{"id":1041,"date":"2026-02-10T12:26:59","date_gmt":"2026-02-10T04:26:59","guid":{"rendered":"https:\/\/www.eutaboo.com\/?p=1041"},"modified":"2026-02-10T12:26:59","modified_gmt":"2026-02-10T04:26:59","slug":"%e4%bb%8e%e9%9b%b6%e7%90%86%e8%a7%a3-mamba%ef%bc%9a%e9%80%89%e6%8b%a9%e6%80%a7%e7%8a%b6%e6%80%81%e7%a9%ba%e9%97%b4%e6%a8%a1%e5%9e%8b%ef%bc%88selective-ssm%ef%bc%89%e5%88%b0-mamba-block%ef%bc%88","status":"publish","type":"post","link":"https:\/\/www.eutaboo.com\/index.php\/2026\/02\/10\/%e4%bb%8e%e9%9b%b6%e7%90%86%e8%a7%a3-mamba%ef%bc%9a%e9%80%89%e6%8b%a9%e6%80%a7%e7%8a%b6%e6%80%81%e7%a9%ba%e9%97%b4%e6%a8%a1%e5%9e%8b%ef%bc%88selective-ssm%ef%bc%89%e5%88%b0-mamba-block%ef%bc%88\/","title":{"rendered":"\u4ece\u96f6\u7406\u89e3 Mamba\uff1a\u9009\u62e9\u6027\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff08Selective SSM\uff09\u5230 Mamba Block\uff08\u9762\u5411\u533b\u5b66\u56fe\u50cf\u5206\u5272\u7684\u57fa\u7840\u94fa\u57ab\uff09"},"content":{"rendered":"<h2>1. \u4e3a\u4ec0\u4e48\u533b\u5b66\u56fe\u50cf\u5206\u5272\u4f1a\u5173\u6ce8 Mamba\uff1f<\/h2>\n<p>\u533b\u5b66\u56fe\u50cf\u5206\u5272\uff082D\/3D\uff09\u7ecf\u5e38\u540c\u65f6\u9700\u8981\uff1a<\/p>\n<ul>\n<li><strong>\u5c40\u90e8\u7ec6\u8282<\/strong>\uff1a\u8fb9\u754c\u3001\u8584\u7ed3\u6784\u3001\u5c0f\u5668\u5b98\uff08CNN \u64c5\u957f\uff09<\/li>\n<li><strong>\u5168\u5c40\u4e00\u81f4\u6027\/\u957f\u7a0b\u4f9d\u8d56<\/strong>\uff1a\u5668\u5b98\u5f62\u6001\u3001\u62d3\u6251\u3001\u8de8\u5207\u7247\/\u8de8\u533a\u57df\u4e00\u81f4\uff08Transformer \u64c5\u957f\uff09<\/li>\n<li><strong>\u53ef\u627f\u53d7\u7684\u8ba1\u7b97\u4e0e\u663e\u5b58<\/strong>\uff1a\u5c24\u5176 3D \u4f53\u6570\u636e\uff0ctoken \u6570\u91cf\u975e\u5e38\u6050\u6016<\/li>\n<\/ul>\n<p>Transformer \u7684\u81ea\u6ce8\u610f\u529b\u6838\u5fc3\u74f6\u9888\u5728\u4e8e\uff1a<strong>\u5e8f\u5217\u957f\u5ea6 (L)<\/strong> \u53d8\u5927\u65f6\u8ba1\u7b97\/\u663e\u5b58\u5927\u591a\u662f <strong>(O(L^2))<\/strong> \u7ea7\u522b\uff08\u5373\u4f7f\u6709\u5404\u79cd\u201c\u9ad8\u6548\u6ce8\u610f\u529b\u201d\uff0c\u4e5f\u5e38\u5e38\u8981\u5728\u6548\u679c\/\u5de5\u7a0b\u4e0a\u505a\u53d6\u820d\uff09\u3002<\/p>\n<p>Mamba \u7684\u6838\u5fc3\u8bc9\u6c42\u662f\uff1a<strong>\u50cf RNN \u4e00\u6837\u7ebf\u6027\u6269\u5c55\uff08\u968f (L) \u7ebf\u6027\uff09\uff0c\u540c\u65f6\u53c8\u5177\u5907\u63a5\u8fd1\u6ce8\u610f\u529b\u7684\u201c\u5185\u5bb9\u9009\u62e9\/\u63a8\u7406\u80fd\u529b\u201d<\/strong>\u3002\u8bba\u6587\u660e\u786e\u63d0\u51fa\u5176\u76ee\u6807\u662f\u4ee5 <strong>\u7ebf\u6027\u65f6\u95f4<\/strong>\u89c4\u6a21\u5efa\u6a21\u957f\u5e8f\u5217\uff0c\u5e76\u7528\u201c\u9009\u62e9\u6027\uff08selective\uff09\u72b6\u6001\u7a7a\u95f4\u201d\u5f15\u5165\u8f93\u5165\u76f8\u5173\u7684\u9009\u62e9\u673a\u5236\u3002<\/p>\n<hr \/>\n<h2>2. \u72b6\u6001\u7a7a\u95f4\u6a21\u578b SSM\uff1a\u4ece\u76f4\u89c9\u5230\u6700\u6838\u5fc3\u7684\u4e09\u7ec4\u516c\u5f0f<\/h2>\n<p>\u5148\u522b\u88ab\u201c\u72b6\u6001\u7a7a\u95f4\u201d\u56db\u4e2a\u5b57\u5413\u5230\u3002\u4f60\u53ef\u4ee5\u628a SSM \u5f53\u4f5c\u4e00\u79cd\u201c<strong>\u5e26\u6709\u8fde\u7eed\/\u79bb\u6563\u52a8\u529b\u5b66\u7684 RNN<\/strong>\u201d\uff0c\u5b83\u7528\u4e00\u4e2a\u9690\u85cf\u72b6\u6001 (h) \u6765\u7d2f\u79ef\u5386\u53f2\u4fe1\u606f\u3002<\/p>\n<h3>2.1 \u8fde\u7eed\u65f6\u95f4\u5f62\u5f0f\uff08\u76f4\u89c9\uff1a\u52a8\u6001\u7cfb\u7edf\uff09<\/h3>\n<p>\u8bba\u6587\u4ece\u7ecf\u5178\u5f62\u5f0f\u51fa\u53d1\uff08\u8fde\u7eed\u7cfb\u7edf\uff09\uff1a<\/p>\n<p>[<br \/>\n\\frac{d h(t)}{dt} = A h(t) + B x(t), \\qquad y(t) = C h(t)<br \/>\n]<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>(x(t))\uff1a\u8f93\u5165\u4fe1\u53f7\uff08\u5e8f\u5217\/\u65f6\u95f4\u4fe1\u53f7\uff09<\/li>\n<li>(h(t))\uff1a\u9690\u85cf\u72b6\u6001\uff08\u7ef4\u5ea6\u901a\u5e38\u662f (N)\uff09<\/li>\n<li>(y(t))\uff1a\u8f93\u51fa<\/li>\n<li>(A)\uff1a\u72b6\u6001\u8f6c\u79fb\uff08\u51b3\u5b9a\u201c\u8bb0\u5fc6\u8870\u51cf\/\u632f\u8361\/\u7a33\u5b9a\u6027\u201d\u7b49\u52a8\u529b\u5b66\uff09<\/li>\n<li>(B)\uff1a\u628a\u8f93\u5165\u5199\u5165\u72b6\u6001<\/li>\n<li>(C)\uff1a\u4ece\u72b6\u6001\u8bfb\u51fa\u8f93\u51fa<\/li>\n<\/ul>\n<p>\u8fd9\u5c31\u662f\u8bba\u6587\u7684\u5f0f (1a)(1b)\u3002<\/p>\n<h3>2.2 \u79bb\u6563\u65f6\u95f4\u5f62\u5f0f\uff08\u66f4\u50cf\u4f60\u719f\u6089\u7684 RNN\uff09<\/h3>\n<p>\u628a\u65f6\u95f4\u79bb\u6563\u5316\u540e\uff08\u6309\u6b65 (t=1,2,\\dots)\uff09\uff1a<\/p>\n<p>[<br \/>\nh<em>t = \\bar{A} h<\/em>{t-1} + \\bar{B} x_t,\\qquad y_t = C h_t<br \/>\n]<\/p>\n<p>\u8fd9\u5bf9\u5e94\u8bba\u6587\u7684\u5f0f (2a)(2b)\u3002<\/p>\n<blockquote>\n<p>\ud83d\udca1 <strong>\u4e00\u53e5\u8bdd\u76f4\u89c9<\/strong>\uff1a<br \/>\n(\\bar{A}) \u63a7\u5236\u201c\u4e0a\u4e00\u65f6\u523b\u72b6\u6001\u7559\u591a\u5c11\u201d\uff0c(\\bar{B}) \u63a7\u5236\u201c\u5f53\u524d\u8f93\u5165\u5199\u591a\u5c11\u201d\uff0c(C) \u63a7\u5236\u201c\u8bfb\u51fa\u4ec0\u4e48\u201d\u3002<\/p>\n<\/blockquote>\n<h3>2.3 \u5377\u79ef\u5f62\u5f0f\uff08SSM \u8fd8\u80fd\u7b49\u4ef7\u6210 1D \u5377\u79ef\uff09<\/h3>\n<p>\u5bf9 <strong>\u7ebf\u6027\u65f6\u4e0d\u53d8\uff08LTI\uff09<\/strong> \u7684 SSM\uff0c\u8f93\u51fa\u8fd8\u53ef\u4ee5\u5199\u6210\u5168\u5c40\u5377\u79ef\uff1a<\/p>\n<p>[<br \/>\nK = (CB,\\; CAB,\\; CA^2B,\\;\\dots), \\qquad y = x * K<br \/>\n]<\/p>\n<p>\u8fd9\u662f\u8bba\u6587\u7684\u5f0f (3a)(3b)\u3002<\/p>\n<p>\u8fd9\u4ef6\u4e8b\u975e\u5e38\u5173\u952e\uff0c\u56e0\u4e3a\uff1a<\/p>\n<ul>\n<li><strong>\u5377\u79ef\u5f62\u5f0f<\/strong>\u8ba9\u8bad\u7ec3\u65f6\u53ef\u4ee5\u5e76\u884c\uff08\u50cf CNN \u4e00\u6837\uff09<\/li>\n<li><strong>\u9012\u63a8\u5f62\u5f0f<\/strong>\u8ba9\u63a8\u7406\u65f6\u53ef\u4ee5\u4e00\u6b65\u4e00\u6b65\u66f4\u65b0\uff08\u50cf RNN \u4e00\u6837\uff09<\/li>\n<\/ul>\n<hr \/>\n<h2>3. \u4f20\u7edf SSM \u7684\u5173\u952e\u9650\u5236\uff1aLTI\uff08\u7ebf\u6027\u65f6\u4e0d\u53d8\uff09<\/h2>\n<p>SSM \u4e4b\u6240\u4ee5\u80fd\u5feb\uff0c\u5386\u53f2\u4e0a\u4e00\u4e2a\u91cd\u8981\u539f\u56e0\u662f\u5b83\u4eec\u901a\u5e38\u88ab\u8bbe\u8ba1\u4e3a <strong>LTI<\/strong>\uff1a\u53c2\u6570 ((\\Delta, A, B, C)) \u5728\u6240\u6709\u65f6\u95f4\u6b65\u90fd\u4e0d\u53d8\uff0c\u56e0\u6b64\u53ef\u4ee5\u8d70\u9ad8\u6548\u7684\u5377\u79ef\/FFT \u7b49\u8ba1\u7b97\u8def\u5f84\u3002\u8bba\u6587\u660e\u786e\u6307\u51fa\uff1a\u6b64\u524d\u7ed3\u6784\u5316 SSM \u57fa\u672c\u90fd\u662f LTI\uff0c\u53d7\u5236\u4e8e\u6548\u7387\u7ea6\u675f\u3002<\/p>\n<p>\u4f46\u662f LTI \u6709\u4e00\u4e2a\u201c\u5929\u7136\u7684\u77ed\u677f\u201d\uff1a<\/p>\n<blockquote>\n<p><strong>\u540c\u4e00\u5957\u52a8\u529b\u5b66\u53c2\u6570\u9762\u5bf9\u6240\u6709 token<\/strong><br \/>\n\u5b83\u5f88\u96be\u50cf\u6ce8\u610f\u529b\u90a3\u6837\u6839\u636e\u5185\u5bb9\u505a\u201c\u9009\u62e9\u201d\uff1a\u8be5\u8bb0\u4f4f\u8c01\u3001\u8be5\u5fd8\u6389\u8c01\u3001\u8be5\u8df3\u8fc7\u54ea\u4e9b\u566a\u58f0 token\u3002<\/p>\n<\/blockquote>\n<p>Mamba \u8bba\u6587\u628a\u8fd9\u4e2a\u95ee\u9898\u6982\u62ec\u6210\uff1a\u5f88\u591a\u6b21\u4e8c\u6b21\u590d\u6742\u5ea6\uff08\u6216\u6b21\u4e8c\u6b21\u590d\u6742\u5ea6\uff09\u7684\u5e8f\u5217\u6a21\u578b\u5728\u79bb\u6563\/\u4fe1\u606f\u5bc6\u96c6\u6570\u636e\uff08\u4f8b\u5982\u6587\u672c\uff09\u4e0a\u4e0d\u5982\u6ce8\u610f\u529b\uff0c\u4e00\u4e2a\u5173\u952e\u5f31\u70b9\u662f\u7f3a\u5c11\u9ad8\u6548\u7684\u8f93\u5165\u4f9d\u8d56\u9009\u62e9\u80fd\u529b\u3002<\/p>\n<hr \/>\n<h2>4. Mamba \u7684\u7b2c\u4e00\u6838\u5fc3\uff1aSelection \u673a\u5236\uff08\u8ba9 SSM \u53c2\u6570\u201c\u770b\u8f93\u5165\u8bf4\u8bdd\u201d\uff09<\/h2>\n<p>Mamba \u6700\u5173\u952e\u7684\u4e00\u5200\uff1a<strong>\u8ba9 SSM \u7684\u90e8\u5206\u53c2\u6570\u53d8\u6210\u8f93\u5165 (x_t) \u7684\u51fd\u6570<\/strong>\u3002\u8bba\u6587\u628a\u5b83\u79f0\u4e3a <strong>selection mechanism<\/strong>\uff1a\u901a\u8fc7\u8f93\u5165\u53bb\u53c2\u6570\u5316 SSM \u53c2\u6570\uff0c\u4f7f\u6a21\u578b\u80fd\u201c\u8fc7\u6ee4\u65e0\u5173\u4fe1\u606f\uff0c\u957f\u4e45\u8bb0\u4f4f\u76f8\u5173\u4fe1\u606f\u201d\u3002<\/p>\n<h3>4.1 \u4ece S4\uff08\u4f20\u7edf\uff09\u5230 S6\uff08\u9009\u62e9\u6027\uff09<\/h3>\n<p>\u8bba\u6587\u7528\u4f2a\u4ee3\u7801\u975e\u5e38\u6e05\u6670\u5730\u533a\u5206\uff1a<\/p>\n<ul>\n<li><strong>Algorithm 1\uff1aSSM\uff08S4\uff09<\/strong>\uff1a\u53c2\u6570\u65f6\u95f4\u4e0d\u53d8  <\/li>\n<li><strong>Algorithm 2\uff1aSSM + Selection\uff08S6\uff09<\/strong>\uff1a\u53c2\u6570\u968f (t) \u53d8\u5316\uff08\u8f93\u5165\u76f8\u5173\uff09<\/li>\n<\/ul>\n<p>Algorithm 2 \u7684\u6838\u5fc3\u662f\uff1a<br \/>\n\u8ba9 (B_t, C_t, \\Delta_t) \u7531\u8f93\u5165\u751f\u6210\uff1a<\/p>\n<ul>\n<li>(B \\leftarrow s_B(x))<\/li>\n<li>(C \\leftarrow s_C(x))<\/li>\n<li>(\\Delta \\leftarrow \\tau<em>\\Delta(\\text{Parameter} + s<\/em>\\Delta(x)))<\/li>\n<\/ul>\n<p>\u5e76\u5728\u6bcf\u4e2a\u65f6\u95f4\u6b65\u79bb\u6563\u5316\u540e\u505a SSM \u9012\u63a8\uff08scan\uff09\u3002<\/p>\n<p>\u4f60\u53ef\u4ee5\u628a\u5b83\u7406\u89e3\u6210\uff1a<\/p>\n<blockquote>\n<p><strong>\u540c\u4e00\u4e2a SSM \u6846\u67b6<\/strong><br \/>\n\u4f46\u6bcf\u4e2a token \u90fd\u4f1a\u201c\u4e34\u65f6\u51b3\u5b9a\u201d\u81ea\u5df1\u8be5\u5199\u591a\u5c11\u8fdb\u72b6\u6001\u3001\u8be5\u8bfb\u51fa\u4ec0\u4e48\u3001\u4ee5\u53ca\u8fd9\u4e00\u6b65\u7684\u201c\u6b65\u957f\/\u95e8\u63a7\u201d\u5927\u5c0f\u3002<\/p>\n<\/blockquote>\n<h3>4.2 \u5173\u952e\u56fe\uff1aSelection \u5728\u7ed3\u6784\u4e0a\u201c\u52a0\u4e86\u4ec0\u4e48\u201d<\/h3>\n<p>\u4e0b\u9762\u8fd9\u5f20\u56fe\u975e\u5e38\u63a8\u8350\u4f60\u5728\u8111\u5b50\u91cc\u8bb0\u4f4f\uff08\u6765\u81ea\u5b98\u65b9\u4ed3\u5e93 assets\uff0c\u5bf9\u5e94\u8bba\u6587\u56fe 1 \u7684\u6838\u5fc3\u542b\u4e49\uff09\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/github.com\/state-spaces\/mamba\/raw\/main\/assets\/selection.png\" alt=\"Selective State Space Model (Selection Mechanism)\" \/><\/p>\n<p><em>\u56fe 1\uff1a\u9009\u62e9\u6027\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff1a\u8f93\u5165 (x_t) \u901a\u8fc7 selection mechanism \u751f\u6210\/\u8c03\u5236 (B_t, C_t, \\Delta_t)\uff0c\u5e76\u914d\u5408\u786c\u4ef6\u53cb\u597d\u7684 state expansion \u8bbe\u8ba1\u3002<\/em>\u3002<\/p>\n<p>\u4f60\u53ef\u4ee5\u5bf9\u7167\u7740\u8bfb\uff1a<\/p>\n<ul>\n<li>(x_t) \u7ecf\u8fc7\u6295\u5f71\uff08Project\uff09<\/li>\n<li>\u4ea7\u751f (B_t, C_t, \\Delta_t)<\/li>\n<li>\u518d\u79bb\u6563\u5316\uff08Discretize\uff09\u8fdb\u5165\u9012\u63a8\u66f4\u65b0<\/li>\n<li>\u8f93\u51fa (y_t)<\/li>\n<\/ul>\n<hr \/>\n<h2>5. \u8ba1\u7b97\u6311\u6218\uff1a\u53c2\u6570\u968f\u65f6\u95f4\u53d8\u4e86\uff0c\u5377\u79ef\u8def\u8d70\u4e0d\u901a\u600e\u4e48\u529e\uff1f<\/h2>\n<p>\u4f60\u53ef\u80fd\u4f1a\u95ee\uff1a<\/p>\n<blockquote>\n<p>\u65e2\u7136\u53c2\u6570 (B_t, C_t, \\Delta_t) \u6bcf\u4e2a\u65f6\u95f4\u6b65\u90fd\u4e0d\u4e00\u6837\uff0c<br \/>\n\u90a3\u4e0d\u5c31\u4e0d\u80fd\u7528\u5377\u79ef\u5f62\u5f0f (y=x*K) \u7684\u9ad8\u6548\u5e76\u884c\u4e86\u5417\uff1f<\/p>\n<\/blockquote>\n<p>\u662f\u7684\u2014\u2014\u8bba\u6587\u660e\u786e\u6307\u51fa\uff1a<strong>\u65f6\u95f4\u53d8\u5316\u7684 SSM \u65e0\u6cd5\u8d70\u5377\u79ef\u8def\u5f84<\/strong>\uff0c\u5fc5\u987b\u7528\u9012\u63a8\uff08scan\uff09\u6765\u8ba1\u7b97\u3002<\/p>\n<p>\u4f46 Mamba \u4ecd\u7136\u5feb\uff0c\u9760\u7684\u662f\u4e24\u4e2a\u601d\u8def\uff1a<\/p>\n<ol>\n<li><strong>\u6570\u5b66\u7ed3\u6784<\/strong>\uff1a\u9012\u63a8\u66f4\u65b0\u662f\u201c\u7ebf\u6027\/\u4eff\u5c04\u201d\u7684\uff08\u53ef\u4ee5\u88ab\u5e76\u884c scan\uff09<\/li>\n<li><strong>\u786c\u4ef6\u5de5\u7a0b<\/strong>\uff1a\u8bbe\u8ba1\u4e86\u786c\u4ef6\u53cb\u597d\u7684\u5e76\u884c scan \u65b9\u6848\uff0c\u907f\u514d\u628a\u5de8\u5927\u7684 state \u5c55\u5f00\u5230\u6162\u663e\u5b58\u91cc\uff08HBM\uff09\uff0c\u5c3d\u91cf\u5728\u66f4\u5feb\u7684\u5c42\u7ea7\uff08SRAM\/\u7247\u4e0a\uff09\u5b8c\u6210\u878d\u5408\u8ba1\u7b97\u3002<\/li>\n<\/ol>\n<blockquote>\n<p>\ud83e\udde0 \u4e00\u4e2a\u975e\u5e38\u6709\u7528\u7684\u201c\u7b80\u5316\u7248\u201d\u9012\u63a8\u5f62\u5f0f<br \/>\n\u628a\u6bcf\u4e2a\u901a\u9053\/\u6bcf\u4e2a state \u7ef4\u5ea6\u4e0a\u7684\u66f4\u65b0\u60f3\u6210\u6807\u91cf\u9012\u63a8\uff1a<\/p>\n<p>[<br \/>\nh_t = a<em>t \\, h<\/em>{t-1} + b_t<br \/>\n]<\/p>\n<p>\u5176\u4e2d (a_t) \u6765\u81ea (\\Delta_t) \u4e0e (A) \u7684\u79bb\u6563\u5316\uff0c(b_t) \u6765\u81ea (B_t x_t)\u3002<br \/>\n\u8fd9\u79cd\u5f62\u5f0f\u53ef\u4ee5\u7528\u5e76\u884c