{"id":15715,"date":"2024-07-10T21:29:00","date_gmt":"2024-07-10T13:29:00","guid":{"rendered":"http:\/\/139.9.1.231\/?p=15715"},"modified":"2024-07-10T09:29:56","modified_gmt":"2024-07-10T01:29:56","slug":"mamba-2","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2024\/07\/10\/mamba-2\/","title":{"rendered":"Mamba-2 \u6a21\u578b\u89e3\u8bfb"},"content":{"rendered":"\n

Github\uff1ahttps:\/\/github.com\/state-spaces\/mamba<\/p>\n\n\n\n

\u8bba\u6587\uff1ahttps:\/\/arxiv.org\/abs\/2405.21060<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Mamba2 \u6a21\u578b\u518d\u6b21\u56de\u5f52\uff0c\u5f15\u53d1 AI\u754c\u65b0\u7684\u96c0\u8dc3\u3002\u5b83\u91cd\u8981\u6027\u5728\u4e8e\u5f88\u53ef\u80fd\u5f00\u542f\u4e86\u4e00\u4e2a\u65b0\u7684\u65f6\u4ee3\uff0c\u6ce8\u610f\u529b\u673a\u52362.0\u65f6\u4ee3\uff0c\u7531\u5355\u4e00\u6ce8\u610f\u529b\u673a\u5236\u53d8\u6210\u6df7\u5408\u6ce8\u610f\u529b\u673a\u5236\u3002\u4eba\u4eec\u82e6Transformer \u8fd9\u4e2a\u5927\u8bed\u8a00\u6a21\u578b\u6838\u5fc3\u6a21\u5757\u7684\u786c\u4f24\u4e45\u77e3(\u4f20\u7edf\u81ea\u6ce8\u610f\u529b\u673a\u5236\u8fd0\u7b97\u6548\u7387\u4f4e)\uff0c\u521d\u4ee3\u7684 Mamba \u7406\u8bba\u4e0a\u4ecd\u7136\u4e0d\u591f\u5b8c\u5584\uff0c\u6240\u4ee5\u624d\u4f1a\u88ab\u4eba\u8bdf\u75c5\u3002\u4e0d\u8fc7\uff0c\u8fd9\u79cd\u4e89\u8bba\u5145\u5206\u8bf4\u660e\u4e86 LLM\u6838\u5fc3\u67b6\u6784\u7684\u53d8\u9769\u5df2\u7ecf\u52bf\u5728\u5fc5\u884c\u3002<\/p>\n\n\n\n\n\n

\u6807\u9898\u5251\u6307\u201cTransformers \u5c31\u662f SSM \u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u201d\uff0c\u4fe8\u7136\u662f\u8981\u505a\u4e2a\u5927\u4e00\u7edf\u7684\u5de5\u4f5c\uff0c\u6c14\u541e\u5c71\u6cb3Generalized models and efficient algorithms \u53eb\u6cd5\u611f\u4eba\uff0c\u53ef\u4ee5\u60f3\u8c61\u540e\u7eed\u5de5\u4f5c\u4f1a\u4e00\u7247\u4e00\u7247\u3002<\/p>\n\n\n\n

\u4e00\u3001\u91cd\u8981\u7ed3\u8bba<\/h2>\n\n\n\n

\u8fd9\u6b21\u7684\u6458\u8981\u975e\u5e38\u7b80\u77ed\uff0c\u4f46\u5b57\u5c11\u4e8b\u66f4\u5927\uff0c\u4eba\u72e0\u8bdd\u4e0d\u591a\u3002\u4e09\u53e5\u8bdd\u4e09\u5c42\u610f\u601d:
1.\u5c3d\u7ba1 Transformers \u591a\u5e74\u6765\u4e00\u76f4\u662f\u6df1\u5ea6\u5b66\u4e60\u5728\u8bed\u8a00\u5efa\u6a21\u9886\u57df\u6210\u529f\u7684\u4e3b\u8981\u67b6\u6784\uff0c\u4f46\u8fd1\u5e74\u6765\uff0c\u72b6\u6001\u7a7a\u95f4\u6a21\u578b(SSMs)\u5982 Mamba \u5df2\u88ab\u8bc1\u660e\u5728\u5c0f\u5230\u4e2d\u7b49\u89c4\u6a21\u4e0a\u80fd\u591f\u5339\u654c\u751a\u81f3\u8d85\u8d8a\u3002\u4eba\u8bdd\u5c31\u662fSSM \u662f\u65b0\u7684\u653f\u6cbb\u6b63\u786e!
2.\u672c\u6587\u5c55\u793a\u8fd9\u4e9b\u6a2a\u578b\u5bb6\u65cf\u5b9e\u9645\u4e0a\u662f\u5bc6\u5207\u76f8\u5173\u7684\uff0c\u53ef\u4ee5\u5728\u4e00\u4e2a\u79f0\u4e3a\u201c\u72b6\u6001\u7a7a\u95f4\u5bf9\u5076\u201c\u7406\u8bba\u6846\u67b6\u4e0b\u8fde\u63a5 SSM \u548c\u6ce8\u610f\u529b\u53d8\u4f53\u3002\u9009\u62e9\u6027 SSM \u5c31\u662f\u4e00\u79cd\u65b0\u7684\u6ce8\u610f\u529b\u673a\u5236\uff0c\u770b\uff0c\u8fd9\u4e48\u5feb\u5c31\u5e94\u9a8c\u4e86\uff0c\u5f53\u7136\u4eba\u5bb6\u725b\u7684\u662f\u6570\u5b66\u4e0a\u8bc1\u660e\u4e86\u3002\u522b\u6b7b\u76ef\u7740\u4f20\u7edf\u7684 Transformer \u67b6\u6784\u4e86\uff0c\u5b83\u7684\u5185\u6838\u5176\u5b9e\u8fd8\u662f\u6ce8\u610f\u529b\u3002\u5c31\u50cf\u96f7\u8fbe\u4e00\u6837\uff0c\u8981\u641e\u65b0\u4f53\u5236\u96f7\u8fbe\u3002\u65b0\u578b\u6ce8\u610f\u529b\u624d\u662f\u6b63\u9014!\u4f46\u65b9\u6cd5\u5e76\u975e\u4ece Transformer \u4fa7\u641e\u3002
3.\u636e\u6b64\u8bbe\u8ba1\u7684 Mamba-2\u901f\u5ea6\u6bd4 Transformers\u5feb 2-8\u500d\uff0c\u800c\u51c6\u786e\u7387\u66f4\u4f18\u3002<\/strong>\u7b97\u529b\u6602\u8d35\u7684\u4eca\u5929\u6548\u7387\u5c06\u662f\u65b0\u6a21\u578b\u7ade\u4e89\u7684\u91cd\u70b9!<\/p>\n\n\n\n

