom:1px solid #f3fbff;color:black}.button-fancy span:after{content:"»";position:relative;opacity:0;top:1px;right:-5px;padding-left:10px;transition:0.5s;font-size:20px;color:#1772a0}.button-fancy:hover span{padding-right:15px}.button-fancy:hover span:after{opacity:1;right:0}.banner-minimal a:hover{background-color:#1c1a17;border-color:#dbc6c6;color:#f9f7f7}.columns .column.banner-minimal.forum a:hover{border-color:transparent;background-color:transparent;color:#fff;text-decoration:none}.tagline-cta:hover{background-color:#d9af0c;text-decoration:none}.tagline-cta:hover p{color:#ffffff}#abs-outer,#abs{margin:-0.7em}#abs-outer .leftcolumn{margin:0 0 1em 0;padding:0px;width:calc(100% - 18em);float:left}#abs-outer .mobile-submission-download{display:none}#abs-outer .extra-services{float:right;margin:0;width:18em}#abs-outer .extra-services button.bib-cite-button{color:rgb(0,0,238);font-weight:bold;padding:.35em;display:block;text-transform:capitalize;background:none;border:none;font-size:inherit;font-family:inherit;text-align:left}#abs-outer .extra-services button.bib-cite-button:hover,#abs-outer .extra-services button.bib-cite-button:focus{text-decoration:underline;cursor:pointer}.bib-modal{position:fixed;z-index:10;left:0;top:0;width:100%;height:100%;overflow:auto;background-color:rgba(0,0,0,0.4)}.bib-modal-close:hover,.bib-modal-close:focus{color:black;text-decoration:none;cursor:pointer}#labstabs{clear:both;margin:1em 1.5em}#labstabs .labstabs{display:flex;flex-wrap:wrap;white-space:normal;justify-content:flex-start}#labstabs .labstabs>label{order:1;display:block;padding:.75em 1.5em;font-size:.85em;color:#4a4a4a;margin-right:0.2rem;cursor:pointer;font-weight:bold;transition:background ease 0.2s;border-radius:6px 6px 0 0;background-color:#eef5f9}#labstabs .labstabs>label:focus-within,#labstabs .labstabs>input:focus+label{outline:2px solid #005ea2;outline-offset:2px}#labstabs .labstabs .tab{order:99;flex-grow:1;width:100%;display:none;padding:1rem;border:1px solid #828282;z-index:1;top:-1px;position:relative}#labstabs .labstabs .tab h1{font-size:1.25em;font-weight:normal}#labstabs .labstabs input[type="radio"]{position:absolute;opacity:0;width:1px;height:1px;margin:-1px;padding:0;overflow:hidden;clip:rect(0,0,0,0);border:0}#labstabs .labstabs input[type="radio"]:focus+label{outline:2px solid #005aa7;outline-offset:2px}#labstabs .labstabs input[type="radio"]:checked+label{background:#ffffff;border:1px solid #828282;border-bottom:0;z-index:2;color:black}#labstabs .labstabs input[type="radio"]:checked+label+.tab{display:block}@media (max-width:45em){#labstabs{padding-bottom:1em;margin:1em}#labstabs .labstabs .tab,#labstabs .labstabs label{order:initial;width:100%;margin-right:0;margin-top:0.2rem;border-radius:0}#labstabs .labstabs>label{font-size:.8em}#labstabs .labstabs .tab{margin-top:-10px!important;border:2px solid #b8b8b8;border-top:0px;background-color:#ffffff}#labstabs .labstabs label{background-color:#eef5f9;color:black;padding:1em .5em}#labstabs .labstabs .labs-display-bib label{background:transparent;color:black;padding:0}#labstabs .labstabs input[type="radio"]:checked+label{background-color:#acd2e8;color:black;border:2px solid #b8b8b8;border-bottom:0px;padding:1em .5em}#labstabs .labstabs input[type="radio"]:hover,#labstabs .labstabs input[type="radio"]:active{background-color:#abb4b9}}#labstabs .toggle{border:1px dotted #c7d3db;padding:.5em;background-color:#eef5f9}#labstabs .toggle .columns.lab-row{align-items:center}#labstabs .toggle .columns.lab-row .column{padding:.5rem .25rem}#labstabs .column.lab-name{flex-basis:auto;flex-grow:0;font-size:.75rem}#labstabs .tab a{display:inline}#labstabs .column.lab-name em{font-size:11px;color:black}#labstabs .column.lab-name em a{line-height:18px;text-decoration:none;padding:0;border:0;font-style:normal;font-size:11px}#labstabs .column.lab-switch{flex-grow:0}#labstabs .toggle .lab-switch label.switch{position:relative;display:inline-block;width:38px;height:20px;padding:0;background-color:transparent;margin:0}#labstabs .toggle .lab-switch .switch input{opacity:0;width:0;height:0}#labstabs .toggle .lab-switch .slider{position:absolute;cursor:pointer;top:0;left:0;right:0;bottom:0;border-radius:24px;background-color:#ccc;-webkit-transition:.4s;transition:.4s}#labstabs .toggle .lab-switch .slider:before{position:absolute;content:"";height:16px;width:16px;left:2px;bottom:2px;border-radius:50%;background-color:white;-webkit-transition:.4s;transition:.4s}#labstabs .toggle .lab-switch input.enabled+.slider:before{-webkit-transform:translateX(18px);-ms-transform:translateX(86px);transform:translateX(18px)}#labstabs .toggle .lab-switch input:focus-visible+.slider{outline:2px solid #005ea2;outline-offset:2px}#labstabs .toggle .lab-switch input:focus+.slider{outline:2px solid #005ea2;outline-offset:2px}#abs-outer .subheader{background-color:#eee;color:#000;padding:.25em 0;border-bottom:1px solid #ccc}#abs-outer .subheader h1{margin:0;font-size:1.1em;padding:0 0 .2em 20px;font-weight:bold;font-style:normal}#abs .descriptor{display:none}#abs-outer .extra-services .descriptor{display:none}#abs h1.title{margin:.5em 0 .5em 20px;font-size:x-large;font-weight:bold;line-height:120%}#abs .authors{margin:.5em 0 .5em 20px;font-size:medium;line-height:150%}#abs .authors a{font-size:medium}#abs .dateline{margin:.5em 0 .5em 20px;font-style:italic;font-size:small}#abs blockquote.abstract{line-height:1.55;font-size:1.05em;margin-bottom:1.5em}#abs .metatable{font-size:0.92em;line-height:1.5;margin:0 0 1.5em 20px}#abs .tablecell{padding:.1em .5em 0em 0em;vertical-align:top}#abs .arxivid a{font-weight:normal}#abs-outer .submission-history{margin:1.5em 0 1.5em 20px;font-size:90%;line-height:1.5em}#abs-outer .submission-history h2{font-size:120%;margin:0 0 .25em 0;font-weight:bold}#abs-outer .endorsers{margin:1em 0 1.5em 20px;font-size:small;font-style:italic;clear:both}#abs-outer .header-breadcrumbs-mobile{display:none}#abs-outer #abs .dateline{margin-top:15px;margin-bottom:0}#abs-outer #abs h1.title{margin-top:.25em}.endorsers .help{display:inline-block}@media screen and (max-width:768px){#abs-outer .header-breadcrumbs-mobile{display:block;color:black;font-size:.85em;margin:.25em 0 .5em 1em}#abs-outer #abs a.mobile-submission-download{display:flex;justify-content:center;margin:.7em .25em;border-radius:10px;background-color:#408bd0;padding:.25em 1em;font-weight:800;color:white;text-decoration:none;font-size:20px;text-align:center}#abs-outer .extra-services h2{font-size:15px;margin-bottom:.5em}#abs-outer .extra-services h3{font-size:14px}#abs-outer .leftcolumn,#abs-outer .extra-services{width:100%;float:left}#abs-outer .extra-services,#abs-outer .extra-services .full-text,#abs-outer .extra-services .browse,#abs-outer .extra-services .extra-ref-cite{border:0px;font-size:12px}#abs-outer .extra-services{-webkit-box-shadow:inset 0px 8px 15px 0px rgba(173,173,173,1);-moz-box-shadow:inset 0px 8px 15px 0px rgba(173,173,173,1);box-shadow:inset 0px 8px 15px 0px rgba(173,173,173,1);background-color:#E6E6E6;margin:0 