{"id":90619,"date":"2026-08-31T16:21:19","date_gmt":"2026-08-31T13:21:19","guid":{"rendered":"https:\/\/twodots.gr\/?p=90619"},"modified":"2026-08-31T16:21:45","modified_gmt":"2026-08-31T13:21:45","slug":"ctqw-gnn-kvantikoi-peripatoi-graph-neural-networks","status":"publish","type":"post","link":"https:\/\/twodots.gr\/bg\/ctqw-gnn-kvantikoi-peripatoi-graph-neural-networks\/","title":{"rendered":"CTQW-GNN: \u03c0\u03ce\u03c2 \u03bf\u03b9 \u03ba\u03b2\u03b1\u03bd\u03c4\u03b9\u03ba\u03bf\u03af \u03c0\u03b5\u03c1\u03af\u03c0\u03b1\u03c4\u03bf\u03b9 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03bb\u03cd\u03c3\u03bf\u03c5\u03bd \u03b4\u03cd\u03bf \u03b1\u03b4\u03c5\u03bd\u03b1\u03bc\u03af\u03b5\u03c2 \u03c4\u03c9\u03bd graph neural networks"},"content":{"rendered":"<div class=\"td-article-lede\">\n<p><strong>\u03a4\u03bf CTQW-GNN \u03b4\u03b5\u03bd \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b2\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ae: \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03c0\u03c1\u03bf\u03c3\u03bf\u03bc\u03bf\u03b9\u03c9\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 continuous-time quantum walks \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b7 \u03c6\u03b1\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b1 \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03af\u03b6\u03b5\u03b9 \u03c4\u03bf over-smoothing \u03c3\u03c4\u03b1 graph neural networks.<\/strong> \u0397 \u03b5\u03c1\u03b5\u03c5\u03bd\u03b7\u03c4\u03b9\u03ba\u03ae \u03c0\u03c1\u03cc\u03c4\u03b1\u03c3\u03b7 \u03c3\u03c5\u03bd\u03b4\u03c5\u03ac\u03b6\u03b5\u03b9 \u03c4\u03c1\u03b5\u03b9\u03c2 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03bb\u03ac\u03b4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03ba\u03bf\u03c1\u03c5\u03c6\u03b1\u03af\u03b1 \u03b5\u03c0\u03af\u03b4\u03bf\u03c3\u03b7 \u03c3\u03b5 14 node-classification benchmarks. \u0391\u03c5\u03c4\u03cc \u03c4\u03b7\u03bd \u03ba\u03ac\u03bd\u03b5\u03b9 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03c3\u03b1 \u03b3\u03b9\u03b1 \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03cc, \u03cc\u03c7\u03b9 \u03ad\u03c4\u03bf\u03b9\u03bc\u03b7 \u03b5\u03b3\u03b3\u03cd\u03b7\u03c3\u03b7 \u03b3\u03b9\u03b1 recommendations, fraud detection \u03ae \u03ac\u03bb\u03bb\u03bf production workload.<\/p>\n<\/div>\n<div class=\"td-article-toc\">\n<div class=\"td-toc-title\">\u03a0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03b1<\/div>\n<ul>\n<li><a href=\"#ti-provlima-lynei-ctqw-gnn\">\u03a4\u03b9 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b5\u03af \u03bd\u03b1 \u03bb\u03cd\u03c3\u03b5\u03b9 \u03c4\u03bf CTQW-GNN<\/a><\/li>\n<li><a href=\"#message-passing-low-pass\">\u0393\u03b9\u03b1\u03c4\u03af \u03c4\u03bf message passing \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03c3\u03c5\u03c7\u03bd\u03ac \u03c3\u03b1\u03bd low-pass \u03c6\u03af\u03bb\u03c4\u03c1\u03bf<\/a><\/li>\n<li><a href=\"#faseis-anti-gia-aposvesi\">\u03a0\u03ce\u03c2 \u03bf\u03b9 \u03c6\u03ac\u03c3\u03b5\u03b9\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03bf\u03cd\u03bd \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03c3\u03b2\u03b5\u03c3\u03b7<\/a><\/li>\n<li><a href=\"#treis-kladoi-ctqw-gnn\">\u03a4\u03c1\u03b5\u03b9\u03c2 \u03ba\u03bb\u03ac\u03b4\u03bf\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03c1\u03af\u03b1 \u03b5\u03af\u03b4\u03b7 \u03c0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b1\u03c2<\/a><\/li>\n<li><a href=\"#sparsification-walk-time\">\u03a0\u03ce\u03c2 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03bd\u03c4\u03b1\u03b9 sparsification \u03ba\u03b1\u03b9 walk time<\/a><\/li>\n<li><a href=\"#dekatessera-benchmarks\">\u03a4\u03b9 \u03ad\u03b4\u03b5\u03b9\u03be\u03b1\u03bd \u03c4\u03b1 14 benchmarks<\/a><\/li>\n<li><a href=\"#ypologistiko-kostos\">\u03a0\u03bf\u03b9\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2<\/a><\/li>\n<li><a href=\"#epixeirimatiki-aksia\">\u03a0\u03bf\u03cd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03be\u03af\u03b1<\/a><\/li>\n<li><a href=\"#periorismoi-preprint\">\u03a0\u03bf\u03b9\u03bf\u03b9 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03af \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03bd\u03bf\u03c5\u03bd<\/a><\/li>\n<li><a href=\"#plano-aksiologisis\">\u03a0\u03ce\u03c2 \u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af\u03c4\u03b1\u03b9 \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae<\/a><\/li>\n<\/ul>\n<\/div>\n<p>\u03a4\u03b1 graph neural networks \u03b5\u03af\u03bd\u03b1\u03b9 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03b1 \u03cc\u03c4\u03b1\u03bd \u03bf\u03b9 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2 \u03b1\u03bd\u03ac\u03bc\u03b5\u03c3\u03b1 \u03c3\u03c4\u03b9\u03c2 \u03bf\u03bd\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03af\u03b4\u03b9\u03b1 \u03c3\u03b7\u03bc\u03b1\u03c3\u03af\u03b1 \u03bc\u03b5 \u03c4\u03b1 \u03af\u03b4\u03b9\u03b1 \u03c4\u03b1 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1: \u03c0\u03c1\u03bf\u03ca\u03cc\u03bd\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03c7\u03c1\u03ae\u03c3\u03c4\u03b5\u03c2, \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03bf\u03af \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b1\u03bb\u03bb\u03b1\u03b3\u03ad\u03c2, \u03c3\u03c5\u03c3\u03ba\u03b5\u03c5\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bc\u03b2\u03ac\u03bd\u03c4\u03b1, \u03ad\u03b3\u03b3\u03c1\u03b1\u03c6\u03b1 \u03ba\u03b1\u03b9 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b5\u03c2. \u03a4\u03bf message passing \u03b5\u03c0\u03b9\u03c4\u03c1\u03ad\u03c0\u03b5\u03b9 \u03c3\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03ba\u03cc\u03bc\u03b2\u03bf \u03bd\u03b1 \u03b5\u03bd\u03b7\u03bc\u03b5\u03c1\u03ce\u03bd\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03ae \u03c4\u03bf\u03c5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03b3\u03b5\u03af\u03c4\u03bf\u03bd\u03b5\u03c2. \u0397 \u03af\u03b4\u03b9\u03b1 \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1 \u03cc\u03bc\u03c9\u03c2 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c3\u03b2\u03ae\u03c3\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ad\u03c2 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03bf \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03b5\u03b9 \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2.<\/p>\n<p>\u0397 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1 <em>Continuous-Time Quantum Walks based Graph Neural Network<\/em> \u03c4\u03c9\u03bd Yuliang Zhan, Zefeng Gao, Jian Li, Yang Liu \u03ba\u03b1\u03b9 Hao Sun \u03c0\u03c1\u03bf\u03c4\u03b5\u03af\u03bd\u03b5\u03b9 \u03c4\u03bf CTQW-GNN \u03c9\u03c2 \u03ba\u03bf\u03b9\u03bd\u03ae \u03b1\u03c0\u03ac\u03bd\u03c4\u03b7\u03c3\u03b7 \u03c3\u03c4\u03b7\u03bd heterophily \u03ba\u03b1\u03b9 \u03c4\u03bf over-smoothing. \u0397 \u03c3\u03cd\u03bd\u03b4\u03b5\u03c3\u03b7 \u03bc\u03b5 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2 \u03cc\u03c0\u03c9\u03c2 \u03c4\u03bf <a href=\"https:\/\/twodots.gr\/pygraphistry-graph-intelligence-security-analytics\/\">graph intelligence \u03b3\u03b9\u03b1 security analytics<\/a> \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03cd\u03bb\u03bf\u03b3\u03b7 \u03bc\u03cc\u03bd\u03bf \u03c9\u03c2 \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 \u03c0\u03c1\u03bf\u03c2 \u03b4\u03bf\u03ba\u03b9\u03bc\u03ae: \u03c4\u03bf paper \u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af node classification \u03c3\u03b5 \u03b4\u03b7\u03bc\u03cc\u03c3\u03b9\u03b1 datasets, \u03cc\u03c7\u03b9 \u03ad\u03c4\u03bf\u03b9\u03bc\u03b1 \u03b5\u03bc\u03c0\u03bf\u03c1\u03b9\u03ba\u03ac \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1.<\/p>\n<h2 id=\"ti-provlima-lynei-ctqw-gnn\">\u03a4\u03b9 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b5\u03af \u03bd\u03b1 \u03bb\u03cd\u03c3\u03b5\u03b9 \u03c4\u03bf CTQW-GNN<\/h2>\n<p>\u0397 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03b1\u03b4\u03c5\u03bd\u03b1\u03bc\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 heterophily. \u03a0\u03bf\u03bb\u03bb\u03ac GNN \u03be\u03b5\u03ba\u03b9\u03bd\u03bf\u03cd\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03c3\u03c5\u03bd\u03b4\u03b5\u03b4\u03b5\u03bc\u03ad\u03bd\u03bf\u03b9 \u03ba\u03cc\u03bc\u03b2\u03bf\u03b9 \u03bc\u03bf\u03b9\u03ac\u03b6\u03bf\u03c5\u03bd. \u0391\u03c5\u03c4\u03cc \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03c3\u03b5 \u03ad\u03bd\u03b1\u03bd \u03b3\u03c1\u03ac\u03c6\u03bf \u03cc\u03c0\u03bf\u03c5 \u03c6\u03af\u03bb\u03bf\u03b9, \u03c0\u03c1\u03bf\u03ca\u03cc\u03bd\u03c4\u03b1 \u03ae \u03ad\u03b3\u03b3\u03c1\u03b1\u03c6\u03b1 \u03bc\u03bf\u03b9\u03c1\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b5\u03c4\u03b9\u03ba\u03ad\u03c4\u03b5\u03c2, \u03b1\u03bb\u03bb\u03ac \u03b1\u03c0\u03bf\u03c4\u03c5\u03b3\u03c7\u03ac\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b1\u03bd \u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03c9\u03bd \u03b3\u03b5\u03b9\u03c4\u03cc\u03bd\u03c9\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2. \u0388\u03bd\u03b1\u03c2 \u03cd\u03c0\u03bf\u03c0\u03c4\u03bf\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03cc\u03c2, \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03c4\u03b1\u03b9 \u03c3\u03ba\u03cc\u03c0\u03b9\u03bc\u03b1 \u03bc\u03b5 \u03ba\u03b1\u03bd\u03bf\u03bd\u03b9\u03ba\u03bf\u03cd\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b1\u03c3\u03bc\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03c3\u03ba\u03b5\u03c5\u03ad\u03c2.