\u7406\u89e3\u6574\u7bc7\u6587\u7ae0\u7684\u6838\u5fc3\u5176\u5b9e\u5c31\u662f\u8fd9\u4e2a\u5bf9\u5076 duality<\/strong>\uff0c\u6211\u4eec\u5c06\u56f4\u7ed5\u7740\u5b83\u5c55\u5f00\uff0c\u660e\u767d\u4e86\u5b83\u4e5f\u5c31\u662f\u5f7b\u5e95\u641e\u61c2\u4e86 Mamba2 \u7684\u7cbe\u9ad3\u3002<\/p>\n\n\n\n

\u4e8c\u3001\u7edf\u4e00 SSM \u548c\u6ce8\u610f\u529b\u673a\u5236(\u4e24\u6027\u8bdd\u9898)<\/h2>\n\n\n\n


2.1 \u4ec0\u4e48\u662f\u5bf9\u5076\u5173\u7cfb<\/h3>\n\n\n\n

\u5728\u6570\u5b66\u3001\u7269\u7406\u5b66\u4e43\u81f3\u54f2\u5b66\u4e2d\uff0c\u201c\u5bf9\u5076\u6027\u201d\u662f\u6307\u4e24\u79cd\u770b\u4f3c\u4e0d\u540c\u7684\u7406\u8bba\u6216\u6a21\u578b\u4e4b\u95f4\u5b58\u5728\u7684\u4e00\u79cd\u6df1\u5c42\u6b21\u7684\u7b49\u4ef7\u5173\u7cfb\u3002\u901a\u8fc7\u8fd9\u79cd\u5bf9\u5076\u5173\u7cfb\uff0c\u53ef\u4ee5\u5c06\u4e00\u4e2a\u590d\u6742\u7684\u95ee\u9898\u8f6c\u5316\u4e3a\u53e6\u4e00\u4e2a\u76f8\u5bf9\u7b80\u5355\u7684\u95ee\u9898\u6765\u89e3\u51b3\uff0c\u6216\u8005\u5728\u4e00\u79cd\u8868\u793a\u5f62\u5f0f\u4e0b\u65e0\u6cd5\u8f7b\u6613\u770b\u5230\u7684\u6027\u8d28\u5728\u53e6\u4e00\u79cd\u8868\u793a\u5f62\u5f0f\u4e0b\u53d8\u5f97\u663e\u800c\u6613\u89c1\u3002<\/strong>\u6bd4\u5982\u592a\u6781\u56fe\u5c31\u662f\u5178\u578b\u7684\u5bf9\u5076\u5173\u7cfb\uff0c\u9634\u9633\u5bf9\u5e94\u3002<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u672c\u6587\u63d0\u51fa\u7684\u72b6\u6001\u7a7a\u95f4\u5bf9\u5076\u4e00\u8fb9\u662f\u7ed3\u6784\u5316\u72b6\u6001\u7a7a\u95f4\u6a21\u578b(SSMS)\uff0c\u4e00\u8fb9\u662f\u6ce8\u610f\u529b\u53d8\u4f53\uff0c\u5173\u8054\u65b9\u5f0f\u4e5f\u5c31\u662f\u5206\u754c\u7ebf\u662f\u5177\u6709\u6b21\u5e73\u65b9\u53c2\u6570\u548c\u4e58\u6cd5\u590d\u6742\u6027\u7684\u7ed3\u6784\u5316\u77e9\u9635<\/strong>\u3002<\/p>\n\n\n\n

\u8fd9\u4e2a\u7406\u8bba\u7684\u57fa\u7840\u5176\u5b9e\u662f\u7ebf\u6027\u6ce8\u610f\u529b(LA)\u6846\u67b6<\/strong>\uff0c\u5b83\u4e5f\u662f\u4e00\u79cd\u5bf9\u5076:\u4e00\u8fb9\u662f\u7ebf\u6027\u9012\u5f52\u795e\u7ecf\u7f51\u7edc(RNN)\uff0c\u4e00\u8fb9\u662f\u4f20\u7edf\u7684\u81ea\u56de\u5f52\u6ce8\u610f\u529b\u673a\u5236<\/strong>\u3002\u4e5f\u5c31\u662f\u521a\u8bf4\u7684Transformeris RNN.<\/p>\n\n\n\n

\u6838\u5fc3\u601d\u8def\u5c31\u662f\u4f20\u7edf\u7684\u81ea\u56de\u5f52\u6ce8\u610f\u529b\u673a\u5236\u5728\u5904\u7406\u957f\u5e8f\u5217\u65f6\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u800c\u901a\u8fc7\u5bf9\u5076\u5173\u7cfb\uff0c\u53ef\u4ee5\u5c06\u5176\u8f6c\u5316\u4e3a\u7ebf\u6027 RNN \u6765\u5904\u7406\uff0c\u4ece\u800c\u663e\u8457\u964d\u4f4e\u8ba1\u7b97\u590d\u6742\u5ea6<\/strong>\u3002\u8fd9\u5c31\u597d\u6bd4\u4e00\u4e2a\u5fd9\u788c\u7684\u5496\u5561\u9986\uff0c\u987e\u5ba2\u4eec\u4e0d\u65ad\u5730\u6392\u961f\u4e0b\u5355\u3002\u81ea\u56de\u5f52\u6ce8\u610f\u529b\u673a\u5236\u4f20\u7edf\u65b9\u6cd5\u4e2d\uff0c\u5496\u5561\u5e08\u9010\u4e2a\u5904\u7406\u6bcf\u4e2a\u8ba2\u5355\uff0c\u8ba1\u7b97\u590d\u6742\u5ea6\u968f\u7740\u8ba2\u5355\u6570\u91cf\u589e\u52a0\u800c\u6210\u5e73\u65b9\u589e\u957f\u3002\u901a\u8fc7\u5bf9\u5076\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u8f6c\u6362\u6210\u4e00\u79cd\u66f4\u9ad8\u6548\u7684\u5904\u7406\u65b9\u6cd5:\u5148\u6536\u96c6\u4e00\u6279\u8ba2\u5355\u6839\u636e\u8ba2\u5355\u7c7b\u578b(\u62ff\u94c1\u3001\u5361\u5e03\u7b49)\u5206\u7c7b\uff0c\u7136\u540e\u6279\u91cf\u5236\u4f5c\u518d\u5206\u53d1\uff0c\u8fd9\u5c31\u662f\u7ebf\u6027 RNN \u5904\u7406\u957f\u5e8f\u5217\u6570\u636e\u7684\u601d\u8def\u3002<\/p>\n\n\n\n