scan\uff08\u7c7b\u4f3c\u524d\u7f00\u548c\uff09\u9ad8\u6548\u8ba1\u7b97\u3002<\/p>\n<\/blockquote>\n<hr \/>\n<h2>6. Mamba Block\uff1a\u628a\u201cConv + Selective SSM + Gated MLP\u201d\u63c9\u6210\u4e00\u4e2a\u53ef\u5806\u53e0\u7684 Block<\/h2>\n<p>\u5230\u8fd9\u91cc\u6211\u4eec\u5df2\u7ecf\u7406\u89e3\u4e86 <strong>Selective SSM\uff08S6\uff09<\/strong>\u3002\u4f46\u5728\u6df1\u5ea6\u7f51\u7edc\u91cc\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a\u50cf Transformer block \u4e00\u6837\u53ef\u5806\u53e0\u7684\u7ed3\u6784\u3002<\/p>\n<p>\u8bba\u6587\u7684\u505a\u6cd5\u662f\uff1a\u628a\u5178\u578b SSM \u67b6\u6784\uff08H3 \u7cfb\uff09\u4e0e\u73b0\u4ee3\u7f51\u7edc\u4e2d\u5e38\u89c1\u7684 gated MLP \u878d\u5408\u6210\u4e00\u4e2a\u7edf\u4e00 block\uff0c\u7136\u540e\u91cd\u590d\u5806\u53e0\u5373\u53ef\uff08\u4e0d\u518d\u9700\u8981 attention \u6216\u5355\u72ec\u7684 MLP block\uff09\u3002<\/p>\n<h3>6.1 \u5173\u952e\u56fe\uff1aH3\u3001Gated MLP \u4e0e Mamba \u7684\u7ec4\u5408\u5173\u7cfb<\/h3>\n<p>\u8fd9\u5f20\u56fe\uff08\u5bf9\u5e94\u8bba\u6587 Figure 3 \u7684\u7ed3\u6784\u6982\u5ff5\uff09\u975e\u5e38\u9002\u5408\u653e\u5728\u535a\u5ba2\u91cc\u5f53\u201c\u603b\u89c8\u201d\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wiki.math.uwaterloo.ca\/statwiki\/images\/7\/78\/Mamba-Architecture.png\" alt=\"Mamba Block Architecture\" \/><\/p>\n<p><em>\u56fe 2\uff1aMamba block \u53ef\u4ee5\u7406\u89e3\u4e3a\u628a H3\uff08Conv+SSM+\u95e8\u63a7\uff09\u548c Gated MLP \u878d\u5408\uff1a\u76f8\u5bf9 H3\uff0c\u7528\u6fc0\u6d3b\u51fd\u6570\u66ff\u4ee3\u7b2c\u4e00\u5904\u4e58\u6cd5\u95e8\uff1b\u76f8\u5bf9\u7eaf MLP\uff0c\u5728\u4e3b\u5206\u652f\u52a0\u5165 SSM\u3002<\/em>\u3002<\/p>\n<blockquote>\n<p>\u2705 \u4f60\u73b0\u5728\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u8bb0\u4f4f Mamba Block\uff1a<br \/>\n<strong>\u201cSwiGLU\uff08gated MLP\uff09+ \u4e00\u4e2a\u989d\u5916\u7684 Conv\u2192SSM \u5e8f\u5217\u901a\u8def\u201d<\/strong>\u3002<\/p>\n<\/blockquote>\n<h3>6.2 Block \u5185\u90e8\u90fd\u5728\u505a\u4ec0\u4e48\uff08\u6309\u6570\u636e\u6d41\u62c6\u5f00\u8bb2\uff09<\/h3>\n<p>\u4e0b\u9762\u6211\u7528\u201c\u5b9e\u73b0\u8005\u89c6\u89d2\u201d\u62c6\u5f00\u4e00\u904d\uff08\u4e0d\u7ea0\u7ed3\u6bcf\u4e2a\u7b26\u53f7\u7684\u547d\u540d\uff0c\u5148\u6293\u4f4f\u7ed3\u6784\uff09\uff1a<\/p>\n<p>\u5047\u8bbe\u8f93\u5165\u4e3a\uff1a<\/p>\n<ul>\n<li>(x \\in \\mathbb{R}^{B\\times L\\times D})\uff08batch, length, dim\uff09<\/li>\n<\/ul>\n<h4>Step 1\uff1a\u7ef4\u5ea6\u6269\u5c55\uff08Expand\uff09+ \u5206\u4e24\u8def<\/h4>\n<p>Mamba block \u4f1a\u628a\u901a\u9053\u7ef4\u6269\u5c55\u4e00\u4e2a\u56e0\u5b50 (E)\uff08\u8bba\u6587\u5b9e\u9a8c\u91cc\u5e38\u56fa\u5b9a (E=2)\uff09\uff0c\u5927\u90e8\u5206\u53c2\u6570\u90fd\u5728\u8f93\u5165\/\u8f93\u51fa\u6295\u5f71\u91cc\u3002<\/p>\n<p>\u4f60\u53ef\u4ee5\u5199\u6210\uff1a<\/p>\n<p>[<br \/>\n[u, v] = x W_{\\text{in}}, \\quad u,v \\in \\mathbb{R}^{B\\times L\\times (E D)}<br \/>\n]<\/p>\n<ul>\n<li>(u)\uff1a\u8d70 <strong>Conv\u2192Selective SSM<\/strong> \u7684\u201c\u5e8f\u5217\u53d8\u6362\u201d\u4e3b\u8def<\/li>\n<li>(v)\uff1a\u4f5c\u4e3a <strong>\u95e8\u63a7\/\u6fc0\u6d3b<\/strong> \u7684\u8f85\u52a9\u8def\uff08\u7c7b\u4f3c SwiGLU \u7684 gate\uff09<\/li>\n<\/ul>\n<h4>Step 2\uff1a\u5c40\u90e8\u6df7\u5408\uff08Conv\uff09<\/h4>\n<p>\u5728\u8fdb\u5165 SSM \u4e4b\u524d\uff0c\u52a0\u4e00\u4e2a\u5c0f\u7a97\u53e3\u7684 1D \u5377\u79ef\uff08\u901a\u5e38\u662f depthwise causal conv\uff0c\u7528\u6765\u8865\u8db3\u5c40\u90e8\u5efa\u6a21\uff09\u3002\u56fe 2 \u91cc Conv \u5c31\u662f\u8fd9\u4e2a\u3002<\/p>\n<blockquote>\n<p>\u76f4\u89c9\uff1a  <\/p>\n<ul>\n<li>SSM \u66f4\u50cf\u201c\u957f\u7a0b\u8bb0\u5fc6\/\u4f20\u64ad\u201d  <\/li>\n<li>\u5c0f\u5377\u79ef\u66f4\u50cf\u201c\u5c40\u90e8\u7eb9\u7406\/\u77ed\u7a0b\u6df7\u5408\u201d<br \/>\n\u4e24\u8005\u4e92\u8865\u3002<\/li>\n<\/ul>\n<\/blockquote>\n<h4>Step 3\uff1a\u751f\u6210\u9009\u62e9\u6027\u53c2\u6570\uff08(\\Delta_t, B_t, C_t)\uff09<\/h4>\n<p>\u8fd9\u662f Mamba \u7684\u7075\u9b42\uff1a\u4ece\u5f53\u524d token \u7684\u8868\u5f81\u91cc\u751f\u6210\u9009\u62e9\u6027\u53c2\u6570\uff1a<\/p>\n<ul>\n<li>(B_t = s_B(u_t))<\/li>\n<li>(C_t = s_C(u_t))<\/li>\n<li>(\\Delta<em>t = \\tau<\/em>\\Delta(\\text{Parameter} + s_\\Delta(u_t)))<\/li>\n<\/ul>\n<p>\u5bf9\u5e94 Algorithm 2 \u7684\u6838\u5fc3\u3002<\/p>\n<h4>Step 4\uff1aSelective SSM\uff08scan\uff09<\/h4>\n<p>\u6bcf\u4e2a\u65f6\u95f4\u6b65\u505a\u79bb\u6563\u5316\u5e76\u9012\u63a8\uff1a<\/p>\n<ul>\n<li>\u5148\u7528\u79bb\u6563\u5316\u89c4\u5219\u628a\u8fde\u7eed\u53c2\u6570\u53d8\u6210\u79bb\u6563\u53c2\u6570  <\/li>\n<li>\u518d\u9012\u63a8\u66f4\u65b0 (h_t)\uff0c\u8bfb\u51fa (y_t)<\/li>\n<\/ul>\n<p>SSM \u7684\u57fa\u7840\u79bb\u6563\u5316\uff08\u8bba\u6587\u7ed9\u51fa ZOH\uff09\uff1a<\/p>\n<p>[<br \/>\n\\bar{A} = e^{\\Delta A},\\qquad<br \/>\n\\bar{B} = (\\Delta A)^{-1}(e^{\\Delta A}-I)\\cdot \\Delta B<br \/>\n]<\/p>\n<p>\u8fd9\u662f\u8bba\u6587\u5f0f (4)\u3002<\/p>\n<p>\u7136\u540e\u6309\u5f0f (2a)(2b) \u66f4\u65b0\u5373\u53ef\u3002<\/p>\n<h4>Step 5\uff1a\u95e8\u63a7\uff08\u4e3a\u4ec0\u4e48\u5b83\u201c\u50cf\u6ce8\u610f\u529b\u201d\u4f46\u4e0d\u662f\u6ce8\u610f\u529b\uff09<\/h4>\n<p>Mamba block \u91cc\u8fd8\u6709\u4e00\u4e2a\u5173\u952e\uff1a<strong>gating\/activation<\/strong>\u3002<\/p>\n<p>\u8bba\u6587\u7ed9\u4e86\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u8fde\u63a5\uff1a\u5f53\u72b6\u6001\u7ef4\u5ea6 (N=1) \u7b49\u7279\u4f8b\u4e0b\uff0c\u9009\u62e9\u6027 SSM \u7684\u9012\u63a8\u4f1a\u9000\u5316\u6210\u7ecf\u5178 RNN \u95e8\u63a7\u5f62\u5f0f\uff1a<\/p>\n<p>[<br \/>\ng_t = \\sigma(\\text{Linear}(x_t)),\\qquad<br \/>\nh_t = (1-g<em>t)h<\/em>{t-1} + g_t x_t<br \/>\n]<\/p>\n<p>\u8fd9\u662f\u8bba\u6587 Theorem 1 \/ \u5f0f (5)\u3002<\/p>\n<blockquote>\n<p>\ud83d\udca1 \u76f4\u89c9\u7ffb\u8bd1\uff1a  <\/p>\n<ul>\n<li>(g_t) \u5927\uff1a\u5f3a\u66f4\u65b0\uff0c\u628a\u5f53\u524d token \u5199\u8fdb\u8bb0\u5fc6\uff08\u751a\u81f3\u201c\u8986\u76d6\u201d\u65e7\u72b6\u6001\uff09  <\/li>\n<li>(g_t) \u5c0f\uff1a\u5f31\u66f4\u65b0\uff0c\u4e3b\u8981\u4fdd\u7559\u65e7\u8bb0\u5fc6\uff0c\u5f53\u524d token \u66f4\u50cf\u201c\u566a\u58f0\u201d\u88ab\u5ffd\u7565<\/li>\n<\/ul>\n<\/blockquote>\n<p>\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48 