<\/p>\n<p>\u0397 \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03b7 \u03b1\u03b4\u03c5\u03bd\u03b1\u03bc\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf over-smoothing. \u038c\u03c4\u03b1\u03bd \u03b7 \u03c3\u03c5\u03bd\u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03b7 \u03b5\u03c0\u03b1\u03bd\u03b1\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03c0\u03bf\u03bb\u03bb\u03ac layers, \u03bf\u03b9 \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u03c4\u03c9\u03bd \u03ba\u03cc\u03bc\u03b2\u03c9\u03bd \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03c3\u03c5\u03b3\u03ba\u03bb\u03af\u03bd\u03bf\u03c5\u03bd \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03b3\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bf\u03bb\u03bf\u03ad\u03bd\u03b1 \u03c0\u03b9\u03bf \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03bf \u03bd\u03b1 \u03b4\u03b9\u03b1\u03ba\u03c1\u03b9\u03b8\u03bf\u03cd\u03bd. \u03a4\u03bf paper \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c6\u03b5\u03b9 \u03c4\u03bf \u03c6\u03b1\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03bc\u03ad\u03c3\u03c9 \u03c4\u03b7\u03c2 \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1\u03c2 Dirichlet: \u03b1\u03bd \u03bf\u03b9 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ad\u03c2 \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03c3\u03c5\u03bd\u03b4\u03b5\u03b4\u03b5\u03bc\u03ad\u03bd\u03c9\u03bd \u03ba\u03cc\u03bc\u03b2\u03c9\u03bd \u03c6\u03b8\u03af\u03bd\u03bf\u03c5\u03bd \u03b5\u03ba\u03b8\u03b5\u03c4\u03b9\u03ba\u03ac \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf \u03bc\u03b7\u03b4\u03ad\u03bd, \u03c4\u03bf \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03bf \u03c7\u03ac\u03bd\u03b5\u03b9 \u03b5\u03ba\u03c6\u03c1\u03b1\u03c3\u03c4\u03b9\u03ba\u03ae \u03c0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b1.<\/p>\n<p>\u03a4\u03bf \u03ba\u03c1\u03af\u03c3\u03b9\u03bc\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03b1\u03c1\u03b1\u03af\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b8\u03b1\u03c1\u03ac \u03bf\u03bc\u03bf\u03c6\u03b9\u03bb\u03b9\u03ba\u03cc\u03c2 \u03ae \u03b5\u03c4\u03b5\u03c1\u03bf\u03c6\u03b9\u03bb\u03b9\u03ba\u03cc\u03c2. \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c7\u03b1\u03bc\u03b7\u03bb\u03ad\u03c2, \u03bc\u03b5\u03c3\u03b1\u03af\u03b5\u03c2 \u03ae \u03c5\u03c8\u03b7\u03bb\u03ad\u03c2 graph frequencies. \u0391\u03c5\u03c4\u03ae \u03b7 \u03c4\u03bf\u03c0\u03b9\u03ba\u03ae \u03c0\u03bf\u03b9\u03ba\u03b9\u03bb\u03af\u03b1 \u03b8\u03c5\u03bc\u03af\u03b6\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03bd\u03ac\u03b3\u03ba\u03b7 \u03c0\u03bf\u03c5 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b1 <a href=\"https:\/\/twodots.gr\/discoformer-ai-analytics-density-score-estimation\/\">AI analytics \u03bc\u03b5 \u03c0\u03c5\u03ba\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1, \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03ac \u03c3\u03ae\u03bc\u03b1\u03c4\u03b1<\/a>: \u03ad\u03bd\u03b1 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03cc score \u03b4\u03b5\u03bd \u03b5\u03be\u03b7\u03b3\u03b5\u03af \u03c0\u03ac\u03bd\u03c4\u03b1 \u03c4\u03b9\u03c2 \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03b5\u03c2 \u03c5\u03c0\u03bf\u03bf\u03bc\u03ac\u03b4\u03b5\u03c2.<\/p>\n<h2 id=\"message-passing-low-pass\">\u0393\u03b9\u03b1\u03c4\u03af \u03c4\u03bf message passing \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03c3\u03c5\u03c7\u03bd\u03ac \u03c3\u03b1\u03bd low-pass \u03c6\u03af\u03bb\u03c4\u03c1\u03bf<\/h2>\n<p>\u0397 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ae \u03b4\u03b9\u03ac\u03b4\u03bf\u03c3\u03b7 \u03b5\u03be\u03bf\u03bc\u03b1\u03bb\u03cd\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03b1\u03c0\u03cc\u03c4\u03bf\u03bc\u03b5\u03c2 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ad\u03c2 \u03c3\u03c4\u03bf\u03bd graph signal. \u03a3\u03c4\u03b7 \u03c6\u03b1\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03bf\u03c0\u03c4\u03b9\u03ba\u03ae, \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af \u03ba\u03c5\u03c1\u03af\u03c9\u03c2 \u03c4\u03b9\u03c2 \u03c7\u03b1\u03bc\u03b7\u03bb\u03ad\u03c2 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03b5\u03b9\u03ce\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03c5\u03c8\u03b7\u03bb\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2. \u0391\u03c5\u03c4\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf \u03cc\u03c4\u03b1\u03bd \u03bf\u03b9 \u03b3\u03b5\u03af\u03c4\u03bf\u03bd\u03b5\u03c2 \u03ad\u03c7\u03bf\u03c5\u03bd \u03c0\u03b1\u03c1\u03cc\u03bc\u03bf\u03b9\u03b5\u03c2 \u03b5\u03c4\u03b9\u03ba\u03ad\u03c4\u03b5\u03c2, \u03b5\u03c0\u03b5\u03b9\u03b4\u03ae \u03bf \u03b8\u03cc\u03c1\u03c5\u03b2\u03bf\u03c2 \u03c5\u03c0\u03bf\u03c7\u03c9\u03c1\u03b5\u03af \u03ba\u03b1\u03b9 \u03c4\u03bf \u03ba\u03bf\u03b9\u03bd\u03cc \u03bc\u03bf\u03c4\u03af\u03b2\u03bf \u03b5\u03bd\u03b9\u03c3\u03c7\u03cd\u03b5\u03c4\u03b1\u03b9.<\/p>\n<p>\u03a3\u03b5 heterophilic \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2, \u03b7 \u03af\u03b4\u03b9\u03b1 \u03b5\u03be\u03bf\u03bc\u03ac\u03bb\u03c5\u03bd\u03c3\u03b7 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b1\u03c6\u03b1\u03b9\u03c1\u03ad\u03c3\u03b5\u03b9 \u03b1\u03ba\u03c1\u03b9\u03b2\u03ce\u03c2 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac \u03c0\u03bf\u03c5 \u03be\u03b5\u03c7\u03c9\u03c1\u03af\u03b6\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03ba\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1. \u0397 \u03bb\u03cd\u03c3\u03b7 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03b1\u03c3\u03c4\u03b1\u03b8\u03b5\u03af \u03c0\u03b1\u03bd\u03c4\u03bf\u03cd \u03c4\u03bf low-pass \u03c6\u03af\u03bb\u03c4\u03c1\u03bf \u03bc\u03b5 \u03ad\u03bd\u03b1 high-pass \u03c6\u03af\u03bb\u03c4\u03c1\u03bf. \u03a4\u03bf CTQW-GNN \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03cc low-frequency \u03ba\u03bb\u03ac\u03b4\u03bf, \u03c0\u03c1\u03bf\u03c3\u03b8\u03ad\u03c4\u03b5\u03b9 all-pass CTQW \u03b4\u03b9\u03ac\u03b4\u03bf\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03ad\u03bd\u03b1\u03bd attention \u03ba\u03bb\u03ac\u03b4\u03bf \u03c0\u03ac\u03bd\u03c9 \u03c3\u03b5 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2.<\/p>\n<aside class=\"td-article-note\">\n<p><strong>\u0397 \u03bb\u03ad\u03be\u03b7 \u00abquantum\u00bb \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c6\u03b5\u03b9 \u03c4\u03bf\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc propagator, \u03cc\u03c7\u03b9 \u03c4\u03bf hardware.<\/strong> \u0397 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b4\u03bf\u03c5\u03bb\u03b5\u03cd\u03b5\u03b9 \u03c3\u03c4\u03bf\u03bd \u03c7\u03ce\u03c1\u03bf \u03c4\u03c9\u03bd N \u03ba\u03cc\u03bc\u03b2\u03c9\u03bd, \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03c4\u03bf\u03bd \u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03bc\u03b5 sparse Krylov \u03ba\u03b1\u03b9 Chebyshev \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03b4\u03b5\u03bd \u03b1\u03c0\u03b1\u03b9\u03c4\u03b5\u03af \u03ba\u03b2\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ae.<\/p>\n<\/aside>\n<p>\u0391\u03c5\u03c4\u03cc\u03c2 \u03bf \u03b4\u03b9\u03b1\u03c7\u03c9\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b3\u03b9\u03b1 \u03bc\u03b9\u03b1 \u03c4\u03b5\u03c7\u03bd\u03b9\u03ba\u03ae \u03b1\u03c0\u03cc\u03c6\u03b1\u03c3\u03b7. \u03a4\u03bf CTQW-GNN \u03b4\u03b5\u03bd \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af\u03c4\u03b1\u03b9 \u03c9\u03c2 \u03c5\u03c0\u03cc\u03c3\u03c7\u03b5\u03c3\u03b7 quantum acceleration, \u03b1\u03bb\u03bb\u03ac \u03c9\u03c2 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03b7 GNN \u03b1\u03c1\u03c7\u03b9\u03c4\u03b5\u03ba\u03c4\u03bf\u03bd\u03b9\u03ba\u03ae. \u0397 \u03c3\u03c9\u03c3\u03c4\u03ae \u03b5\u03c1\u03ce\u03c4\u03b7\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bd \u03b2\u03b5\u03bb\u03c4\u03b9\u03ce\u03bd\u03b5\u03b9 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf failure mode \u03c3\u03c4\u03bf \u03b4\u03b9\u03ba\u03cc \u03bc\u03b1\u03c2 dataset \u03bc\u03b5 \u03b1\u03c0\u03bf\u03b4\u03b5\u03ba\u03c4\u03cc \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2, \u03cc\u03c0\u03c9\u03c2 \u03c3\u03c5\u03bc\u03b2\u03b1\u03af\u03bd\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03bc\u03b5 \u03ba\u03ac\u03b8\u03b5 <a href=\"https:\/\/twodots.gr\/transition-complexity-profile-ai-world-models\/\">benchmark \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c9\u03c3\u03c4\u03cc \u03c0\u03c1\u03bf\u03c6\u03af\u03bb \u03b4\u03c5\u03c3\u03ba\u03bf\u03bb\u03af\u03b1\u03c2<\/a>.<\/p>\n<h2 id=\"faseis-anti-gia-aposvesi\">\u03a0\u03ce\u03c2 \u03bf\u03b9 \u03c6\u03ac\u03c3\u03b5\u03b9\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03bf\u03cd\u03bd \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03c3\u03b2\u03b5\u03c3\u03b7<\/h2>\n<p>\u03a3\u03b5 \u03ad\u03bd\u03b1\u03bd \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03cc continuous-time random walk, \u03bf\u03b9 \u03bc\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2 \u03c6\u03b1\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c3\u03c5\u03bd\u03b9\u03c3\u03c4\u03ce\u03c3\u03b5\u03c2 \u03b1\u03c0\u03bf\u03c3\u03b2\u03ad\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c1\u03c5\u03b8\u03bc\u03bf\u03cd\u03c2. \u03a3\u03c4\u03bf\u03bd continuous-time quantum walk, \u03bf \u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae\u03c2 \u03b5\u03be\u03ad\u03bb\u03b9\u03be\u03b7\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03b1\u03af\u03bf\u03c2: \u03ba\u03ac\u03b8\u03b5 eigenmode \u03b1\u03c0\u03bf\u03ba\u03c4\u03ac \u03c6\u03ac\u03c3\u03b7, \u03b5\u03bd\u03ce \u03c4\u03bf \u03bc\u03ad\u03c4\u03c1\u03bf \u03c4\u03bf\u03c5 \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af\u03c4\u03b1\u03b9. \u0388\u03c4\u03c3\u03b9 \u03bf CTQW \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03c9\u03c2 all-pass \u03c6\u03af\u03bb\u03c4\u03c1\u03bf \u03ba\u03b1\u03b9 \u03b4\u03b5\u03bd \u03ba\u03cc\u03b2\u03b5\u03b9 \u03b1\u03c0\u03cc \u03bc\u03cc\u03bd\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03c4\u03b9\u03c2 \u03bc\u03b5\u03c3\u03b1\u03af\u03b5\u03c2 \u03ae \u03c5\u03c8\u03b7\u03bb\u03ad\u03c2 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2.