\u7b80\u5355\u603b\u7ed3\u4e00\u53e5\u8bdd:\u9633\u8c0b\u4e0d\u884c\u54b1\u4eec\u6765\u9634\u8c0b\u554a\uff0c\u54ea\u4e2a\u7ba1\u7528\u6765\u54ea\u4e2a\uff0c\u6548\u679c\u7c7b\u4f3c\u80fd\u8fbe\u5230\u76ee\u7684\u5c31\u884c<\/p>\n\n\n\n

\u65e2\u7136\u662f\u5728 SSM \u548c\u6ce8\u610f\u529b\u4e4b\u95f4\u8fdb\u884c\u5bf9\u5076\uff0c\u6211\u4eec\u5206\u522b\u56de\u5f52\u4e00\u4e0b\u5b83\u4eec\u90fd\u662f\u5565\u3002<\/p>\n\n\n\n

2.2 \u65f6\u7a7a\u6a21\u578b SSM \u7684\u672c\u8d28<\/h3>\n\n\n\n

2.1\u6d0b\u6d0b\u9152\u9152\u516c\u5f0f\u4e0d\u5c11\uff0c\u770b\u8d77\u6765\u8d39\u52b2\uff0c\u5176\u5b9e\u5c31\u662f\u5728\u8bb2\u4e0b\u9762\u8fd9\u5e45\u56fe\uff0c\u4e0a\u4e0a\u671f\u6211\u4eec\u5206\u6790\u8fc7\u3002\u672c\u8d28\u4e0a\u5de6\u8fb9\u5c31\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u65f6\u4e0d\u53d8\u7cfb\u7edf\u5efa\u6a21\uff0c\u4e2d\u95f4\u662f\u79bb\u6563\u5316\u540e\u7684\u6a21\u578b\u5c31\u662f\u4e2aRNN\uff0c\u6700\u53f3\u8fb9\u662f\u5e76\u884c\u5316\u7528\u5377\u79ef\u6838\u8fdb\u884c\u5904\u7406\uff0c\u4e5f\u5c31\u662f CNN \u5316\u7684\u6a21\u578b\u3002\u8fd9\u79cd\u8868\u793a\u65b9\u5f0f\u662f\u7528\u56fe\u6a21\u578b\u6765\u5efa\u6a21\uff0c\u5f3a\u8c03\u7684\u662f\u5e8f\u5217\u6570\u636e\u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u548c\u52a8\u6001\u53d8\u5316\u3002\u6240\u8c13\u7684 SSM \u5176\u5b9e\u53ef\u4ee5\u7406\u89e3\u4e3a\u5c31\u662f RNN\uff0c\u53ea\u4e0d\u8fc7\u66f4\u5f3a\u8c03\u901a\u8fc7\u7ebf\u6027\u4ee3\u6570\u65b9\u7a0b\u6765\u63cf\u8ff0\u7cfb\u7edf\u72b6\u6001\u7684\u53d8\u5316\uff0c\u5229\u7528\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u4e2d\u7684\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u548c\u89c2\u6d4b\u77e9\u9635\u6765\u8fdb\u884c\u5efa\u6a21\u3002\u4e5f\u5c31\u662f\u4e0b\u9762\u7684\u4e24\u7ec4\u516c\u5f0f\u3002<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u524d\u8005 ABC \u90fd\u662f\u65f6\u4e0d\u53d8\u7684\uff0c\u540e\u8005\u53d8\u6210\u4e86\u968f\u65f6\u95f4\u53d8\u5316\u7684\uff0c\u4e5f\u5c31\u662f Mamba \u6a21\u578b\u7684\u5de5\u4f5c\uff0c\u653e\u5bbd\u4e86\u5bf9\u7cfb\u6570\u77e9\u9635\u7684\u7ea6\u675f\u3002\u56e0\u6b64\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u8bf4\uff0cSSM \u5c31\u662f\u7ebf\u6027\u4ee3\u6570\u7248\u7684RNN\uff0c\u501f\u52a9\u7ebf\u4ee3\u8fd9\u4e2a\u6570\u5b66\u5de5\u5177\u6765\u66f4\u6df1\u5165\u7684\u5206\u6790 RNN\u3002\u5dee\u5206\u65b9\u7a0b\u8fdb\u884c\u65f6\u5e8f\u52a8\u6001\u5efa\u6a21\uff0cCNN\u80fd\u5e76\u884c\u5316\u5904\u7406\uff0c\u800c ABC \u7cfb\u6570\u77e9\u9635\u80fd\u5b9e\u73b0\u7279\u5f81\u7a7a\u95f4\u7684\u7ed3\u6784\u5316\u5206\u6790\u3002<\/p>\n\n\n\n