0 1em 0;padding:1em 0}#abs-outer .extra-ref-cite ul li{float:left}#abs-outer .extra-services .full-text ul,#abs-outer .extra-services .extra-ref-cite ul{list-style:none;margin:0;padding:0}#abs-outer .extra-services .full-text ul li,#abs-outer .extra-services .extra-ref-cite ul li{display:inline-block;margin:0 0 .25em 0;padding:0}#abs-outer .extra-services .bookmarks{margin:1em 0 0 0;border-left:0;padding:.25em .5em 0 1em;border-top:2px solid #cccccc;font-size:1em}#abs-outer .extra-services .bookmarks .abs-button-small{margin-top:.25em}#abs-outer .extra-services .browse{margin-top:.5em;border-top:2px solid #cccccc;padding-top:1em}#abs-outer .extra-services .prevnext{margin-top:.5em}#abs-outer .extra-services .browse .current{color:#AB4B02;display:inline}.abs-switch-cat{margin:0 0 1em 0}.browse .abs-switch-cat .switch{display:inline}.browse .abs-switch-cat .switch a{font-weight:bold}.browse .abs-switch-cat .switch .subclass{padding:0;margin-left:-3px}.abs-switch-cat .subclass:before{content:", "}.abs-button{display:inline-block;border-radius:5px;border:1px solid #046BAF;font-size:1.25em;color:#046BAF!important;padding:.5em;background:#E6E6E6;margin-right:.3em}.abs-button-small{font-size:1em;padding:.25em 1em;margin:.75em .5em 0 0}.abs-button-grey{border:1px solid #666666;color:#666666!important}#abs-outer .extra-services button.bib-cite-button{margin:.5em .5em 0 0;display:inline-block!important;border-radius:5px;background:#E6E6E6;border:1px solid #046BAF;font-size:1em!important;padding:.25em 1em;font-weight:normal;text-transform:capitalize}#abs-outer .extra-services .extra-ref-cite ul li{margin:.5em 0;padding:0;height:auto}#abs-outer .extra-services .extra-ref-cite ul li a{margin:.25em .5em .25em 0}#abs-outer .subheader{background-color:#fefefe;padding:.25em 0;border-bottom:1px solid #ccc}#abs-outer .subheader h1{margin:0;font-size:.75em;padding:.2em 0 .2em 1em;font-weight:normal;font-style:normal;color:#b55c06}#abs-outer #abs .dateline{color:#767676;font-size:.85em;font-style:normal;margin:2em 0 0 1em}#abs-outer .submission-history{padding:1em;margin:0;background-color:#f5f5f5;-webkit-box-shadow:inset 0px -6px 15px 0px rgba(219,219,219,1);-moz-box-shadow:inset 0px -6px 15px 0px rgba(219,219,219,1);box-shadow:inset 0px -6px 15px 0px rgba(219,219,219,1)}#abs-outer #abs h1.title{margin:0 .25em 0 .5em;font-size:1.5em}#abs-outer #abs .authors{margin:1em .25em 0 1em;font-size:.9em;line-height:1.5em}#abs-outer #abs .authors a{font-size:inherit}#abs-outer #abs blockquote.abstract{margin:0 1em}#abs-outer #abs .metatable{margin:.75em 0 1.5em 1.5em}#abs-outer #abs a,#abs-outer a,#abs-outer .endorsers a{color:#1777bc}#abs-outer .abs-license a,#abs-outer .submission-history a,#abs-outer .abs-switch-cat .switch a,#abs-outer .extra-services .full-text .abs-license a{color:#046BAF}#abs-outer .endorsers{display:block;float:left;border:1px solid #eee;padding:1em;margin:1em}#abs-outer .endorsers .help{display:none}}.mobile-header .toggle-target{max-height:0;visibility:hidden}.mobile-header{background-color:#b31b1b}.mobile-header .columns{height:65px;align-items:center}.mobile-header .column{border-left:1px solid #fc5554;border-right:1px solid #731515;height:65px;padding:0 1em;display:flex;align-items:center}.mobile-header .column:first-child{border-left:0}.mobile-header .column:last-child{border-right:0}.mobile-header .column.logo-arxiv{width:100px;flex:none}.mobile-header .column.logo-arxiv img{height:25px}.mobile-header .column.logo-cornell{display:flex}.mobile-header .column.logo-cornell img{height:45px}.mobile-header .column.nav{justify-content:flex-end;align-self:flex-end}.mobile-header #toggle-container button.toggle-control{background-color:transparent;border-radius:0;border:0;font-size:25px;padding:3px;margin-left:.5em}.mobile-header #toggle-container button.toggle-control svg.icon{width:1.25rem;margin:0}.mobile-header .mobile-toggle-block{margin:0;width:100%;flex:none;transition:max-height 3s;position:absolute;top:64px;left:0;background-color:#b31a1a;overflow:hidden}.mobile-header .mobile-toggle-block form.mobile-search-form{margin:.5em 1em 1em 1em}.mobile-header .mobile-toggle-block form.mobile-search-form input::-webkit-input-placeholder{color:#94908c}.mobile-header .mobile-toggle-block form.mobile-search-form input:-ms-input-placeholder{color:#94908c}.mobile-header .mobile-toggle-block form.mobile-search-form input::placeholder{color:#94908c}.mobile-header .mobile-toggle-block form.mobile-search-form input{width:calc(100% - 50px);background:#fef6f6;border-radius:10px 0 0 10px;border:0;padding:5px;color:black;font-size:1.5em}.mobile-header .mobile-toggle-block form.mobile-search-form button.button{width:50px;background:#fc5554;border:0;border-left:1px solid #b31b1b;border-radius:0 10px 10px 0;padding:3px;font-size:20px;font-weight:bold;color:#fffaf4}.mobile-header .mobile-toggle-block nav.mobile-menu{padding:.75em 1em}.mobile-header .mobile-toggle-block nav.mobile-menu h2{margin:0;font-size:12px;color:#fcd7d7;text-transform:uppercase}.mobile-header .mobile-toggle-block nav.mobile-menu ul{list-style:none;margin:.75em 0 0 0;padding:0}.mobile-header .mobile-toggle-block nav.mobile-menu ul li{display:inline-flex;align-items:stretch;padding:.1em .2em;margin:0 0 .5em 0;border-top:2px solid #fc5554;margin-right:.75em}.mobile-header .mobile-toggle-block nav.mobile-menu ul li a{color:#fef6f6;font-weight:normal;font-size:12px}@media screen and (min-width:769px){.mobile-header{display:none}}@media screen and (min-width:426px){.mobile-header .column.nav{flex:none;width:100px}}@media screen and (max-width:500px){.mobile-header .columns{height:80px}.mobile-header .column{height:80px;padding:0 .5em}.mobile-header .column.logo-arxiv{border-right:0!important}.mobile-header .column.logo-cornell{justify-content:flex-end;border-left:0!important}.mobile-header .column.logo-cornell img{height:73px}.mobile-header .column.nav{width:65px;flex:none}.mobile-header .mobile-toggle-block{top:80px}}@media screen and (min-width:501px){.mobile-header .column{height:65px}.mobile-header .column.logo-cornell img{height:45px}.mobile-header .column.nav{width:65px}}.extra-services{border-bottom:.35em solid #ddd}.extra-services h3{font-size:medium;font-weight:normal;margin:0 0 0.3em 0;padding-top:0.3em}.full-text{margin:0;padding:.5em 1em .5em 1em;font-size:110%;font-weight:normal;border-bottom:medium solid #ddd;border-left:.35em solid #ddd}.full-text h2{font-size:140%;font-weight:bold;margin:0.1em 0 0 0}.full-text ul{margin:.3em 0 0 1em;padding:0;list-style-type:none}.extra-ref-cite{margin:0;padding:0 1em 0 1em;font-size:90%;border-bottom:medium solid #ddd;border-left:.35em solid #ddd}.extra-ref-cite ul{font-weight:normal;margin:0.3em 0 0 20px;padding-left:0;padding-bottom:0.3em;list-style-type:none}.browse{padding:0 1em 0 1em;font-size:90%;border-bottom:medium solid #ddd;border-left:.35em solid #ddd}.browse .current{padding:0;font-weight:bold}.browse .prevnext{padding:0.2em 0 0 0}.browse .list{padding:0.2em 0 0.5em 0;font-weight:normal}.browse .switch{font-weight:normal;padding:.2em 0em .7em 0em}.browse .switch .subclass{padding-left:1.5em}.bookmarks{clear:both;margin:0;padding:0 1em .5em 1em;font-size:90%;border-left:.35em solid #ddd}.abs-license{font-size:xx-small;padding-top:0.3em}.abs-license .has_license{display:flex;align-items:center;gap:5px}#header #search-arxiv .wrapper-search-arxiv ::-webkit-input-placeholder{color:#222}#header #search-arxiv .wrapper-search-arxiv ::-moz-placeholder{color:#222}#header #search-arxiv .wrapper-search-arxiv :-ms-input-placeholder{color:#222}#header #search-arxiv .wrapper-search-arxiv :-moz-placeholder{color:#222}#header #search-semantic .wrapper-search-semantic ::-webkit-input-placeholder{color:#264D71}#header #search-semantic .wrapper-search-semantic ::-moz-placeholder{color:#2B6195}#header #search-semantic .wrapper-search-semantic :-ms-input-placeholder{color:#264D71}#header #search-semantic .wrapper-search-semantic :-moz-placeholder{color:#264D71}#header.cs #search-arxiv .wrapper-search-arxiv ::-webkit-input-placeholder{color:#222}#header.cs #search-arxiv .wrapper-search-arxiv ::-moz-placeholder{color:#222}#header.cs #search-arxiv .wrapper-search-arxiv :-ms-input-placeholder{color:#222}#header.cs #search-arxiv .wrapper-search-arxiv :-moz-placeholder{color:#222}#header.cs #search-semantic .wrapper-search-semantic ::-webkit-input-placeholder{color:#264D71}#header.cs #search-semantic .wrapper-search-semantic ::-moz-placeholder{color:#2B6195}#header.cs #search-semantic .wrapper-search-semantic :-ms-input-placeholder{color:#264D71}#header.cs #search-semantic .wrapper-search-semantic :-moz-placeholder{color:#264D71}@media screen and (max-width:768px){#cu-identity{flex-direction:column}}@media screen and (max-width:768px){.is-hidden-mobile{display:none!important}.columns.is-mobile{display:flex}}.is-sr-only{border:none!important;clip:rect(0,0,0,0)!important;height:0.01em!important;overflow:hidden!important;padding:0!important;position:absolute!important;white-space:nowrap!important;width:0.01em!important}.browse-context-heading{display:inline}.button{border-width:1px;cursor:pointer;justify-content:center;padding-bottom:calc(0.5em - 1px);padding-left:1em;padding-right:1em;padding-top:calc(0.5em - 1px);text-align:center;white-space:nowrap}.tabs a:hover{border-bottom-color:#363636;color:#363636}.tabs.is-boxed a:hover{background-color:whitesmoke;border-bottom-color:#dbdbdb}.column{display:block;flex-basis:0;flex-grow:1;flex-shrink:1;padding:0.75rem}.columns.is-vcentered{align-items:center}@media screen and (min-width:769px),print{.columns:not(.is-desktop){display:flex}}@media screen and (min-width:1024px){.columns.is-desktop{display:flex}}.large-data-list .accordion-toggle:focus{outline:none}.large-data-list .accordion-toggle:focus-visible{outline:2px solid #005ea2;outline-offset:2px}.large-data-list .accordion-toggle .accordion-caret:before{content:"˅";padding-right:0.5em;font-size:1.25em;font-weight:100}.large-data-list .accordion-toggle[aria-expanded="true"] .accordion-caret:before{content:"˄";color:#b7b8b9}.large-data-list .accordion-head:after{content:"˅";padding-left:1em;position:relative;top:.25em;font-size:1.25em;font-weight:100}.large-data-list .accordion-head.open:after{content:"˄";color:#b7b8b9}.large-data-list .accordion-head:has(.accordion-toggle):after{display:none}.trackback-styles .trackback-source a:visited{text-decoration:underline;color:#6c6c6c}.trackback-styles .trackback-source a:hover,.trackback-styles .trackback-source a:active{text-decoration:underline;color:#000000}.bold-divided-list .bold-divided-column ul li:before{color:#000;content:"-";margin:0 6px 0 0;font-weight:bold}svg.icon{height:1em!important}.icon.filter-white{fill:#FFFFFF}.icon.filter-black{fill:#000000}.filter-dark_grey{fill:#cccccc}a .icon{transition:fill 0.3s ease}a:hover .icon.filter-white{fill:#f5f5f5}a:hover .icon.filter-black,a:hover .icon.filter-grey,a:hover .icon.filter-blue,a:hover .icon.filter-red{fill:#ffffff}</style>
+<style media=screen>.field.has-addons{display:flex}.search-block .select::after{position:absolute;display:block;z-index:4;top:50%;right:.65em;width:0.5em;height:0.5em;content:" ";border:3px solid #0068AC;border-radius:2px;border-right:0;border-top:0;transform:rotate(-45deg);transform-origin:center;pointer-events:none;margin-top:-1.125em}.search-block .select.is-small select::-ms-expand{display:none}.search-block .button:hover,.search-block .button:focus{background-color:#440A0A;color:#FFF}</style>
+<link rel=canonical href=https://arxiv.org/abs/2602.05013>
+<meta name=description content="Abstract page for arXiv paper 2602.05013: Untwisting RoPE: Frequency Control for Shared Attention in DiTs"><meta property=og:type content=website>
+<meta property=og:site_name content=arXiv.org>
+<meta property=og:title content="Untwisting RoPE: Frequency Control for Shared Attention in DiTs">
+<meta property=og:url content=https://arxiv.org/abs/2602.05013v1>
+<meta property=og:image content=/static/browse/0.3.4/images/arxiv-logo-fb.png>
+<meta property=og:image:secure_url content=/static/browse/0.3.4/images/arxiv-logo-fb.png>
+<meta property=og:image:width content=1200>
+<meta property=og:image:height content=700>
+<meta property=og:image:alt content="arXiv logo">
+<meta property=og:description content="Positional encodings are essential to transformer-based generative models, yet their behavior in multimodal and attention-sharing settings is not fully understood. In this work, we present a principled analysis of Rotary Positional Embeddings (RoPE), showing that RoPE naturally decomposes into frequency components with distinct positional sensitivities. We demonstrate that this frequency structure explains why shared-attention mechanisms, where a target image is generated while attending to tokens from a reference image, can lead to reference copying, in which the model reproduces content from the reference instead of extracting only its stylistic cues. Our analysis reveals that the high-frequency components of RoPE dominate the attention computation, forcing queries to attend mainly to spatially aligned reference tokens and thereby inducing this unintended copying behavior. Building on these insights, we introduce a method for selectively modulating RoPE frequency bands so that attention reflects semantic similarity rather than strict positional alignment. Applied to modern transformer-based diffusion architectures, where all tokens share attention, this modulation restores stable and meaningful shared attention. As a result, it enables effective control over the degree of style transfer versus content copying, yielding a proper style-aligned generation process in which stylistic attributes are transferred without duplicating reference content.">
+<meta name=twitter:site content=@arxiv>
+<meta name=twitter:card content=summary>
+<meta name=twitter:title content="Untwisting RoPE: Frequency Control for Shared Attention in DiTs">