<\/p>\n<p>\u0397 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03ae \u03b5\u03b3\u03b3\u03cd\u03b7\u03c3\u03b7 \u03ad\u03c7\u03b5\u03b9 \u03cc\u03c1\u03b9\u03b1. \u0391\u03bd \u03bf Hamiltonian \u03bc\u03b5\u03c4\u03b1\u03c4\u03af\u03b8\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03bf\u03bd Laplacian \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7\u03bd \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1 Dirichlet, \u03b7 \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5 CTQW \u03ba\u03bb\u03ac\u03b4\u03bf\u03c5 \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03bd\u03b5\u03b9 \u03b1\u03bd\u03b1\u03bb\u03bb\u03bf\u03af\u03c9\u03c4\u03b7. \u039c\u03b5 \u03c4\u03b7\u03bd \u03c0\u03c1\u03bf\u03b5\u03c0\u03b9\u03bb\u03b5\u03b3\u03bc\u03ad\u03bd\u03b7 sparse adjacency, \u03bf\u03b9 \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03b5\u03af\u03c2 \u03b4\u03af\u03bd\u03bf\u03c5\u03bd \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03c4\u03ce\u03c4\u03b5\u03c1\u03bf \u03cc\u03c1\u03b9\u03bf \u03ba\u03b1\u03c4\u03ac \u03bc\u03ad\u03c3\u03bf \u03cc\u03c1\u03bf \u03c5\u03c0\u03cc \u03c3\u03c5\u03bd\u03b8\u03ae\u03ba\u03b7 \u03bc\u03b7 \u03c3\u03c5\u03bd\u03c4\u03bf\u03bd\u03b9\u03c3\u03bc\u03bf\u03cd. \u039a\u03b1\u03b9 \u03c3\u03c4\u03b9\u03c2 \u03b4\u03cd\u03bf \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2, \u03bf \u03bc\u03b5\u03c4\u03b1\u03b3\u03b5\u03bd\u03ad\u03c3\u03c4\u03b5\u03c1\u03bf\u03c2 mixer \u03b4\u03b5\u03bd \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03bc\u03b7\u03b4\u03b5\u03bd\u03af\u03c3\u03b5\u03b9 \u03c4\u03bf\u03bd CTQW \u03ba\u03bb\u03ac\u03b4\u03bf.<\/p>\n<p>\u0386\u03c1\u03b1 \u03c4\u03bf paper \u03b4\u03b5\u03bd \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c1\u03c7\u03b9\u03ba\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7, nonlinearity \u03ba\u03b1\u03b9 learned projection \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c3\u03c6\u03b1\u03bb\u03ae\u03c2. \u0391\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 branch-level \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b4\u03b5\u03bd \u03c5\u03c0\u03bf\u03c7\u03c1\u03b5\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03ba\u03b1\u03c4\u03b1\u03c1\u03c1\u03b5\u03cd\u03c3\u03b5\u03b9 \u03b5\u03ba\u03b8\u03b5\u03c4\u03b9\u03ba\u03ac. \u0393\u03b9\u03b1 production \u03bf\u03bc\u03ac\u03b4\u03b1, \u03b1\u03c5\u03c4\u03cc \u03bc\u03b5\u03c4\u03b1\u03c6\u03c1\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1\u03c2 \u03b1\u03bd\u03ac layer, ablations \u03ba\u03b1\u03b9 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf \u03c4\u03bf\u03c5 mixing, \u03cc\u03c7\u03b9 \u03c3\u03b5 \u03b5\u03bc\u03c0\u03b9\u03c3\u03c4\u03bf\u03c3\u03cd\u03bd\u03b7 \u03bc\u03cc\u03bd\u03bf \u03c3\u03c4\u03bf \u03cc\u03bd\u03bf\u03bc\u03b1 \u03c4\u03b7\u03c2 \u03b1\u03c1\u03c7\u03b9\u03c4\u03b5\u03ba\u03c4\u03bf\u03bd\u03b9\u03ba\u03ae\u03c2.<\/p>\n<h2 id=\"treis-kladoi-ctqw-gnn\">\u03a4\u03c1\u03b5\u03b9\u03c2 \u03ba\u03bb\u03ac\u03b4\u03bf\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03c1\u03af\u03b1 \u03b5\u03af\u03b4\u03b7 \u03c0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b1\u03c2<\/h2>\n<p>\u03a4\u03bf CTQW-GNN \u03b4\u03b5\u03bd \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03ac \u03cc\u03bb\u03bf \u03c4\u03bf message passing \u03bc\u03b5 \u03ad\u03bd\u03b1\u03bd \u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae. \u03a3\u03c5\u03bd\u03b5\u03bd\u03ce\u03bd\u03b5\u03b9 \u03c4\u03c1\u03b5\u03b9\u03c2 outputs \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03ba\u03ac\u03b8\u03b5 \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf layer. \u0397 \u03c3\u03c7\u03b5\u03b4\u03af\u03b1\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03c5\u03c3\u03b9\u03b1\u03c3\u03c4\u03b9\u03ba\u03ac \u03ad\u03bd\u03b1 ensemble \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ce\u03bd \u03c6\u03b1\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03ba\u03b1\u03b9 \u03c7\u03c9\u03c1\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03b4\u03c1\u03bf\u03bc\u03ce\u03bd.<\/p>\n<div class=\"td-comparison td-comparison-cards td-comparison-cards--horizontal\">\n<div class=\"td-comparison-grid td-comparison-grid--three\">\n<div class=\"td-platform-card\">\n<p class=\"td-comparison-title\">CTQW-based Aggregation<\/p>\n<p>\u0395\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03c4\u03b7 \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03b1\u03af\u03b1 \u03b5\u03be\u03ad\u03bb\u03b9\u03be\u03b7 \u03c3\u03c4\u03b1 node features \u03ba\u03b1\u03b9 \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03c6\u03b1\u03bd\u03c4\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc \u03bc\u03ad\u03c1\u03bf\u03c2. \u03a3\u03c4\u03bf\u03c7\u03b5\u03cd\u03b5\u03b9 \u03bc\u03b5\u03c3\u03b1\u03af\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03c5\u03c8\u03b7\u03bb\u03ad\u03c2 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ad\u03c7\u03b5\u03b9 \u03c4\u03bf\u03bd \u03bc\u03b7 \u03c6\u03b8\u03af\u03bd\u03bf\u03bd\u03c4\u03b1 \u03ba\u03bb\u03ac\u03b4\u03bf \u03b1\u03c0\u03ad\u03bd\u03b1\u03bd\u03c4\u03b9 \u03c3\u03c4\u03bf over-smoothing.<\/p>\n<div class=\"td-badge-row\"><span class=\"td-badge\">All-pass<\/span><span class=\"td-badge\">Energy floor<\/span><\/div>\n<\/div>\n<div class=\"td-platform-card td-platform-card--navy\">\n<p class=\"td-comparison-title\">CTQW-Attention<\/p>\n<p>\u03a7\u03c4\u03af\u03b6\u03b5\u03b9 sparse multi-hop \u03b3\u03c1\u03ac\u03c6\u03bf \u03b1\u03c0\u03cc \u03c4\u03b1 \u03c0\u03bb\u03ac\u03c4\u03b7 \u03c4\u03bf\u03c5 quantum walk \u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 attention. \u03a3\u03c4\u03cc\u03c7\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bd\u03b1 \u03b2\u03c1\u03af\u03c3\u03ba\u03b5\u03b9 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03bf\u03cd\u03c2, \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf\u03c5\u03c2 \u03ba\u03cc\u03bc\u03b2\u03bf\u03c5\u03c2 \u03c0\u03bf\u03c5 \u03bb\u03b5\u03af\u03c0\u03bf\u03c5\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03ac\u03bc\u03b5\u03c3\u03b7 \u03b3\u03b5\u03b9\u03c4\u03bf\u03bd\u03b9\u03ac.<\/p>\n<div class=\"td-badge-row\"><span class=\"td-badge\">Long range<\/span><span class=\"td-badge\">Attention<\/span><\/div>\n<\/div>\n<div class=\"td-platform-card\">\n<p class=\"td-comparison-title\">LF Aggregation<\/p>\n<p>\u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af GAT \u03c9\u03c2 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03cc low-frequency \u03ba\u03bb\u03ac\u03b4\u03bf. \u0394\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af \u03c4\u03b7\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03b5\u03be\u03bf\u03bc\u03ac\u03bb\u03c5\u03bd\u03c3\u03b7\u03c2 \u03c3\u03b5 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2 \u03cc\u03c0\u03bf\u03c5 \u03b7 \u03bf\u03bc\u03bf\u03c6\u03b9\u03bb\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03c3\u03c7\u03c5\u03c1\u03ae \u03ba\u03b1\u03b9 \u03c4\u03bf low-pass \u03c6\u03af\u03bb\u03c4\u03c1\u03bf \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03bd\u03b5\u03b9 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf.<\/p>\n<div class=\"td-badge-row\"><span class=\"td-badge\">GAT<\/span><span class=\"td-badge\">Homophily<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u039f\u03b9 ablations \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03bf\u03c5\u03bd \u03bf\u03b9 \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03b5\u03af\u03c2 \u03c3\u03c4\u03bf Minesweeper \u03c3\u03c5\u03bd\u03b4\u03ad\u03bf\u03c5\u03bd \u03ba\u03ac\u03b8\u03b5 \u03ba\u03bb\u03ac\u03b4\u03bf \u03bc\u03b5 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ae \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ae \u03bf\u03bc\u03bf\u03c6\u03b9\u03bb\u03af\u03b1\u03c2: \u03bf attention \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03b2\u03bf\u03b7\u03b8\u03ac \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf \u03c7\u03b1\u03bc\u03b7\u03bb\u03ac homophily ratios, \u03bf LF \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03c4\u03b1 \u03c5\u03c8\u03b7\u03bb\u03ac \u03ba\u03b1\u03b9 \u03bf CTQW-based \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03c4\u03b9\u03c2 \u03b5\u03bd\u03b4\u03b9\u03ac\u03bc\u03b5\u03c3\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b7 \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1\u03c2. \u0391\u03c5\u03c4\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03c3\u03c7\u03c5\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf \u03b1\u03c0\u03cc \u03bc\u03b9\u03b1 \u03b1\u03cc\u03c1\u03b9\u03c3\u03c4\u03b7 \u03b4\u03ae\u03bb\u03c9\u03c3\u03b7 \u00ab\u03c4\u03bf ensemble \u03b4\u03bf\u03c5\u03bb\u03b5\u03cd\u03b5\u03b9\u00bb, \u03b1\u03bb\u03bb\u03ac \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b5\u03c0\u03b1\u03bd\u03ac\u03bb\u03b7\u03c8\u03b7 \u03c3\u03c4\u03bf \u03b4\u03b9\u03ba\u03cc \u03bc\u03b1\u03c2 \u03b3\u03c1\u03ac\u03c6\u03bf.