{"id":44745,"date":"2023-08-29T20:50:07","date_gmt":"2023-08-29T12:50:07","guid":{"rendered":"https:\/\/swarma.org\/?p=44745"},"modified":"2023-08-29T20:50:07","modified_gmt":"2023-08-29T12:50:07","slug":"%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e4%b8%8e%e6%95%b0%e5%ad%a6%e8%af%bb%e4%b9%a6%e4%bc%9a%e5%90%af%e5%8a%a8%ef%bc%9aai-for-math%ef%bc%8cmath-for-ai","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=44745","title":{"rendered":"\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1aAI for Math\uff0cMath for AI"},"content":{"rendered":"<div class='wxsyncmain'>\n<section powered-by=\"xiumi.us\" style=\"margin-bottom: 0px;outline: 0px;letter-spacing: 0.544px;white-space: normal;color: rgb(63, 63, 63);font-family: PingFangSC-light;font-size: 15px;background-color: rgb(255, 255, 255);visibility: visible;\" data-mpa-powered-by=\"yiban.io\">\n<section style=\"outline: 0px;display: inline-block;width: 661px;vertical-align: top;background-color: rgb(246, 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4px;background-color: rgb(221, 239, 249);overflow: hidden;\" data-width=\"100%\"><br  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ece\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u5230 AI \u53d1\u73b0\u6570\u5b66\u89c4\u5f8b\uff0c\u4ee5\u53ca\u51e0\u4f55\u62d3\u6251\u3001\u52a8\u529b\u7cfb\u7edf\u7b49\u6570\u5b66\u5206\u652f\u5728AI\u7684\u5e94\u7528\uff0c\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u4e00\u76f4\u6709\u7740\u975e\u5e38\u5bc6\u5207\u7684\u8054\u7cfb\u3002\u5728\u5373\u5c06\u53ec\u5f00\u7684\u8bfb\u4e66\u4f1a\u4e2d\uff0c\u6211\u4eec\u5c06\u4ece AI\u3000for\u3000Math\uff0cMath\u3000for\u3000AI \u4e24\u4e2a\u65b9\u9762\u6df1\u5165\u63a2\u8ba8\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u7684\u5bc6\u5207\u8054\u7cfb\u3002\u9996\u5148\uff0c\u6211\u4eec\u5c06\u6982\u8ff0\u4eba\u5de5\u667a\u80fd\u5728\u6570\u5b66\u7684\u5e94\u7528\uff0c\u5e76\u6df1\u5165\u63a2\u8ba8\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u63a8\u7406\u3001\u5b9a\u7406\u81ea\u52a8\u8bc1\u660e\u3001AI\u53d1\u73b0\u6570\u5b66\u89c4\u5f8b\u3001\u7b26\u53f7\u8ba1\u7b97\u7b49\u65b9\u5411\u7684\u7814\u7a76\u5de5\u4f5c\u3002\u968f\u540e\uff0c\u6211\u4eec\u5c06\u8f6c\u5411\u5927\u6a21\u578b\u4e0e\u795e\u7ecf\u7f51\u7edc\u7684\u6570\u5b66\u57fa\u7840\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u63a2\u8ba8\u51e0\u4f55\u4e0e\u62d3\u6251\u5728\u673a\u5668\u5b66\u4e60\u7684\u5e94\u7528\u3002\u6211\u4eec\u7684\u76ee\u7684\u662f\u901a\u8fc7\u8fd9\u6837\u6df1\u5165\u7684\u63a2\u8ba8\uff0c\u4e0e\u5927\u5bb6\u4e00\u8d77\u4ea4\u6d41\u5b66\u4e60\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u7684\u8054\u7cfb\uff0c\u540c\u65f6\u63ed\u793a\u672a\u6765\u53ef\u80fd\u7684\u7814\u7a76\u53d1\u5c55\u65b9\u5411<strong>\u3002<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><img class=\"rich_pages wxw-img\" data-backh=\"215\" data-backw=\"562\" data-ratio=\"0.38333333333333336\"  data-type=\"png\" data-w=\"1080\" style=\"width: 100%;height: auto;\" src=\"\/wp-content\/uploads\/2023\/08\/wxsync-2023-08-135393c440eccb26d342262039387497.png\"  \/><\/section>\n<p style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;\"><br  \/><\/p>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><strong><br  \/><\/strong><\/span><\/section>\n<section data-role=\"title\" data-tools=\"135\u7f16\u8f91\u5668\" data-id=\"131868\" style=\"letter-spacing: 0.578px;white-space: normal;\">\n<section style=\"margin: 10px auto;display: flex;justify-content: center;\">\n<section>\n<section data-width=\"100%\" style=\"width: 146.891px;\">\n<section data-width=\"30%\" style=\"width: 44.0625px;height: 10px;background-color: rgb(181, 234, 242);overflow: hidden;\"><br  \/><\/section>\n<\/section>\n<section style=\"margin-top: -6px;padding-left: 4px;\">\n<section style=\"padding: 5px 25px;font-size: 16px;color: rgb(255, 255, 255);background-color: rgb(14, 115, 220);\"><span style=\"font-size: 18px;\"><strong data-brushtype=\"text\">\u4e0e\u590d\u6742\u79d1\u5b66\u7684\u5173\u7cfb<\/strong><\/span><\/section>\n<section data-width=\"100%\" style=\"width: 142.891px;height: 4px;background-color: rgb(221, 239, 249);overflow: hidden;\"><br  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;letter-spacing: 0.578px;white-space: normal;line-height: 1.75em;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.034em;\">\u6570\u5b66\u7ed3\u6784\u672c\u8eab\u53ef\u4ee5\u770b\u4f5c\u4e00\u4e2a\u590d\u6742\u7cfb\u7edf\uff0c\u4ece\u5206\u6790\u3001\u4ee3\u6570\u3001\u51e0\u4f55\u5230\u62d3\u6251\uff0c\u6570\u5b66\u5bf9\u8c61\u6784\u6210\u4e86\u76f8\u4e92\u5173\u8054\u7684\u590d\u6742\u7cfb\u7edf\u3002<\/span><span style=\"color: rgb(63, 63, 63);font-size: 15px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.034em;\">\u53e6\u4e00\u65b9\u9762\uff0c\u590d\u6742\u79d1\u5b66\u7684\u7814\u7a76\u4e5f\u79bb\u4e0d\u5f00\u6570\u5b66\u5de5\u5177\u3002<\/span><span style=\"color: rgb(63, 63, 63);font-size: 15px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.034em;\">\u6df7\u6c8c\u3001\u975e\u7ebf\u6027\u7b49\u65e2\u662f\u91cd\u8981\u7684\u6570\u5b66\u6982\u5ff5\uff0c\u4e5f\u662f\u590d\u6742\u79d1\u5b66\u7684\u57fa\u7840\u6982\u5ff5\u3002<\/span><span style=\"color: rgb(63, 63, 63);font-size: 15px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.034em;\">\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u6df1\u5165\u53d1\u5c55\uff0c\u5c06\u8fdb\u4e00\u6b65\u52a0\u5f3a\u6570\u5b66\u4e0e\u590d\u6742\u79d1\u5b66\u7684\u6df1\u523b\u8054\u7cfb\u3002<\/span><span style=\"color: rgb(63, 63, 63);font-size: 15px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.034em;\">\u6570\u5b66\u4e0e\u590d\u6742\u79d1\u5b66\u7684\u65b9\u6cd5\u6b63\u9010\u6b65\u6e17\u5165\u5230\u4eba\u5de5\u667a\u80fd\u7684\u7814\u7a76\uff0c\u5e76\u4e3a\u6784\u5efa\u795e\u7ecf\u7f51\u7edc\u4e0e\u5927\u6a21\u578b\u7684\u53ef\u89e3\u91ca\u6027\u63d0\u4f9b\u575a\u5b9e\u7684\u7406\u8bba\u57fa\u7840\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4e0e\u5df2\u6709\u7684\u673a\u5668\u5b66\u4e60\u7406\u8bba\u4e0d\u540c\uff0c\u5927\u6a21\u578b\u57fa\u7840\u7406\u8bba\u5e76\u4e0d\u5173\u6ce8\u5177\u4f53\u7684\u4f18\u5316\u7b97\u6cd5\u6216\u5176\u6cdb\u5316\u8868\u73b0\uff0c\u800c\u5c1d\u8bd5\u5206\u6790\u6a21\u578b\u8bad\u7ec3\u7684\u7406\u60f3\u76ee\u6807\u662f\u4ec0\u4e48\u3002\u901a\u8fc7\u5206\u6790\u7406\u60f3\u60c5\u51b5\u5f97\u5230\u7684\u7406\u8bba\u867d\u7136\u7b80\u5355\u62bd\u8c61\uff0c\u4f46\u5374\u80fd\u63cf\u7ed8\u5404\u79cd\u6a21\u578b\u5404\u79cd\u6570\u636e\u4e0b\u7684\u5171\u6027\uff0c\u8fdb\u800c\u5e2e\u52a9\u4eba\u4eec\u8bbe\u8ba1\u51fa\u66f4\u597d\u7684\u7b97\u6cd5\uff0c\u6216\u8005\u5bf9\u6a21\u578b\u8868\u73b0\u6709\u66f4\u6df1\u523b\u7684\u7406\u89e3\u3002\u8fd9\u548c\u7269\u7406\u5b66\u7684\u601d\u7ef4\u65b9\u5f0f\u975e\u5e38\u7c7b\u4f3c\uff1a\u7269\u7406\u5b66\u5bb6\u4f1a\u8003\u8651\u5728\u771f\u7a7a\u4e2d\u6216\u8005\u65e0\u6469\u64e6\u7684\u60c5\u51b5\u4e0b\u7684\u4e8b\u7269\u4e0e\u73b0\u8c61\uff0c\u54ea\u6015\u8fd9\u4e9b\u5047\u8bbe\u5728\u73b0\u5b9e\u4e2d\u5e76\u4e0d\u5b8c\u7f8e\u6210\u7acb\u3002\u5bf9\u4e8e\u590d\u6742\u79d1\u5b66\u6765\u8bf4\uff0c\u8fd9\u4e2a\u601d\u8def\u4e5f\u5e94\u8be5\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u5207\u5165\u53e3\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;\">\n<section style=\"margin: 10px auto;display: flex;justify-content: center;\">\n<section>\n<section style=\"width: 100%;\" data-width=\"100%\">\n<section style=\"width: 30%;height: 10px;background-color: rgb(181, 234, 242);overflow: hidden;\" data-width=\"30%\"><br  \/><\/section>\n<\/section>\n<section style=\"padding-left: 4px;margin-top: -6px;\">\n<section style=\"font-size: 16px;color: rgb(255, 255, 255);background-color: rgb(14, 115, 220);padding: 5px 25px;\"><span style=\"font-size: 18px;\"><strong data-brushtype=\"text\">\u53d1\u8d77\u4eba\u4ecb\u7ecd<\/strong><\/span><\/section>\n<section style=\"width: 100%;height: 4px;background-color: rgb(221, 239, 249);overflow: hidden;\" data-width=\"100%\"><br  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;text-align: center;margin-left: 8px;margin-right: 8px;\"><img class=\"rich_pages wxw-img\" data-ratio=\"1.2564814814814815\"  data-type=\"jpeg\" data-w=\"1080\" style=\"width: 156px;height: 196px;\" src=\"\/wp-content\/uploads\/2023\/08\/wxsync-2023-08-bb91f9ca775d57d6a6ed6bc17bd1c74c.jpeg\"  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(63, 63, 63);\"><strong><span style=\"font-size: 15px;\">\u9648\u5c0f\u6768<\/span><\/strong><\/span><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff0c\u540c\u6d4e\u5927\u5b66\u7279\u8058\u7814\u7a76\u5458\u30022014\u5e745\u6708\u83b7\u5f97\u7f8e\u56fd\u5723\u6bcd\u5927\u5b66\u6570\u5b66\u535a\u58eb\u5b66\u4f4d\uff0c2014-2016\u5e74\u5728\u6fb3\u95e8\u5927\u5b66\u4ece\u4e8b\u535a\u58eb\u540e\u7814\u7a76\uff0c\u5e76\u4e8e2016\u5e74\u5e95\u5165\u804c\u540c\u6d4e\u5927\u5b66\u3002\u9648\u5c0f\u6768\u7684\u4e3b\u8981\u7814\u7a76\u65b9\u5411\u4e3a\u9ece\u66fc\u51e0\u4f55\uff0c\u5728 