+<meta name=twitter:description content="Positional encodings are essential to transformer-based generative models, yet their behavior in multimodal and attention-sharing settings is not fully understood. In this work, we present a...">
+<meta name=twitter:image content=https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png>
+<meta name=twitter:image:alt content="arXiv logo">
+<style media=screen>.visually-hidden{clip-path:inset(100%);clip:rect(1px,1px,1px,1px);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}.button-and-tooltip{position:relative;display:inline}.button-and-tooltip button{background:transparent;border:none;box-shadow:none;position:relative;padding:0 0 0 6px}[role="tooltip"]{display:none;position:absolute;top:-6px;left:28px;width:250px;background-color:#f7fafc;border:1px solid black;padding:4px 10px;border-radius:5px}button:hover+[role="tooltip"],button:focus+[role="tooltip"]{display:block}td.tablecell.arxivdoi{display:inline-flex;align-items:center}@media screen and (max-width:480px){[role="tooltip"]{width:250px;left:-273px}}</style><style media=screen>.arrow{width:0;height:0;border-left:8px solid transparent;border-right:8px solid transparent}.bib-sort-arrow a:hover{text-decoration:none;cursor:pointer}.bib-authors a:after{content:","}.bib-authors a:last-of-type:after{content:""}h1.bib-header:before{border-top:2px solid #dfdfdf;content:"";margin:0 auto;position:absolute;top:50%;left:0;right:0;bottom:0;width:95%;z-index:-1}.bib-sidebar-msgs .msg:hover .hover{visibility:visible}@-webkit-keyframes pulsate{0%{-webkit-transform:scale(.1);transform:scale(.1);opacity:0}30%{opacity:1}60%{-webkit-transform:scale(.8);transform:scale(.8);opacity:0}}@keyframes pulsate{0%{-webkit-transform:scale(.1);transform:scale(.1);opacity:0}30%{opacity:1}60%{-webkit-transform:scale(.8);transform:scale(.8);opacity:0}}.tooltiptext:after{opacity:1;content:" ";position:absolute;top:100%;left:50%;margin-left:-5px;border-width:5px;border-style:solid;border-color:#000 transparent transparent}.modal-close:focus,.modal-close:hover{color:#000;text-decoration:none;cursor:pointer}.cite:hover{cursor:pointer}</style>
+<meta name=citation_title content="Untwisting RoPE: Frequency Control for Shared Attention in DiTs"><meta name=citation_author content="Mikaeili, Aryan"><meta name=citation_author content="Patashnik, Or"><meta name=citation_author content="Tagliasacchi, Andrea"><meta name=citation_author content="Cohen-Or, Daniel"><meta name=citation_author content="Mahdavi-Amiri, Ali"><meta name=citation_date content=2026/02/04><meta name=citation_online_date content=2026/02/04><meta name=citation_pdf_url content=https://arxiv.org/pdf/2602.05013><meta name=citation_arxiv_id content=2602.05013><meta name=citation_abstract content="Positional encodings are essential to transformer-based generative models, yet their behavior in multimodal and attention-sharing settings is not fully understood. In this work, we present a principled analysis of Rotary Positional Embeddings (RoPE), showing that RoPE naturally decomposes into frequency components with distinct positional sensitivities. We demonstrate that this frequency structure explains why shared-attention mechanisms, where a target image is generated while attending to tokens from a reference image, can lead to reference copying, in which the model reproduces content from the reference instead of extracting only its stylistic cues. Our analysis reveals that the high-frequency components of RoPE dominate the attention computation, forcing queries to attend mainly to spatially aligned reference tokens and thereby inducing this unintended copying behavior. Building on these insights, we introduce a method for selectively modulating RoPE frequency bands so that attention reflects semantic similarity rather than strict positional alignment. Applied to modern transformer-based diffusion architectures, where all tokens share attention, this modulation restores stable and meaningful shared attention. As a result, it enables effective control over the degree of style transfer versus content copying, yielding a proper style-aligned generation process in which stylistic attributes are transferred without duplicating reference content.">
+<style>#MathJax_Message{position:fixed;left:1px;bottom:2px;background-color:#E6E6E6;border:1px solid #959595;margin:0px;padding:2px 8px;z-index:102;color:black;font-size:80%;width:auto;white-space:nowrap}</style><style>.MathJax_MenuDisabled:focus,.MathJax_MenuLabel:focus{background-color:#E8E8E8}.MathJax_ContextMenu:focus{outline:none}.MathJax_ContextMenu .MathJax_MenuItem:focus{outline:none}.MathJax_MenuClose:hover{color:white!important;border:2px solid #CCC!important}.MathJax_MenuClose:hover span{background-color:#CCC!important}.MathJax_MenuClose:hover:focus{outline:none}</style><meta name=referrer content=no-referrer><link rel=icon type=image/png sizes=32x32 href="data:image/png;base64,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"><style>.sf-hidden{display:none!important}</style><meta http-equiv=content-security-policy content="default-src 'none'; font-src 'self' data:; img-src 'self' data:; style-src 'unsafe-inline'; media-src 'self' data:; script-src 'unsafe-inline' data:; object-src 'self' data:; frame-src 'self' data:;"></head>
+<body class=with-cu-identity><div id=MathJax_Message style=display:none></div>
+ <div class=flex-wrap-footer>
+ <header>
+ <a href=#content class=is-sr-only>Skip to main content</a>
+ <div class="columns is-vcentered is-hidden-mobile sf-hidden" id=cu-identity>
+ </div>
+ <div id=header class="is-hidden-mobile sf-hidden">
+ </div>
+ <div class=mobile-header>
+ <div class="columns is-mobile">
+ <div class="column logo-arxiv"><a href=https://arxiv.org/><img src="data:image/svg+xml;base64,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" alt="arXiv logo" style=height:60px></a></div>
+ <div class="column logo-cornell"><a href=https://www.cornell.edu/>
+ <picture>
+ <img src=data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8"?>
<!-- Generator: Adobe Illustrator 19.2.1, SVG Export Plug-In . SVG Version: 6.00 Build 0)  -->
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
	 viewBox="0 0 120 120" style="enable-background:new 0 0 120 120;" xml:space="preserve">
<g>
	<path d="M45.9,91.7c6.8,5.3,13.5,8.2,13.8,8.3l0.5,0.2l0.5-0.2c0.3-0.1,6.9-3,13.7-8.3c9.1-7.1,13.9-15.2,13.9-23.5l0-37.6l-56.4,0
		l0,37C31.9,76.1,36.7,84.5,45.9,91.7z M58.8,80.1c-0.3-0.1-0.6-0.2-1-0.2c0,0,0,0-0.1,0c-1.4,0-2.4,0.1-3.5,0.2
		c-1.1,0.1-2.2,0.2-3.8,0.2c-0.7,0-1.4,0-1.9,0V62.7c0.1,0,0.2,0,0.2,0c0.7,0,1.5,0,2.6,0c0.9,0,1.9-0.1,3-0.2
		c0.6-0.1,1.3-0.1,2-0.2c1.2-0.1,2.2,0.1,2.2,0.1c0.1,0,0.2,0.1,0.3,0.1C58.8,62.4,58.8,80.1,58.8,80.1z M85.6,68.2
		c0,15.4-18.9,25.8-24.5,28.6v-14c0.1-0.1,0.2-0.2,0.3-0.3c0.3-0.3,0.5-0.5,1-0.5c1.3,0,2.3,0.1,3.4,0.2c1.1,0.1,2.2,0.2,3.9,0.2
		c1.7,0,3,0,3,0l0.9,0l0-5.2h2.2v-2.8h-2.2l0-5.1h2.2v-2.8h-2.2l0-5.7l-1,0c-0.4,0-0.8,0-1.3,0c-0.7,0-1.5,0-2.5,0
		c-0.8,0-1.7-0.1-2.8-0.2c-0.6-0.1-1.3-0.1-2-0.2c-1.5-0.2-2.8,0.1-2.9,0.1c0,0,0,0-0.1,0V55h24.5L85.6,68.2z M61.1,80.2V62.5