2.3 \u6ce8\u610f\u529b\u673a\u5236\u7684\u672c\u8d28<\/h3>\n\n\n\n

\u518d\u6765\u770b\u770b\u6ce8\u610f\u529b\u673a\u5236\u3002\u672c\u610f\u662f\u7ed9\u5e8f\u5217\u4e2d\u6bcf\u4e2a\u4f4d\u7f6e\u7684\u5143\u7d20\u5206\u914d\u5206\u6570\uff0c\u4f7f\u6bcf\u4e2a\u5143\u7d20\u80fd\u591f\u201c\u5173\u6ce8\u201d\u5e8f\u5217\u4e2d\u7684\u5176\u4ed6\u5143\u7d20\u3002\u524d\u6700\u5e38\u89c1\u548c\u91cd\u8981\u7684\u6ce8\u610f\u529b\u673a\u5236\u53d8\u4f53\u662f softmax \u81ea\u6ce8\u610f\u529b
Y = softmax(QKT).V
\u5176\u4e2d QK \u6210\u5bf9\u6bd4\u8f83\u7684\u673a\u5236\u5f15\u53d1\u4e86\u6ce8\u610f\u529b\u673a\u5236\u7684\u5e73\u65b9\u8bad\u7ec3\u6210\u672c\u3002\u4f60\u770b\u5b83\u7684\u672c\u8d28\u4e0a\u5c31\u662f\u77e9\u9635\u8fd0\u7b97\u3002\u8fd9\u4e0e SSM(\u7ed3\u6784\u5316\u72b6\u6001\u7a7a\u95f4\u6a2a\u578b)\u662f\u4e00\u81f4\u7684\uff0c\u4e24\u8005\u5728\u7ebf\u6027\u4ee3\u6570\u5c42\u9762\u4e0a\u6709\u5f88\u5f3a\u7684\u5173\u8054\u6027\uff0c\u7edf\u4e00\u5206\u6790\u548c\u4f18\u5316\u7684\u89c6\u89d2\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u7406\u89e3\u5b83\u4eec\u7684\u5185\u90e8\u673a\u5236\uff0c\u5e76\u53d1\u73b0\u65b0\u7684\u6539\u8fdb\u65b9\u6cd5\u3002<\/strong>
\u4ee5\u524d\u5b66\u6df1\u5ea6\u5b66\u4e60\uff0c\u5766\u7387\u8bf4 CS \u5360\u4f18\u52bf\uff0c\u9700\u8981\u7684\u6570\u5b66\u77e5\u8bc6\u4e0d\u591a\uff0c\u4ee3\u7801\u5b9e\u73b0\u80fd\u529b\u5f3a\u5c31\u53ef\u4ee5\u4e86\u3002\u4f46\u73b0\u5728\u7684\u8d8b\u52bf\u660e\u663e\u4e0d\u540c\u4e86\uff0c\u5bf9\u7ebf\u6027\u4ee3\u6570\u7b49\u719f\u6089\u7406\u8bba\u77e5\u8bc6\u7684\u529f\u529b\u8981\u6c42\u8d8a\u6765\u8d8a\u9ad8\uff0c\u81ea\u52a8\u5316\u6216\u8005\u5e94\u7528\u6570\u5b66\u80cc\u666f\u7684\u540c\u5b66\u4f18\u52bf\u66f4\u52a0\u660e\u663e\u3002<\/p>\n\n\n\n

2.3 \u600e\u4e48\u5b9e\u73b0\u4e8c\u8005\u7684\u5bf9\u5076<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u4f8b\u5982\uff0cToeplitz \u77e9\u9635\u662f\u6307\u6bcf\u6761\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u90fd\u76f8\u540c\u7684\u77ed\u9635\u3002Cauchy \u77e9\u9635\u662f\u6307\u6bcf\u4e2a\u5143\u7d20\u90fd\u7531\u4e24\u4e2a\u5411\u91cf\u7684\u5143\u7d20\u4e4b\u95f4\u7684\u5dee\u7684\u5012\u6570\u6765\u5b9a\u4e49\u7684\u77e9\u9635\u3002Vandermonde \u77e9\u9635\u662f\u7531\u4e00\u4e2a\u5411\u91cf\u7684\u5e42\u7ec4\u6210\u7684\u77e9\u9635\u3002\u4f4e\u79e9\u77e9\u9635\u662f\u6307\u5176\u79e9\u8fdc\u5c0f\u4e8e\u5176\u884c\u6216\u5217\u6570\u7684\u77e9\u9635\u3002\u7c7b\u4f3c\u7684\u7279\u6b8a\u7ed3\u6784\u77e9\u9635\uff0c\u901a\u8fc7\u538b\u7f29\u8868\u793a\u53ef\u4ee5\u7528\u66f4\u5c11\u53c2\u6570\u548c\u66f4\u5feb\u7b97\u6cd5\u8ba1\u7b97\uff0c\u51cf\u5c11\u5b58\u50a8\u9700\u6c42\uff0c\u52a0\u5feb\u8fd0\u7b97\u901f\u5ea6\uff0c\u5728\u5927\u89c4\u6a21\u6570\u636e\u5904\u7406\u548c\u673a\u5668\u5b66\u4e60\u4e2d\u5c24\u4e3a\u91cd\u8981\u3002SSM \u672c\u8d28\u4e0a\u4e5f\u662f\u4e00\u79cd\u7ed3\u6784\u5316\u77e9\u9635\u3002\u8bb2\u5230\u8fd9\u4f60\u660e\u767d\u4e86\u5427\uff0c\u8fd9\u6587\u7ae0\u5c31\u662f\u73a9\u513f\u7ebf\u6027\u4ee3\u6570\uff0c\u5728\u6ce8\u610f\u529b\u673a\u5236\u548c SSM \u4e4b\u95f4\u5efa\u7acb\u7edf\u4e00\u7684\u5bf9\u5076\u5173\u8054\u5173\u7cfb\u3002<\/p>\n\n\n\n

\u90a3\u5230\u5e95\u662f\u600e\u4e48\u7528\u6240\u8c13\u7684\u7ed3\u6784\u5316\u77e9\u9635\u8ba9\u4e8c\u8005\u52fe\u8fde\u7684\u5462?\u5176\u5b9e\u4e5f\u5f88\u7b80\u5355\u5c31\u662f\u5728 SSM \u7684\u8ba1\u7b97\u4e2d\uff0c\u7279\u522b\u662f\u77e9\u9635 A\uff0c\u5f15\u5165\u4e86\u7c7b\u4f3c\u6ce8\u610f\u529b\u673a\u5236\u7684\u516c\u5f0f\u548c\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u5177\u4f53\u6765\u8bf4:<\/p>\n\n\n\n