Geometry and Topology, Advances in Mathematics\u7b49\u671f\u520a\u53d1\u8868\u4e86\u591a\u7bc7\u7814\u7a76\u8bba\u6587\u3002\u8fd1\u671f\uff0c\u9648\u5c0f\u6768\u4e0e\u7814\u7a76\u56e2\u961f\u5f00\u5c55\u4e86\u5927\u6a21\u578b\u5728\u57fa\u7840\u6570\u5b66\u7684\u5e94\u7528\u7814\u7a76\uff0c\u5e76\u8ba1\u5212\u5f00\u53d1\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u7528\u4e8e\u53d1\u73b0\u6570\u5b66\u89c4\u5f8b\uff0c\u6784\u9020\u6570\u5b66\u731c\u60f3\u53cd\u4f8b\u7b49\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;text-align: center;margin-left: 8px;margin-right: 8px;\"><img class=\"rich_pages wxw-img\" data-ratio=\"1.262037037037037\"  data-type=\"jpeg\" data-w=\"1080\" style=\"width: 165px;height: 208px;\" src=\"\/wp-content\/uploads\/2023\/08\/wxsync-2023-08-e3eb8d344e430b71e502321e10320c12.jpeg\"  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8881\u6d0b<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff0c\u6e05\u534e\u5927\u5b66\u4ea4\u53c9\u4fe1\u606f\u5b66\u9662\u52a9\u7406\u6559\u6388\u30022012\u5e74\u6bd5\u4e1a\u4e8e\u5317\u4eac\u5927\u5b66\u8ba1\u7b97\u673a\u7cfb\uff0c2018\u5e74\u83b7\u5f97\u7f8e\u56fd\u5eb7\u5948\u5c14\u5927\u5b66\u8ba1\u7b97\u673a\u535a\u58eb\u5b66\u4f4d\uff0c\u5e08\u4eceRobert Kleinberg\u6559\u6388\u3002\u5728\u535a\u58eb\u671f\u95f4\uff0c\u4e8e2014\u5e74-2015\u5e74\u524d\u5f80\u5fae\u8f6f\u65b0\u82f1\u683c\u5170\u7814\u7a76\u9662\u505a\u8bbf\u95ee\u5b66\u751f\uff0c\u5e76\u4e8e2016\u5e74\u79cb\u5b63\u524d\u5f80\u7f8e\u56fd\u666e\u6797\u65af\u987f\u5927\u5b66\u505a\u8bbf\u95ee\u5b66\u751f\u30022018-2019\u5e74\u524d\u5f80\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u5927\u6570\u636e\u79d1\u5b66\u5b66\u9662\uff08MIFODS\uff09\u505a\u535a\u58eb\u540e\u3002\u8881\u6d0b\u7684\u4e3b\u8981\u7814\u7a76\u65b9\u5411\u662f\u667a\u80fd\u533b\u7597\u3001AI\u57fa\u7840\u7406\u8bba\u3001\u5e94\u7528\u8303\u7574\u8bba\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;text-align: center;margin-left: 8px;margin-right: 8px;\"><img class=\"rich_pages wxw-img\" data-ratio=\"1.1962962962962962\"  data-type=\"jpeg\" data-w=\"1080\" style=\"width: 160px;height: 191px;\" src=\"\/wp-content\/uploads\/2023\/08\/wxsync-2023-08-66f884ff7587b4d5925bc571a65a03ea.jpeg\"  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u590f\u514b\u6797<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff0c\u5357\u6d0b\u7406\u5de5\u5927\u5b66\u526f\u6559\u6388\u30022013\u5e741\u6708\u83b7\u5f97\u4e2d\u56fd\u79d1\u5b66\u9662\u535a\u58eb\u5b66\u4f4d\uff0c\u4e8e2009\u5e7412\u6708\u81f32012\u5e7412\u6708\u5728\u7f8e\u56fd\u5bc6\u6b47\u6839\u5dde\u7acb\u5927\u5b66\u6570\u5b66\u7cfb\u4f5c\u4e3a\u8bbf\u95ee\u5b66\u8005\u3002\u4ece2013\u5e741\u6708\u81f32016\u5e745\u6708\uff0c\u5728\u5bc6\u6b47\u6839\u5dde\u7acb\u5927\u5b66\u62c5\u4efb\u8bbf\u95ee\u52a9\u7406\u6559\u6388\u30022016\u5e746\u6708\uff0c\u52a0\u5165\u5357\u6d0b\u7406\u5de5\u5927\u5b66\uff0c\u5e76\u4e8e2023\u5e743\u6708\u664b\u5347\u4e3a\u526f\u6559\u6388\u3002\u590f\u514b\u6797\u7684\u7814\u7a76\u4e13\u6ce8\u4e8e\u5206\u5b50\u79d1\u5b66\u7684\u6570\u5b66\u4eba\u5de5\u667a\u80fd\uff0c\u5728\u300aSIAM Review\u300b\u3001\u300aScience Advances\u300b\u3001\u300anpj Computational Materials\u300b\u3001\u300aACS nano\u300b\u7b49\u671f\u520a\u4e0a\u53d1\u8868\u4e8670\u591a\u7bc7\u8bba\u6587\uff0c\u5e76\u62c5\u4efb\u4e86\u8d85\u8fc710\u9879\u8d44\u52a9\u9879\u76ee\u7684\u4e3b\u6301\u4eba\u548c\u5408\u4f5c\u4e3b\u6301\u4eba\uff0c\u603b\u91d1\u989d\u8d85\u8fc7300\u4e07\u65b0\u52a0\u5761\u5143\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"vertical-align: inherit;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;\">\n<section style=\"margin: 10px auto;display: flex;justify-content: center;\">\n<section>\n<section style=\"width: 100%;\" data-width=\"100%\">\n<section style=\"width: 30%;height: 10px;background-color: rgb(181, 234, 242);overflow: hidden;\" data-width=\"30%\"><br  \/><\/section>\n<\/section>\n<section style=\"padding-left: 4px;margin-top: -6px;\">\n<section style=\"font-size: 16px;color: rgb(255, 255, 255);background-color: rgb(14, 115, 220);padding: 5px 25px;\"><span style=\"font-size: 18px;\"><strong data-brushtype=\"text\">\u62a5\u540d\u53c2\u4e0e\u8bfb\u4e66\u4f1a<\/strong><\/span><\/section>\n<section style=\"width: 100%;height: 4px;background-color: rgb(221, 239, 249);overflow: hidden;\" data-width=\"100%\"><br  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 0px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u672c\u8bfb\u4e66\u4f1a\u9002\u5408\u53c2\u4e0e\u7684\u5bf9\u8c61<\/strong><\/span><\/section>\n<section style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;\">\u2022&nbsp;<\/span>\u6570\u5b66\u548cAI\u4ea4\u53c9\u9886\u57df\u7684\u7814\u7a76\u8005\uff0c\u5305\u62ec\u6570\u5b66\u5bb6\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u548c\u673a\u5668\u5b66\u4e60\u7814\u7a76\u4eba\u5458\u7b49\uff0c\u53ef\u4ee5\u901a\u8fc7\u5206\u4eab\u6700\u65b0\u7684\u7814\u7a76\u6210\u679c\u548c\u7406\u8bba\u63a2\u8ba8\uff0c\u4fc3\u8fdb\u77e5\u8bc6\u4ea4\u6d41\u548c\u5408\u4f5c\uff1b<\/span><\/section>\n<section style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;\">\u2022&nbsp;<\/span>\u6559\u80b2\u4ece\u4e1a\u8005\uff0c\u6570\u5b66\u548cAI\u5728\u6559\u80b2\u4e2d\u5177\u6709\u6f5c\u5728\u7684\u5e94\u7528\uff0c\u6559\u5e08\u548c\u6559\u80b2\u673a\u6784\u5de5\u4f5c\u4eba\u5458\u53ef\u4ee5\u53c2\u4e0e\uff0c\u4e86\u89e3\u5982\u4f55\u5c06\u8fd9\u4e9b\u6982\u5ff5\u878d\u5165\u5230\u6559\u5b66\u4e2d\uff0c\u6fc0\u53d1\u5b66\u751f\u7684\u5174\u8da3\u3002<\/span><\/section>\n<section style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;\">\u2022&nbsp;<\/span>\u5bf9\u8ba1\u7b97\u673a\u548c\u6570\u5b66\u611f\u5174\u8da3\u7684\u672c\u79d1\u751f\u548c\u7814\u7a76\u751f\uff0c\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e2a\u8bfb\u4e66\u4f1a\u4e86\u89e3\u5230\u6700\u65b0\u7684\u7814\u7a76\u52a8\u6001\u548c\u524d\u6cbf\u9886\u57df\uff0c\u4fc3\u8fdb\u5b66\u672f\u4ea4\u6d41\uff0c\u63d0\u9ad8\u81ea\u5df1\u7684\u79d1\u7814\u80fd\u529b\uff1b<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;letter-spacing: 0.578px;\">\u2022&nbsp;<\/span>\u5bf9AI\u548c\u6570\u5b66\u4ea4\u53c9\u9886\u57df\u611f\u5174\u8da3\uff0c\u4f46\u6ca1\u6709\u4e13\u4e1a\u80cc\u666f\u7684\u4eba\u3002\u8fd9\u4e2a\u8bfb\u4e66\u4f1a\u53ef\u4ee5\u5e2e\u52a9\u4ed6\u4eec\u5efa\u7acb\u57fa\u7840\u77e5\u8bc6\uff0c\u5e76\u4e86\u89e3\u5982\u4f55\u5c06\u6570\u5b66\u4e0eAI\u7ed3\u5408\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u672c\u8bfb\u4e66\u4f1a\u8c22\u7edd\u53c2\u4e0e\u7684\u5bf9\u8c61<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4e3a\u786e\u4fdd\u4e13\u4e1a\u6027\u548c\u8ba8\u8bba\u7684\u805a\u7126\uff0c\u672c\u8bfb\u4e66\u4f1a\u8c22\u7edd\u8131\u79bb\u8bfb\u4e66\u4f1a\u6587\u672c\u548c\u590d\u6742\u79d1\u5b66\u95ee\u9898\u672c\u8eab\u7684\u7a7a\u6cdb\u7684\u54f2\u5b66\u548c\u601d\u8fa8\u5f0f\u8ba8\u8bba\uff1b\u4e0d\u63d0\u5021\u8fc7\u5ea6\u5f15\u7533\u5728\u793e\u4f1a\u3001\u4eba\u6587\u3001\u7ba1\u7406\u3001\u653f\u6cbb\u3001\u7ecf\u6d4e\u7b49\u5e94\u7528\u5c42\u9762\u7684\u8ba8\u8bba\u3002<strong>\u6211\u4eec\u5c06\u5bf9\u53c2\u4e0e\u4eba\u5458\u8fdb\u884c\u7b5b\u9009\uff0c\u5982\u679c\u51fa\u73b0\u8ba8\u8bba\u5185\u5bb9\u4e0d\u7b26\u5408\u8981\u6c42\u3001\u7ecf\u63d0\u9192\u65e0\u6548\u8005\uff0c\u4f1a\u88ab\u79fb\u9664\u7fa4\u804a\u5e76\u5bf9\u672a\u53c2\u4e0e\u90e8\u5206\u9000\u8d39\uff0c\u89e3\u91ca\u6743\u5f52\u96c6\u667a\u4ff1\u4e50\u90e8\u6240\u6709\u3002<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u8fd0\u884c\u6a21\u5f0f<\/strong><\/span><\/section>\n<section style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u5b63\u8bfb\u4e66\u4f1a\u9884\u8ba1\u8ba8\u8bba\u5206\u4eab8-10\u6b21\uff0c\u6309\u6682\u5b9a\u6846\u67b6\u8d2f\u6b21\u5c55\u5f00\uff1b<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u6bcf\u5468\u8fdb\u884c\u7ebf\u4e0a\u4f1a\u8bae\uff0c\u7531 1-2 \u540d\u8bfb\u4e66\u4f1a\u6210\u5458\u4ee5PPT\u8bb2\u89e3\u7684\u5f62\u5f0f\u9886\u8bfb\u76f8\u5173\u8bba\u6587\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a\u6210\u5458\u53ef\u4ee5\u52a0\u5165\u793e\u7fa4\uff0c\u53c2\u4e0e\u8ba8\u8bba\uff0c\u4f1a\u540e\u53ef\u4ee5\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6301\u7eed\u5b66\u4e60\uff0c\u672a\u62a5\u540d\u6210\u5458\u53ef\u4ee5\u5728\u96c6\u667a\u4ff1\u4e50\u90e8B\u7ad9\u6216\u8005\u89c6\u9891\u53f7\u770b\u516c\u5f00\u76f4\u64ad\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u4e3e\u529e\u65f6\u95f4<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ece<strong> 2023 \u5e74 9 \u6708 15 \u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e94\u665a\u4e0a 20:00-22:00<\/strong>\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba1<strong>8-10 \u5468<\/strong>\u3002\u6211\u4eec\u4e5f\u4f1a\u5bf9\u6bcf\u6b21\u5206\u4eab\u7684\u5185\u5bb9\u8fdb\u884c\u5f55\u5236\uff0c\u526a\u8f91\u540e\u53d1\u5e03\u5728\u96c6\u667a\u6591\u56fe\u7f51\u7ad9\u4e0a\uff0c\u4f9b\u8bfb\u4e66\u4f1a\u6210\u5458\u56de\u770b\uff0c\u56e0\u6b64\u62a5\u540d\u7684\u6210\u5458\u53ef\u4ee5\u6839\u636e\u81ea\u5df1\u7684\u65f6\u95f4\u81ea\u7531\u5b89\u6392\u5b66\u4e60\u65f6\u95f4\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u53c2\u4e0e\u65b9\u5f0f<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u6b64\u6b21\u8bfb\u4e66\u4f1a\u4e3a\u7ebf\u4e0a\u95ed\u95e8\u8bfb\u4e66\u4f1a\uff0c\u91c7\u7528\u7684\u4f1a\u8bae\u8f6f\u4ef6\u662f\u817e\u8baf\u4f1a\u8bae\uff08\u8bf7\u63d0\u524d\u4e0b\u8f7d\u5b89\u88c5\uff09\u3002<strong>\u5728\u626b\u7801\u5b8c\u6210\u62a5\u540d\u5e76\u6dfb\u52a0\u8d1f\u8d23\u4eba\u5fae\u4fe1\u540e\uff0c\u8d1f\u8d23\u4eba\u4f1a\u5c06\u60a8\u62c9\u5165\u4ea4\u6d41\u793e\u533a\uff08\u5fae\u4fe1\u7fa4\uff09\uff0c\u5165\u7fa4\u540e\u544a\u77e5\u5177\u4f53\u7684\u4f1a\u8bae\u53f7\u7801\u3002<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u62a5\u540d\u65b9\u5f0f<\/strong><\/span><\/section>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e00\u6b65\uff1a\u626b\u7801\u586b\u5199\u62a5\u540d\u4fe1\u606f\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: center;margin-bottom: 8px;\"><img class=\"rich_pages wxw-img\" data-ratio=\"1\"  data-type=\"png\" data-w=\"400\" style=\"width: 138px;height: 138px;\" src=\"\/wp-content\/uploads\/2023\/08\/wxsync-2023-08-23e7eddb03c801c65b7b764dad411ae5.png\"  \/><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e8c\u6b65\uff1a\u586b\u5199\u4fe1\u606f\u540e\uff0c\u4ed8\u8d39299\u5143\u3002<\/span><span style=\"font-size: 15px;color: rgb(136, 136, 136);\">\uff08\u53ef\u53c2\u4e0e\u5171\u521b\u4efb\u52a1\u83b7\u53d6\u79ef\u5206\uff0c\u79ef\u5206\u7b26\u5408\u6807\u51c6\u53ef\u4ee5\u7533\u8bf7\u9000\u8d39\uff09<\/span><\/p>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e09\u6b65\uff1a\u6dfb\u52a0\u8d1f\u8d23\u4eba\u5fae\u4fe1\uff0c\u62c9\u5165\u5bf9\u5e94\u4e3b\u9898\u7684\u8bfb\u4e66\u4f1a\u793e\u533a\/\u5fae\u4fe1\u7fa4\u3002<\/span><span style=\"font-size: 15px;color: rgb(136, 136, 136);\">\uff08\u672c\u8bfb\u4e66\u4f1a\u53ef\u5f00\u53d1\u7968\u7b49\u8bc1\u660e\u6750\u6599\uff0c\u8bf7\u8054\u7cfb\u76f8\u5173\u8d1f\u8d23\u4eba\u6c9f\u901a\u8be6\u60c5\uff09<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u9488\u5bf9\u5b66\u751f\u7684\u9000\u8d39\u673a\u5236<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfb\u4e66\u4f1a\u901a\u8fc7\u5171\u5b66\u5171\u7814\u7684\u673a\u5236\uff0c\u56f4\u7ed5\u524d\u6cbf\u4e3b\u9898\u8fdb\u884c\u5185\u5bb9\u68b3\u7406\u548c\u6c89\u6dc0\uff0c\u6240\u4ee5\u9488\u5bf9\u4e8e\u5b66\u751f\uff0c\u53ef\u4ee5\u901a\u8fc7\u53c2\u4e0e\u5171\u521b\u4efb\u52a1\uff0c\u83b7\u53d6\u79ef\u5206\uff0c\u79ef\u5206\u8fbe\u5230\u9000\u8d39\u6807\u51c6\u4e4b\u540e\uff0c\u53ef\u4ee5\u76f4\u63a5\u9000\u8d39\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u52a0\u5165\u793e\u533a\u540e\u53ef\u4ee5\u83b7\u5f97\u7684\u8d44\u6e90<\/strong><\/span><\/section>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u5728\u7ebf\u4f1a\u8bae\u5ba4\u6c89\u6d78\u5f0f\u8ba8\u8bba\uff1a\u4e0e\u4e3b\u8bb2\u4eba\u5373\u65f6\u8ba8\u8bba\u4ea4\u6d41<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ea4\u4e92\u5f0f\u64ad\u653e\u5668\u9ad8\u6548\u56de\u770b\uff1a\u5feb\u901f\u5b9a\u4f4d\u4e3b\u8bb2\u4eba\u63d0\u5230\u7684\u672f\u8bed\u3001\u8bba\u6587\u3001\u5927\u7eb2\u3001\u8ba8\u8bba\u7b49\u91cd\u8981\u65f6\u95f4\u70b9<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u9ad8\u8d28\u91cf\u7684\u4e3b\u9898\u5fae\u4fe1\u793e\u7fa4\uff1a\u7855\u535a\u6bd4\u4f8b\u8d85\u8fc780%\u7684\u6210\u5458\u5fae\u4fe1\u793e\u533a\uff0c\u95ed\u95e8\u591c\u8c08\u548c\u4ea4\u6d41<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8d85\u591a\u5b66\u4e60\u8d44\u6e90\u968f\u624b\u53ef\u5f97\uff1a\u4ece\u4e0d\u540c\u5c3a\u5ea6\u8bb0\u5f55\u4e3b\u9898\u4e0b\u7684\u8def\u5f84\u3001\u8bcd\u6761\u3001\u524d\u6cbf\u89e3\u8bfb\u3001\u7b97\u6cd5\u3001\u5b66\u8005\u7b49<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u53c2\u4e0e\u793e\u533a\u5185\u5bb9\u5171\u521b\u4efb\u52a1\uff1a\u8bfb\u4e66\u4f1a\u7b14\u8bb0\u3001\u767e\u79d1\u8bcd\u6761\u3001\u516c\u4f17\u53f7\u6587\u7ae0\u3001\u8bba\u6587\u89e3\u8bfb\u5206\u4eab\u7b49\u4e0d\u540c\u96be\u5ea6\u5171\u521b\u4efb\u52a1\uff0c\u5728\u5b66\u4e60\u4e2d\u8d21\u732e\uff0c\u5728\u4ed8\u51fa\u4e2d\u6536\u83b7\u3002<\/span><\/p>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u5171\u4eab\u8ffd\u8e2a\u4e3b\u9898\u524d\u6cbf\u8fdb\u5c55\uff1a\u5728\u7fa4\u5185\u548c\u516c\u4f17\u53f7\u5206\u4eab\u6700\u65b0\u8fdb\u5c55\uff0c\u9886\u57df\u8bba\u6587\u901f\u9012<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u53c2\u4e0e\u5171\u521b\u4efb\u52a1\uff0c\u5171\u5efa\u5b66\u672f\u793e\u533a<\/strong><\/span><\/section>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u2022 <strong>\u8bfb\u4e66\u4f1a\u7b14\u8bb0\uff1a<\/strong>\u5728\u4ea4\u4e92\u5f0f\u64ad\u653e\u5668\u4e0a\u8bb0\u5f55\u672f\u8bed\u548c\u53c2\u8003\u6587\u732e<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u2022 <strong>\u96c6\u667a\u767e\u79d1\u8bcd\u6761\uff1a<\/strong>\u56f4\u7ed5\u8bfb\u4e66\u4f1a\u4e3b\u9898\u4e2d\u91cd\u8981\u4e14\u524d\u6cbf\u7684\u77e5\u8bc6\u6982\u5ff5\u68b3\u7406\u6210\u8bcd\u6761\u3002\u4f8b\u5982\uff1a<\/span><\/p>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: circle;margin-left: 16px;margin-right: 16px;\">\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247611863&amp;idx=4&amp;sn=3e76dcdd60a9a3970edcffff1a59dc88&amp;chksm=e8966f5adfe1e64c7fd31411f7b4abeff57cdef630e8fa433f313728441bfb39569e4df10750&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u5927\u89c4\u6a21\u4eba\u7fa4\u6a21\u62df\uff1a\u89c2\u5bdf\u96c6\u4f53\u611a\u8822\u4e0e\u96c6\u4f53\u667a\u6167 | \u96c6\u667a\u767e\u79d1<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247614758&amp;idx=4&amp;sn=9517e1a5383b72d2593d95131969aab6&amp;chksm=e8965babdfe1d2bd09a71513dceb851069d7acc571d6126d597a7a251884568d50898518cdc7&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u884c\u4e3a\u7ecf\u6d4e\u5b66\uff1a\u7ecf\u6d4e\u7cfb\u7edf\u7684\u884c\u4e3a\u4e3b\u4f53\u662f\u5426\u7406\u6027\uff1f| \u96c6\u667a\u767e\u79d1<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247613356&amp;idx=4&amp;sn=5256c39b6fc3c77fa314c0b5d701f698&amp;chksm=e8966121dfe1e837eb54d42d3e14e7b07e0bfec2ea31666fa20656b364c74c4aa85c4555314f&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u7f51\u7edc\u53ef\u63a7\u6027\uff1a\u7ed3\u6784\u53ef\u63a7\u6027\u4e0e\u6700\u5927\u5339\u914d | \u96c6\u667a\u767e\u79d1<\/span><\/a><\/p>\n<\/li>\n<\/ul>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u2022 <strong>\u8bba\u6587\u89e3\u8bfb\u5206\u4eab\uff1a<\/strong>\u8ba4\u9886\u5f85\u8bfb\u5217\u8868\u4e2d\u7684\u8bba\u6587\uff0c\u4ee5\u4e3b\u9898\u62a5\u544a\u7684\u5f62\u5f0f\u5728\u793e\u533a\u5206\u4eab<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"> \u2022 <strong>\u8bba\u6587\u6458\u8981\u7ffb\u8bd1\uff1a<\/strong>\u7ffb\u8bd1\u793e\u533a\u63a8\u8350\u8bba\u6587\u4e2d\u7684\u6458\u8981\u548c\u56fe\u6ce8<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"> \u2022 <strong>\u516c\u4f17\u53f7\u6587\u7ae0\uff1a<\/strong>\u4ee5\u7ffb\u8bd1\u6574\u7406\u6216\u8005\u539f\u521b\u751f\u4ea7\u5f62\u5f0f\u751f\u4ea7\u516c\u4f17\u53f7\u6587\u7ae0\uff0c\u4ee5\u4ecb\u7ecd\u524d\u6cbf\u8fdb\u5c55\u3002<strong>\u4f8b\u5982\uff1a\u8bba\u6587\u7ffb\u8bd1<\/strong><\/span><\/p>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: circle;margin-left: 16px;margin-right: 16px;\">\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247627615&amp;idx=1&amp;sn=be379353aea95a746f4b0eb8e99c6c49&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u591a\u8005\u5f02\u4e5f\uff1a\u7834\u7f3a\u7684\u5bf9\u79f0\u6027\u4e0e\u79d1\u5b66\u5c42\u7ea7\u7ed3\u6784\u7684\u672c\u8d28<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247584281&amp;idx=1&amp;sn=f1bd965a7e690202324947cb4f931be7&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u8bfa\u5956\u59d4\u5458\u4f1a\u4e07\u5b57\u8bc4\u8ff0\uff1a\u4e3a\u4ec0\u4e48\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u53d7\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u9752\u7750\uff1f<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247631378&amp;idx=1&amp;sn=2214710d9c092b6d75587e3737c9ff3c&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u4ece\u751f\u547d\u8d77\u6e90\u5230\u6d41\u884c\u75c5\uff1a\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u591a\u5c3a\u5ea6\u6d8c\u73b0\u73b0\u8c61<\/span><\/a><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247611133&amp;idx=1&amp;sn=af5e995e3a218f7bfe38a8cdcf8593b7&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u6d8c\u73b0\uff1a21\u4e16\u7eaa\u79d1\u5b66\u7684\u7edf\u4e00\u4e3b\u9898<\/span><\/a><\/p>\n<\/li>\n<\/ul>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u79d1\u666e\u6587\u7ae0\u7ffb\u8bd1<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><\/span><\/p>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: circle;margin-left: 16px;margin-right: 