		c0.1-0.1,0.3-0.1,0.5-0.2c0,0,1.1-0.2,2.3-0.1c0.7,0.1,1.4,0.1,2,0.2c1.1,0.1,2.1,0.2,3,0.2c0.9,0,1.6,0,2.3,0c0.2,0,0.4,0,0.5,0
		l0,17.7c-0.5,0-1.2,0-1.9,0c-1.6,0-2.7-0.1-3.8-0.2c-1.1-0.1-2.1-0.2-3.5-0.2C61.9,80,61.5,80.1,61.1,80.2z M34.6,33.3l51,0l0,19.1
		h-51L34.6,33.3z M34.6,55h24.3v5.3c-0.4-0.1-1.5-0.2-2.7-0.1c-0.7,0.1-1.4,0.1-2,0.2c-1.1,0.1-2,0.2-2.8,0.2c-1,0-1.8,0-2.5,0
		c-0.5,0-0.9,0-1.3,0l-1,0v5.1h-2.4v2.8h2.4v5.1h-2.4v2.8h2.4v5.7l0.9,0c0.1,0,1.4,0.1,3,0c1.7,0,2.9-0.1,3.9-0.2
		c1.1-0.1,2-0.2,3.3-0.2c0.5,0,0.7,0.2,0.9,0.5c0,0,0.1,0.1,0.1,0.1v14.1C53,93.8,34.6,83.5,34.6,67.6L34.6,55z"/>
	<path d="M55.9,35.2H41.6v1c0,3.1,0,8.4,0,8.6c0.1,1.1,0.8,2.1,2.2,3c1.7,1.2,4.3,2.7,4.4,2.7l0.5,0.3l0.5-0.3
		c0.1-0.1,2.9-1.6,4.6-2.7c2-1.3,2.1-2.6,2.1-3c0-0.2,0-4.8,0-8.6V35.2z M43.6,37.2h10.2c0,0.8,0,1.7,0,2.6H43.6
		C43.6,38.9,43.6,38,43.6,37.2z M53.9,44.7c0,0.5-0.7,1-1.2,1.4c-1.2,0.8-3.1,1.9-4,2.4c-0.8-0.5-2.6-1.5-3.8-2.4
		c-0.8-0.5-1.3-1.1-1.3-1.5c0-0.1,0-1.3,0-2.9h10.2C53.9,43.3,53.9,44.5,53.9,44.7z"/>
	<path d="M80.1,34.8H65.6v1c0,3.9,0,8.6,0,8.9c0.1,1.1,0.8,2.1,2.2,3c1.8,1.2,4.4,2.7,4.5,2.8l0.5,0.3l0.5-0.3
		c0.1-0.1,3-1.6,4.7-2.8c2.1-1.4,2.1-2.6,2.1-3c0-0.2,0-4.9,0-8.8L80.1,34.8z M78.1,44.5c0,0.5-0.7,1.1-1.2,1.4
		c-1.3,0.8-3.2,1.9-4.1,2.4c-0.9-0.5-2.6-1.6-3.9-2.4c-0.4-0.3-1.3-0.9-1.3-1.5c0-0.1,0-0.2,0-0.5l5-3.6l5.5,3.7
		C78.1,44.3,78.1,44.5,78.1,44.5z M72.6,37.8l-5,3.6c0-1.4,0-3.2,0-4.7h10.6c0,1.6,0,3.3,0,4.8L72.6,37.8z"/>
	<path d="M63.7,66.5l1,0.1c0.6,0.1,1.2,0.1,1.7,0.1l2.9,0.1l0-2l-2.9-0.1c-0.4,0-0.9-0.1-1.5-0.1l-1-0.1c-0.3,0-0.5,0-0.7,0l0.1,2
		C63.4,66.4,63.6,66.4,63.7,66.5z"/>
	<path d="M66.4,70.2c-0.4,0-0.9-0.1-1.5-0.1c-0.3,0-0.7-0.1-1-0.1c-0.3,0-0.5,0-0.7,0l0,2c0.1,0,0.3,0,0.5,0c0.4,0,0.7,0.1,1,0.1
		c0.6,0.1,1.1,0.1,1.6,0.1c0.6,0,1.5,0,2.2,0l0.8,0l0-2l-0.8,0C67.9,70.3,67,70.2,66.4,70.2z"/>
	<path d="M66.4,75.8c-0.4,0-0.9-0.1-1.5-0.1c-0.3,0-0.7-0.1-1-0.1c-0.3,0-0.5,0-0.7,0l0.1,2c0.1,0,0.3,0,0.5,0c0.4,0,0.7,0.1,1,0.1
		c0.6,0.1,1.2,0.1,1.6,0.1l0.8,0c0.8,0,1.8,0,2.1,0.1l0-2c-0.3,0-1.3,0-2.1-0.1L66.4,75.8z"/>
	<path d="M53.8,66.7c0.5,0,1-0.1,1.7-0.1c0.3,0,0.6-0.1,1-0.1c0.2,0,0.3,0,0.5,0l0-2c-0.2,0-0.4,0-0.7,0c-0.4,0-0.7,0.1-1,0.1
		c-0.6,0.1-1.1,0.1-1.5,0.1l-2.9,0.1l0,2L53.8,66.7z"/>
	<path d="M55.3,70.1c-0.6,0.1-1.1,0.1-1.5,0.1l-2.9,0.1l0,2l2.9-0.1c0.5,0,1-0.1,1.7-0.1l0.9-0.1c0.2,0,0.3,0,0.4,0l0.1-2
		c-0.2,0-0.4,0-0.7,0L55.3,70.1z"/>
	<path d="M55.3,75.6c-0.6,0.1-1.1,0.1-1.6,0.1c-0.9,0-2.4,0.1-2.8,0.1l0,2c0.4,0,1.9-0.1,2.9-0.1c0.5,0,1-0.1,1.7-0.1l1-0.1
		c0.1,0,0.3,0,0.4,0l0-2c-0.2,0-0.4,0-0.7,0L55.3,75.6z"/>
	<path d="M9.3,60.3c2.5,0,4-1.6,4.2-4.4c0-0.5,0-1.2-0.1-1.9l0-0.2l-2.1,0l0.2,0.4c0.1,0.3,0.2,1,0.2,1.6c-0.1,1.4-1.2,2.3-2.7,2.2
		c-1.6-0.1-2.5-1.1-2.5-2.5c0-0.5,0.1-1,0.5-1.5l0.3-0.4l-2-0.3l-0.1,0.2c-0.3,0.6-0.4,1.3-0.5,1.9c-0.2,2.9,1.4,4.8,4.3,4.9
		C9.1,60.3,9.2,60.3,9.3,60.3z"/>
	<path d="M9.7,50.5c0.6,0.2,1.1,0.2,1.6,0.2c1.9,0,3.3-1.1,3.9-3c0.3-1.2,0.2-2.2-0.3-3.2c-0.6-1-1.6-1.7-2.9-2.1
		c-0.5-0.2-1.1-0.2-1.5-0.2c-1.9,0-3.3,1.1-3.9,3C5.8,47.7,7,49.7,9.7,50.5z M8.3,45.8c0.3-1.1,1.2-1.3,1.9-1.3
		c0.3,0,0.7,0.1,1.1,0.2c0.9,0.3,1.6,0.7,1.9,1.3c0.2,0.4,0.3,0.8,0.1,1.3c-0.3,1.1-1.2,1.3-1.9,1.3c-0.4,0-0.7-0.1-1.1-0.2
		C9.1,48,7.9,47.1,8.3,45.8z"/>
	<path d="M18.3,39.3l-2.9-1.6l0.1-0.2c0.3-0.5,0.5-0.5,0.9-0.4l2.9,0.4l1.1-2.1l-3.8-0.4c-0.3,0-0.5,0-0.7,0c0-0.8-0.4-1.6-1.2-2
		c-0.4-0.2-0.8-0.3-1.2-0.3c-1.4,0-2.1,1.4-2.8,2.7l-1,1.9l7.6,4.1L18.3,39.3z M13.8,36.6l-0.1,0.2l-1.4-0.7l0.1-0.2
		c0.3-0.6,0.7-1.2,1.3-0.9c0.2,0.1,0.3,0.2,0.4,0.4C14.2,35.8,14,36.3,13.8,36.6z"/>
	<polygon points="23,31.7 19.1,28.5 24.7,29.8 26.2,27.9 19.6,22.4 18.2,24 22.2,27.3 16.6,26 15,27.9 21.7,33.4 	"/>
	<polygon points="32.7,22.4 31.5,21 29.1,22.9 28,21.6 30.2,19.8 29,18.4 26.8,20.2 26,19.1 28.4,17.2 27.2,15.7 23.1,19 28.5,25.7 
			"/>
	<polygon points="39.8,18.1 38.9,16.5 36.2,18 32.9,12.1 31,13.2 35.2,20.7 	"/>
	<polygon points="47.1,15.3 46.4,13.6 43.6,14.6 41.3,8.3 39.2,9 42.1,17.1 	"/>
	<path d="M55.8,13.9c0.2,0,0.3,0,0.5,0c1.2-0.1,2.1-0.5,2.6-1.1c0.5-0.6,0.7-1.5,0.6-2.5l-0.4-5.4L56.9,5l0.4,4.9
		c0.1,1.7-0.6,2-1.2,2.1c-0.1,0-0.1,0-0.2,0c-0.5,0-1.2-0.2-1.4-1.9l-0.4-4.9l-2.2,0.2l0.4,5.4C52.7,12.8,53.8,13.9,55.8,13.9z"/>
	<polygon points="65.7,8.8 67.5,14.1 70,14.5 71.1,5.9 69,5.6 68.3,10.7 66.5,5.3 64.1,5 62.9,13.5 65,13.8 	"/>
	<polygon points="77.6,7.8 75.5,7.1 72.9,15.3 75,16 	"/>
	<polygon points="88.4,12.6 86.5,11.6 82.3,15.9 83.2,10 81.1,8.9 79.8,18 82,19 	"/>
	<polygon points="90.6,25 91.7,23.5 89.3,21.6 90.3,20.3 92.5,22 93.7,20.5 91.5,18.8 92.3,17.7 94.7,19.6 95.9,18.1 91.7,14.9 
		86.4,21.7 	"/>
	<path d="M94.2,28.6l2.5-2.2l0.1,0.2c0.3,0.4,0.3,0.5,0.1,1l-1.4,2.6l1.6,1.8l1.7-3.4c0.1-0.1,0.2-0.4,0.2-0.7
		c0.7,0.3,1.6,0.2,2.3-0.4c1.9-1.6,0.4-3.3-0.7-4.6l-1.4-1.6L92.7,27L94.2,28.6z M99.3,24.1l0.1,0.2c0.3,0.4,0.6,0.8,0.6,1.1
		c0,0.2-0.1,0.3-0.3,0.4C99.6,26,99.4,26,99.3,26c-0.4,0-0.8-0.4-1-0.7l-0.1-0.2L99.3,24.1z"/>
	<path d="M102.2,35.5c-0.4,0.3-1-0.2-1.2-0.6c-0.3-0.5-0.4-1-0.4-1.7l0-0.5l-2,0.9l0.1,0.4c0.2,0.7,0.3,1.1,0.7,1.8
		c0.7,1.2,1.6,1.8,2.6,1.8c0.5,0,0.9-0.1,1.4-0.4c1.5-0.9,1.3-2.3,1.1-3.4c-0.1-0.7-0.2-1.2,0.1-1.4c0.2-0.1,0.3-0.1,0.4-0.1
		c0.4,0,0.7,0.4,0.8,0.5c0.3,0.4,0.4,0.9,0.5,1.4l0.1,0.4l1.8-0.8l0-0.2c-0.1-0.6-0.4-1.2-0.8-1.9c-0.9-1.6-2.5-2.1-3.9-1.2
		c-1.5,0.9-1.3,2.3-1.1,3.3C102.5,34.8,102.6,35.3,102.2,35.5z"/>
	<rect x="102.5" y="39.6" transform="matrix(0.9259 -0.3777 0.3777 0.9259 -7.4559 43.3568)" width="8.6" height="2.2"/>
	<polygon points="111.2,46.2 104.7,47.8 105.2,49.9 111.8,48.3 112.3,50.5 114.1,50.1 112.5,43.5 110.7,44 	"/>
	<polygon points="106.2,56.6 106.3,58.8 109.7,58.6 115.1,61.4 115,59 111.8,57.5 114.8,55.6 114.6,53 109.6,56.5 	"/>
	<polygon points="11,76.4 12.8,75.9 12.1,73.3 13.4,72.9 14.2,75.7 16,75.1 14.6,70.3 6.3,72.7 6.9,74.8 10.3,73.8 	"/>
	<path d="M18.7,83.6c0.3-1,0.2-2.1-0.3-3.2c-0.8-1.6-2-2.4-3.6-2.4c-0.7,0-1.5,0.2-2.3,0.6c-1.3,0.6-2.1,1.5-2.5,2.6
		c-0.3,1-0.2,2.1,0.3,3.2c0.8,1.5,2,2.4,3.6,2.4c0.7,0,1.5-0.2,2.3-0.6C17.5,85.5,18.4,84.7,18.7,83.6z M15.3,84.1
		c-0.5,0.3-1.1,0.4-1.6,0.4c-0.8,0-1.3-0.3-1.6-1c-0.2-0.5-0.3-0.9-0.1-1.3c0.2-0.6,0.8-1.2,1.6-1.6c0.5-0.2,1-0.4,1.5-0.4
		c0.8,0,1.3,0.3,1.6,1c0.2,0.5,0.3,0.9,0.1,1.3C16.6,83.1,16.1,83.7,15.3,84.1z"/>
	<path d="M24.7,90.3l-3.9,3.1c-1,0.8-1.8,0.9-2.4,0.2c-0.2-0.3-0.3-0.6-0.3-0.9c0.1-0.4,0.4-0.9,1-1.4l3.9-3.1l-1.4-1.7l-4.3,3.4
		c-0.9,0.7-1.4,1.5-1.4,2.4c0,0.8,0.3,1.6,1,2.5c0.8,1.1,1.7,1.6,2.7,1.6c0.7,0,1.4-0.3,2.1-0.9L26,92L24.7,90.3z"/>
	<polygon points="32,97.3 28.8,101.3 30,95.7 28.1,94.1 22.6,100.8 24.3,102.2 27.5,98.2 26.3,103.8 28.2,105.4 33.7,98.7 	"/>
	<path d="M38.4,101.4l-2.2-1.1l-3.9,7.7l2.2,1.1c1.1,0.5,2,0.8,2.9,0.8c1.5,0,2.7-0.8,3.5-2.4C42.2,104.9,41.3,102.9,38.4,101.4z
		 M38.8,106.5c-0.4,0.9-1.2,1.4-2.1,1.4c-0.4,0-0.7-0.1-1.1-0.3l-0.5-0.3l2.2-4.4l0.5,0.3c0.6,0.3,1,0.8,1.2,1.3
		C39.2,105.2,39.1,105.8,38.8,106.5z"/>
	<polygon points="43.2,112.8 48.3,114.2 48.8,112.4 45.8,111.6 46.2,110 49,110.7 49.5,108.9 46.7,108.2 47,106.8 50.1,107.6 
		50.5,105.8 45.4,104.5 	"/>
	<path d="M55.9,106.5l-2.5-0.1l-0.5,8.6l2.5,0.1c0.2,0,0.4,0,0.6,0c2.9,0,4.4-1.4,4.6-4.1c0.1-1.3-0.2-2.4-0.9-3.2
