{"id":6685,"date":"2025-12-30T11:10:31","date_gmt":"2025-12-30T03:10:31","guid":{"rendered":"https:\/\/nullthought.net\/?p=6685"},"modified":"2025-12-30T11:10:33","modified_gmt":"2025-12-30T03:10:33","slug":"%e5%a4%a7%e6%a8%a1%e5%9e%8b%e7%9a%84%e5%87%a0%e4%bd%95%e5%bc%8f%e8%ae%b0%e5%bf%86%ef%bc%88geometric-memory%ef%bc%89%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=6685","title":{"rendered":"\u5927\u6a21\u578b\u7684\u51e0\u4f55\u5f0f\u8bb0\u5fc6\uff08Geometric Memory\uff09\uff1f"},"content":{"rendered":"\n<p>\u8bba\u6587<strong><a href=\"https:\/\/arxiv.org\/abs\/2510.26745\" target=\"_blank\" rel=\"noreferrer noopener\">\u201cDeep sequence models tend to memorize geometrically; it is unclear why\u201d<\/a><\/strong>\u8ba8\u8bba\u4e00\u4e2a\u770b\u8d77\u6765\u201c\u53cd\u76f4\u89c9\u201d\u7684\u73b0\u8c61\uff1a\u5728\u5e8f\u5217\u5efa\u6a21\u91cc\uff0c\u6a21\u578b\u5bf9\u4e00\u5806\u201c\u539f\u5b50\u4e8b\u5b9e\u201d\uff08\u6ca1\u6709\u7edf\u8ba1\u5197\u4f59\u3001\u5f88\u96be\u538b\u7f29\u7684\u4fe1\u606f\uff09\u8fdb\u884c\u8bb0\u5fc6\u65f6\uff0c\u5e38\u89c1\u76f4\u89c9\u662f\u628a\u5b83\u4eec\u5f53\u4f5c\u201c\u5171\u73b0\u5173\u7cfb\u7684\u67e5\u8868\u201d\uff08\u4f5c\u8005\u79f0\u4e3a<strong>\u8054\u60f3\u5f0f\u8bb0\u5fc6<\/strong>\uff09\u3002\u4f46\u4f5c\u8005\u901a\u8fc7\u53ef\u63a7\u7684\u56fe\u4efb\u52a1\u53d1\u73b0\uff0c\u6df1\u5ea6\u5e8f\u5217\u6a21\u578b\uff08Transformer\u3001Mamba \u7b49\uff09\u5f80\u5f80\u4f1a\u81ea\u53d1\u5f62\u6210\u4e00\u79cd<strong>\u51e0\u4f55\u5f0f\u8bb0\u5fc6<\/strong>\uff1a\u4e0d\u4ec5\u8bb0\u4f4f\u8bad\u7ec3\u4e2d\u51fa\u73b0\u7684\u5c40\u90e8\u90bb\u63a5\u5173\u7cfb\uff0c\u8fd8\u5728\u5d4c\u5165\u7a7a\u95f4\u91cc\u7ec4\u7ec7\u51fa\u53cd\u6620\u5168\u5c40\u7ed3\u6784\u7684\u201c\u51e0\u4f55\u5e03\u5c40\u201d\uff0c\u8ba9\u539f\u672c\u9700\u8981\u591a\u6b65\u7ec4\u5408\u7684\u63a8\u7406\u53d8\u6210\u66f4\u5bb9\u6613\u5b66\u7684\u201c\u51e0\u4f55\u4e00\u6b65\u5224\u65ad\u201d\u3002<\/p>\n\n\n\n<p>\u8bba\u6587\u4f5c\u8005\u4e3aShahriar Noroozizadeh, Vaishnavh Nagarajan, Elan Rosenfeld, Sanjiv Kumar\uff0c\u6765\u81eaCMU\u548cGoogle