<\/p>\n<p>\u0397 \u03af\u03b4\u03b9\u03b1 \u03bb\u03bf\u03b3\u03b9\u03ba\u03ae \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03c3\u03b5 production \u03b1\u03c1\u03c7\u03b9\u03c4\u03b5\u03ba\u03c4\u03bf\u03bd\u03b9\u03ba\u03ad\u03c2: \u03b7 \u03cd\u03c0\u03b1\u03c1\u03be\u03b7 \u03c0\u03bf\u03bb\u03bb\u03ce\u03bd branches \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b9\u03ba\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9 \u03c4\u03bf\u03bd \u03c7\u03ce\u03c1\u03bf \u03c0\u03b9\u03b8\u03b1\u03bd\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03c5\u03c7\u03b9\u03ce\u03bd. \u03a4\u03bf monitoring \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03b9 \u03c4\u03bf \u03cc\u03c6\u03b5\u03bb\u03bf\u03c2 \u03c3\u03c4\u03bf\u03bd \u03c3\u03c9\u03c3\u03c4\u03cc \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc, \u03cc\u03c0\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03b5 \u03ad\u03bd\u03b1 <a href=\"https:\/\/twodots.gr\/hybrid-ai-search-papers-with-code\/\">hybrid AI search \u03bc\u03b5 \u03bb\u03ad\u03be\u03b5\u03b9\u03c2, embeddings \u03ba\u03b1\u03b9 \u03b1\u03c3\u03c6\u03b1\u03bb\u03ae fallbacks<\/a>.<\/p>\n<h2 id=\"sparsification-walk-time\">\u03a0\u03ce\u03c2 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03bd\u03c4\u03b1\u03b9 sparsification \u03ba\u03b1\u03b9 walk time<\/h2>\n<p>\u039f \u03c0\u03bb\u03ae\u03c1\u03b7\u03c2 CTQW propagator \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03c5\u03ba\u03bd\u03cc\u03c2. \u0397 \u03c5\u03bb\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03b4\u03b5\u03bd \u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03af\u03b6\u03b5\u03b9 \u03c0\u03bf\u03c4\u03ad \u03bf\u03bb\u03cc\u03ba\u03bb\u03b7\u03c1\u03bf \u03c4\u03bf\u03bd \u03c0\u03c5\u03ba\u03bd\u03cc \u03c0\u03af\u03bd\u03b1\u03ba\u03b1. \u039a\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ac\u03b6\u03b5\u03b9 \u03bc\u03af\u03b1 \u03c6\u03bf\u03c1\u03ac \u03ad\u03bd\u03b1\u03bd \u03bd\u03ad\u03bf \u03b3\u03c1\u03ac\u03c6\u03bf \u03bc\u03b5 Chebyshev expansion, \u03b1\u03c0\u03bf\u03c1\u03c1\u03af\u03c0\u03c4\u03b5\u03b9 \u03c0\u03bb\u03ac\u03c4\u03b7 \u03ba\u03ac\u03c4\u03c9 \u03b1\u03c0\u03cc threshold \u03ba\u03b1\u03b9 \u03ba\u03c1\u03b1\u03c4\u03ac sparse \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2. \u03a3\u03c4\u03b9\u03c2 \u03b4\u03bf\u03ba\u03b9\u03bc\u03ad\u03c2, \u03bc\u03b9\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b9\u03b1 \u03c4\u03b9\u03bc\u03ae epsilon \u03af\u03c3\u03b7 \u03bc\u03b5 5\u00d710<sup>-3<\/sup> \u03ad\u03b4\u03c9\u03c3\u03b5 \u03b9\u03c3\u03bf\u03c1\u03c1\u03bf\u03c0\u03af\u03b1 \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03b5\u03c0\u03af\u03b4\u03bf\u03c3\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03b1\u03c1\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2.<\/p>\n<p>\u03a4\u03bf paper \u03b4\u03bf\u03ba\u03b9\u03bc\u03ac\u03b6\u03b5\u03b9 epsilon \u03b1\u03c0\u03cc 10<sup>-4<\/sup> \u03ad\u03c9\u03c2 5\u00d710<sup>-2<\/sup> \u03c3\u03b5 \u03c4\u03ad\u03c3\u03c3\u03b5\u03c1\u03b1 datasets. \u039f\u03b9 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03b1\u03c0\u03cc 10<sup>-4<\/sup> \u03ad\u03c9\u03c2 10<sup>-2<\/sup> \u03bc\u03ad\u03bd\u03bf\u03c5\u03bd \u03ba\u03bf\u03bd\u03c4\u03ac \u03c3\u03c4\u03b1 \u03ba\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1, \u03b5\u03bd\u03ce \u03c4\u03bf 5\u00d710<sup>-2<\/sup> \u03ba\u03cc\u03b2\u03b5\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03b5\u03c2 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2. \u0391\u03c5\u03c4\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03c9\u03bd \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03ac\u03c4\u03c9\u03bd, \u03cc\u03c7\u03b9 \u03ba\u03b1\u03b8\u03bf\u03bb\u03b9\u03ba\u03ae \u03b1\u03c3\u03c6\u03b1\u03bb\u03ae\u03c2 \u03c1\u03cd\u03b8\u03bc\u03b9\u03c3\u03b7.<\/p>\n<p>\u0397 \u03c0\u03b1\u03c1\u03ac\u03bc\u03b5\u03c4\u03c1\u03bf\u03c2 t \u03b5\u03bb\u03ad\u03b3\u03c7\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b5\u03bc\u03b2\u03ad\u03bb\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03c0\u03ac\u03c4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ae \u03c6\u03ac\u03c3\u03b7\u03c2. \u03a0\u03bf\u03bb\u03cd \u03bc\u03b9\u03ba\u03c1\u03cc t \u03ba\u03c1\u03b1\u03c4\u03ac \u03c4\u03b7\u03bd \u03b5\u03be\u03ad\u03bb\u03b9\u03be\u03b7 \u03c3\u03c7\u03b5\u03b4\u03cc\u03bd \u03c4\u03bf\u03c0\u03b9\u03ba\u03ae. \u039c\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf t \u03b5\u03c0\u03b9\u03c4\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03ba\u03bf\u03c1\u03c5\u03c6\u03ad\u03c2, \u03b1\u03bb\u03bb\u03ac \u03c5\u03c0\u03b5\u03c1\u03b2\u03bf\u03bb\u03b9\u03ba\u03ae \u03c4\u03b9\u03bc\u03ae \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c6\u03ad\u03c1\u03b5\u03b9 \u03ad\u03bd\u03c4\u03bf\u03bd\u03b7 \u03bc\u03af\u03be\u03b7. \u03a4\u03bf Lieb\u2013Robinson-type \u03cc\u03c1\u03b9\u03bf \u03c4\u03b7\u03c2 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 \u03b4\u03b9\u03ba\u03b1\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af \u03bc\u03b9\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03ba\u03c4\u03af\u03bd\u03b1 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 t, \u03c0\u03c1\u03b9\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03c4\u03b5\u03af \u03c4\u03bf empirical threshold.<\/p>\n<p>\u0393\u03b9\u03b1 engineering \u03bf\u03bc\u03ac\u03b4\u03b1, epsilon \u03ba\u03b1\u03b9 t \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b4\u03ad\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 peak memory, \u03bd\u03ad\u03bf \u03bc\u03ad\u03c3\u03bf degree, latency \u03ba\u03b1\u03b9 \u03c0\u03bf\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b1\u03bd\u03ac subgroup. \u0391\u03bd \u03bf sparsified \u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03bc\u03b5\u03b3\u03b1\u03bb\u03ce\u03bd\u03b5\u03b9 \u03c0\u03bf\u03bb\u03cd, \u03b7 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b1\u03c3\u03c5\u03bc\u03c0\u03c4\u03c9\u03c4\u03b9\u03ba\u03ae \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03b1\u03c6\u03ae \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03ba\u03c1\u03cd\u03b2\u03b5\u03b9 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc \u03c0\u03c1\u03b1\u03ba\u03c4\u03b9\u03ba\u03cc \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae.<\/p>\n<h2 id=\"dekatessera-benchmarks\">\u03a4\u03b9 \u03ad\u03b4\u03b5\u03b9\u03be\u03b1\u03bd \u03c4\u03b1 14 benchmarks<\/h2>\n<p>\u0397 \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7 \u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03b5\u03b9 \u03b5\u03bd\u03bd\u03ad\u03b1 heterophilic \u03ba\u03b1\u03b9 \u03c0\u03ad\u03bd\u03c4\u03b5 homophilic datasets. \u0393\u03b9\u03b1 \u03c4\u03b1 \u03b4\u03c5\u03b1\u03b4\u03b9\u03ba\u03ac Minesweeper \u03ba\u03b1\u03b9 Tolokers \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 ROC-AUC, \u03b5\u03bd\u03ce \u03c3\u03c4\u03b1 \u03c5\u03c0\u03cc\u03bb\u03bf\u03b9\u03c0\u03b1 accuracy. \u039f\u03b9 baselines \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03c5\u03bd ResNet \u03c7\u03c9\u03c1\u03af\u03c2 graph structure, \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac GCN, GAT \u03ba\u03b1\u03b9 GraphSAGE, heterophily-specific \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1 \u03ba\u03b1\u03b9 \u03bc\u03b5\u03b8\u03cc\u03b4\u03bf\u03c5\u03c2 \u03c0\u03bf\u03c5 \u03c3\u03c4\u03bf\u03c7\u03b5\u03cd\u03bf\u03c5\u03bd \u03bc\u03b1\u03b6\u03af heterophily \u03ba\u03b1\u03b9 over-smoothing.<\/p>\n<div class=\"td-chart td-chart--metrics\">\n<div class=\"td-chart-head\">\n<p class=\"td-chart-title\">\u0397 \u03ad\u03ba\u03c4\u03b1\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7\u03c2 CTQW-GNN<\/p>\n<p class=\"td-chart-subtitle\">\u03a3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03c4\u03bf arXiv v1 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b4\u03b9\u03ba\u03cc \u03c4\u03bf\u03c5 \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03c0\u03c1\u03c9\u03c4\u03cc\u03ba\u03bf\u03bb\u03bb\u03bf. \u0394\u03b5\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03bd \u03b1\u03bd\u03b5\u03be\u03ac\u03c1\u03c4\u03b7\u03c4\u03b7 \u03b5\u03c0\u03b9\u03ba\u03cd\u03c1\u03c9\u03c3\u03b7 \u03bf\u03cd\u03c4\u03b5 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b5\u03c8\u03b7 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7\u03c2.