1.\u7b80\u5316A\u77e9\u9635\u7684\u7ed3\u6784\uff0c\u4f7f\u5176\u53ef\u4ee5\u7528\u6807\u91cf\u4e58\u4ee5\u5355\u4f4d\u77e9\u9635\u8868\u793a\uff0c\u4ece\u800c\u51cf\u5c11\u8ba1\u7b97\u590d\u6742\u5ea6<\/p>\n\n\n\n

2.\u7c7b\u4f3c Transformer \u4e2d\u591a\u5934\u6ce8\u610f\u529b\u7684\u6982\u5ff5\uff0c\u589e\u52a0\u4e86\u5934\u7ef4\u5ea6(P)\u4ee5\u589e\u5f3a\u6a21\u578b\u7684\u8868\u8fbe\u80fd\u529b\u3002<\/p>\n\n\n\n

3.\u4f7f\u7528\u7c7b\u4f3c\u6ce8\u610f\u529b\u7684\u5bf9\u5076\u5f62\u5f0f\uff0c\u53bb\u9664\u4e86softmax\uff0c\u5e76\u5f15\u5165\u4e86\u4e00\u4e2a\u989d\u5916\u7684\u63a9\u7801\u77e9\u9635L\uff0c\u6839\u636e\u6570\u636e\u751f\u6210\uff0c\u63a7\u5236\u4fe1\u606f\u5728\u65f6\u95f4\u4e0a\u7684\u4f20\u9012\u91cf\u3002<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u5706\u5708\u8868\u793a\u5143\u7d20\u76f8\u4e58\uff0c\u4e5f\u5c31\u662f\u54c8\u5fb7\u9a6c\u79ef\u3002\u53f3\u8fb9\u7684\u5f0f\u5b50\u6709\u70b9\u96be\u61c2\uff0c\u7ed9\u4f60\u5199\u6210\u77e9\u9635\u5f62\u5f0f\u597d\u7406\u89e3\uff0c\u5047\u8bbea =[a1, a2, a3]\u8fd9\u4e2a mask \u5176\u5b9e\u5c31\u662f\u4e2a\u4e0b\u4e09\u89d2\u77e9\u9635:<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u8fd8\u662f\u770b\u4e0d\u61c2\u662f\u5427\uff0c\u884c\u6807\u662fi\uff0c\u5217\u6807\u662fj\uff0ci<j \u7684\u90e8\u5206\u5168\u662f\u96f6\uff0c\u610f\u5473\u7740\u53ea\u8003\u8651\u65f6\u95f4\u4e0a\u65e9\u4e8e\u6216\u540c\u4e00\u65f6\u95f4\u70b9\u7684\u5143\u7d20\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u662f\u4e00\u79cd\u7c7b\u4f3c GPT \u6a21\u578b\u4e2d\u7684\u5355\u5411\u6ce8\u610f\u529b\u673a\u5236\uff0c\u53ea\u8003\u8651\u8fc7\u53bb\u7684\u65f6\u95f4\u6b65\uff0c\u800c\u4e0d\u8003\u8651\u672a\u6765\u7684\u65f6\u95f4\u6b65\u3002\u901a\u8fc7\u8fd9\u79cd\u4e0b\u4e09\u89d2\u77e9\u9635\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u63a7\u5236\u4fe1\u606f\u5728\u65f6\u95f4\u4e0a\u7684\u6d41\u52a8\uff0c\u786e\u4fdd\u4fe1\u606f\u53ea\u80fd\u4ece\u8fc7\u53bb\u4f20\u9012\u5230\u73b0\u5728\uff0c\u800c\u4e0d\u80fd\u53cd\u5411\u4f20\u64ad\u3002 <\/p>\n\n\n\n

\u5f88\u591a\u4eba\u5230\u8fd9\u91cc\u53ef\u80fd\u4f1a\u5f88\u56f0\u60d1?\u4e3a\u4ec0\u4e48\u8fd9\u5c31\u662f\u5bf9\u5076\u554a?\u660e\u660e\u5c31\u662f\u5728 A\u4e2d\u5e94\u7528\u4e86\u7c7b\u4f3c\u6ce8\u610f\u529b\u7684\u8ba1\u7b97\u65b9\u5f0f\u561b!\u6211\u4eec\u6253\u4e24\u4e2a\u6bd4\u65b9\u52a0\u6df1\u4f60\u7684\u7406\u89e3\u3002\u5982\u540c\u592a\u6781\u56fe\u4e2d\u7684\u9634\u9633\u4e92\u8865\u76f8\u4e92\u8f6c\u6362\u4e00\u6837\uff0c\u65e0\u8bba\u662f\u6ce8\u610f\u529b\u673a\u5236\u8fd8\u662f SSM\uff0c\u5b83\u4eec\u7684\u6838\u5fc3\u90fd\u662f\u5904\u7406\u548c\u66f4\u65b0\u4fe1\u606f\u72b6\u6001\uff0c\u53ea\u662f\u65b9\u5f0f\u4e0d\u540c\u3002SSM \u50cf\u4e2a\u7537\u4eba\u5f3a\u8c03\u903b\u8f91\u548c\u987a\u5e8f\uff0c\u6ce8\u610f\u529b\u673a\u5236\u50cf\u4e2a\u5973\u4eba\u672c\u5f3a\u8c03\u7ec6\u8282\u548c\u5173\u8054\uff0c\u5bf9\u5076\u5c31\u50cf\u662f\u4e8c\u8005\u7684\u7ed3\u5a5a\uff0c\u4f60\u4e2d\u6709\u6211\u6211\u4e2d\u6709\u4f60\uff0c\u5230\u5e95\u662f\u8c01\u5e72\u8c01\u4e5f\u8bf4\u4e0d\u6e05\u3002\u7ad9\u5728SSM \u89c6\u89d2\uff0c\u5185\u5d4c\u4e86\u6ce8\u610f\u529b\uff0c\u7ad9\u5728\u6ce8\u610f\u529b\u673a\u5236\u7684\u89c6\u89d2\uff0c\u8fd9\u662f\u65b0\u578b\u8ba1\u7b97\u65b9\u5f0f\u3002<\/strong>\u5b83\u4e0d\u662f\u4e00\u79cd\u7b80\u5355\u7684\u5185\u5d4c\uff0c\u800c\u662f\u6709\u7740\u6570\u5b66\u548c\u529f\u80fd\u4e0a\u7684\u6df1\u5c42\u8054\u7cfb\uff0c\u8fd9\u5c31\u725b\u903c\u4e86\u3002\u6b63\u5982\u4f60\u80fd\u8bf4\u751f\u6d3b\u4e0d\u9700\u8981\u6280\u5de7\uff0c\u968f\u968f\u4fbf\u4fbf\u5c31\u80fd\u767b\u5cf0\u9020\u6781\u5417?<\/p>\n\n\n\n