Research\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e00\u3001\u6838\u5fc3\u4efb\u52a1\uff1a\u628a\u201c\u8def\u5f84\u641c\u7d22\u201d\u53d8\u6210\u68c0\u9a8c\u8bb0\u5fc6\u5f62\u6001\u7684\u8bd5\u91d1\u77f3<\/h4>\n\n\n\n<p>\u4f5c\u8005\u4f7f\u7528\u4e00\u79cd\u4e13\u95e8\u8bbe\u8ba1\u6765\u201c\u5361\u4f4f\u201d\u4e0b\u4e00\u8bcd\u9884\u6d4b\u5b66\u4e60\u7684\u56fe\u62d3\u6251\uff08path-star\uff09\uff0c\u6bd4\u8f83\u4e24\u79cd\u8bbe\u7f6e\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>in-context<\/strong>\uff1a\u628a\u56fe\u653e\u5728\u4e0a\u4e0b\u6587\u91cc\u8ba9\u6a21\u578b\u73b0\u7b97\u8def\u5f84\uff08\u6b64\u524d\u5de5\u4f5c\u663e\u793a\u8fd9\u7c7b\u8bbe\u7f6e\u5bb9\u6613\u5931\u8d25\uff09\u3002<\/li>\n\n\n\n<li><strong>in-weights<\/strong>\uff1a\u8ba9\u6a21\u578b\u628a\u56fe\u7684\u8fb9\u5173\u7cfb\u5148\u8bb0\u8fdb\u53c2\u6570\u91cc\uff0c\u518d\u5728\u6d4b\u8bd5\u65f6\u505a\u8def\u5f84\u76f8\u5173\u9884\u6d4b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728 in-weights \u8bbe\u7f6e\u4e0b\uff0c\u4f5c\u8005\u7528\u4ece\u96f6\u8bad\u7ec3\u7684 decoder-only Transformer\uff08\u4e5f\u5728 Mamba \u4e0a\u590d\u73b0\uff09\uff0c\u8bad\u7ec3\u65f6\u628a\u201c\u8bb0\u8fb9\u6837\u672c\u201d\u548c\u201c\u627e\u8def\u5f84\u6837\u672c\u201d\u4ea4\u9519\uff0c\u5e76\u5f15\u5165 pause token \u7b49\u6280\u5de7\uff1b\u540c\u65f6\u4e3a\u4e86\u907f\u514d\u5df2\u77e5\u7684\u201c\u53cd\u8f6c\u8bc5\u5492\u201d\uff0c\u5728\u8bb0\u8fb9\u9636\u6bb5\u52a0\u5165\u6b63\u5411\u4e0e\u53cd\u5411\u8fb9\u7684\u6570\u636e\u589e\u5f3a\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e8c\u3001\u5173\u952e\u53d1\u73b0\uff1a\u5927\u89c4\u6a21\u201c\u9690\u5f0f\u63a8\u7406\u201d\u786e\u5b9e\u53d1\u751f\u4e86<\/h4>\n\n\n\n<p>\u6700\u91cd\u8981\u7684\u7ecf\u9a8c\u7ed3\u679c\u662f\uff1a\u5728\u89c4\u6a21\u5f88\u5927\u7684 path-star \u56fe\u4e0a\uff08\u8282\u70b9\u6570\u91cf\u53ef\u5230\u7ea6\u4e94\u4e07\u91cf\u7ea7\u3001\u8bad\u7ec3\u53ea\u8986\u76d6\u90e8\u5206\u8def\u5f84\uff09\uff0cTransformer \u4e0e Mamba \u4ecd\u80fd\u5728\u672a\u89c1\u8fc7\u7684\u53f6\u5b50\u8282\u70b9\u4e0a\u9884\u6d4b\u6b63\u786e\u7684\u8def\u5f84\u4fe1\u606f\uff0c\u7cbe\u5ea6\u53ef\u8fbe\u5230\u51e0\u4e4e\u6ee1\u5206\u3002<br>\u4f5c\u8005\u8fdb\u4e00\u6b65\u7528\u4e00\u4e9b\u63a7\u5236\u5b9e\u9a8c\u8bf4\u660e\uff1a\u6210\u529f\u5e76\u4e0d\u4f9d\u8d56\u201c\u4ece\u540e\u5f80\u524d\u731c\u7b54\u6848\u201d\u8fd9\u79cd\u6295\u673a\u6377\u5f84\uff08\u4f8b\u5982\u6a21\u578b\u5e76\u6ca1\u6709\u6309\u201c\u53cd\u5411\u987a\u5e8f\u201d\u5148\u5b66\u5bb9\u6613\u7684 token \u518d\u5b66\u96be\u7684 token\uff09\uff0c\u800c\u662f\u66f4\u50cf\u771f\u7684\u5b66\u5230\u4e86\u67d0\u79cd\u80fd\u6cdb\u5316\u7684\u5185\u90e8\u7ed3\u6784\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e09\u3001\u8bc1\u636e\u6307\u5411\u201c\u51e0\u4f55\u5f0f\u8bb0\u5fc6\u201d\uff1a\u5d4c\u5165\u7a7a\u95f4\u51fa\u73b0\u5168\u5c40\u7ed3\u6784<\/h4>\n\n\n\n<p>\u8bba\u6587\u7ed9\u51fa\u76f4\u63a5\u8bc1\u636e\u8868\u660e\u6a21\u578b\u7684 