<\/p>\n<\/div>\n<div class=\"td-chart-body\">\n<div class=\"td-metric-grid\">\n<div class=\"td-metric-card\"><span class=\"td-metric-value\">14<\/span><span class=\"td-metric-label\">datasets \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ac<\/span><span class=\"td-metric-note\">Node classification<\/span><\/div>\n<div class=\"td-metric-card\"><span class=\"td-metric-value\">9<\/span><span class=\"td-metric-label\">heterophilic datasets<\/span><span class=\"td-metric-note\">\u039a\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03bd\u03b5\u03cc\u03c4\u03b5\u03c1\u03b1<\/span><\/div>\n<div class=\"td-metric-card\"><span class=\"td-metric-value\">5<\/span><span class=\"td-metric-label\">homophilic datasets<\/span><span class=\"td-metric-note\">Cora, Citeseer, PubMed, Computers, Photo<\/span><\/div>\n<div class=\"td-metric-card\"><span class=\"td-metric-value\">+1,07%<\/span><span class=\"td-metric-label\">\u03bc\u03ad\u03c3\u03b7 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ae \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7<\/span><span class=\"td-metric-note\">\u0388\u03bd\u03b1\u03bd\u03c4\u03b9 \u03c4\u03bf\u03c5 \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf\u03c5 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03bf\u03c5 paper<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>\u039f\u03b9 \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03b5\u03af\u03c2 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03bd \u03ba\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b1 14 datasets \u03ba\u03b1\u03b9 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ae \u03bc\u03ad\u03c3\u03b7 \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7 1,07% \u03ad\u03bd\u03b1\u03bd\u03c4\u03b9 \u03c4\u03bf\u03c5 \u03b1\u03bc\u03ad\u03c3\u03c9\u03c2 \u03b5\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf\u03c5 score. \u03a3\u03c4\u03b1 \u03c0\u03ad\u03bd\u03c4\u03b5 \u03ce\u03c1\u03b9\u03bc\u03b1 homophilic benchmarks \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03bd \u03ba\u03ad\u03c1\u03b4\u03b7 \u03b1\u03c0\u03cc 0,84% \u03ad\u03c9\u03c2 3,31% \u03b1\u03bd\u03ac dataset, \u03b5\u03bd\u03ce \u03b7 \u03c3\u03cd\u03bd\u03bf\u03c8\u03b7 \u03b5\u03c0\u03b9\u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03b5\u03cd\u03c1\u03bf\u03c2 1,06%\u20133,31% \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03b2\u03b1\u03c3\u03b9\u03ba\u03ad\u03c2 saturated \u03c3\u03c5\u03b3\u03ba\u03c1\u03af\u03c3\u03b5\u03b9\u03c2. \u039f\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03b2\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b1\u03b6\u03af \u03bc\u03b5 splits, metric, hyperparameter budget \u03ba\u03b1\u03b9 variance.<\/p>\n<p>\u0397 \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u03b1\u03bd\u03ac node subgroup \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03c9\u03c2 \u03c0\u03b9\u03bf \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03b7 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03ba\u03bf\u03c1\u03c5\u03c6\u03b1\u03af\u03b1 \u03bc\u03ad\u03c3\u03b7 \u03c4\u03b9\u03bc\u03ae. \u0388\u03bd\u03b1\u03c2 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ac \u03bf\u03bc\u03bf\u03c6\u03b9\u03bb\u03b9\u03ba\u03cc\u03c2 \u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9 \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03bf\u03c5\u03c2 \u03b5\u03c4\u03b5\u03c1\u03bf\u03c6\u03b9\u03bb\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03cc\u03bc\u03b2\u03bf\u03c5\u03c2. \u0397 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03b9\u03ba\u03ae \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 slices \u03b1\u03bd\u03ac node-level homophily, degree, class, recency \u03ba\u03b1\u03b9 business impact. \u0391\u03c5\u03c4\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03af\u03b4\u03b9\u03b1 \u03c0\u03b5\u03b9\u03b8\u03b1\u03c1\u03c7\u03af\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03b9\u03c4\u03bf\u03cd\u03bd \u03c4\u03b1 <a href=\"https:\/\/twodots.gr\/ai-agents-behavioral-testing\/\">behavioral tests \u03b3\u03b9\u03b1 AI \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1<\/a>: \u03b7 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ae \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1 \u03b4\u03b5\u03bd \u03b1\u03c1\u03ba\u03b5\u03af \u03c7\u03c9\u03c1\u03af\u03c2 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf \u03c4\u03c9\u03bd \u03ba\u03c1\u03af\u03c3\u03b9\u03bc\u03c9\u03bd \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b9\u03c6\u03bf\u03c1\u03ce\u03bd.<\/p>\n<aside class=\"td-article-note\">\n<p><strong>\u039c\u03b7\u03bd \u03bc\u03b5\u03c4\u03b1\u03c6\u03c1\u03ac\u03b6\u03b5\u03c4\u03b5 \u03c4\u03bf +1,07% \u03c3\u03b5 \u03c0\u03c9\u03bb\u03ae\u03c3\u03b5\u03b9\u03c2, \u03bb\u03b9\u03b3\u03cc\u03c4\u03b5\u03c1\u03b7 \u03b1\u03c0\u03ac\u03c4\u03b7 \u03ae \u03c7\u03b1\u03bc\u03b7\u03bb\u03cc\u03c4\u03b5\u03c1\u03bf \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2.<\/strong> \u0395\u03af\u03bd\u03b1\u03b9 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ae \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7 benchmark \u03bc\u03ad\u03c3\u03b1 \u03c3\u03c4\u03bf \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf paper. \u0397 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03be\u03af\u03b1 \u03b1\u03c0\u03b1\u03b9\u03c4\u03b5\u03af \u03b4\u03b9\u03ba\u03cc \u03c3\u03b1\u03c2 temporal test set, calibration, thresholds \u03ba\u03b1\u03b9 \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2 \u03bb\u03b1\u03b8\u03ce\u03bd.<\/p>\n<\/aside>\n<h2 id=\"ypologistiko-kostos\">\u03a0\u03bf\u03b9\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2<\/h2>\n<p>\u039f CTQW \u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03b5\u03af\u03c4\u03b1\u03b9 \u03bc\u03af\u03b1 \u03c6\u03bf\u03c1\u03ac \u03bc\u03b5 sparse Chebyshev expansion \u03c4\u03ac\u03be\u03b7\u03c2 20. \u03a3\u03b5 \u03ba\u03ac\u03b8\u03b5 layer, \u03bf CTQW \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03c4\u03bf\u03bd propagator \u03bc\u03b5 Krylov projection \u03ad\u03c9\u03c2 20 \u03b2\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd. \u03a5\u03c0\u03cc \u03c4\u03bf\u03bd \u03ba\u03b1\u03bd\u03cc\u03bd\u03b1 \u03cc\u03c4\u03b9 \u03bf \u03bd\u03ad\u03bf\u03c2 \u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03bd\u03b5\u03b9 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03cc\u03c2 \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b1 \u03b1\u03c1\u03c7\u03b9\u03ba\u03ac edges, \u03bf\u03b9 \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03b5\u03af\u03c2 \u03b4\u03af\u03bd\u03bf\u03c5\u03bd \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03cc per-layer \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03cc \u03c3\u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c4\u03c9\u03bd edges, \u03bc\u03b5 \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae \u03ad\u03c9\u03c2 k+1, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03ad\u03c9\u03c2 21 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03cc \u03cc\u03c1\u03bf.<\/p>\n<p>\u0397 \u03b1\u03c3\u03c5\u03bc\u03c0\u03c4\u03c9\u03c4\u03b9\u03ba\u03ae \u03c0\u03bf\u03bb\u03c5\u03c0\u03bb\u03bf\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b4\u03b5\u03bd \u03b1\u03c1\u03ba\u03b5\u03af \u03b3\u03b9\u03b1 \u03b1\u03b3\u03bf\u03c1\u03ac \u03c5\u03c0\u03bf\u03b4\u03bf\u03bc\u03ae\u03c2 \u03ae SLA. \u03a7\u03c1\u03b5\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 preprocessing time, peak GPU memory, training throughput, inference latency, \u03bc\u03ad\u03b3\u03b5\u03b8\u03bf\u03c2 \u03c4\u03bf\u03c5 CTQW edge set \u03ba\u03b1\u03b9 \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2 \u03b5\u03bd\u03b7\u03bc\u03ad\u03c1\u03c9\u03c3\u03b7\u03c2 \u03cc\u03c4\u03b1\u03bd \u03bf \u03b3\u03c1\u03ac\u03c6\u03bf\u03c2 \u03b1\u03bb\u03bb\u03ac\u03b6\u03b5\u03b9. \u03a3\u03b5 dynamic recommender \u03ae fraud graph, \u03b7 \u03b1\u03bd\u03ac\u03b3\u03ba\u03b7 \u03b5\u03c0\u03b1\u03bd\u03b1\u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ce\u03bd \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03c9\u03bd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b7 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc per-layer \u03c4\u03cd\u03c0\u03bf.<\/p>\n<p>\u0397 \u03b4\u03af\u03ba\u03b1\u03b9\u03b7 baseline \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03c3\u03c5\u03b3\u03ba\u03c1\u03af\u03c3\u03b9\u03bc\u03bf parameter budget \u03ba\u03b1\u03b9 tuning effort. \u03a4\u03bf triple-branch design \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03b9 \u03c7\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03c0\u03bf\u03bb\u03c5\u03c0\u03bb\u03bf\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1. \u0388\u03bd\u03b1 \u03c6\u03b8\u03b7\u03bd\u03cc\u03c4\u03b5\u03c1\u03bf GraphSAGE \u03ae GAT \u03c0\u03bf\u03c5 \u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03b5\u03b9 \u03c4\u03bf operational target \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b7 \u03b1\u03c0\u03cc\u03c6\u03b1\u03c3\u03b7, \u03b1\u03ba\u03cc\u03bc\u03b7 \u03ba\u03b9 \u03b1\u03bd \u03c7\u03ac\u03bd\u03b5\u03b9 \u03bb\u03af\u03b3\u03bf \u03c3\u03b5 aggregate benchmark.<\/p>\n<h2 id=\"epixeirimatiki-aksia\">\u03a0\u03bf\u03cd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03be\u03af\u03b1<\/h2>\n<p>\u03a3\u03c4\u03b1 \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd, \u03c7\u03c1\u03ae\u03c3\u03c4\u03b5\u03c2, \u03c0\u03c1\u03bf\u03ca\u03cc\u03bd\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03b1\u03bb\u03bb\u03b7\u03bb\u03b5\u03c0\u03b9\u03b4\u03c1\u03ac\u03c3\u03b5\u03b9\u03c2 \u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03af\u03b6\u03bf\u03c5\u03bd \u03bc\u03b9\u03ba\u03c4\u03ac \u03bc\u03bf\u03c4\u03af\u03b2\u03b1. \u0397 \u03b4\u03b9\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ce\u03bd graph frequencies \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b2\u03bf\u03b7\u03b8\u03ae\u03c3\u03b5\u03b9 \u03cc\u03c4\u03b1\u03bd \u03b7 \u03b5\u03be\u03b5\u03c1\u03b5\u03c5\u03bd\u03b7\u03c4\u03b9\u03ba\u03ae \u03b1\u03b3\u03bf\u03c1\u03ac \u03ae \u03b7 \u03c3\u03c0\u03ac\u03bd\u03b9\u03b1 \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b9\u03c6\u03bf\u03c1\u03ac \u03c7\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03bc\u03ad\u03c3\u03b1 \u03c3\u03c4\u03b7\u03bd \u03b5\u03be\u03bf\u03bc\u03ac\u03bb\u03c5\u03bd\u03c3\u03b7. \u03a4\u03bf paper \u03b4\u03b5\u03bd \u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af \u03b5\u03bc\u03c0\u03bf\u03c1\u03b9\u03ba\u03cc recommender, \u03ac\u03c1\u03b1 \u03c4\u03bf \u03cc\u03c6\u03b5\u03bb\u03bf\u03c2 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03c7\u03b8\u03b5\u03af \u03bc\u03b5 offline ranking metrics \u03ba\u03b1\u03b9 \u03b5\u03bb\u03b5\u03b3\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf online experiment.