		C58.9,107.1,57.7,106.6,55.9,106.5z M55.8,113.3l-0.6,0l0.3-4.9l0.6,0c1.2,0.1,2.3,1,2.2,2.6C58.2,112.6,57,113.3,55.8,113.3z"/>
	<path d="M68.2,105.8l-1.5,9.1l2.3-0.5l0.3-1.9l2.8-0.6l1.1,1.7l2.4-0.5l-5.1-7.7L68.2,105.8z M69.6,110.6l0.3-2.3l1.2,1.9
		L69.6,110.6z"/>
	<polygon points="76.4,110.3 77.2,112.4 79.2,111.6 78.5,109.6 	"/>
	<path d="M80.6,101.6l-2.2,1.2l4.1,7.6l2.2-1.2c2.9-1.6,3.6-3.6,2.3-6.1C85.7,100.5,83.5,100,80.6,101.6z M84.1,107.4l-0.5,0.3
		l-2.3-4.3l0.5-0.3c0.3-0.2,0.7-0.3,1.1-0.3c0.9,0,1.6,0.5,2.1,1.3C85.8,105.5,85.1,106.8,84.1,107.4z"/>
	<polygon points="88.7,104.3 89.9,106.1 91.7,104.8 90.5,103 	"/>
	<polygon points="92.1,93.2 91.7,96.6 93.6,96.9 93.8,95.5 97.9,99.6 99.5,98.1 93.4,91.9 	"/>
	<path d="M103.8,88.7c-0.7-0.5-1.5-0.6-2.4-0.3c0-0.8-0.4-1.6-1-2c-1.1-0.8-2.5-0.3-3.6,1.1c-1,1.4-0.9,2.8,0.3,3.7
		c0.6,0.4,1.4,0.5,2.1,0.3c-0.1,0.9,0.2,1.6,0.9,2.1c0.5,0.4,1,0.5,1.5,0.5c0.9,0,1.7-0.5,2.5-1.5c0.6-0.8,0.9-1.6,0.8-2.4
		C104.8,89.7,104.4,89.2,103.8,88.7z M99.7,89.3c-0.3,0.2-0.6,0.4-0.9,0.4c-0.1,0-0.3,0-0.4-0.1c-0.4-0.3-0.2-0.8,0-1.1
		c0.1-0.2,0.3-0.3,0.5-0.3c0.1,0,0.3,0.1,0.5,0.2C99.7,88.6,99.8,89,99.7,89.3z M102.7,91.7c-0.3,0.4-0.8,0.5-1.2,0.2
		c-0.3-0.3-0.5-0.6-0.4-1.2c0.6-0.4,1.1-0.5,1.5-0.2c0.2,0.1,0.3,0.3,0.3,0.5C102.9,91.2,102.8,91.5,102.7,91.7z"/>
	<path d="M107.7,80.3c-1.5-0.7-2.9-0.3-3.6,1.1c-0.2,0.4-0.3,0.8-0.2,1.2c-0.5-0.4-1-1.1-0.6-2c0.2-0.4,0.5-0.7,0.8-1l0.3-0.2
		l-1.6-1.1l-0.2,0.2c-0.4,0.4-0.8,0.9-1.1,1.5c-0.4,0.9-0.5,1.7-0.2,2.5c0.5,1.4,1.9,2.4,3,2.9c1,0.5,1.8,0.7,2.5,0.7
		c1.1,0,1.9-0.5,2.5-1.6C110.1,82.7,109.5,81.2,107.7,80.3z M107.7,83.5c-0.1,0.3-0.4,0.4-0.7,0.4c-0.2,0-0.5-0.1-0.7-0.2
		c-0.4-0.2-0.7-0.5-0.8-0.7c-0.1-0.2,0-0.3,0-0.5c0.1-0.3,0.3-0.4,0.7-0.4c0.2,0,0.5,0.1,0.8,0.2c0.4,0.2,0.6,0.4,0.7,0.7
		C107.8,83.2,107.7,83.4,107.7,83.5z"/>
	<path d="M110.8,71.5c-1.7-0.5-3.1,0.3-3.6,1.9c0,0.2-0.1,0.3-0.1,0.4l-1-0.3l0.9-3l-1.7-0.5l-1.5,5l4.8,1.5l0-0.4
		c0-0.5,0.1-0.9,0.2-1.4c0.1-0.4,0.6-1.4,1.5-1.2c1,0.3,0.8,1.4,0.7,1.7c-0.2,0.6-0.5,1-0.8,1.4l-0.3,0.3l2,0.7l0.1-0.2
		c0.3-0.6,0.6-1.3,0.8-1.8c0.3-1,0.3-1.9-0.1-2.7C112.3,72.3,111.6,71.8,110.8,71.5z"/>
	<path d="M16.3,60c0,24,19.5,43.6,43.5,43.6c24,0,43.5-19.5,43.5-43.6c0-24-19.5-43.5-43.5-43.5C35.9,16.4,16.3,36,16.3,60z
		 M59.9,17.9c23.2,0,42,18.9,42,42c0,23.2-18.9,42-42,42c-23.2,0-42-18.9-42-42C17.8,36.8,36.7,17.9,59.9,17.9z"/>
	<path d="M59.9,0.4C27,0.4,0.3,27.1,0.3,60c0,32.8,26.7,59.6,59.6,59.6c32.8,0,59.6-26.7,59.6-59.6C119.4,27.1,92.7,0.4,59.9,0.4z
		 M59.9,118c-32,0-58-26-58-58c0-32,26-58,58-58c32,0,58,26,58,58C117.9,92,91.9,118,59.9,118z"/>
</g>
</svg>
 alt="Cornell University Logo" srcset sizes>
+ </picture>
+ </a></div>
+ <div class="column nav" id=toggle-container>
+ <button class=toggle-control aria-label="Open search"><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-white" aria-hidden=true><path d="M505 442.7L405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9 0 208 0S0 93.1 0 208s93.1 208 208 208c48.3 0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9 0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7 0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7 0 128 57.2 128 128 0 70.7-57.2 128-128 128z"></path></svg></button>
+ <div class="mobile-toggle-block toggle-target">
+ <form class=mobile-search-form method=GET action=https://arxiv.org/search>
+ <div class="field has-addons">
+ <input class=input type=text name=query placeholder=Search... aria-label="Search term or terms" value>
+ <button class=button>GO</button>
+ </div>
+ </form>
+ </div>
+ <button class=toggle-control aria-label="Open navigation menu"><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 448 512" class="icon filter-white" aria-hidden=true><path d="M16 132h416c8.837 0 16-7.163 16-16V76c0-8.837-7.163-16-16-16H16C7.163 60 0 67.163 0 76v40c0 8.837 7.163 16 16 16zm0 160h416c8.837 0 16-7.163 16-16v-40c0-8.837-7.163-16-16-16H16c-8.837 0-16 7.163-16 16v40c0 8.837 7.163 16 16 16zm0 160h416c8.837 0 16-7.163 16-16v-40c0-8.837-7.163-16-16-16H16c-8.837 0-16 7.163-16 16v40c0 8.837 7.163 16 16 16z"></path></svg></button>
+ <div class="mobile-toggle-block toggle-target">
+ <nav class=mobile-menu aria-labelledby=mobilemenulabel>
+ <h2 id=mobilemenulabel>quick links</h2>
+ <ul>
+ <li><a href=https://arxiv.org/login>Login</a></li>
+ <li><a href=https://info.arxiv.org/help>Help Pages</a></li>
+ <li><a href=https://info.arxiv.org/about>About</a></li>
+ </ul>
+ </nav>
+ </div>
+ </div>
+ </div>
+ </div>
+ </header>
+ <main>
+ <div id=content>
+<div id=abs-outer>
+ <div class=leftcolumn>
+ <div class=subheader>
+ <h1>Computer Science &gt; Graphics</h1>
+ </div>
+ <div class=header-breadcrumbs-mobile>
+ <strong>arXiv:2602.05013</strong> (cs)
+ </div>
+<style>#abs{font-family:"Lucida Grande",Helvetica,Arial,sans-serif!important}#abs h1.title{display:block;font-size:1.8em!important;font-weight:700;margin-block-end:12px;margin-block-start:12px;margin-bottom:12px;margin-inline-end:0px;margin-inline-start:20px;margin-left:20px;margin-right:0px;margin-top:12px}#abs div.authors{font-size:1.2em;line-height:24px;margin-bottom:8px;margin-left:20px;margin-right:0px;margin-top:8px}#abs div.dateline{font-size:0.9em;font-style:italic;margin-bottom:6.5px;margin-left:20px;margin-right:0px;margin-top:6.5px}#abs blockquote.abstract{font-size:1.05em;margin-block-end:21.6px;margin-block-start:14.4px;margin-bottom:21.6px;margin-inline-end:40px;margin-inline-start:40px;background-color:white;border-left:0px;padding:0px}#abs div.metatable{font-size:0.95em!important;margin-bottom:19px;margin-left:20px;margin-right:0px;margin-top:0px;border:0px;padding:0px}#abs div.metatable tbody{vertical-align:middle}#abs tr{margin-top:0px;margin-bottom:0px}#abs td.tablecell{padding-top:0px;padding-bottom:0px;padding-right:6.5px;padding-left:0px;vertical-align:top;font-size:0.95em!important;margin-top:0px;margin-bottom:0px;border:0px}#abs td.tablecell.label{font-weight:400!important}#abs span.primary-subject{font-weight:700}#abs span.arxivid{font-weight:700}</style>
+<div id=content-inner>
+ <div id=abs>
+ <div class=dateline>
+ [Submitted on 4 Feb 2026]</div>
+ <h1 class="title mathjax"><span class="descriptor sf-hidden">Title:</span>Untwisting RoPE: Frequency Control for Shared Attention in DiTs</h1>
+ <div class=authors><span class="descriptor sf-hidden">Authors:</span><a href="https://arxiv.org/search/cs?searchtype=author&amp;query=Mikaeili,+A" rel=nofollow>Aryan Mikaeili</a>, <a href="https://arxiv.org/search/cs?searchtype=author&amp;query=Patashnik,+O" rel=nofollow>Or Patashnik</a>, <a href="https://arxiv.org/search/cs?searchtype=author&amp;query=Tagliasacchi,+A" rel=nofollow>Andrea Tagliasacchi</a>, <a href="https://arxiv.org/search/cs?searchtype=author&amp;query=Cohen-Or,+D" rel=nofollow>Daniel Cohen-Or</a>, <a href="https://arxiv.org/search/cs?searchtype=author&amp;query=Mahdavi-Amiri,+A" rel=nofollow>Ali Mahdavi-Amiri</a></div> <div id=download-button-info hidden class=sf-hidden>View a PDF of the paper titled Untwisting RoPE: Frequency Control for Shared Attention in DiTs, by Aryan Mikaeili and 4 other authors</div>