token\/\u8282\u70b9\u5d4c\u5165\u5e76\u975e\u4efb\u610f\uff0c\u800c\u662f\u5448\u73b0\u51fa\u201c\u540c\u4e00\u8def\u5f84\u7684\u53f6\u5b50\u4e0e\u5173\u952e\u8282\u70b9\u66f4\u9760\u8fd1\u201d\u7684\u7c07\u7ed3\u6784\uff0c\u8fd9\u79cd\u7ed3\u6784\u53cd\u6620\u4e86\u56fe\u7684\u5168\u5c40\u5173\u7cfb\uff0c\u800c\u4e0d\u4ec5\u662f\u8bad\u7ec3\u4e2d\u51fa\u73b0\u8fc7\u7684\u5c40\u90e8\u5171\u73b0\u3002<br>\u8fd9\u4f7f\u5f97\u539f\u672c\u9700\u8981\u6cbf\u7740\u8fb9\u5173\u7cfb\u591a\u6b65\u7ec4\u5408\u7684\u4efb\u52a1\uff0c\u5728\u51e0\u4f55\u7a7a\u95f4\u91cc\u66f4\u50cf\u662f\u201c\u627e\u5230\u4e0e\u76ee\u6807\u6700\u5339\u914d\u7684\u90bb\u5c45\/\u65b9\u5411\u201d\u7684\u95ee\u9898\uff0c\u4ece\u800c\u663e\u8457\u964d\u4f4e\u5b66\u4e60\u96be\u5ea6\uff08\u81f3\u5c11\u4ece\u7ecf\u9a8c\u4e0a\u770b\u662f\u8fd9\u6837\uff09\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u56db\u3001\u4e3a\u4ec0\u4e48\u4f5c\u8005\u8bf4\u201c\u5f88\u96be\u89e3\u91ca\u201d\uff1a\u5e38\u89c1\u538b\u529b\u673a\u5236\u90fd\u4e0d\u591f<\/h4>\n\n\n\n<p>\u4f5c\u8005\u7cfb\u7edf\u6027\u5730\u53cd\u9a73\u4e86\u51e0\u7c7b\u76f4\u89c9\u89e3\u91ca\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5bb9\u91cf\/\u74f6\u9888\u538b\u529b\u5e76\u4e0d\u80fd\u89e3\u91ca<\/strong>\uff1a\u4ed6\u4eec\u5c55\u793a\u4e86\u5728\u76f8\u540c\u7684\u4f18\u5316\u8bbe\u7f6e\u4e0b\uff0c\u628a\u5d4c\u5165\u51bb\u7ed3\u3001\u4ec5\u5b66\u4e60\u4e00\u4e2a\u201c\u7eaf\u8054\u60f3\u5f0f\u201d\u7684\u8868\u5f81\u4e5f\u80fd\u62df\u5408\u6570\u636e\uff0c\u8bf4\u660e\u201c\u7ed3\u6784\u4e0a\u505a\u4e0d\u5230\u8054\u60f3\u8bb0\u5fc6\u201d\u5e76\u4e0d\u662f\u539f\u56e0\uff1b\u51e0\u4f55\u7ed3\u6784\u662f\u201c\u81ea\u7136\u957f\u51fa\u6765\u7684\u201d\uff0c\u4e0d\u662f\u88ab\u8feb\u7684\u3002<\/li>\n\n\n\n<li><strong>\u201c\u51e0\u4f55\u66f4\u7701\u53c2\u6570\/\u66f4\u7b80\u6d01\u201d\u4e5f\u672a\u5fc5\u6210\u7acb<\/strong>\uff1a\u5728\u8fd9\u4e9b\u8bb0\u5fc6\u578b\u56fe\u4efb\u52a1\u91cc\uff0c\u8054\u60f3\u5f0f\u5b58\u50a8\u4e0e\u51e0\u4f55\u5f0f\u5b58\u50a8\u5728\u5e38\u89c1\u590d\u6742\u5ea6\u5ea6\u91cf\u4e0b\u5dee\u8ddd\u53ef\u80fd\u53ea\u662f\u5e38\u6570\u500d\uff0c\u5e76\u4e0d\u4f1a\u968f\u7740\u56fe\u89c4\u6a21\u663e\u8457\u62c9\u5f00\uff0c\u56e0\u6b64\u5f88\u96be\u8