<\/p>\n<p>\u03a3\u03c4\u03bf fraud detection, \u03ad\u03bd\u03b1\u03c2 \u03cd\u03c0\u03bf\u03c0\u03c4\u03bf\u03c2 \u03ba\u03cc\u03bc\u03b2\u03bf\u03c2 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c0\u03bf\u03bb\u03bb\u03ad\u03c2 \u03ba\u03b1\u03bd\u03bf\u03bd\u03b9\u03ba\u03ad\u03c2 \u03bf\u03bd\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2. \u0397 heterophily \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf \u03c3\u03ae\u03bc\u03b1, \u03b1\u03bb\u03bb\u03ac \u03bc\u03b9\u03b1 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ae \u03c3\u03cd\u03bd\u03b4\u03b5\u03c3\u03b7 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03bd\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b8\u03ad\u03c3\u03b5\u03b9 \u03b8\u03cc\u03c1\u03c5\u03b2\u03bf \u03ae leakage. \u03a7\u03c1\u03b5\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 temporal splits, \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 false positives \u03ba\u03b1\u03b9 \u03b5\u03c1\u03bc\u03b7\u03bd\u03b5\u03af\u03b1 \u03c3\u03b5 \u03b5\u03c0\u03af\u03c0\u03b5\u03b4\u03bf investigation, \u03cc\u03c7\u03b9 \u03bc\u03cc\u03bd\u03bf node accuracy.<\/p>\n<p>\u03a3\u03b5 knowledge graphs, \u03bf\u03b9 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03bf\u03af \u03c4\u03cd\u03c0\u03bf\u03b9 \u03bf\u03bd\u03c4\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03b5\u03be\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2 \u03c4\u03b1\u03b9\u03c1\u03b9\u03ac\u03b6\u03bf\u03c5\u03bd \u03b5\u03bd\u03bd\u03bf\u03b9\u03bf\u03bb\u03bf\u03b3\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03b7 CTQW-Attention. \u0397 \u03c0\u03c1\u03b1\u03ba\u03c4\u03b9\u03ba\u03ae \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b4\u03b5\u03b8\u03b5\u03af \u03bc\u03b5 \u03cc\u03c3\u03b1 \u03b4\u03b5\u03af\u03c7\u03bd\u03bf\u03c5\u03bd \u03c4\u03b1 <a href=\"https:\/\/twodots.gr\/fred-pos-knowledge-graphs-fotizoun-dedomena-ai\/\">knowledge graphs \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03c1\u03bf\u03ad\u03bb\u03b5\u03c5\u03c3\u03b7 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03af\u03c3\u03c9 \u03b1\u03c0\u03cc \u03ad\u03bd\u03b1 AI<\/a>: \u03ba\u03ac\u03b8\u03b5 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03b7 \u03c3\u03cd\u03bd\u03b4\u03b5\u03c3\u03b7 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03c7\u03bd\u03b7\u03bb\u03ac\u03c3\u03b9\u03bc\u03b7 \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03bc\u03b7\u03bd \u03ba\u03c1\u03cd\u03b2\u03b5\u03b9 \u03bb\u03ac\u03b8\u03bf\u03c2 relationship semantics.<\/p>\n<p>\u03a3\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03c7\u03c1\u03ae\u03c3\u03b7, \u03b7 \u03b1\u03c0\u03cc\u03c6\u03b1\u03c3\u03b7 \u03be\u03b5\u03ba\u03b9\u03bd\u03ac \u03b1\u03c0\u03cc \u03c4\u03bf failure mode. \u0391\u03bd \u03b7 \u03c4\u03c1\u03ad\u03c7\u03bf\u03c5\u03c3\u03b1 baseline \u03ba\u03b1\u03c4\u03b1\u03c1\u03c1\u03ad\u03b5\u03b9 \u03bc\u03b5 \u03b2\u03ac\u03b8\u03bf\u03c2, \u03b1\u03c0\u03bf\u03c4\u03c5\u03b3\u03c7\u03ac\u03bd\u03b5\u03b9 \u03c3\u03b5 heterophilic subgroups \u03ba\u03b1\u03b9 \u03c7\u03ac\u03bd\u03b5\u03b9 \u03b1\u03c0\u03bf\u03b4\u03b5\u03b4\u03b5\u03b9\u03b3\u03bc\u03ad\u03bd\u03b1 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2, \u03c4\u03bf CTQW-GNN \u03b5\u03af\u03bd\u03b1\u03b9 \u03bb\u03bf\u03b3\u03b9\u03ba\u03cc\u03c2 \u03c5\u03c0\u03bf\u03c8\u03ae\u03c6\u03b9\u03bf\u03c2 \u03b3\u03b9\u03b1 pilot. \u0391\u03bd \u03b4\u03b5\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03c4\u03ad\u03c4\u03bf\u03b9\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1, \u03b7 \u03c0\u03bf\u03bb\u03c5\u03c0\u03bb\u03bf\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03b1 \u03b4\u03b9\u03ba\u03b1\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af\u03c4\u03b1\u03b9.<\/p>\n<h2 id=\"periorismoi-preprint\">\u03a0\u03bf\u03b9\u03bf\u03b9 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03af \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03bd\u03bf\u03c5\u03bd<\/h2>\n<p>\u0397 \u03c0\u03b7\u03b3\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 arXiv v1 \u03c4\u03b7\u03c2 21\u03b7\u03c2 \u0391\u03c5\u03b3\u03bf\u03cd\u03c3\u03c4\u03bf\u03c5 2026. \u0397 HTML \u03ad\u03ba\u03b4\u03bf\u03c3\u03b7 \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03b9 placeholder conference \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1, \u03bf\u03c0\u03cc\u03c4\u03b5 \u03b4\u03b5\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03b2\u03ac\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03b9\u03c3\u03c7\u03c5\u03c1\u03b9\u03c3\u03bc\u03cc \u03b1\u03c0\u03bf\u03b4\u03bf\u03c7\u03ae\u03c2 \u03c3\u03b5 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf venue. \u03a4\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03bc\u03b5\u03c4\u03c9\u03c0\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c9\u03c2 claims \u03c4\u03c9\u03bd \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03ad\u03c9\u03bd \u03ad\u03c9\u03c2 \u03cc\u03c4\u03bf\u03c5 \u03c5\u03c0\u03ac\u03c1\u03be\u03b5\u03b9 \u03b1\u03bd\u03b5\u03be\u03ac\u03c1\u03c4\u03b7\u03c4\u03b7 \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae \u03ae peer review.<\/p>\n<p>\u0397 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03ae \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u03b1\u03c6\u03bf\u03c1\u03ac \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c5\u03c0\u03bf\u03b8\u03ad\u03c3\u03b5\u03b9\u03c2 \u03b3\u03b9\u03b1 Hamiltonian, Laplacian, \u03bc\u03b7 \u03c3\u03c5\u03bd\u03c4\u03bf\u03bd\u03b9\u03c3\u03bc\u03cc \u03ba\u03b1\u03b9 non-degenerate mixing. \u03a4\u03bf \u03c0\u03bb\u03ae\u03c1\u03b5\u03c2 \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03bf \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03b9 sparsification, attention, nonlinearities \u03ba\u03b1\u03b9 learnable projection. \u0397 branch-level \u03c0\u03c1\u03bf\u03c3\u03c4\u03b1\u03c3\u03af\u03b1 \u03b4\u03b5\u03bd \u03b9\u03c3\u03bf\u03b4\u03c5\u03bd\u03b1\u03bc\u03b5\u03af \u03bc\u03b5 \u03ba\u03b1\u03b8\u03bf\u03bb\u03b9\u03ba\u03ae \u03b5\u03b3\u03b3\u03cd\u03b7\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 training run.<\/p>\n<p>\u0397 \u03c3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf \u03b3\u03b9\u03b1 \u03af\u03b4\u03b9\u03b1 splits, seeds, hyperparameter search \u03ba\u03b1\u03b9 compute budget. \u0388\u03bd\u03b1 \u03ba\u03bf\u03c1\u03c5\u03c6\u03b1\u03af\u03bf score \u03c3\u03b5 \u03b4\u03b7\u03bc\u03cc\u03c3\u03b9\u03bf benchmark \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03cc \u03bc\u03cc\u03bd\u03bf \u03c4\u03bf\u03c5 production readiness. \u0397 \u03b1\u03c1\u03c7\u03ae \u03b1\u03c5\u03c4\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b5\u03bd\u03c4\u03c1\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b1 <a href=\"https:\/\/twodots.gr\/model-cards-open-weight-ai-governance\/\">model cards \u03c7\u03c9\u03c1\u03af\u03c2 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b9\u03ba\u03ad\u03c2 \u03b5\u03b3\u03b3\u03c5\u03ae\u03c3\u03b5\u03b9\u03c2<\/a>: \u03b7 \u03c4\u03b5\u03ba\u03bc\u03b7\u03c1\u03af\u03c9\u03c3\u03b7 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac controls.<\/p>\n<div class=\"td-decision-band\">\n<p class=\"td-decision-label\">Gate \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf CTQW-GNN pilot<\/p>\n<p><strong>\u03a0\u03c1\u03bf\u03c7\u03c9\u03c1\u03ae\u03c3\u03c4\u03b5 \u03bc\u03cc\u03bd\u03bf \u03b1\u03bd \u03ad\u03c7\u03b5\u03c4\u03b5 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b7 \u03b1\u03c0\u03bf\u03c4\u03c5\u03c7\u03af\u03b1 \u03c4\u03b7\u03c2 baseline \u03c3\u03b5 heterophilic \u03ae \u03b2\u03b1\u03b8\u03b9\u03ac graph regions \u03ba\u03b1\u03b9 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af\u03c4\u03b5 \u03bd\u03b1 \u03b5\u03c0\u03b1\u03bd\u03b1\u03bb\u03ac\u03b2\u03b5\u03c4\u03b5 \u03c4\u03bf \u03c0\u03b5\u03af\u03c1\u03b1\u03bc\u03b1 \u03bc\u03b5 \u03af\u03b4\u03b9\u03bf compute budget.<\/strong><\/p>\n<p>\u0391\u03bd \u03bb\u03b5\u03af\u03c0\u03bf\u03c5\u03bd temporal split, subgroup metrics, memory profile, ablations \u03ba\u03b1\u03b9 \u03c3\u03c7\u03ad\u03b4\u03b9\u03bf rollback, \u03c4\u03bf \u03c3\u03c9\u03c3\u03c4\u03cc \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u00ab\u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b7 \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7\u00bb \u03ba\u03b1\u03b9 \u03cc\u03c7\u03b9 production deployment.<\/p>\n<\/div>\n<p>\u0397 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03b9\u03ba\u03ae \u03b4\u03b9\u03b1\u03ba\u03c5\u03b2\u03ad\u03c1\u03bd\u03b7\u03c3\u03b7 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03b5\u03b9 dataset version, graph snapshot, edge semantics, code commit, seeds, t, epsilon, CTQW degree growth, model artifacts \u03ba\u03b1\u03b9 thresholds. \u0391\u03c5\u03c4\u03ae \u03b7 traceability \u03c4\u03b1\u03b9\u03c1\u03b9\u03ac\u03b6\u03b5\u03b9 \u03bc\u03b5 \u03bc\u03b9\u03b1 <a href=\"https:\/\/twodots.gr\/enterprise-ai-harnesses-diakyvernisi-architektoniki\/\">enterprise AI harness \u03cc\u03c0\u03bf\u03c5 \u03c4\u03b1 controls \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03b1\u03c1\u03c7\u03b9\u03c4\u03b5\u03ba\u03c4\u03bf\u03bd\u03b9\u03ba\u03ae\u03c2<\/a>.