16px;\">\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247611133&amp;idx=1&amp;sn=af5e995e3a218f7bfe38a8cdcf8593b7&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u6d8c\u73b0\uff1a21\u4e16\u7eaa\u79d1\u5b66\u7684\u7edf\u4e00\u4e3b\u9898<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247519456&amp;idx=1&amp;sn=c5db1636e9b70fb50b9db85e08a44128&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u4ece\u9ea6\u514b\u65af\u97e6\u5996\u5230\u91cf\u5b50\u751f\u7269\u5b66\uff0c\u751f\u547d\u7269\u8d28\u4e2d\u662f\u5426\u6f5c\u85cf\u7740\u65b0\u7269\u7406\u5b66\uff1f<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247604504&amp;idx=1&amp;sn=a54df1c24b5d7317c9ac594a20f5f4fa&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u5927\u8111\u70ed\u529b\u5b66\uff1a\u5229\u7528\u201c\u6e4d\u6d41\u201d\u8fdc\u79bb\u5e73\u8861\u6001<\/span><\/a><\/p>\n<\/li>\n<\/ul>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bb2\u5ea7\u6574\u7406<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><\/span><\/p>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: circle;margin-left: 16px;margin-right: 16px;\">\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247511098&amp;idx=1&amp;sn=0bc2f2027a3148cc53385bea6de3305d&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u5f20\u6c5f\uff1a\u4ece\u56fe\u7f51\u7edc\u5230\u56e0\u679c\u63a8\u65ad\uff0c\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u4e94\u90e8\u66f2<\/span><\/a><\/p>\n<\/li>\n<li>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247509774&amp;idx=1&amp;sn=d9a211a83fc650a64622fa8c86a56b1b&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;color: rgb(0, 122, 170);text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">\u7c97\u770b\u957f\u5c3e\uff0c\u7ec6\u8fa8\u5e42\u5f8b\uff1a\u8de8\u4e16\u7eaa\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u7814\u7a76\u7eb7\u4e89\u53f2<\/span><\/a><\/p>\n<\/li>\n<li>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247601490&amp;idx=1&amp;sn=8d3e68b08af6b411b72607d92212a297&amp;scene=21#wechat_redirect\" style=\"font-size: 15px;text-decoration: underline;\" data-linktype=\"2\"><span style=\"font-size: 15px;color: rgb(0, 122, 170);\">Erik Hoel\uff1a\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u600e\u6837\u8fde\u901a\u590d\u6742\u7cfb\u7edf\u7684\u5b8f\u89c2\u4e0e\u5fae\u89c2<\/span><\/a><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">PS\uff1a\u5177\u4f53\u53c2\u4e0e\u65b9\u5f0f\u53ef\u4ee5\u52a0\u5165\u8bfb\u4e66\u4f1a\u540e\u67e5\u770b\u5bf9\u5e94\u7684\u5171\u521b\u4efb\u52a1\u5217\u8868\uff0c\u9886\u53d6\u4efb\u52a1\uff0c\u4e0e\u8fd0\u8425\u8d1f\u8d23\u4eba\u6c9f\u901a\u8be6\u60c5\uff0c\u4e0a\u8ff0\u89c4\u5219\u7684\u6700\u7ec8\u89e3\u91ca\u6743\u5f52\u96c6\u667a\u4ff1\u4e50\u90e8\u6240\u6709\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;\">\n<section style=\"margin: 10px auto;display: flex;justify-content: center;\">\n<section>\n<section style=\"width: 100%;\" data-width=\"100%\">\n<section style=\"width: 30%;height: 10px;background-color: rgb(181, 234, 242);overflow: hidden;\" data-width=\"30%\"><br  \/><\/section>\n<\/section>\n<section style=\"padding-left: 4px;margin-top: -6px;\">\n<section style=\"font-size: 16px;color: rgb(255, 255, 255);background-color: rgb(14, 115, 220);padding: 5px 25px;\"><span style=\"font-size: 18px;\"><strong data-brushtype=\"text\">\u9605\u8bfb\u6750\u6599<\/strong><\/span><\/section>\n<section style=\"width: 100%;height: 4px;background-color: rgb(221, 239, 249);overflow: hidden;\" data-width=\"100%\"><br  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ee5\u4e0b\u662f\u75313\u4f4d\u53d1\u8d77\u4eba\u8001\u5e08\u548c\u591a\u4f4d\u4e3b\u8bb2\u4eba\u63a8\u8350\u7684\u6587\u732e\u5217\u8868\u4e0e\u76f8\u5173\u5b66\u4e60\u8d44\u6e90\u3002\u6b22\u8fce\u626b\u7801\u67e5\u770b\u6536\u85cf\uff0c\u53ef\u4ee5\u76f4\u63a5\u8df3\u8f6c\u94fe\u63a5\uff0c\u4e0b\u8f7dPDF\u6587\u4ef6\uff0c\u6536\u85cf\u53c2\u8003\u6587\u732e\u5217\u8868\uff1a<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;text-align: center;margin-left: 8px;margin-right: 8px;\"><img class=\"rich_pages wxw-img\" data-ratio=\"1\"  data-type=\"png\" data-w=\"400\" style=\"width: 139px;height: 139px;\" src=\"\/wp-content\/uploads\/2023\/08\/wxsync-2023-08-e0938f190e93ec74956dc770b68ddc28.png\"  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u4e00\u3001AI for Math<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u968f\u7740\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u98de\u901f\u53d1\u5c55\uff0c\u5176\u5728\u6570\u5b66\u9886\u57df\u7684\u5e94\u7528\u6b63\u65e5\u76ca\u5f15\u8d77\u4eba\u4eec\u7684\u5173\u6ce8\u4e0e\u70ed\u60c5\u3002AI\u5728\u6570\u5b66\u7814\u7a76\u4e2d\u7684\u5e94\u7528\u4e00\u76f4\u662f\u4e00\u4e2a\u91cd\u8981\u7684\u7814\u7a76\u65b9\u5411\uff0c\u5e76\u53d6\u5f97\u4e86\u8bb8\u591a\u91cd\u8981\u6210\u679c\uff0c\u4ece\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5230\u81ea\u52a8\u8bc1\u660e\uff0c\u518d\u5230\u6570\u5b66\u89c4\u5f8b\u7684\u53d1\u73b0\uff0c\u4eba\u5de5\u667a\u80fd\u6b63\u9010\u6e10\u6210\u4e3a\u6570\u5b66\u9886\u57df\u7684\u5f97\u529b\u52a9\u624b\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u5728<strong>\u6570\u5b66\u63a8\u7406<\/strong>\u65b9\u9762\uff0c\u7814\u7a76\u4eba\u5458\u901a\u8fc7\u8bad\u7ec3\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff0c\u5982Llama2\uff0c\u63a2\u7d22\u4e86\u5f00\u6e90\u6a21\u578b\u7684\u57fa\u672c\u539f\u7406\u4e0e\u8bad\u7ec3\u6280\u5de7\uff0c\u8fdb\u4e00\u6b65\u63d0\u5347\u4e86\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u3002\u901a\u8fc7\u601d\u7ef4\u94fe\u7684\u5f15\u5bfc\uff0c\u5927\u8bed\u8a00\u6a21\u578b\u5728\u63a8\u7406\u80fd\u529b\u65b9\u9762\u53d6\u5f97\u4e86\u663e\u8457\u8fdb\u5c55\u3002\u6b64\u5916\uff0c\u5c06\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u8bc1\u660e\u76f8\u7ed3\u5408\uff0c\u5982LeanDojo\u7684\u5b9e\u8df5\uff0c\u4e3a\u6570\u5b66\u5b9a\u7406\u7684\u81ea\u52a8\u8bc1\u660e\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><strong>\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e<\/strong>\u65b9\u9762\u7684\u7814\u7a76\u4e5f\u53d6\u5f97\u4e86\u7a81\u7834\uff0cGPT-f\u7b49\u6a21\u578b\u5728\u81ea\u52a8\u8bc1\u660e\u641c\u7d22\u65b9\u9762\u5c55\u73b0\u51fa\u5f3a\u5927\u7684\u6f5c\u529b\uff0c\u800c\u8fdb\u4e00\u6b65\u7684\u7b97\u6cd5\u6539\u8fdb\u5219\u4f7f\u6a21\u578b\u80fd\u591f\u81ea\u52a8\u8bc1\u660e\u5404\u79cd\u6570\u5b66\u95ee\u9898\uff0c\u751a\u81f3\u5305\u62ec\u56fd\u9645\u6570\u5b66\u5965\u6797\u5339\u514b\uff08IMO\uff09\u7684\u9898\u76ee\u3002\u5229\u7528\u81ea\u7136\u8bed\u8a00\u6307\u5bfc\u5b9a\u7406\u81ea\u52a8\u8bc1\u660e\uff0c\u4e5f\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u89e3\u51b3\u4e86\u5f62\u5f0f\u5316\u8bc1\u660e\u7684\u96be\u9898\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">AI\u8fd8\u5728<strong>\u53d1\u73b0\u6570\u5b66\u89c4\u5f8b<\/strong>\u65b9\u9762\u53d1\u6325\u4e86\u91cd\u8981\u4f5c\u7528\u3002\u901a\u8fc7\u8f85\u52a9\u4eba\u7c7b\u76f4\u89c9\uff0cAI\u5e2e\u52a9\u53d1\u73b0\u4e86\u65b0\u7684\u6570\u5b66\u89c4\u5f8b\uff0c\u5982\u626d\u7ed3\u4e0d\u53d8\u91cf\u3001\u77e9\u9635\u4e58\u6cd5\u7b97\u6cd5\u3001\u57fa\u672c\u5e38\u6570\u7b49\u3002\u5229\u7528\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\uff0c\u7814\u7a76\u4eba\u5458\u751a\u81f3\u80fd\u591f\u81ea\u52a8\u751f\u6210\u6570\u5b66\u731c\u60f3\u7684\u53cd\u4f8b\uff0c\u63a8\u52a8\u4e86\u6570\u5b66\u9886\u57df\u7684\u524d\u6cbf\u63a2\u7d22\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u540c\u65f6\uff0c<strong>\u7b26\u53f7\u8ba1\u7b97<\/strong>\u4f5c\u4e3a\u6570\u5b66\u9886\u57df\u7684\u5173\u952e\u5de5\u5177\uff0c\u4e5f\u5f97\u5230\u4e86AI\u7684\u9769\u65b0\u3002\u57fa\u4e8e\u7b7e\u540d\u7684Grobner\u57fa\u7b97\u6cd5\u7b49\u65b9\u6cd5\u4e3a\u7b26\u53f7\u8ba1\u7b97\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\uff0c\u4f7f\u8ba1\u7b97\u66f4\u52a0\u9ad8\u6548\u51c6\u786e\u3002\u5b66\u4e60\u9009\u62e9\u7b56\u7565\u4f18\u5316\u7b97\u6cd5\uff0c\u4ee5\u53ca\u5728Gvw\u7b97\u6cd5\u6846\u67b6\u4e0b\u6539\u8fdb\u7b7e\u540d\u57fa\u7b97\u6cd5\u7b49\u7814\u7a76\uff0c\u8fdb\u4e00\u6b65\u63a8\u52a8\u4e86\u7b26\u53f7\u8ba1\u7b97\u9886\u57df\u7684\u53d1\u5c55\u3002<\/span><\/p>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u603b\u4e4b\uff0cAI\u5728\u6570\u5b66\u9886\u57df\u7684\u5e94\u7528\u4e0d\u4ec5\u4ec5\u662f\u4e00\u79cd\u6280\u672f\u9769\u65b0\uff0c\u66f4\u662f\u5728\u62d3\u5c55\u4eba\u7c7b\u6570\u5b66\u8ba4\u77e5\u8fb9\u754c\u65b9\u9762\u7684\u91cd\u8981\u52a9\u529b\u3002\u901a\u8fc7\u5927\u578b\u6a21\u578b\u3001\u81ea\u52a8\u8bc1\u660e\u3001\u6570\u5b66\u89c4\u5f8b\u53d1\u73b0\u7b49\u9886\u57df\u7684\u7814\u7a76\uff0cAI\u6b63\u5f15\u9886\u7740\u6570\u5b66\u9886\u57df\u7684\u521b\u65b0\u4e0e\u7a81\u7834\uff0c\u4e3a\u6570\u5b66\u5bb6\u548c\u7814\u7a76\u8005\u63d0\u4f9b\u4e86\u524d\u6240\u672a\u6709\u7684\u5de5\u5177\u4e0e\u65b9\u6cd5\u3002\u8fd9\u4e00\u7cfb\u5217\u7814\u7a76\u4e0d\u4ec5\u5c55\u793a\u4e86AI\u5728\u6570\u5b66\u9886\u57df\u7684\u5a01\u529b\uff0c\u4e5f\u542f\u793a\u4e86\u672a\u6765\u6570\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u6df1\u5ea6\u878d\u5408\u7684\u53ef\u80fd\u6027\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">1. <strong>\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u63a8\u7406<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Hugo Touvron et al. Llama 2: Open Foundation and Fine-Tuned Chat Models. <br  \/>arXiv:2307.09288 [cs.CL]<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u8be6\u7ec6\u8bb2\u89e3\u4e86\u5f00\u6e90\u5927\u8bed\u8a00\u6a21\u578b Llama2 \u7684\u57fa\u672c\u539f\u7406\u4e0e\u8bad\u7ec3\u6280\u5de7\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Jason Wei, et al. &nbsp;Chain-of-Thought Prompting Elicits Reasoning in Large Language Models. <br  \/>arXiv:2201.11903 [cs.CL]<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed: \u5229\u7528\u601d\u7ef4\u94fe\u63d0\u5347\u5927\u8bed\u8a00\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Kaiyu Yang et al. &nbsp;LeanDojo: Theorem Proving with Retrieval-Augmented Language Models.