+ <a class=mobile-submission-download href=https://arxiv.org/pdf/2602.05013>View PDF</a>
+ <a class=mobile-submission-download href=https://arxiv.org/html/2602.05013v1>HTML (experimental)</a>
+ <blockquote class="abstract mathjax">
+ <span class="descriptor sf-hidden">Abstract:</span>Positional encodings are essential to transformer-based generative models, yet their behavior in multimodal and attention-sharing settings is not fully understood. In this work, we present a principled analysis of Rotary Positional Embeddings (RoPE), showing that RoPE naturally decomposes into frequency components with distinct positional sensitivities. We demonstrate that this frequency structure explains why shared-attention mechanisms, where a target image is generated while attending to tokens from a reference image, can lead to reference copying, in which the model reproduces content from the reference instead of extracting only its stylistic cues. Our analysis reveals that the high-frequency components of RoPE dominate the attention computation, forcing queries to attend mainly to spatially aligned reference tokens and thereby inducing this unintended copying behavior. Building on these insights, we introduce a method for selectively modulating RoPE frequency bands so that attention reflects semantic similarity rather than strict positional alignment. Applied to modern transformer-based diffusion architectures, where all tokens share attention, this modulation restores stable and meaningful shared attention. As a result, it enables effective control over the degree of style transfer versus content copying, yielding a proper style-aligned generation process in which stylistic attributes are transferred without duplicating reference content.
+ </blockquote>
+ <div class=metatable>
+ <table summary="Additional metadata"><tbody><tr>
+ <td class="tablecell label">Subjects:</td>
+ <td class="tablecell subjects">
+ <span class=primary-subject>Graphics (cs.GR)</span>; Computer Vision and Pattern Recognition (cs.CV)</td>
+ <tr>
+ <td class="tablecell label">Cite as:</td>
+ <td class="tablecell arxivid"><span class=arxivid><a href=https://arxiv.org/abs/2602.05013>arXiv:2602.05013</a> [cs.GR]</span></td>
+ </tr>
+ <tr>
+ <td class="tablecell label">&nbsp;</td>
+ <td class="tablecell arxividv">(or <span class=arxivid>
+ <a href=https://arxiv.org/abs/2602.05013v1>arXiv:2602.05013v1</a> [cs.GR]</span> for this version)
+ </td>
+ </tr>
+ <tr>
+ <td class="tablecell label">&nbsp;</td>
+ <td class="tablecell arxivdoi"> <a href=https://doi.org/10.48550/arXiv.2602.05013 id=arxiv-doi-link>https://doi.org/10.48550/arXiv.2602.05013</a><div class=button-and-tooltip>
+ <button class=more-info aria-describedby=more-info-desc-1>
+ <svg height=15 role=presentation xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512"><path fill=currentColor d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z"></path></svg>
+ <span class=visually-hidden>Focus to learn more</span>
+ </button>
+ <div role=tooltip id=more-info-desc-1 class=sf-hidden>
+ arXiv-issued DOI via DataCite</div>
+ </div>
+ </td>
+ </table>
+ </div>
+ </div>
+</div>
+ <div class=submission-history>
+ <h2>Submission history</h2> From: Aryan Mikaeili [<a href=https://arxiv.org/show-email/4568aed9/2602.05013 rel=nofollow>view email</a>] <br> <strong>[v1]</strong>
+ Wed, 4 Feb 2026 20:01:59 UTC (34,443 KB)<br>
+</div>
+ </div>
+<div class=extra-services> <div class=full-text>
+ <a name=other></a>
+ <span class="descriptor sf-hidden">Full-text links:</span>
+ <h2>Access Paper:</h2>
+ <ul>
+ <div id=download-button-info hidden class=sf-hidden>
+View a PDF of the paper titled Untwisting RoPE: Frequency Control for Shared Attention in DiTs, by Aryan Mikaeili and 4 other authors</div><li><a href=https://arxiv.org/pdf/2602.05013 aria-describedby=download-button-info accesskey=f class="abs-button download-pdf">View PDF</a><li><a href=https://arxiv.org/html/2602.05013v1 class=abs-button id=latexml-download-link>HTML (experimental)</a><li><a href=https://arxiv.org/src/2602.05013 class="abs-button download-eprint">TeX Source
+ </a></ul>
+ <div class=abs-license><a href=http://creativecommons.org/licenses/by/4.0/ title="Rights to this article" class=has_license>
+ <img alt="license icon" role=presentation src="data:image/png;base64,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">
+ <span>view license</span>
+ </a></div>
+ </div>
+ <div class=browse>
+ <h3 class=browse-context-heading>Current browse context:</h3>
+ <div class=current>cs.GR</div>
+ <div class=prevnext>
+<span class=arrow>
+ <a class="abs-button prev-url" href="https://arxiv.org/prevnext?id=2602.05013&amp;function=prev&amp;context=cs.GR" accesskey=p title="previous in cs.GR (accesskey p)" rel=nofollow>&lt;&nbsp;prev</a>
+ </span>
+ <span class="is-hidden-mobile sf-hidden">&nbsp; | &nbsp;</span> <span class=arrow>
+ <a class="abs-button next-url" href="https://arxiv.org/prevnext?id=2602.05013&amp;function=next&amp;context=cs.GR" accesskey=n title="next in cs.GR (accesskey n)" rel=nofollow>next&nbsp;&gt;</a>
+ </span><br>
+ </div><div class=list>
+ <a class="abs-button abs-button-grey abs-button-small context-new" href=https://arxiv.org/list/cs.GR/new rel=nofollow>new</a>
+ <span class="is-hidden-mobile sf-hidden"> | </span>
+ <a class="abs-button abs-button-grey abs-button-small context-recent" href=https://arxiv.org/list/cs.GR/recent rel=nofollow>recent</a>
+ <span class="is-hidden-mobile sf-hidden"> | </span><a class="abs-button abs-button-grey abs-button-small context-id" href=https://arxiv.org/list/cs.GR/2026-02 rel=nofollow>2026-02</a>
+ </div><div class=abs-switch-cat>
+ Change to browse by:
+ <div class="switch context-change">
+ <a href="https://arxiv.org/abs/2602.05013?context=cs" rel=nofollow>cs</a><br class="is-hidden-mobile sf-hidden">
+ <a class=subclass href="https://arxiv.org/abs/2602.05013?context=cs.CV" rel=nofollow>cs.CV</a><br class="is-hidden-mobile sf-hidden">
+ </div>
+ </div>
+ </div>
+ <div class=extra-ref-cite>
+ <h3>References &amp; Citations</h3>
+ <ul>
+ <li><a class="abs-button abs-button-small cite-ads" href=https://ui.adsabs.harvard.edu/abs/arXiv:2602.05013>NASA ADS</a><li><a class="abs-button abs-button-small cite-google-scholar" href="https://scholar.google.com/scholar_lookup?arxiv_id=2602.05013" target=_blank rel=noopener>Google Scholar</a></li>
+ <li><a class="abs-button abs-button-small cite-semantic-scholar" href=https://api.semanticscholar.org/arXiv:2602.05013 target=_blank rel=noopener>Semantic Scholar</a></li>
+ </ul>
+ <div style=clear:both></div>
+ </div>
+<div class=extra-ref-cite>
+ <button type=button id=bib-cite-trigger class="bib-cite-button abs-button">export BibTeX citation</button>
+ <span id=bib-cite-loading hidden class=sf-hidden>Loading...</span>
+</div>
+<div id=bib-cite-modal class="bib-modal sf-hidden" hidden>
+</div><div class=bookmarks>