Mamba \u7684 \u201cselection\u201d \u53ef\u4ee5\u88ab\u7406\u89e3\u6210\u4e00\u79cd\u66f4\u5e7f\u4e49\u3001\u52a8\u529b\u5b66\u66f4\u5f3a\u7684 gating\u3002<\/p>\n<h4>Step 6\uff1a\u8f93\u51fa\u6295\u5f71 + \u6b8b\u5dee<\/h4>\n<p>\u6700\u540e\u628a (ED) \u6295\u56de (D)\uff1a<\/p>\n<p>[<br \/>\n\\text{out} = x + \\text{ProjOut}( \\; \\text{SSM}(u) \\odot \\phi(v) \\;)<br \/>\n]<\/p>\n<p>\u5176\u4e2d (\\phi) \u5e38\u7528 SiLU\/Swish\uff0c\u4f7f\u5176 gated MLP \u5bf9\u5e94 SwiGLU \u98ce\u683c\u3002<\/p>\n<hr \/>\n<h2>7. \u628a Mamba \u5f53\u4f5c\u201c\u533b\u5b66\u56fe\u50cf\u5206\u5272\u7684\u9aa8\u5e72\u6a21\u5757\u201d\u65f6\uff0c\u4f60\u9700\u8981\u77e5\u9053\u4ec0\u4e48\uff1f<\/h2>\n<blockquote>\n<p>\u8fd9\u90e8\u5206\u53ea\u505a\u201c\u57fa\u7840\u5bf9\u63a5\u201d\uff0c\u4e0d\u5c55\u5f00\u89c6\u89c9\u4e13\u7528 scanning\/\u7ed3\u6784\u53d8\u4f53\u3002<\/p>\n<\/blockquote>\n<h3>7.1 \u628a\u56fe\u50cf\u53d8\u6210\u5e8f\u5217\uff1atoken length \u662f\u5173\u952e\u77db\u76fe<\/h3>\n<p>\u4e8c\u7ef4\u56fe\u50cf\uff08\u6216\u4e09\u7ef4\u4f53\u6570\u636e\uff09\u8fdb\u5165 Mamba \u7684\u6700\u6734\u7d20\u65b9\u5f0f\uff1a<\/p>\n<ol>\n<li>patch embedding\uff08Conv\/Linear\uff09  <\/li>\n<li>\u5c55\u5e73\u6210 token \u5e8f\u5217  <\/li>\n<li>\u9001\u5165\u4e00\u5806 Mamba blocks<\/li>\n<\/ol>\n<p>\u4f8b\u5982 2D\uff1a<\/p>\n<ul>\n<li>\u56fe\u50cf (H\\times W)<\/li>\n<li>patch \u5927\u5c0f (P\\times P)<\/li>\n<li>token \u6570 (L=(H\/P)(W\/P))<\/li>\n<\/ul>\n<p>\u5bf9 3D\uff1a<\/p>\n<ul>\n<li>(H\\times W\\times Z)<\/li>\n<li>patch (P\\times P\\times P)<\/li>\n<li>(L=(H\/P)(W\/P)(Z\/P))<\/li>\n<\/ul>\n<p><strong>\u4f60\u9a6c\u4e0a\u5c31\u80fd\u7406\u89e3 Mamba \u7684\u4ef7\u503c\u70b9\uff1a<\/strong><br \/>\n\u5f53 (L) \u5f88\u5927\u65f6\uff0c\u6ce8\u610f\u529b\u7684 (L^2) \u4f1a\u53d8\u5f97\u975e\u5e38\u5403\u529b\uff0c\u800c Mamba \u7684\u6838\u5fc3\u8ba1\u7b97\u968f (L) \u7ebf\u6027\u6269\u5c55\u3002<\/p>\n<h3>7.2 \u4f4d\u7f6e\/\u7a7a\u95f4\u7ed3\u6784\uff1aSSM \u5929\u751f\u662f 1D \u5e8f\u5217\uff0c\u4f60\u8981\u7ed9\u5b83\u201c\u7a7a\u95f4\u611f\u201d<\/h3>\n<p>\u5bf9\u533b\u5b66\u5206\u5272\uff0c\u4f60\u4e00\u822c\u4f1a\u5173\u5fc3\uff1a<\/p>\n<ul>\n<li>\u5c40\u90e8\u90bb\u57df\uff08\u8fb9\u754c\u7ec6\u8282\uff09<\/li>\n<li>\u5168\u5c40\u7a7a\u95f4\u4e00\u81f4\u6027\uff08\u5668\u5b98\u6574\u4f53\u5f62\u72b6\uff09<\/li>\n<\/ul>\n<p>\u539f\u59cb Mamba \u662f <strong>\u5e8f\u5217\u6a21\u578b<\/strong>\uff0c\u6240\u4ee5<strong>\u201c\u5e8f\u5217\u5316\u65b9\u5f0f\u201d<\/strong>\u4f1a\u5f3a\u70c8\u5f71\u54cd\u5b83\u5b66\u4e60\u5230\u7684\u7a7a\u95f4\u5173\u7cfb\uff08\u6bd4\u5982 raster scan \u4f1a\u628a 2D \u90bb\u5c45\u53d8\u6210 1D \u90bb\u5c45\uff0c\u8ddd\u79bb\u53ef\u80fd\u88ab\u62c9\u957f\uff09\u3002<\/p>\n<p><strong>\u8fd9\u4e00\u70b9\u6b63\u662f\u5f88\u591a\u89c6\u89c9 Mamba \u53d8\u4f53\u8981\u89e3\u51b3\u7684\u95ee\u9898<\/strong>\uff0c\u4f46\u4f60\u5728\u5199\u201c\u57fa\u7840\u7bc7\u201d\u65f6\u53ef\u4ee5\u5148\u628a\u5b83\u5f53\u4f5c\uff1a<\/p>\n<ul>\n<li>\u201c\u4e00\u79cd\u6bd4 