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/arxiv.org\/pdf\/2306.15626.pdf. 2306.15626. &nbsp;[cs.LG].<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed: \u5c06\u5927\u8bed\u8a00\u6a21\u578b\u4e0elean\u4ea4\u4e92\uff0c\u8f85\u52a9\u6570\u5b66\u5b9a\u7406\u8bc1\u660e\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">2. <strong>\u5927\u6a21\u578b\u4e0e\u81ea\u52a8\u8bc1\u660e<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Polu, Stanislas, and Ilya Sutskever. &#8220;Generative language modeling for automated theorem proving.&#8221;<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">arXiv preprint arXiv:2009.03393 (2020).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u63d0\u51faGPT-f\uff0c\u4f7f\u7528GPT-3\u7ea7\u5927\u6a21\u578b\u8fdb\u884c\u81ea\u52a8\u8bc1\u660e\u641c\u7d22\u7684\u5f00\u5c71\u4f5c\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Lample, Guillaume, et al. &#8220;Hypertree proof search for neural theorem proving.&#8221;<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Advances in Neural Information Processing Systems 35 (2022): 26337-26349.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u7528\u66f4\u5148\u8fdb\u7684\u641c\u7d22\u7b97\u6cd5\u6539\u8fdb\u4e86GPT-f\uff0c\u81ea\u52a8\u8bc1\u660e\u4e86\u5341\u9053IMO\u9898\u76ee\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Jiang, Albert Q., et al. &#8220;Draft, sketch, and prove: Guiding formal theorem provers with informal proofs.&#8221;<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">arXiv preprint arXiv:2210.12283 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Alex, et al. \u201cAdvancing mathematics by guiding human intuition with AI. \u201d Nature 600 (2021): 70-74.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1aAI\u8f85\u52a9\u53d1\u73b0\u626d\u7ed3\u4e0d\u53d8\u91cf\uff0cKazhdan-Lusztig\u591a\u9879\u5f0f\u7b49\u65b0\u89c4\u5f8b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u76f8\u5173\u6587\u7ae0\uff1a\u300a<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247595745&amp;idx=1&amp;sn=7f706e2c1b01491f4884836c04b97f48&amp;chksm=e8962c6cdfe1a57aac107cd0cfed1697ff06547bcd71e3a560d03f65c4d8abb5cc93c5c0a6cc&amp;scene=21#wechat_redirect\" textvalue=\"Nature\uff1aAI \u5f15\u5bfc\u4eba\u7c7b\u76f4\u89c9\uff0c\u5e2e\u52a9\u53d1\u73b0\u6570\u5b66\u5b9a\u7406\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">Nature\uff1aAI \u5f15\u5bfc\u4eba\u7c7b\u76f4\u89c9\uff0c\u5e2e\u52a9\u53d1\u73b0\u6570\u5b66\u5b9a\u7406<\/a>\u300b<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Fawzi. 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Wagner . \u201cConstructions in combinatorics via neural networks\u201d.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">arXiv.org\/abs\/2104.14516.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1aAI\u81ea\u52a8\u53d1\u73b0\u6570\u5b66\u731c\u60f3\u53cd\u4f8b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Gal Raayoni ,et al. &nbsp;Generating conjectures on fundamental constants with the Ramanujan Machine. 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Ph.D. Thesis, Harvard University, June 1982. 168 pages.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">math.columbia.edu\/~bayer\/papers\/Bayer-thesis.pdf<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1aMacaulay\u4f5c\u8005\u4e4b\u4e00\u7684Bayer\u7684\u535a\u58eb\u8bba\u6587\uff0c\u662f\u5f53\u4ee3\u4ee3\u6570\u51e0\u4f55\u4e0e\u9664\u6cd5\u7b97\u6cd5\u7406\u8bba\u76f8\u7ed3\u5408\u7684\u5f00\u5c71\u4e4b\u4f5c\u3002<br  \/><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Vlad, Raluca. 2022. A Discussion of Gr\u00f6bner Bases and the Hilbert Scheme. Bachelor&#8217;s thesis, Harvard College. https:\/\/dash.harvard.edu\/bitstream\/handle\/1\/37371732\/thesis.pdf?sequence=1<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u975e\u5e38\u9002\u5408\u5feb\u901f\u4e86\u89e3Grobner\u57fa\u7684\u57fa\u672c\u6982\u5ff5\u548c\u7b80\u5355\u5e94\u7528\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><strong>\u5f00\u6e90\u7b26\u53f7\u8f6f\u4ef6\u7b80\u4ecb<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">A Tour of Sage<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/doc.sagemath.org\/html\/en\/a_tour_of_sage\/<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">SageMath\u662f\u975e\u5e38\u5f3a\u5927\u7684\u5f00\u6e90\u6570\u5b66\u8f6f\u4ef6\uff0c\u57fa\u4e8ePython\uff0c\u53ef\u76f4\u63a5\u8fd0\u884cPython\uff0c\u5341\u5206\u5168\u9762\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">GAP \u2013 A Tutorial<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/docs.gap-system.org\/doc\/tut\/chap0_mj.html<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">GAP\u662f\u4e00\u6b3e\u4e13\u95e8\u9488\u5bf9\u7fa4\u8bba\u548c\u7ebf\u6027\u4ee3\u6570\u7684\u7b26\u53f7\u8ba1\u7b97\u7cfb\u7edf\uff0c\u57fa\u4e8eC\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Macaulay2Doc \u2014\u2014 Macaulay2 documentation<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">http:\/\/www2.macaulay2.com\/Macaulay2\/doc\/Macaulay2\/share\/doc\/Macaulay2\/Macaulay2Doc\/html\/<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Macaulay2\u662f\u4e00\u6b3e\u8ba1\u7b97Grobner\u57fa\u7684\u8ba1\u7b97\u673a\u4ee3\u6570\u7cfb\u7edf\uff0c\u4e3b\u8981\u7528\u4e8e\u5904\u7406\u4ea4\u6362\u73af\u53ca\u5176\u6a21\u4e0a\u7684\u7b26\u53f7\u8ba1\u7b97\u95ee\u9898\uff0c\u662f\u4ee3\u6570\u51e0\u4f55\u4e2d\u5e38\u7528\u7684\u8f6f\u4ef6\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">PARI\/GP documentation<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/pari.math.u-bordeaux.fr\/doc.html<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Pari\/GP\u662f\u4e00\u6b3e\u7528\u6765\u8ba1\u7b97\u7b97\u672f\u51e0\u4f55\u4e0e\u4ee3\u6570\u6570\u8bba\u3001\u57df\u6269\u5f20\u76f8\u5173\u9886\u57df\u7684\u4ee3\u6570\u7cfb\u7edf\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Maxima 5.47.0 Manual<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/maxima.sourceforge.io\/docs\/manual\/maxima_toc.html<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Maxima\u662f\u4e00\u6b3e\u5e38\u7528\u7684\u8ba1\u7b97\u673a\u4ee3\u6570\u7cfb\u7edf\uff0c\u5bf9\u6807Mathematica, Maple\u7b49\u8f6f\u4ef6\uff0c\u662f\u4e16\u754c\u4e0a\u6700\u65e9\u7684\u901a\u7528\u8ba1\u7b97\u673a\u4ee3\u6570\u7cfb\u7edf\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"color: rgb(61, 170, 214);font-size: 16px;\"><strong>\u4e8c\u3001Math for AI<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u6570\u5b66\u662f\u4eba\u5de5\u667a\u80fd\uff08AI\uff09\u7684\u7075\u9b42\uff0c\u5b83\u4e0d\u4ec5\u662fAI\u53d1\u5c55\u7684\u57fa\u7840\uff0c\u4e5f\u662f\u5176\u5404\u4e2a\u9886\u57df\u548c\u5e94\u7528\u7684\u6838\u5fc3\u9a71\u52a8\u529b\u3002\u4ece\u6570\u636e\u5904\u7406\u5230\u6a21\u578b\u4f18\u5316\uff0c\u4ece\u7b97\u6cd5\u8bbe\u8ba1\u5230\u51b3\u7b56\u63a8\u65ad\uff0c\u6570\u5b66\u5728AI\u4e2d\u626e\u6f14\u7740\u591a\u91cd\u89d2\u8272\uff0c\u65e0\u5904\u4e0d\u5728\uff0c\u4e0d\u53ef\u6216\u7f3a\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><strong>\u5927\u6a21\u578b\u4e0e\u795e\u7ecf\u7f51\u7edc<\/strong>\u7684\u6210\u529f\u79bb\u4e0d\u5f00\u6570\u5b66\u7684\u5173\u952e\u8d21\u732e\u3002\u8303\u7574\u8bba\u4e3a\u6784\u5efa\u66f4\u62bd\u8c61\u3001\u901a\u7528\u7684\u6a21\u578b\u6846\u67b6\u63d0\u4f9b\u57fa\u7840\uff0c\u5e2e\u52a9\u6211\u4eec\u4ece\u66f4\u5b8f\u89c2\u7684\u89d2\u5ea6\u7406\u89e3\u7f51\u7edc\u7ed3\u6784\u548c\u64cd\u4f5c\u3002\u5bf9\u6bd4\u5b66\u4e60\u501f\u52a9\u6570\u5b66\u7684\u8ddd\u79bb\u5ea6\u91cf\u548c\u76f8\u4f3c\u6027\u6982\u5ff5\uff0c\u4f7f\u6a21\u578b\u80fd\u66f4\u51c6\u786e\u5730\u6355\u6349\u6570\u636e\u7684\u5173\u7cfb\u3002\u63a7\u5236\u7406\u8bba\u4e3a\u4f18\u5316\u7b97\u6cd5\u63d0\u4f9b\u6307\u5bfc\uff0c\u4ece\u5fae\u5206\u65b9\u7a0b\u5230\u6700\u4f18\u63a7\u5236\u65b9\u6cd5\uff0c\u6709\u52a9\u4e8e\u5728\u53c2\u6570\u7a7a\u95f4\u4e2d\u5bfb\u627e\u6700\u4f73\u89e3\u3002\u8fd9\u4e9b\u6570\u5b66\u6982\u5ff5\u5728