\u5230\u6b64\uff0c\u4f60\u5df2\u7ecf get\u4e86\u672c\u6587\u7684\u6838\u5fc3\u601d\u60f3\uff0c\u6765\u770b\u770b\u5b83\u7684\u7ec4\u7ec7\u7ed3\u6784\u3002<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u8fd9\u5f20\u56fe\u4e4d\u4e00\u770b\u662f\u4e00\u8138\u60dc\u903c\u7684\uff0c\u4e0d\u8fc7\u501f\u7528\u521a\u624d\u6253\u7684\u6bd4\u65b9\u8ba9\u4f60\u79d2\u61c2\u3002SSM \u662f\u4e2a\u7537\u7684\uff0cAttention \u662f\u4e2a\u5973\u7684\uff0cSSD \u662f\u4e8c\u8005\u7684\u5bf9\u5076\u5c31\u662f\u6027\u751f\u6d3b\uff0c\u8fd9\u79cd\u7ed3\u5408\u4e0d\u4ec5\u4ec5\u662f\u8868\u9762\u7684\u53e0\u52a0\uff0c\u800c\u662f\u6df1\u5c42\u6b21\u7684\u878d\u5408\u3002\u90a3\u6211\u95ee\u4f60 Mamba-2\u662f\u5565?\u9020\u4eba\u751f\u5a03\u554a!\u901a\u8fc7\u6df1\u5c42\u6b21\u7ed3\u5408\uff0c\u8fbe\u5230\u6700\u4f73\u7684\u8ba1\u7b97\u6548\u679c\u548c\u6027\u80fd\u3002\u4e0a\u8fb9\u7684 Structured Matrices \u5c31\u662f\u7231\u7231\u7684\u7ed3\u54c1\uff0c\u53d7\u5b55\u7684\u80da\u80ce\uff0c\u53eb\u7ed3\u6784\u5316\u77e9\u9635\uff0c\u5b83\u80fd\u5e26\u6765\u66f4\u52a0\u9ad8\u6548\u7684\u7b97\u6cd5\u3002<\/p>\n\n\n\n

\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u8bb2\u5b8c\u4e86\u539f\u65871\u548c2\u90e8\u5206\u7684\u5185\u5bb9\uff0c\u63a5\u4e0b\u6765\u6b63\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u5206\u522b\u8be6\u7ec6\u8bb2\u8ff0\u51e0\u6761\u8fb9\u3002\u9996\u5148\u662f SSM \u5982\u4f55\u751f\u6210\u7ed3\u6784\u5316\u77ed\u9635\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u6240\u8c13\u7684\u534a\u53ef\u5206\u77e9\u9635\u3002<\/p>\n\n\n\n

\u4e09\u3001SSM \u77e9\u9635\u7684\u5de7\u5999\u8bbe\u8ba1(MAN)<\/h2>\n\n\n\n

\u534a\u53ef\u5206\u77e9\u9635\u5bf9\u5e94\u539f\u6587\u7b2c3\u90e8\u5206\uff0c\u5145\u65a5\u5927\u91cf\u7ebf\u6027\u4ee3\u6570\u5b9a\u7406\u63a8\u5bfc\uff0c\u8bfb\u8d77\u6765\u57fa\u7840\u4e0d\u624e\u5b9e\u90a3\u662f\u76f8\u5f53\u7684\u8d39\u52b2\u3002\u4eba\u8bdd\u603b\u7ed3\u5f52\u7eb3\uff0c\u5176\u5b9e\u8bf4\u7a7f\u4e86\u5c31\u662f\u4e24\u5c42\u610f\u601d:\u4e00\u662f SSM \u53ef\u4ee5\u8868\u793a\u4e3a y=Mx \u7684\u5f62\u5f0f\uff0c\u5176\u4e2d M \u662f ABC \u7684\u8868\u8fbe\u5f0f:\u4e8c\u662f M \u5177\u6709\u4e13\u95e8\u8bbe\u8ba1\u7684\u534a\u53ef\u5206\u7ed3\u6784\uff0c\u80fd\u7b80\u5316\u8fd0\u7b97\u3002<\/strong><\/p>\n\n\n\n

3.1 SSM\u7684\u8868\u8fbe\u5f0f<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u539f\u6765\u7684 RNN \u4e5f\u597d\uff0c\u65f6\u5e8f\u7cfb\u7edf\u4e5f\u597d\uff0c\u53ef\u4ee5\u5377\u79ef\u5316\uff0c\u5199\u6210y=Mx\u7684\u5f62\u5f0f\u3002\u8fd9\u91cc\u7684M \u662f\u4ec0\u4e48\u5c31\u6709\u8bb2
\u5934\u4e86\u3002<\/p>\n\n\n\n