<\/p>\n<h2 id=\"plano-aksiologisis\">\u03a0\u03ce\u03c2 \u03b1\u03be\u03b9\u03bf\u03bb\u03bf\u03b3\u03b5\u03af\u03c4\u03b1\u03b9 \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae<\/h2>\n<p>\u0397 \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7 \u03be\u03b5\u03ba\u03b9\u03bd\u03ac \u03bc\u03b5 \u03b4\u03b9\u03ac\u03b3\u03bd\u03c9\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03cc\u03c7\u03b9 \u03bc\u03b5 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03bf\u03c5. \u039c\u03b5\u03c4\u03c1\u03ae\u03c3\u03c4\u03b5 graph-level \u03ba\u03b1\u03b9 node-level homophily, \u03b1\u03c0\u03cc\u03b4\u03bf\u03c3\u03b7 \u03b1\u03bd\u03ac degree \u03ba\u03b1\u03b9 class, Dirichlet energy \u03b1\u03bd\u03ac layer \u03ba\u03b1\u03b9 \u03c4\u03bf \u03b1\u03ba\u03c1\u03b9\u03b2\u03ad\u03c2 business cost \u03c4\u03c9\u03bd \u03bb\u03b1\u03b8\u03ce\u03bd. \u0388\u03c0\u03b5\u03b9\u03c4\u03b1 \u03ba\u03c1\u03b1\u03c4\u03ae\u03c3\u03c4\u03b5 \u03b9\u03c3\u03c7\u03c5\u03c1\u03ad\u03c2, \u03b1\u03c0\u03bb\u03bf\u03cd\u03c3\u03c4\u03b5\u03c1\u03b5\u03c2 baselines \u03ba\u03b1\u03b9 \u03b1\u03bb\u03bb\u03ac\u03be\u03c4\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf \u03ba\u03ac\u03b8\u03b5 \u03c6\u03bf\u03c1\u03ac.<\/p>\n<p>\u03a4\u03bf test protocol \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03c7\u03c9\u03c1\u03af\u03b6\u03b5\u03b9 \u03c4\u03c1\u03af\u03b1 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ac claims: \u03b1\u03bd \u03bf CTQW-based \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03b5\u03af \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1, \u03b1\u03bd \u03bf attention \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03b2\u03c1\u03af\u03c3\u03ba\u03b5\u03b9 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf\u03c5\u03c2 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03bf\u03cd\u03c2 \u03ba\u03cc\u03bc\u03b2\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03b1\u03bd \u03bf LF \u03ba\u03bb\u03ac\u03b4\u03bf\u03c2 \u03c0\u03c1\u03bf\u03c3\u03c4\u03b1\u03c4\u03b5\u03cd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03bf\u03bc\u03bf\u03c6\u03b9\u03bb\u03b9\u03ba\u03ad\u03c2 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2. \u03a7\u03c9\u03c1\u03af\u03c2 ablations, \u03b7 \u03c4\u03b5\u03bb\u03b9\u03ba\u03ae \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7 \u03b4\u03b5\u03bd \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03b1\u03c3\u03c6\u03ac\u03bb\u03b5\u03b9\u03b1 \u03c3\u03c4\u03bf\u03bd \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc \u03c0\u03bf\u03c5 \u03c5\u03c0\u03bf\u03c4\u03af\u03b8\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03bb\u03cd\u03bd\u03b5\u03b9 \u03c4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1.<\/p>\n<div class=\"td-step-list\">\n<p class=\"td-step-list-title\">\u0395\u03c0\u03c4\u03ac gates \u03b3\u03b9\u03b1 \u03ad\u03bd\u03b1 CTQW-GNN pilot<\/p>\n<ol>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 1<\/span><strong>\u039f\u03c1\u03af\u03c3\u03c4\u03b5 \u03c4\u03bf failure mode<\/strong>\n<p>\u039a\u03b1\u03c4\u03b1\u03b3\u03c1\u03ac\u03c8\u03c4\u03b5 \u03b1\u03bd \u03b7 baseline \u03b1\u03c0\u03bf\u03c4\u03c5\u03b3\u03c7\u03ac\u03bd\u03b5\u03b9 \u03b1\u03c0\u03cc heterophily, over-smoothing, \u03b1\u03bd\u03b5\u03c0\u03b1\u03c1\u03ba\u03ad\u03c2 receptive field \u03ae \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03cc \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03b4\u03b5\u03bd \u03bb\u03cd\u03bd\u03b5\u03b9 \u03b7 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2.<\/p>\n<\/li>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 2<\/span><strong>\u03a7\u03b1\u03c1\u03c4\u03bf\u03b3\u03c1\u03b1\u03c6\u03ae\u03c3\u03c4\u03b5 \u03c4\u03b7 \u03b4\u03bf\u03bc\u03ae \u03c4\u03bf\u03c5 \u03b3\u03c1\u03ac\u03c6\u03bf\u03c5<\/strong>\n<p>\u039c\u03b5\u03c4\u03c1\u03ae\u03c3\u03c4\u03b5 graph \u03ba\u03b1\u03b9 node homophily, degree distribution, components, edge types, leakage \u03ba\u03b1\u03b9 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ae \u03c3\u03c4\u03bf\u03bd \u03c7\u03c1\u03cc\u03bd\u03bf.<\/p>\n<\/li>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 3<\/span><strong>\u039a\u03c1\u03b1\u03c4\u03ae\u03c3\u03c4\u03b5 \u03c3\u03c5\u03b3\u03ba\u03c1\u03af\u03c3\u03b9\u03bc\u03b5\u03c2 baselines<\/strong>\n<p>\u03a4\u03c1\u03ad\u03be\u03c4\u03b5 graph-agnostic \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03bf, GraphSAGE \u03ae GAT \u03ba\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac\u03bb\u03bb\u03b7\u03bb\u03b7 heterophily-specific \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf \u03bc\u03b5 \u03ba\u03bf\u03b9\u03bd\u03ac splits \u03ba\u03b1\u03b9 compute budget.<\/p>\n<\/li>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 4<\/span><strong>\u0395\u03c0\u03b1\u03bd\u03b1\u03bb\u03ac\u03b2\u03b5\u03c4\u03b5 \u03c4\u03b1 \u03c4\u03c1\u03af\u03b1 ablations<\/strong>\n<p>\u0391\u03c6\u03b1\u03b9\u03c1\u03ad\u03c3\u03c4\u03b5 \u03b4\u03b9\u03b1\u03b4\u03bf\u03c7\u03b9\u03ba\u03ac CTQW, attention \u03ba\u03b1\u03b9 LF branch \u03ce\u03c3\u03c4\u03b5 \u03bd\u03b1 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03c4\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7 \u03bc\u03b5 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b7 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03af\u03b1.<\/p>\n<\/li>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 5<\/span><strong>\u03a3\u03b1\u03c1\u03ce\u03c3\u03c4\u03b5 t \u03ba\u03b1\u03b9 epsilon<\/strong>\n<p>\u039c\u03b5\u03c4\u03c1\u03ae\u03c3\u03c4\u03b5 \u03bc\u03b1\u03b6\u03af accuracy \u03ae ROC-AUC, \u03bd\u03ad\u03bf \u03bc\u03ad\u03c3\u03bf degree, peak memory \u03ba\u03b1\u03b9 latency\u00b7 \u03bc\u03b7\u03bd \u03b1\u03bd\u03c4\u03b9\u03b3\u03c1\u03ac\u03c8\u03b5\u03c4\u03b5 \u03c4\u03c5\u03c6\u03bb\u03ac \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 paper.<\/p>\n<\/li>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 6<\/span><strong>\u0395\u03bb\u03ad\u03b3\u03be\u03c4\u03b5 subgroups \u03ba\u03b1\u03b9 \u03c7\u03c1\u03cc\u03bd\u03bf<\/strong>\n<p>\u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03c4\u03b5 temporal split \u03ba\u03b1\u03b9 metrics \u03b1\u03bd\u03ac homophily, degree, class \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2, \u03cc\u03c7\u03b9 \u03bc\u03cc\u03bd\u03bf aggregate score.<\/p>\n<\/li>\n<li><span class=\"td-step-kicker\">\u0392\u03ae\u03bc\u03b1 7<\/span><strong>\u0391\u03c0\u03bf\u03c6\u03b1\u03c3\u03af\u03c3\u03c4\u03b5 deploy, narrow \u03ae stop<\/strong>\n<p>\u03a0\u03c1\u03bf\u03c7\u03c9\u03c1\u03ae\u03c3\u03c4\u03b5 \u03bc\u03cc\u03bd\u03bf \u03b1\u03bd \u03c4\u03bf \u03cc\u03c6\u03b5\u03bb\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c0\u03b1\u03bd\u03b1\u03bb\u03ae\u03c8\u03b9\u03bc\u03bf, \u03c4\u03bf \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2 \u03b1\u03c0\u03bf\u03b4\u03b5\u03ba\u03c4\u03cc \u03ba\u03b1\u03b9 \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd monitoring, rollback \u03ba\u03b1\u03b9 \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03b7 \u03b4\u03b9\u03b5\u03c1\u03b5\u03cd\u03bd\u03b7\u03c3\u03b7.<\/p>\n<\/li>\n<\/ol>\n<\/div>\n<p>\u0415\u0434\u0438\u043d <a href=\"https:\/\/twodots.gr\/rail-ai-4-erotimata-prin-tin-paragogi\/\">RAIL \u03bc\u03b5 \u03c3\u03b1\u03c6\u03ae \u03b5\u03c1\u03c9\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae<\/a> \u03b2\u03bf\u03b7\u03b8\u03ac \u03bd\u03b1 \u03bc\u03b5\u03c4\u03b1\u03c4\u03c1\u03b1\u03c0\u03b5\u03af \u03c4\u03bf paper \u03c3\u03b5 \u03b5\u03bb\u03b5\u03b3\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03c0\u03b5\u03af\u03c1\u03b1\u03bc\u03b1. \u03a4\u03bf \u03c0\u03c1\u03b1\u03ba\u03c4\u03b9\u03ba\u03cc \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 GNN \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b3\u03af\u03bd\u03b5\u03b9 \u00ab\u03ba\u03b2\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u00bb. \u0395\u03af\u03bd\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03b7 \u03b4\u03b9\u03ac\u03b4\u03bf\u03c3\u03b7 \u03c3\u03b5 \u03b3\u03c1\u03ac\u03c6\u03bf\u03c5\u03c2 \u03b4\u03b5\u03bd \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03b9\u03c3\u03bf\u03b4\u03c5\u03bd\u03b1\u03bc\u03b5\u03af \u03bc\u03b5 \u03c3\u03c5\u03bd\u03b5\u03c7\u03ae \u03b5\u03be\u03bf\u03bc\u03ac\u03bb\u03c5\u03bd\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03ba\u03ac\u03b8\u03b5 \u03c0\u03c1\u03cc\u03c3\u03b8\u03b5\u03c4\u03bf\u03c2 \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03b9 \u03c4\u03bf \u03cc\u03c6\u03b5\u03bb\u03cc\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf \u03b4\u03b9\u03ba\u03cc \u03bc\u03b1\u03c2 failure mode.<\/p>\n<section class=\"td-service-cta\">\n<div class=\"td-service-cta-content\">\n<p class=\"td-service-cta-kicker\">\u0391\u03c0\u03cc \u03c4\u03bf graph AI paper \u03c3\u03b5 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf pilot<\/p>\n<h3>\u03a3\u03c7\u03b5\u03b4\u03b9\u03ac\u03c3\u03c4\u03b5 \u03bc\u03b1\u03b6\u03af benchmark, data pipeline \u03ba\u03b1\u03b9 \u03b1\u03c3\u03c6\u03b1\u03bb\u03ad\u03c2 production gate<\/h3>\n<p>\u0397 TWO DOTS \u03c7\u03b1\u03c1\u03c4\u03bf\u03b3\u03c1\u03b1\u03c6\u03b5\u03af \u03c4\u03bf business use case, \u03bf\u03c1\u03b3\u03b1\u03bd\u03ce\u03bd\u03b5\u03b9 task-specific test sets \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03b9 \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1, \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1, monitoring \u03ba\u03b1\u03b9 \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03bf handoff \u03c0\u03c1\u03b9\u03bd \u03ad\u03bd\u03b1 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03bf AI \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03c0\u03b7\u03c1\u03b5\u03ac\u03c3\u03b5\u03b9 \u03c0\u03b5\u03bb\u03ac\u03c4\u03b7 \u03ae \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1.