\u5927\u6a21\u578b\u4e0e\u795e\u7ecf\u7f51\u7edc\u7684\u8bbe\u8ba1\u3001\u8bad\u7ec3\u548c\u4f18\u5316\u4e2d\u53d1\u6325\u7740\u4e0d\u53ef\u6216\u7f3a\u7684\u4f5c\u7528\uff0c\u63a8\u52a8\u4e86\u4eba\u5de5\u667a\u80fd\u9886\u57df\u7684\u524d\u6cbf\u7814\u7a76\u548c\u5e94\u7528\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><strong>\u62d3\u6251\u6570\u636e\u5206\u6790<\/strong>\u51ed\u501f\u6570\u5b66\u7684\u6df1\u8fdc\u8d21\u732e\u5728\u6570\u636e\u7406\u89e3\u9886\u57df\u5d2d\u9732\u5934\u89d2\u3002\u6301\u7eed\u540c\u8c03\u63ed\u793a\u6570\u636e\u7684\u62d3\u6251\u7279\u5f81\uff0c\u901a\u8fc7\u5bf9\u5f62\u72b6\u548c\u8fde\u63a5\u6027\u7684\u91cf\u5316\uff0c\u5e2e\u52a9\u63ed\u793a\u6570\u636e\u5185\u90e8\u7ed3\u6784\u3002\u62d3\u6251\u673a\u5668\u5b66\u4e60\u878d\u5408\u4e86\u51e0\u4f55\u548c\u4ee3\u6570\u7684\u601d\u60f3\uff0c\u5c06\u62d3\u6251\u6982\u5ff5\u5f15\u5165\u6a21\u578b\u4e2d\uff0c\u52a0\u6df1\u5bf9\u6570\u636e\u7684\u8ba4\u77e5\u3002\u800c\u6301\u7eed\u8c31\u56fe\u6cd5\u901a\u8fc7\u6620\u5c04\u6570\u636e\u5230\u7279\u5f81\u7a7a\u95f4\uff0c\u5e76\u5206\u6790\u5176\u6301\u7eed\u8c31\uff0c\u63d0\u4f9b\u4e86\u66f4\u4e30\u5bcc\u7684\u6570\u636e\u8868\u5f81\uff0c\u6709\u52a9\u4e8e\u53d1\u73b0\u6570\u636e\u4e2d\u7684\u6a21\u5f0f\u548c\u5173\u7cfb\u3002\u8fd9\u4e9b\u6570\u5b66\u5de5\u5177\u5171\u540c\u4fc3\u8fdb\u4e86\u5728\u590d\u6742\u6570\u636e\u4e2d\u7684\u6df1\u5165\u63a2\u7d22\u548c\u53d1\u73b0\uff0c\u4e3a\u6570\u636e\u5206\u6790\u6ce8\u5165\u4e86\u65b0\u7684\u89c6\u89d2\u548c\u80fd\u529b\u3002<\/span><\/p>\n<p style=\"line-height: 1.75em;margin-left: 8px;margin-right: 8px;margin-bottom: 16px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><strong>\u56fe\u795e\u7ecf\u7f51\u7edc<\/strong>\u5728\u6570\u5b66\u7684\u5f15\u5bfc\u4e0b\u53d6\u5f97\u7a81\u7834\u6027\u8fdb\u5c55\u3002\u6d88\u606f\u4f20\u9012\u8303\u5f0f\u8fd0\u7528\u7ebf\u6027\u4ee3\u6570\u4e0e\u56fe\u8bba\uff0c\u5c06\u4fe1\u606f\u5728\u56fe\u8282\u70b9\u95f4\u4f20\u9012\uff0c\u589e\u5f3a\u8282\u70b9\u8868\u793a\u3002\u7a81\u7834GNN\u74f6\u9888\u9700\u8981\u6df1\u5165\u56fe\u7ed3\u6784\u7684\u6570\u5b66\u6d1e\u5bdf\uff0c\u63a7\u5236\u7406\u8bba\u548c\u52a8\u6001\u7cfb\u7edf\u6709\u52a9\u4e8e\u89e3\u51b3\u52a8\u6001\u56fe\u95ee\u9898\u3002\u5728\u5316\u5b66\u548c\u7ec6\u80de\u9886\u57df\uff0c\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u6570\u5b66\u5efa\u6a21\u4ece\u5206\u5b50\u76f8\u4e92\u4f5c\u7528\u5230\u86cb\u767d\u8d28\u7ed3\u6784\uff0c\u4e3a\u751f\u547d\u79d1\u5b66\u63ed\u793a\u65b0\u7684\u89c1\u89e3\u3002<\/span><\/p>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u603b\u4e4b\uff0c\u6570\u5b66\u4e3aAI\u7684\u6838\u5fc3\u63d0\u4f9b\u4e86\u575a\u5b9e\u57fa\u7840\u3002\u5927\u6a21\u578b\u4e0e\u795e\u7ecf\u7f51\u7edc\u7684\u6570\u5b66\u57fa\u7840\u9a71\u52a8\u7740\u521b\u65b0\u7b97\u6cd5\u7684\u53d1\u5c55\u3002\u62d3\u6251\u6570\u636e\u5206\u6790\u5f15\u9886\u6211\u4eec\u4ece\u6570\u636e\u4e2d\u6316\u6398\u6df1\u5c42\u6a21\u5f0f\u3002\u56fe\u795e\u7ecf\u7f51\u7edc\u5219\u5c06\u6570\u5b66\u5e94\u7528\u4e8e\u66f4\u590d\u6742\u7684\u5173\u7cfb\u6570\u636e\u89e3\u6790\u3002\u8fd9\u4e9b\u6570\u5b66\u9886\u57df\u5171\u540c\u63a8\u52a8AI\u9886\u57df\u7684\u524d\u8fdb\uff0c\u5f00\u521b\u51fa\u66f4\u5e7f\u9614\u7684\u53ef\u80fd\u6027\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">1. <strong>\u5927\u6a21\u578b\u4e0e\u795e\u7ecf\u7f51\u7edc\u7684\u6570\u5b66\u57fa\u7840<\/strong><\/span><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u9884\u8bad\u7ec3\u5927\u6a21\u578b\u7684\u80fd\u529b\u8fb9\u754c\uff1a<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Yuan, Yang. &#8220;On the Power of Foundation Models.&#8221; <em>Proceedings of the 40th International Conference on Machine Learning<\/em>. Ed. Andreas, Krause, et al.s.: PMLR, 2023.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u4f7f\u7528\u8303\u7574\u8bba\uff0c\u5bf9\u9884\u8bad\u7ec3\u5927\u6a21\u578b\u7684\u80fd\u529b\u8fb9\u754c\u8fdb\u884c\u4e86\u7406\u8bba\u523b\u753b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Kashiwara, Masaki, and Pierre Schapira. <em>Categories and Sheaves<\/em>. Springer Berlin, Heidelberg, 2006.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u8303\u7574\u8bba\u6559\u79d1\u4e66\uff0c\u96be\u5ea6\u8f83\u5927\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Riehl, Emily. <em>Category Theory in Context<\/em>. Courier Dover Publications, 2017. Print.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u8303\u7574\u8bba\u6559\u79d1\u4e66\uff0c\u6bd4\u8f83\u9002\u5408\u521d\u5b66\u8005\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Radford, Alec, et al. &#8220;Improving Language Understanding by Generative Pre-Training.&#8221; &nbsp;(2018).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u9884\u6d4b\u4e0b\u4e00\u4e2a\u8bcd\u7684GPT\u7b97\u6cd5\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chen, Ting, et al. &#8220;A simple framework for contrastive learning of visual representations.&#8221; <em>International conference on machine learning<\/em>. PMLR, 2020.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u9884\u6d4b\u76f8\u4f3c\u56fe\u5bf9\u7684SimCLR\u7b97\u6cd5\uff0c\u5bf9\u4e8e\u56fe\u50cf\u5206\u7c7b\u4efb\u52a1\u975e\u5e38\u6709\u6548\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">He, Kaiming, et al. &#8220;Masked autoencoders are scalable vision learners.&#8221; <em>Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition<\/em>. 2022.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u57fa\u4e8e\u906e\u6321\u9884\u6d4b\u7684MAE\u7b97\u6cd5\uff0c\u5728\u5404\u7c7b\u56fe\u50cf\u4e0b\u6e38\u4efb\u52a1\u4e2d\u90fd\u6709\u5f88\u597d\u7684\u8868\u73b0\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Gidaris, Spyros, Praveer Singh, and Nikos Komodakis. &#8220;Unsupervised Representation Learning by Predicting Image Rotations.&#8221; <em>arXiv preprint arXiv:1803.07728 <\/em> (2018).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u57fa\u4e8e\u65cb\u8f6c\u9884\u6d4b\u7684\u7b97\u6cd5\uff0c\u662f\u975e\u5e38\u7b80\u5355\u800c\u4e14\u65e9\u671f\u7684\u9884\u8bad\u7ec3\u7b97\u6cd5\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u76f8\u5173\u6587\u7ae0\uff1a\u300a<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247663512&amp;idx=1&amp;sn=8d1863a5926300cf4aee3f05c2d06195&amp;chksm=e8992515dfeeac03bf58e73696d37c1ee341ceaeb09f24ec66e754d1b6e1918fc711d98390c3&amp;scene=21#wechat_redirect\" textvalue=\"\u667a\u80fd\u662f\u4ec0\u4e48\uff1f\u8303\u7574\u8bba\u4e3a\u901a\u7528\u4eba\u5de5\u667a\u80fd\u63d0\u4f9b\u666e\u9002\u6846\u67b6\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u667a\u80fd\u662f\u4ec0\u4e48\uff1f\u8303\u7574\u8bba\u4e3a\u901a\u7528\u4eba\u5de5\u667a\u80fd\u63d0\u4f9b\u666e\u9002\u6846\u67b6<\/a>\u300b<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u5bf9\u6bd4\u5b66\u4e60\u7684\u7406\u8bba\u57fa\u7840\uff1a<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Tan, Zhiquan, et al. &#8220;Contrastive Learning Is Spectral Clustering on Similarity Graph.&#8221; <em>arXiv preprint arXiv:2303.15103 <\/em> (2023).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/arxiv.org\/abs\/2303.15103v2<\/span> <\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u4e25\u683c\u523b\u753b\u4e86SimCLR\u4e0eCLIP\u8fd9\u4e24\u4e2a\u5e38\u7528\u9884\u8bad\u7ec3\u7b97\u6cd5\uff0c\u8bc1\u660e\u5176\u4e0e\u76f8\u4f3c\u56fe\u7684\u8c31\u805a\u7c7b\u662f\u7b49\u4ef7\u7684\u3002\u8be5\u7b49\u4ef7\u6027\u5e76\u4e0d\u5e73\u51e1\uff0c\u5b83\u53ef\u4ee5\u770b\u4f5c\u662f\u300aOn the Power of Foundation Models\u300b\u7684\u4e00\u4e2a\u6700\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u4e3a\u7c73\u7530\u5d4c\u5165\u5728\u518d\u751f\u6838\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\u7684\u5177\u4f53\u8868\u73b0\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Van Assel, Hugues, et al. &#8220;A Probabilistic Graph Coupling View of Dimension Reduction.&#8221; <em>Advances in Neural Information Processing Systems <\/em>35 (2022): 10696-708.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u63d0\u51fa\u4e86\u5206\u6790SimCLR\/CLIP\u4f7f\u7528\u7684\u7406\u8bba\u6846\u67b6<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Fan, Lijie, et al. &#8220;Improving Clip Training with Language Rewrites.&#8221; <em>arXiv preprint arXiv:2305.20088 <\/em> (2023).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/arxiv.org\/pdf\/2305.20088.pdf<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u662f\u6539\u8fdbCLIP\u7684\u6700\u65b0\u5de5\u4f5c\uff0c\u80cc\u540e\u7684\u57fa\u7840\u539f\u7406\u53ef\u4ee5\u7531\u540c\u6837\u7684\u7406\u8bba\u6846\u67b6\u89e3\u91ca\uff0c\u6709\u5f88\u597d\u7684\u6548\u679c\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">HaoChen, Jeff Z, et al. &#8220;Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss.&#8221; <em>Advances in Neural Information Processing Systems <\/em>34 (2021): 5000-11.