+ <div><h3>Bookmark</h3></div><a class="abs-button abs-button-grey abs-button-small" href="http://www.bibsonomy.org/BibtexHandler?requTask=upload&amp;url=https://arxiv.org/abs/2602.05013&amp;description=Untwisting%20RoPE:%20Frequency%20Control%20for%20Shared%20Attention%20in%20DiTs" title="Bookmark on BibSonomy">
+ <img src=data:image/png;base64,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 alt=BibSonomy>
+ </a>
+ <a class="abs-button abs-button-grey abs-button-small" href="https://reddit.com/submit?url=https://arxiv.org/abs/2602.05013&amp;title=Untwisting%20RoPE:%20Frequency%20Control%20for%20Shared%20Attention%20in%20DiTs" title="Bookmark on Reddit">
+ <img src="data:image/png;base64,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" alt=Reddit>
+ </a>
+</div> </div>
+<div id=labstabs>
+ <div class=labstabs role=tablist aria-label="arXivLabs tools"><input type=radio name=tabs id=tabone checked class=labs-tab-input value=on>
+ <label for=tabone role=tab aria-selected=true aria-controls=tabpanel-one id=tab-label-one>Bibliographic Tools</label>
+ <div class="tab labs-display-bib" role=tabpanel id=tabpanel-one aria-labelledby=tab-label-one>
+ <h1>Bibliographic and Citation Tools</h1>
+ <div class=toggle>
+ <div class="columns is-mobile lab-row">
+ <div class="column lab-switch">
+ <label class=switch>
+ <input id=bibex-toggle type=checkbox class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/bibex/bibex.js?20241202 value=on>
+ <span class=slider></span>
+ <span class=is-sr-only>Bibliographic Explorer Toggle</span>
+ </label>
+ </div>
+ <div class="column lab-name">
+ <span id=label-for-bibex>Bibliographic Explorer</span> <em>(<a href=https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer>What is the Explorer?</a>)</em>
+ </div>
+ </div>
+ <div class="columns is-mobile lab-row">
+ <div class="column lab-switch">
+ <label class=switch>
+ <input id=connectedpapers-toggle type=checkbox class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/connectedpapers.js aria-labelledby=label-for-connected-papers value=on>
+ <span class=slider></span>
+ <span class=is-sr-only>Connected Papers Toggle</span>
+ </label>
+ </div>
+ <div class="column lab-name">
+ <span id=label-for-connected-papers>Connected Papers</span> <em>(<a href=https://www.connectedpapers.com/about target=_blank>What is Connected Papers?</a>)</em>
+ </div>
+ </div><div class="columns is-mobile lab-row">
+ <div class="column lab-switch">
+ <label class=switch>
+ <input id=litmaps-toggle type=checkbox class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/litmaps.js?20210617 aria-labelledby=label-for-litmaps value=on>
+ <span class=slider></span>
+ <span class=is-sr-only>Litmaps Toggle</span>
+ </label>
+ </div>
+ <div class="column lab-name">
+ <span id=label-for-litmaps>Litmaps</span> <em>(<a href=https://www.litmaps.co/ target=_blank>What is Litmaps?</a>)</em>
+ </div>
+ </div>
+ <div class="columns is-mobile lab-row">
+ <div class="column lab-switch">
+ <label class=switch>
+ <input id=scite-toggle type=checkbox class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/scite.js?20210617 aria-labelledby=label-for-scite value=on>
+ <span class=slider></span>
+ <span class=is-sr-only>scite.ai Toggle</span>
+ </label>
+ </div>
+ <div class="column lab-name">
+ <span id=label-for-scite>scite Smart Citations</span> <em>(<a href=https://www.scite.ai/ target=_blank>What are Smart Citations?</a>)</em>
+ </div>
+ </div>
+ </div>
+ <div class="labs-content-placeholder labs-display" style=display:none></div>
+ <div style=min-height:15px id=connectedpapers-output></div>
+ <div style=min-height:15px id=litmaps-open-in></div>
+ <div style=min-height:15px id=scite-open-in></div>
+ </div>
+ <input type=radio name=tabs id=tabtwo class=labs-tab-input value=on>
+ <label for=tabtwo role=tab aria-selected=false aria-controls=tabpanel-two id=tab-label-two>Code, Data, Media</label>
+ <div class="tab sf-hidden" role=tabpanel id=tabpanel-two aria-labelledby=tab-label-two>
+ </div>
+ <input type=radio name=tabs id=labstabs-demos-input class=labs-tab-input value=on>
+ <label for=labstabs-demos-input id=labstabs-demos-label role=tab aria-selected=false aria-controls=tabpanel-demos>Demos</label>
+ <div class="tab sf-hidden" role=tabpanel id=tabpanel-demos aria-labelledby=labstabs-demos-label>
+ </div>
+ <input type=radio name=tabs id=tabfour class=labs-tab-input value=on>
+ <label for=tabfour role=tab aria-selected=false aria-controls=tabpanel-four id=tab-label-four>Related Papers</label>
+ <div class="tab sf-hidden" role=tabpanel id=tabpanel-four aria-labelledby=tab-label-four>
+ </div>
+ <input type=radio name=tabs id=tabfive class=labs-tab-input value=on>
+ <label for=tabfive role=tab aria-selected=false aria-controls=tabpanel-five id=tab-label-five>
+ About arXivLabs
+ </label>
+ <div class="tab sf-hidden" role=tabpanel id=tabpanel-five aria-labelledby=tab-label-five>
+ </div>
+ </div>
+</div>
+ <div class=endorsers>
+ <a href=https://arxiv.org/auth/show-endorsers/2602.05013 class=endorser-who rel=nofollow>Which authors of this paper are endorsers?</a> |
+ <a id=mathjax_toggle href=javascript:void(0)>Disable MathJax</a> (<a href=https://info.arxiv.org/help/mathjax.html>What is MathJax?</a>)
+ <span class="help sf-hidden" style=font-style:normal;float:right;margin-top:0;margin-right:1em></span>
+ </div>
+</div>
+ </div>
+ </main>
+ <footer style=clear:both>
+ <div class="columns is-desktop" role=navigation aria-label=Secondary style="margin:-0.75em -0.75em 0.75em -0.75em">
+ <div class=column style=padding:0>
+ <div class=columns>
+ <div class=column>
+ <ul style=list-style:none;line-height:2>
+ <li><a href=https://info.arxiv.org/about>About</a></li>
+ <li><a href=https://info.arxiv.org/help>Help</a></li>
+ </ul>
+ </div>
+ <div class=column>
+ <ul style=list-style:none;line-height:2>
+ <li>
+ <svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg>
+ <a href=https://info.arxiv.org/help/contact.html> Contact</a>
+ </li>
+ <li>
+ <svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"></path></svg>
+ <a href=https://info.arxiv.org/help/subscribe> Subscribe</a>
+ </li>
+ </ul>
+ </div>
+ </div>
+ </div>
+ <div class=column style=padding:0>
+ <div class=columns>
+ <div class=column>
+ <ul style=list-style:none;line-height:2>
+ <li><a href=https://info.arxiv.org/help/license/index.html>Copyright</a></li>
+ <li><a href=https://info.arxiv.org/help/policies/privacy_policy.html>Privacy Policy</a></li>
+ </ul>
+ </div>
+ <div class="column sorry-app-links">
+ <ul style=list-style:none;line-height:2>
+ <li><a href=https://info.arxiv.org/help/web_accessibility.html>Web Accessibility Assistance</a></li>
+ <li>
+ <p class=help>
+ <a class=a11y-main-link href=https://status.arxiv.org/ target=_blank>arXiv Operational Status <svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 256 512" class="icon filter-dark_grey" role=presentation><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"></path></svg></a><br>
+ </p>
+ </li>
+ </ul>
+ </div>
+ </div>
+ </div>
+ </div>
+ </footer>
+ </div>