3.2 \u987a\u5e8f\u534a\u53ef\u5206\u77e9\u9635 SSS<\/h3>\n\n\n\n

\u5bf9\u77e9\u9635 M \u4e13\u95e8\u8bbe\u8ba1\uff0c\u53ef\u4ee5\u5b9e\u73b0\u66f4\u9ad8\u6548\u7684\u8ba1\u7b97\u3002\u770b\u56fe\u4e00\u76ee\u4e86\u7136<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u9996\u5148\u662f\u5e8f\u5217\u5316\u7684\uff0c\u5176\u6b21\u662f\u4e0b\u4e09\u89d2\u7684\uff0c\u7b2c\u4e09\u662f\u4f4e\u79e9\u7684\u3002\u987a\u5e8f\u534a\u53ef\u5206\u77e9\u9635(sss\uff0cSequentiallySemiseparable Structure)\u7684\u539f\u56e0\u662f:\u534a\u6307\u4e3b\u8981\u5173\u6ce8\u4e0b\u4e09\u89d2\u90e8\u5206\uff0c\u53ef\u5206\u6307\u7684\u662f\u6bcf\u4e2a\u84dd\u8272\u5c0f\u5757\u7684\u79e9\u8f83\u5c0f\uff0c\u4e0d\u8d85\u8fc7N\uff0c\u610f\u5473\u7740\u53ef\u4ee5\u7528\u66f4\u5c11\u7684\u72ec\u7acb\u6210\u5206\u8868\u793a\uff0c\u4ece\u800c\u5b9e\u73b0\u9ad8\u6548\u8ba1\u7b97\u3002 y=SSS(A, B,C)\u00b7x
\u800c\u5b9a\u7406 3.5\u6307\u51fa\uff0c\u4eba\u8bdd\u72b6\u6001\u7a7a\u95f4\u6a21\u578b SSM\uff0c\u5982\u679c\u72b6\u6001\u7684\u7ef4\u5ea6\u4e3a N\uff0c\u7b49\u4ef7\u4e8e\u4e00\u4e2a\u79e9\u4e3a N \u7684SSS<\/p>\n\n\n\n

\u7ed5\u6765\u7ed5\u53bb\uff0c\u5c31\u662f\u8bf4\u4efb\u4f55 SSM \u5176\u5b9e\u90fd\u53ef\u4ee5\u8f6c\u5199\u6210\u4e00\u4e2a\u7b49\u4ef7\u7684\u5c40\u90e8\u4e0b\u5bf9\u89d2\u9635M \u7684\u5f62\u5f0f\u3002<\/p>\n\n\n\n

SSM \u662f\u4e00\u4e2a\u6574\u4f53\u7684\u6846\u67b6\uff0c\u7528\u4e8e\u5904\u7406\u8f93\u5165x\u5e76\u751f\u6210\u8f93\u51fay\uff0c\u5982\u679c\u628a\u5b83\u7c7b\u6bd4\u4e3a\u4e00\u4e2a\u7537\u4eba\uff0c\u90a3\u4e48 M\u77ed\u9635\u5728\u5176\u4e2d\u8d77\u5230\u6838\u5fc3\u4f5c\u7528\u3002\u63d0\u5347\u4e86\u8ba1\u7b97\u6548\u7387\u3002
\u6bd4\u5982\u6765\u4e2a\u66f4\u7279\u522b\u7684\uff0c\u8ba9\u79e9 N=1\uff0c\u5c31\u662f M=1SS<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5f52\u7eb3\u8d77\u6765\uff0c\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u548c Mamba \u521d\u4ee3\u7684\u533a\u522b\u5728\u4e8e\u4e24\u4e2a:<\/p>\n\n\n\n

\u4e00\u662f\u5728 A \u77e9\u9635\u7684\u8ba1\u7b97\u4e2d\u5d4c\u5165\u4e86\u6ce8\u610f\u529b\u516c\u5f0f;<\/p>\n\n\n\n

\u4e8c\u662f\u8ba9 M \u77e9\u9635\u8bbe\u8ba1\u4e3a\u987a\u5e8f\u534a\u53ef\u5206\u7684\u5f62\u5f0f;<\/p>\n\n\n\n

\u8bf4\u5230\u5e95\uff0c\u90fd\u662f\u5728\u8bbe\u8ba1\u66f4\u4e3a\u673a\u5de7\u7279\u6b8a\u7684\u77e9\u9635\u7ed3\u6784\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u5148\u524d\u6240\u8bf4\u7684\u9600\u95e8\u7ed3\u6784\uff0c\u4ece\u800c\u80fd\u66f4\u597d\u7684\u63a7\u5236\u8bb0\u5fc6\u7684\u6d41\u6dcc\u878d\u5408\uff0c\u4e5f\u662f\u4e00\u79cd\u65b0\u578b\u6ce8\u610f\u529b\u673a\u5236\u7684\u4f53\u73b0\u3002\u8fd9\u91cc\u6ca1\u6709\u8bf4\u6e05\u695aA\u548cM\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5176\u5b9e\u662fA\u8bbe\u8ba1\u6210\u4e86\u534a\u53ef\u5206\uff0c\u4e5f\u5c31\u662f\u4e0b\u5bf9\u89d2\u9635\u7684\u5f62\u5f0f\uff0c\u7136\u540eM\u7ee7\u627f\u4e86\u8fc7\u6765\uff0c\u800cBC \u6ca1\u53d8<\/p>\n\n\n\n