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/arxiv.org\/pdf\/2106.04156.pdf<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u662f\u9996\u7bc7\u5206\u6790SimCLR\uff08\u53d8\u4f53\uff09\u7684\u7406\u8bba\u5de5\u4f5c\uff0c\u7a81\u7834\u6027\u5730\u63d0\u51fa\u4e86\u5728Population\u5206\u5e03\u4e2d\u5206\u6790\u7b97\u6cd5\uff0c\u8bc1\u660e\u4e86SimCLR\u53d8\u4f53\u5728\u505a\u67d0\u79cd\u8c31\u805a\u7c7b\uff08\u53d8\u4f53\uff09\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Radford, Alec, et al. &#8220;Learning transferable visual models from natural language supervision.&#8221; 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PMLR, 2021.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u8fde\u63a5\u56fe\u50cf\u4e0e\u6587\u5b57\u7684CLIP\u7b97\u6cd5\uff0c\u662fDall-E\/EVA\/MILAN\u7b49\u591a\u6a21\u6001\u6a21\u578b\u7684\u91cd\u8981\u7ec4\u6210\u90e8\u5206\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><\/span><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u6700\u5927\u5316\u539f\u7406\u89c6\u89d2\u4e0b\u7684\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\u3001\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u5e73\u5747\u573a\u6700\u4f18\u63a7\u5236\u5efa\u6a21\uff1a<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Li, Qianxiao, Long Chen, and Cheng Tai. &#8220;Maximum Principle Based Algorithms for Deep Learning.&#8221; <em>arXiv preprint arXiv:1710.09513 <\/em> (2017).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u7814\u7a76\u8ba8\u8bba\u4e86\u5982\u4f55\u7528\u73b0\u4ee3\u63a7\u5236\u7406\u8bba\u4e2d\u7684\u5e9e\u7279\u91cc\u4e9a\u91d1\u6700\u5927\u539f\u7406\u5bf9\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u4f18\u5316\u8fc7\u7a0b\u8fdb\u884c\u5efa\u6a21\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">E, Weinan, Jiequn Han, and Qianxiao Li. &#8220;A Mean-Field Optimal Control Formulation of Deep Learning.&#8221; <em>Research in the Mathematical Sciences <\/em>6.1 (2018): 10.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u7814\u7a76\u4ecb\u7ecd\u4e86\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7fa4\u4f53\u98ce\u9669\u6700\u5c0f\u5316\u95ee\u9898\u4f5c\u4e3a\u5747\u503c\u573a\u6700\u4f18\u63a7\u5236\u95ee\u9898\u7684\u6570\u5b66\u8868\u8ff0\uff0c\u9648\u8ff0\u5e76\u8bc1\u660e\u4e86\u54c8\u5bc6\u5c14\u987f-\u96c5\u53ef\u6bd4-\u8d1d\u5c14\u66fc\u7c7b\u578b\u548c\u5e9e\u7279\u91cc\u4e9a\u91d1\u7c7b\u578b\u7684\u6700\u4f18\u6761\u4ef6\u3002\u8fd9\u4e9b\u5e73\u5747\u573a\u7ed3\u679c\u53cd\u6620\u4e86\u5b66\u4e60\u95ee\u9898\u7684\u6982\u7387\u6027\u8d28\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">2. <strong>\u62d3\u6251\u6570\u636e\u5206\u6790<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Edelsbrunner, Herbert, and John Harer. &#8220;Persistent Homology-a Survey.&#8221; <em>Contemporary mathematics <\/em>453.26 (2008): 257-82.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u6301\u7eed\u540c\u8c03\uff08Persistent Homology\uff09\u662f\u62d3\u6251\u6570\u636e\u5904\u7406\uff08Topological data analysis: TDA\uff09\u6838\u5fc3\u6a21\u578b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Tauzin, Guillaume, et al. &#8220;giotto-tda: A topological data analysis toolkit for machine learning and data exploration.&#8221; <em>The Journal of Machine Learning Research<\/em> 22.1 (2021): 1834-1839.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u8fd9\u8fd9\u7bc7\u6587\u7ae0\u603b\u7ed3\u4e86\u62d3\u6251\u6570\u636e\u548c\u673a\u5668\u5b66\u4e60\u7684\u7ed3\u5408\u7684\u76f8\u5173\u7406\u8bba\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Cang, Zixuan, Lin Mu, and Guo-Wei Wei. &#8220;Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening.&#8221; 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Vol. 16: Cambridge university press, 2005.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Otter, Nina, et al. &#8220;A Roadmap for the Computation of Persistent Homology.&#8221; <em>EPJ Data Science <\/em>6 (2017): 1-38.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Zomorodian, Afra, and Gunnar Carlsson. &#8220;Computing persistent homology.&#8221; <em>Proceedings of the twentieth annual symposium on Computational geometry<\/em>. 2004.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u62d3\u6251\u673a\u5668\u5b66\u4e60\u4ee5\u53ca\u5176\u5728\u5206\u5b50\u751f\u7269\u5e94\u7528\uff1a<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Pun, Chi Seng, Si Xian Lee, and Kelin Xia. &#8220;Persistent-Homology-Based Machine Learning: A Survey and a Comparative Study.&#8221; <em>Artificial Intelligence Review <\/em>55.7 (2022): 5169-213.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Nguyen, Duc Duy, Zixuan Cang, and Guo-Wei Wei. &#8220;A Review of Mathematical Representations of Biomolecular Data.&#8221; <em>Physical Chemistry Chemical Physics <\/em>22.8 (2020): 4343-67.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chen, Jiahui, et al. &#8220;Mutations Strengthened Sars-Cov-2 Infectivity.&#8221; <em>Journal of molecular biology <\/em>432.19 (2020): 5212-26.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u6301\u7eed\u8c31\u56fe\u6cd5\uff1a<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Meng, Zhenyu, and Kelin Xia. &#8220;Persistent spectral\u2013based machine learning (PerSpect ML) for protein-ligand binding affinity prediction.&#8221; <em>Science advances<\/em> 7.19 (2021): eabc5329.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">M\u00e9moli, Facundo, Zhengchao Wan, and Yusu Wang. &#8220;Persistent Laplacians: Properties, algorithms and implications.&#8221; <em>SIAM Journal on Mathematics of Data Science<\/em> 4.2 (2022): 858-884.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">3. <strong>\u56fe\u795e\u7ecf\u7f51\u7edc<\/strong><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Gilmer, Justin, et al. &#8220;Neural message passing for quantum chemistry.&#8221; <em>International conference on machine learning<\/em>. PMLR, 2017.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u4f5c\u4e3a\u56fe\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u4e00\u4e2a\u91cc\u7a0b\u7891\u4e4b\u4f5c\uff0c\u63d0\u51fa\u4e86\u6d88\u606f\u4f20\u9012\u8303\u5f0f\uff0c\u4ece\u800c\u5c06\u4e3b\u6d41\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u90fd\u7eb3\u5165\u5230\u8fd9\u4e00\u8303\u5f0f\u4e4b\u4e2d\uff0c\u4e3a\u672a\u6765\u5bf9\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u7406\u8bba\u7814\u7a76\u63d0\u4f9b\u4e00\u4e2a\u6846\u67b6\u3002\u6b64\u5916\u672c\u6587\u4f7f\u7528QM9\u9a8c\u8bc1\u4e86\u57fa\u4e8e\u6d88\u606f\u4f20\u9012\u8303\u5f0f\u6240\u8bbe\u8ba1\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\u5728\u91cf\u5b50\u5316\u5b66\u6027\u8d28\u9884\u6d4b\u4e0a\u7684\u6027\u80fd\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Sch\u00fctt, Kristof T, et al. &#8220;Schnet\u2013a Deep Learning Architecture for Molecules and Materials.&#8221; <em>The Journal of Chemical Physics <\/em>148.24 (2018).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u4f5c\u4e3a\u6df1\u5ea6\u5b66\u4e60\u5728\u5316\u5b66\u6027\u8d28\u8ba1\u7b97\u65b9\u9762\u7684\u6df1\u5ea6\u5e94\u7528\uff0c\u5e76\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5b8c\u6574\u7684\u9488\u5bf9\u91cf\u5b50\u5316\u5b66\u8ba1\u7b97\u7684\u5f00\u6e90\u6846\u67b6\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Xu, Keyulu, et al. &#8220;How Powerful Are Graph Neural Networks?&#8221; <em>arXiv preprint arXiv:1810.00826 <\/em> (2018).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u8fd9\u7bc7\u6587\u7ae0\u4ece\u7406\u8bba\u4e0a\u5206\u6790\u4e86GNN\u7684\u8868\u8fbe\u80fd\u529b\u7684\u4e0a\u9650\uff0c\u4e3a\u4e4b\u540eGNN\u7684\u74f6\u9888\u7a81\u7834\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7406\u8bba\u65b9\u5411\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Ebli, Stefania, Micha\u00ebl Defferrard, and Gard Spreemann. &#8220;Simplicial Neural Networks.&#8221; <em>arXiv preprint arXiv:2010.03633 <\/em> (2020).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u5f15\u5165\u4e86\u5355\u7eaf\u590d\u5f62\u4f5c\u4e3a\u56fe\u6570\u636e\u7684\u66f4\u4e00\u822c\u5316\u5f62\u5f0f\uff0c\u6b64\u5916\u8bbe\u8ba1\u4e86\u5377\u79ef\u64cd\u4f5c\u5e76\u5728\u6b64\u57fa\u7840\u4e0a\u6784\u5efa\u6a21\u578b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Bodnar, Cristian, et al. &#8220;Weisfeiler and lehman go topological: Message passing simplicial networks.&#8221; <em>International Conference on Machine Learning<\/em>. PMLR, 2021.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u901a\u8fc7\u5f15\u5165\u5355\u7eaf\u5f62\u7684\u6982\u5ff5\uff0c\u6765\u7a81\u7834GNN\u6536\u5230\u7684WL-test\u7684\u9650\u5236\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Bodnar, Cristian, et al. &#8220;Weisfeiler and Lehman Go Cellular: Cw Networks.&#8221; <em>Advances in Neural Information Processing Systems <\/em>34 (2021): 2625-40.