attention \u66f4\u7701 (L) \u7684\u957f\u7a0b mixer\u201d<\/li>\n<li>\u201c\u914d\u5408\u5c40\u90e8\u5377\u79ef\u8865\u8db3\u5c40\u90e8\u5efa\u6a21\u201d<\/li>\n<\/ul>\n<h3>7.3 \u4f60\u53ef\u4ee5\u76f4\u63a5\u7c7b\u6bd4 U-Net\uff1a\u628a\u201cTransformer block\u201d\u6362\u6210 \u201cMamba block\u201d<\/h3>\n<p>\u539f\u8bba\u6587\u5728\u97f3\u9891\u5b9e\u9a8c\u91cc\u5c31\u660e\u786e\u63d0\u5230\uff1a\u4ed6\u4eec\u5728\u4e00\u4e2a <strong>U-Net backbone<\/strong>\uff08\u542b pooling\u3001\u591a stage\uff09\u91cc\uff0c\u628a\u539f\u672c\u4ea4\u66ff\u7684 S4+MLP blocks \u66ff\u6362\u6210 Mamba blocks\u3002<\/p>\n<p>\u5bf9\u533b\u5b66\u56fe\u50cf\u5206\u5272\uff0c\u4f60\u53ef\u4ee5\u5148\u7528\u540c\u6837\u7684\u201c\u66ff\u6362\u601d\u8def\u201d\u5efa\u7acb baseline\uff1a<\/p>\n<ul>\n<li>Encoder\uff1aConv\/patch embed + \u4e0b\u91c7\u6837 + Mamba blocks<\/li>\n<li>Bottleneck\uff1a\u66f4\u591a Mamba blocks<\/li>\n<li>Decoder\uff1a\u4e0a\u91c7\u6837 + skip connections +\uff08Conv \u6216 Mamba blocks\uff09<\/li>\n<\/ul>\n<hr \/>\n<h2>8. \u6700\u5c0f\u53ef\u8dd1\u793a\u4f8b\uff1a\u7528\u5b98\u65b9 <code>mamba_ssm<\/code> \u5148\u628a Block \u8dd1\u8d77\u6765<\/h2>\n<p>\u4e0b\u9762\u662f\u5b98\u65b9\u4ed3\u5e93 README \u4e2d\u7684\u6700\u5c0f\u7528\u6cd5\uff08\u8f93\u5165\u8f93\u51fa\u540c\u5f62\u72b6\uff09\uff1a<\/p>\n<pre><code class=\"language-python\">\nimport torch\nfrom mamba_ssm import Mamba\n\nbatch, length, dim = 2, 64, 16\nx = torch.randn(batch, length, dim).to(\"cuda\")\n\nmodel = Mamba(\n    d_model=dim,  # \u901a\u9053\u7ef4 D\n    d_state=16,   # \u72b6\u6001\u7ef4 N\uff08\u6bcf\u901a\u9053\u7684 state size\uff09\n    d_conv=4,     # \u5c40\u90e8\u5377\u79ef\u5bbd\u5ea6\n    expand=2,     # \u901a\u9053\u6269\u5c55\u500d\u6570 E\n).to(\"cuda\")\n\ny = model(x)\nassert y.shape == x.shape<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>1. \u4e3a\u4ec0\u4e48\u533b\u5b66\u56fe\u50cf\u5206\u5272\u4f1a\u5173\u6ce8 Mamba\uff1f \u533b\u5b66\u56fe\u50cf\u5206\u5272\uff082D\/3D\uff09\u7ecf\u5e38\u540c\u65f6\u9700\u8981\uff1a \u5c40\u90e8\u7ec6\u8282\uff1a\u8fb9\u754c\u3001\u8584\u7ed3\u6784\u3001\u5c0f\u5668\u5b98\uff08CNN \u64c5 &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[83],"tags":[84],"class_list":["post-1041","post","type-post","status-publish","format-standard","hentry","category-83","tag-mamba"],"_links":{"self":[{"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/posts\/1041","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/comments?post=1041"}],"version-history":[{"count":1,"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/posts\/1041\/revisions"}],"predecessor-version":[{"id":1042,"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/posts\/1041\/revisions\/1042"}],"wp:attachment":[{"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/media?parent=1041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/categories?post=1041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.eutaboo.com\/index.php\/wp-json\/wp\/v2\/tags?post=1041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}