<\/p>\n<div class=\"td-service-cta-actions\"><a class=\"td-service-cta-button\" href=\"https:\/\/twodots.gr\/aftomatismoi-epicheiriseon-ai\/\">\u0394\u03b5\u03af\u03c4\u03b5 \u03c4\u03bf\u03c5\u03c2 \u0391\u03c5\u03c4\u03bf\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2 \u0395\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd &amp; AI<\/a><\/div>\n<\/div>\n<\/section>\n<section id=\"sychnes-erotiseis\" class=\"td-faq-section\">\n<div class=\"td-faq\">\n<p class=\"td-faq-heading\">\u0427\u0435\u0441\u0442\u043e \u0437\u0430\u0434\u0430\u0432\u0430\u043d\u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u0438<\/p>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf CTQW-GNN;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u0395\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03b5\u03c1\u03b5\u03c5\u03bd\u03b7\u03c4\u03b9\u03ba\u03ae \u03b1\u03c1\u03c7\u03b9\u03c4\u03b5\u03ba\u03c4\u03bf\u03bd\u03b9\u03ba\u03ae graph neural network \u03c0\u03bf\u03c5 \u03c3\u03c5\u03bd\u03b4\u03c5\u03ac\u03b6\u03b5\u03b9 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03c0\u03c1\u03bf\u03c3\u03bf\u03bc\u03bf\u03b9\u03c9\u03bc\u03ad\u03bd\u03bf continuous-time quantum walk, attention \u03c3\u03b5 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 low-frequency GAT.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b2\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ae\u03c2;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u038c\u03c7\u03b9. \u03a4\u03bf paper \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03c4\u03bf\u03bd \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03b1\u03af\u03bf propagator \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03c3\u03c4\u03bf\u03bd \u03c7\u03ce\u03c1\u03bf \u03c4\u03c9\u03bd \u03ba\u03cc\u03bc\u03b2\u03c9\u03bd \u03bc\u03b5 sparse Krylov \u03ba\u03b1\u03b9 Chebyshev \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03c3\u03b5\u03b9\u03c2.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a0\u03bf\u03b9\u03b1 \u03b4\u03cd\u03bf \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 \u03b5\u03c0\u03b9\u03c7\u03b5\u03b9\u03c1\u03b5\u03af \u03bd\u03b1 \u03bb\u03cd\u03c3\u03b5\u03b9;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u03a3\u03c4\u03bf\u03c7\u03b5\u03cd\u03b5\u03b9 \u03c4\u03b7 \u03c7\u03b1\u03bc\u03b7\u03bb\u03ae \u03b5\u03c0\u03af\u03b4\u03bf\u03c3\u03b7 \u03c3\u03b5 heterophilic graphs \u03ba\u03b1\u03b9 \u03c4\u03bf over-smoothing \u03c0\u03bf\u03c5 \u03ba\u03ac\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u03ba\u03cc\u03bc\u03b2\u03c9\u03bd \u03bf\u03bb\u03bf\u03ad\u03bd\u03b1 \u03c0\u03b9\u03bf \u03cc\u03bc\u03bf\u03b9\u03b5\u03c2 \u03cc\u03c3\u03bf \u03b1\u03c5\u03be\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c4\u03b1 layers.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u0393\u03b9\u03b1\u03c4\u03af \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03c4\u03c1\u03b5\u03b9\u03c2 aggregators;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c7\u03ad\u03c2 \u03b5\u03bd\u03cc\u03c2 \u03b3\u03c1\u03ac\u03c6\u03bf\u03c5 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5\u03c3\u03b1\u03af\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03c5\u03c8\u03b7\u03bb\u03ad\u03c2 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2, \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03b5\u03c2 \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2 \u03ae \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ae low-frequency \u03b5\u03be\u03bf\u03bc\u03ac\u03bb\u03c5\u03bd\u03c3\u03b7.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a4\u03b9 \u03ad\u03b4\u03b5\u03b9\u03be\u03b1\u03bd \u03c4\u03b1 14 benchmarks;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u039f\u03b9 \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03b5\u03af\u03c2 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03bf\u03c5\u03bd \u03c4\u03bf \u03ba\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03c3\u03b5 \u03b5\u03bd\u03bd\u03ad\u03b1 heterophilic \u03ba\u03b1\u03b9 \u03c0\u03ad\u03bd\u03c4\u03b5 homophilic datasets, \u03bc\u03b5 \u03bc\u03ad\u03c3\u03b7 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ae \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b7 1,07% \u03ad\u03bd\u03b1\u03bd\u03c4\u03b9 \u03c4\u03bf\u03c5 \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf\u03c5 score \u03c4\u03bf\u03c5 \u03c0\u03b5\u03b9\u03c1\u03ac\u03bc\u03b1\u03c4\u03bf\u03c2.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a4\u03b9 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5\u03bd \u03bf\u03b9 \u03c0\u03b1\u03c1\u03ac\u03bc\u03b5\u03c4\u03c1\u03bf\u03b9 t \u03ba\u03b1\u03b9 epsilon;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u03a4\u03bf t \u03b5\u03c0\u03b7\u03c1\u03b5\u03ac\u03b6\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b5\u03bc\u03b2\u03ad\u03bb\u03b5\u03b9\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03c6\u03ac\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03c0\u03ac\u03c4\u03bf\u03c5, \u03b5\u03bd\u03ce \u03c4\u03bf epsilon \u03ba\u03b1\u03b8\u03bf\u03c1\u03af\u03b6\u03b5\u03b9 \u03c0\u03cc\u03c3\u03b5\u03c2 CTQW \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9\u03c2 \u03b4\u03b9\u03b1\u03c4\u03b7\u03c1\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf\u03bd sparse \u03b3\u03c1\u03ac\u03c6\u03bf.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a0\u03bf\u03cd \u03b1\u03be\u03af\u03b6\u03b5\u03b9 \u03bd\u03b1 \u03b4\u03bf\u03ba\u03b9\u03bc\u03b1\u03c3\u03c4\u03b5\u03af;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u03a3\u03b5 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 \u03cc\u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03bc\u03b5\u03c4\u03c1\u03b7\u03b8\u03b5\u03af \u03bc\u03b9\u03ba\u03c4\u03ae \u03bf\u03bc\u03bf\u03c6\u03b9\u03bb\u03af\u03b1, over-smoothing \u03ae \u03b1\u03bd\u03ac\u03b3\u03ba\u03b7 \u03b3\u03b9\u03b1 \u03bc\u03b1\u03ba\u03c1\u03b9\u03bd\u03ad\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2, \u03cc\u03c0\u03c9\u03c2 \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b1 recommendation, fraud \u03ba\u03b1\u03b9 knowledge-graph workloads.<\/p>\n<\/div>\n<\/details>\n<details class=\"td-faq-item\">\n<summary class=\"td-faq-title\">\u03a0\u03bf\u03b9\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc gate \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf production;<\/summary>\n<div class=\"td-faq-content\">\n<p>\u039d\u03b1 \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03b1\u03c7\u03b8\u03b5\u03af \u03c4\u03bf \u03cc\u03c6\u03b5\u03bb\u03bf\u03c2 \u03c3\u03b5 temporal \u03ba\u03b1\u03b9 subgroup tests \u03bc\u03b5 \u03b4\u03af\u03ba\u03b1\u03b9\u03b5\u03c2 baselines, \u03b1\u03c0\u03bf\u03b4\u03b5\u03ba\u03c4\u03ae \u03bc\u03bd\u03ae\u03bc\u03b7 \u03ba\u03b1\u03b9 latency, \u03c3\u03b1\u03c6\u03ae ablations, monitoring \u03ba\u03b1\u03b9 rollback.<\/p>\n<\/div>\n<\/details>\n<\/div>\n<\/section>\n<div class=\"td-source-list\">\n<p id=\"piges\" class=\"td-source-list-title\">\u0418\u0437\u0442\u043e\u0447\u043d\u0438\u0446\u0438<\/p>\n<ul>\n<li><a href=\"https:\/\/arxiv.org\/abs\/2608.20738\" target=\"_blank\" rel=\"noopener\">arXiv \u2014 Continuous-Time Quantum Walks based Graph Neural Network<\/a><\/li>\n<li><a href=\"https:\/\/pytorch-geometric.readthedocs.io\/en\/latest\/tutorial\/create_gnn.html\" target=\"_blank\" rel=\"noopener\">PyTorch Geometric \u2014 Creating Message Passing Networks<\/a><\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/2302.11640\" target=\"_blank\" rel=\"noopener\">arXiv \u2014 A Critical Look at Evaluation of GNNs under Heterophily<\/a><\/li>\n<li><a href=\"https:\/\/arxiv.org\/abs\/1710.10903\" target=\"_blank\" rel=\"noopener\">arXiv \u2014 Graph Attention Networks<\/a><\/li>\n<\/ul>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u03a0\u03ce\u03c2 \u03c4\u03bf CTQW-GNN \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03c0\u03c1\u03bf\u03c3\u03bf\u03bc\u03bf\u03b9\u03c9\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 \u03ba\u03b2\u03b1\u03bd\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03ac\u03c4\u03bf\u03c5\u03c2 \u03b3\u03b9\u03b1 heterophily \u03ba\u03b1\u03b9 over-smoothing \u03ba\u03b1\u03b9 \u03c4\u03b9 \u03c7\u03c1\u03b5\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf production.<\/p>","protected":false},"author":1,"featured_media":90639,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_gspb_post_css":"","content-type":"","footnotes":""},"categories":[199],"tags":[19812,19813,7477,19815,19814],"class_list":["post-90619","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-techniti-noimosyni","tag-ctqw-gnn","tag-graph-neural-networks","tag-machine-learning","tag-over-smoothing","tag-quantum-inspired-ai"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":7}},"_links":{"self":[{"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/posts\/90619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/comments?post=90619"}],"version-history":[{"count":1,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/posts\/90619\/revisions"}],"predecessor-version":[{"id":90640,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/posts\/90619\/revisions\/90640"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/media\/90639"}],"wp:attachment":[{"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/media?parent=90619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/categories?post=90619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/twodots.gr\/bg\/wp-json\/wp\/v2\/tags?post=90619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}