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u57fa\u4e8e2\u9636\u5355\u7eaf\u5f62\u5bf9\u5e94\u7684\u662f\u4e09\u89d2\u5f62\uff0c\u4ece\u800c\u96be\u4ee5\u5bf9\u82ef\u73af\u7b49\u542b\u6709\u8d85\u8fc73\u4e2a\u539f\u5b50\u6784\u6210\u7684\u5206\u5b50\u73af\u72b6\u7ed3\u6784\u8fdb\u884c\u6709\u6548\u7684\u5904\u7406\uff0c\u56e0\u6b64\u5f15\u5165\u4e86\u5143\u80de\u590d\u5f62\u5bf9\u5355\u7eaf\u590d\u5f62\u7684\u6d88\u606f\u4f20\u9012\u7f51\u7edc\u8fdb\u884c\u6cdb\u5316\uff0c\u4f7f\u5176\u66f4\u52a0\u9002\u7528\u4e8e\u5316\u5b66\u6027\u8d28\u9884\u6d4b\u4efb\u52a1\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Jiang, Yi, et al. &#8220;Topological Representations of Crystalline Compounds for the Machine-Learning Prediction of Materials Properties.&#8221; <em>npj computational materials <\/em>7.1 (2021): 28.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u901a\u8fc7\u5f15\u5165\u4e00\u79cd\u57fa\u4e8e\u62d3\u6251\u5b66\u7684\u539f\u5b50\u7279\u5f02\u6027\u6301\u4e45\u540c\u8c03\uff08ASPH\uff09\u65b9\u6cd5\uff0c\u89e3\u51b3\u4e86\u5982\u4f55\u4e3a\u6676\u4f53\u5316\u5408\u7269\u7b49\u590d\u6742\u6570\u636e\u96c6\u6784\u5efa\u5177\u6709\u5316\u5b66\u6d1e\u5bdf\u529b\u7684\u4f4e\u7ef4\u8868\u793a\u7684\u95ee\u9898\uff0c\u5e76\u4e14\u5f00\u53d1\u4e86\u4e00\u4e2a\u9ad8\u5ea6\u51c6\u786e\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u7528\u4e8e\u9884\u6d4b\u6676\u4f53\u5316\u5408\u7269\u7684\u5f62\u6210\u80fd\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Bodnar, Cristian, et al. &#8220;Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in gnns.&#8221; <em>Advances in Neural Information Processing Systems<\/em> 35 (2022): 18527-18541.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u7ec6\u80de\u5c42\u7ea7\u7ed3\u6784\u7684\u6269\u6563\u8fc7\u7a0bSheaf Diffusion\uff0c\u53ef\u4ee5\u5728\u65e0\u9650\u65f6\u95f4\u6781\u9650\u4e0b\u5904\u7406\u8d8a\u6765\u8d8a\u590d\u6742\u7684\u8282\u70b9\u5206\u7c7b\u4efb\u52a1\uff0c\u4ee5\u89e3\u51b3\u56fe\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5f02\u8d28\u6027\u548c\u8fc7\u5ea6\u5e73\u6ed1\u95ee\u9898\uff0c\u6b64\u5916\u8bc1\u660e\u4e86\u5176\u6bd4Graph Convolutional Networks\u66f4\u52a0\u7075\u6d3b\uff0c\u5bf9\u6e10\u8fd1\u884c\u4e3a\u5177\u6709\u66f4\u5927\u7684\u63a7\u5236\u80fd\u529b\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Qiao, Zhuoran, et al. &#8220;Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry.&#8221; <em>Proceedings of the National Academy of Sciences <\/em>119.31 (2022): e2205221119.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u540d\u4e3aOrbNet-Equi\u7684\u65b0\u65b9\u6cd5\uff0c\u4f7f\u7528\u53d7\u7269\u7406\u542f\u53d1\u7684\u795e\u7ecf\u7f51\u7edc\u6765\u5b66\u4e60\u57fa\u4e8e\u539f\u5b50\u8f68\u9053\u4e4b\u95f4\u7684\u7535\u5b50\u76f8\u4e92\u4f5c\u7528\u7684\u5206\u5b50\u8868\u793a\uff0c\u4ee5\u89e3\u91ca\u5982\u4f55\u5229\u7528\u7535\u5b50\u76f8\u4e92\u4f5c\u7528\u6765\u52a0\u901f\u91cf\u5b50\u5316\u5b66\u8ba1\u7b97\u7684\u95ee\u9898\uff0c\u5e76\u4e14\u8bc1\u660e\u6bd4\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u548c\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\u66f4\u51c6\u786e\u548c\u66f4\u5feb\u3002<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Fu, Xiang, et al. &#8220;Simulate Time-Integrated Coarse-Grained Molecular Dynamics with Geometric Machine Learning.&#8221; <em>arXiv preprint arXiv:2204.10348 <\/em> (2022).<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\uff0c\u7ed3\u5408\u7c97\u7c92\u5316\u548c\u65f6\u95f4\u79ef\u5206\u5efa\u6a21\u4e0e\u56fe\u795e\u7ecf\u7f51\u7edc\uff0c\u7528\u4e8e\u6a21\u62df\u5206\u5b50\u52a8\u529b\u5b66\uff0c\u8be5\u6a21\u578b\u4f18\u4e8e\u57fa\u4e8eGNN\u548c\u957f\u77ed\u671f\u8bb0\u5fc6\uff08LSTM\uff09\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u7684\u4e24\u4e2a\u76d1\u7763\u5b66\u4e60\u57fa\u51c6\u6a21\u578b\u3002\u4e0e\u4f20\u7edf\u529b\u573a\u76f8\u6bd4\uff0c\u8be5\u6a21\u578b\u53ef\u4ee5\u5728\u9700\u8981\u957f\u65f6\u95f4\u6a21\u62df\u7684\u4f30\u8ba1\u95ee\u9898\u4e2d\u63d0\u4f9b\u51e0\u4e2a\u6570\u91cf\u7ea7\u7684\u52a0\u901f\u3002\u901a\u8fc7\u6a21\u62df\u9690\u5f0f\u6eb6\u5242\u4e2d\u7684\u5355\u94fe\u7c97\u7c92\u5316\u805a\u5408\u7269\uff0c\u5e76\u53ef\u9760\u5730\u4f30\u8ba1\u9700\u8981\u957f\u65f6\u95f4\u6a21\u62df\u7684\u805a\u5408\u7269\u6027\u8d28\uff0c\u8bc1\u660e\u4e86\u8be5\u6a21\u578b\u7684\u6027\u80fd\u3002<\/span><span style=\"color: rgb(63, 63, 63);font-size: 15px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.034em;\"><\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u76f8\u5173\u8bfb\u4e66\u4f1a\uff1a<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247659349&amp;idx=1&amp;sn=5e0bcad718d122a04e1b34a8bf94f906&amp;chksm=e89935d8dfeebcceb72a61c9c7602a6042eefad7bf106147d81c3110e04c6f61fbde5214aec9&amp;scene=21#wechat_redirect\" textvalue=\"AI+Science \u8bfb\u4e66\u4f1a\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">AI+Science \u8bfb\u4e66\u4f1a<\/a>\u4e2d\u4ed8\u8944\u5173\u4e8e\u5206\u5b50\u52a8\u529b\u5b66\u6a21\u62df\u7684\u4ecb\u7ecd<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">https:\/\/pattern.swarma.org\/study_group_issue\/484<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Xu, Hao, et al. &#8220;Retention time prediction for chromatographic enantioseparation by quantile geometry-enhanced graph neural network.&#8221; <em>Nature Communications<\/em> 14.1 (2023): 3095.<\/span><\/section>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u63a8\u8350\u8bed\uff1a\u672c\u6587\u63d0\u51fa\u7684\u7814\u7a76\u6846\u67b6\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u6280\u672f\u6539\u8fdb\u8272\u8c31\u624b\u6027\u5206\u79bb\u7684\u6548\u7387\u3002\u8be5\u6846\u67b6\u89e3\u51b3\u4e86\u6570\u636e\u83b7\u53d6\u3001\u624b\u6027\u5206\u5b50\u7684\u4e09\u7ef4\u8868\u793a\u548c\u6570\u636e\u4e0d\u786e\u5b9a\u6027\u7b49\u95ee\u9898\u3002\u5b83\u901a\u8fc7\u4ece\u73b0\u6709\u6587\u732e\u4e2d\u63d0\u53d6\u5b9e\u9a8c\u7ed3\u679c\u6784\u5efa\u4e86\u4e00\u4e2a\u624b\u6027\u5206\u5b50\u4fdd\u7559\u65f6\u95f4\u6570\u636e\u96c6\uff0c\u5e76\u4f7f\u7528\u4e00\u79cd\u4e13\u95e8\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\uff08QGeoGNN\uff09\u8fdb\u884c\u9884\u6d4b\u3002QGeoGNN\u5728\u5355\u67f1\u548c\u591a\u67f1\u9884\u6d4b\u4e2d\u51c6\u786e\u9884\u6d4b\u4e86\u624b\u6027\u5206\u5b50\u7684\u4fdd\u7559\u65f6\u95f4\uff0c\u4ee5\u53ca\u5728\u4e0d\u540c\u6761\u4ef6\u4e0b\u7684\u5206\u79bb\u6982\u7387\u3002\u7136\u800c\uff0c\u6570\u636e\u7684\u4ee3\u8868\u6027\u548c\u8d28\u91cf\u3001\u6570\u636e\u7684\u4e0d\u786e\u5b9a\u6027\u3001\u4f4e\u76f8\u4f3c\u6027\u5206\u5b50\u7684\u9884\u6d4b\u51c6\u786e\u6027\u4ee5\u53ca\u7279\u5f81\u63d0\u53d6\u8fc7\u7a0b\u5b58\u5728\u4e00\u5b9a\u7684\u9650\u5236\u3002\u5c3d\u7ba1\u5b58\u5728\u8fd9\u4e9b\u9650\u5236\uff0c\u8be5\u6846\u67b6\u5728\u8272\u8c31\u624b\u6027\u5206\u79bb\u4e2d\u786e\u5b9a\u9002\u5f53\u5b9e\u9a8c\u6761\u4ef6\u65b9\u9762\u5177\u6709\u91cd\u8981\u6f5c\u529b\u3002<\/span><\/section>\n<p style=\"margin-bottom: 0px;line-height: 1.75em;\"><br  \/><\/p>\n<section style=\"line-height: 1.75em;margin-bottom: 0px;\"><br  \/><\/section>\n<section style=\"line-height: 1.75em;margin-left: 0px;margin-right: 0px;margin-bottom: 0px;\"><strong style=\"outline: 0px;letter-spacing: 0.544px;white-space: normal;font-size: 15px;text-align: left;color: rgb(255, 255, 255);font-family: PingFangSC-light;\"><span style=\"outline: 0px;background-color: rgb(12, 130, 169);\">\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u52a0\u5165\u8bfb\u4e66\u4f1a<\/span><\/strong><\/section>\n<p style=\"display: none;\"><mp-style-type data-value=\"3\"><\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5bfc\u8bed \u6570\u5341\u5e74\u6765\uff0c\u4eba\u5de5\u667a\u80fd\u7684\u7406\u8bba\u53d1\u5c55\u548c\u6280\u672f\u5b9e\u8df5\u4e00\u76f4\u4e0e\u79d1\u5b66\u63a2\u7d22\u76f8\u4f34\u800c\u751f\uff0c\u5c24\u5176\u5728\u4ee5\u5927\u6a21\u578b\u4e3a\u4ee3\u8868\u7684\u4eba\u5de5\u667a\u80fd\u6280\u672f\u5e94\u7528\u96c6\u4e2d\u7206\u53d1\u7684\u5f53\u4e0b\uff0c\u4eba\u5de5\u667a\u80fd\u6b63\u5728\u52a0\u901f\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7b49\u57fa\u7840\u79d1\u5b66\u7684\u9769\u65b0\uff0c\u800c\u8fd9\u4e9b\u5b66\u79d1\u4e5f\u5728\u53cd\u8fc7\u6765\u542f\u53d1\u4eba\u5de5\u667a\u80fd\u6280\u672f\u521b\u65b0\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u4f5c\u4e3a\u517c\u5177\u7406\u8bba\u5c5e\u6027\u4e0e\u5de5\u5177\u5c5e\u6027\u7684\u91cd\u8981\u57fa\u7840\u5b66\u79d1\uff0c\u4e0e\u4eba\u5de5\u667a\u80fd\u5173\u7cfb\u751a\u5bc6\uff0c\u76f8\u8f85\u76f8\u6210&#8230;<\/p>\n","protected":false},"author":0,"featured_media":44737,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/44745"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=44745"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/44745\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/44737"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=44745"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=44745"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=44745"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=44745"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}