bf4\u4f18\u5316\u5668\u662f\u56e0\u4e3a\u201c\u66f4\u7701\u201d\u624d\u504f\u597d\u51e0\u4f55\u3002<\/li>\n\n\n\n<li><strong>\u76d1\u7763\u4fe1\u53f7\u7684\u201c\u5168\u5c40\u6027\u201d\u4e5f\u4e0d\u8db3\u4ee5\u89e3\u91ca<\/strong>\uff1a\u5373\u4f7f\u53ea\u7528\u5c40\u90e8\u76d1\u7763\uff08\u53ea\u8bad\u7ec3\u8bb0\u8fb9\u3001\u4e0d\u76f4\u63a5\u8bad\u7ec3\u8def\u5f84\uff09\uff0c\u6a21\u578b\u5d4c\u5165\u91cc\u4ecd\u4f1a\u51fa\u73b0\u5168\u5c40\u51e0\u4f55\uff1b\u800c\u4e14\u8fd9\u79cd\u53ea\u5b66\u5c40\u90e8\u7684\u6a21\u578b\u518d\u5fae\u8c03\u5230\u8def\u5f84\u76f8\u5173\u76ee\u6807\u65f6\u4e5f\u80fd\u53d6\u5f97\u8f83\u9ad8\u6d4b\u8bd5\u8868\u73b0\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4f5c\u8005\u56e0\u6b64\u5f3a\u8c03\uff1a\u8fd9\u662f\u4e00\u79cd\u53d1\u751f\u5728\u201c\u7f3a\u5c11\u7edf\u8ba1\u5197\u4f59\u7684\u7eaf\u8bb0\u5fc6\u4efb\u52a1\u201d\u4e2d\u7684\u51e0\u4f55\u7ed3\u6784\u6d8c\u73b0\uff0c\u4e0d\u80fd\u8f7b\u6613\u5f52\u56e0\u4e8e\u6211\u4eec\u719f\u6089\u7684\u67b6\u6784\u3001\u4f18\u5316\u6216\u76d1\u7763\u538b\u529b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e94\u3001\u4ece Node2Vec \u5f97\u5230\u7684\u7ebf\u7d22\uff1a\u51e0\u4f55\u53ef\u80fd\u6765\u81ea\u201c\u8c31\u504f\u7f6e\u201d\uff0c\u800c\u4e14\u4e0d\u9700\u8981\u4f20\u7edf\u5047\u8bbe<\/h4>\n\n\n\n<p>\u4e3a\u7406\u89e3\u201c\u5c40\u90e8\u8bad\u7ec3\u5982\u4f55\u5408\u6210\u5168\u5c40\u51e0\u4f55\u201d\uff0c\u4f5c\u8005\u8f6c\u5411\u66f4\u7b80\u5355\u3001\u4e14\u5728\u7ed3\u6784\u4e0a\u7981\u6b62\u8054\u60f3\u5f0f\u8bb0\u5fc6\u7684 Node2Vec \u7c7b\u6a21\u578b\uff0c\u53d1\u73b0\u5176\u5d4c\u5165\u5f80\u5f80\u5bf9\u9f50\u56fe\u62c9\u666e\u62c9\u65af\u77e9\u9635\u7684\u201c\u4e3b\u5bfc\u7ed3\u6784\u65b9\u5411\u201d\uff08\u5e38\u88ab\u7528\u6765\u523b\u753b\u56fe\u7684\u5168\u5c40\u5f62\u72b6\uff09\uff0c\u8fd9\u53ef\u89c6\u4e3a\u4e00\u79cd\u8c31\u504f\u7f6e\uff1b\u66f4\u5173\u952e\u7684\u662f\uff0c\u4f5c\u8005\u6307\u51fa\u8fd9\u79cd\u504f\u7f6e\u5728\u4ed6\u4eec\u7684\u8bbe\u5b9a\u4e2d\u4f1a<strong>\u81ea\u7136\u51fa\u73b0<\/strong>\uff0c\u5e76\u4e0d\u4f9d\u8d56\u6587\u732e\u91cc\u5e38\u89c1\u7684\u90a3\u4e9b\u524d\u63d0\uff08\u4f8b\u5982\u5f3a\u74f6\u9888\u3001\u663e\u5f0f\u6b63\u5219\u3001\u591a\u8df3\u76d1\u7763\u7b49\uff09\u3002<br>\u540c\u65f6\uff0cNode2Vec \u7684\u51e0\u4f55\u5f80\u5f80\u6bd4 Transformer \u66f4\u201c\u89c4\u6574\u201d\uff0c\u63d0\u793a Transformer 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