3.3 \u5f20\u91cf\u6536\u7f29\u4e0b\u7684 SSM \u8ba1\u7b97<\/h3>\n\n\n\n

\u8fd9\u90e8\u5206\u5199\u7684\u582a\u79f0\u6df7\u4e71\uff0c\u4e0d\u8fc7\u8bf4\u7a7f\u4e86\u5c31\u4e00\u53e5\u8bdd:SSS \u7684\u8ba1\u7b97\u8fc7\u7a0b\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u4e00\u7cfb\u5217\u5f20\u91cf\u6536\u7f29\u64cd\u4f5c<\/strong>\uff0c\u501f\u52a9\u987a\u5e8f\u534a\u53ef\u5206\u77e9\u9635\u7684\u7279\u6b8a\u7ed3\u6784\u80fd\u5b9e\u73b0\u9ad8\u6548\u8ba1\u7b97\u3002\u7406\u8bba\u4e0a\uff0c\u6240\u6709 SSM \u7684\u8ba1\u7b97\u90fd\u53ef\u4ee5\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\u4f18\u5316\uff0c\u4ece\u800c\u5728\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u65f6\u663e\u8457\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e09\u4e2a\u6b65\u7403:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u6211\u4eec\u77e5\u9053\uff0c\u5f20\u867d\u6536\u7f29\u662f\u77e9\u9635\u4e58\u6cd5\u7684\u6269\u5c55\uff0c\u5141\u8bb8\u5904\u7406\u66f4\u9ad8\u7ef4\u7684\u5f20\u91cf\uff0c\u5e76\u8fdb\u884c\u590d\u6742\u7684\u7ef4\u5ea6\u53d8\u6362\u548c\u6c42\u548c\u64cd\u4f5c\u3002\u4f7f\u7528\u8bf8\u5982 NumPy \u7684 einsum \u51fd\u6570(\u7231\u56e0\u65af\u5766\u6c42\u548c\u7ea6\u5b9a)\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u5b9e\u73b0\u8fd9\u79cd\u64cd\u4f5c\u3002\u5982\u4e0b\u56fe\u6240\u793a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u4e09\u4e2a\u6b65\u9aa4\u7b2c\u4e00\u6b65\u5c06\u8f93\u5165\u77e9\u9635X \u4e0e\u77e9\u9635 B \u8fdb\u884c\u7ed3\u5408\uff0c\u4ee5\u4ea7\u751f\u4e00\u4e2a\u4e2d\u95f4\u7ed3\u679c Z\u3002\u77e9\u9635A\u6ca1\u6709\u51fa\u73b0\uff0c\u5b83\u4f53\u73b0\u5728\u7b2c\u4e8c\u6b65\u56e0\u72b6\u6001\u66f4\u65b0\u4e2d\uff0cL\u7684\u5b9a\u4e49\u4f9d\u8d56\u4e8e A\u3002\u7b2c\u4e09\u6b65\u662f\u6700\u7ec8\u8f93\u51fa\u3002<\/p>\n\n\n\n

\u8bb2\u5b8c\u4e86 SSM \u5e76\u884c\u5316\u65f6\u77e9\u9635 M\u7684\u5f62\u5f0f\u8fdb\u884c\u4e86\u54ea\u4e9b\u673a\u5de7\u8bbe\u8ba1\uff0c\u4ee5\u53ca\u5f20\u91cf\u6536\u7f29\u89c6\u89d2\u4e0b\u7684 SSM \u8ba1\u7b97\u3002\u518d\u6765\u770b\u770b\u6ce8\u610f\u529b\u673a\u5236\u600e\u4e48\u4e5f\u80fd\u7edf\u4e00\u5230\u540c\u6837\u7684\u6846\u67b6\u4e0b\u3002<\/p>\n\n\n\n

\u56db\u3001\u6ce8\u610f\u529b\u673a\u5236\u7684\u901a\u7528\u5b9e\u73b0(WOMAN)<\/h2>\n\n\n\n

\u8fd9\u90e8\u5206\u539f\u6587\u5199\u7684\u6bd4\u8f83\u5570\u55e6\uff0c\u8ba9\u4eba\u6709\u70b9\u6655\u5934\u8f6c\u5411\u3002\u6897\u76f4\u54e5\u628a\u5176\u8868\u8fbe\u7684\u610f\u601d\u7528\u4eba\u8bdd\u7ffb\u8bd1\u5e2e\u4f60\u7406\u89e3<\/p>\n\n\n\n

4.1 \u5f20\u91cf\u6536\u7f29\u89c6\u89d2\u4e0b\u6ce8\u610f\u529b\u8ba1\u7b97<\/h3>\n\n\n\n

\u7b80\u5355\u8bf4\uff0c\u5c31\u662f\u6362\u4e00\u79cd\u89c6\u89d2\uff0c\u628a\u4e0d\u540c\u6ce8\u610f\u529b\u673a\u5236\u7684\u8ba1\u7b97\u4e00\u822c\u5316\uff0c\u7528\u66f4\u52a0\u901a\u7528\u7684\u5f62\u5f0f\u6765\u63cf\u8ff0\uff0c\u5177\u4f53\u6765\u8bf4\uff0c\u5c31\u662f\u7ad9\u5230\u5f20\u867d\u6536\u7f29\u7684\u89c6\u89d2\u6765\u770b\uff0c\u7eb3\u5165\u4e00\u4e2a\u7edf\u4e00\u7684\u6846\u67b6
\u6bd4\u5982\uff0c\u5e38\u89c1\u7684\u6ce8\u610f\u529b\u8ba1\u7b97\u5f62\u5f0f\u5982\u4e0b:
Q=input (T,N)
K=input (S,N)
V =input(S,P)
G =QKT(T, S)
M=f(G)(T,S)
Y= GV(T,P)
\u8fd9\u91cc\u7684S \u548c T \u4ee3\u8868\u6e90\u5e8f\u5217\u548c\u76ee\u6807\u5e8f\u5217\u7684\u957f\u5ea6\uff0cN \u4ee3\u8868\u7279\u5f81\u7ef4\u5ea6\uff0cP \u4ee3\u8868\u5934\u90e8\u7ef4\u5ea6\uff0c\u6700\u5e38\u89c1\u7684 softmax \u8fd9\u91cc\u7528f\u6765\u66f4\u4e00\u822c\u5316\u7684\u8868\u793a\u3002\u81ea\u6ce8\u610f\u529b\u673a\u5236\u6bd4\u8f83\u7b80\u5355\uff0c\u5c31\u662f\u6e90\u5e8f\u5217\u548c\u76ee\u6807\u5e8f\u5217\u76f8\u540cS=T,\u7279\u5f81\u7ef4\u5ea6\u548c\u5934\u90e8\u7ef4\u5ea6\u76f8\u540c N=P\u30024.1.1-4.1.3:\u4e3b\u8981\u662f\u56de\u987e\u548c\u603b\u7ed3\u5df2\u6709\u7684\u6ce8\u610f\u529b\u673a\u5236\u548c\u65b9\u6cd5\uff0c\u6ca1\u6709\u5565\u65b0\u5185\u5bb9\u3002<\/p>\n\n\n\n

4.1.4 \u56de\u987e\u4e86\u77e9\u9635 A \u4e2d\u5d4c\u5165\u6ce8\u610f\u529b\u673a\u5236\u7684\u63a9\u7801\u6ce8\u610f\u529b
y=(L\u00b0(QKT))\u00b7V
\u6240\u6709\u7684\u8fd9\u4e9b\u8ba1\u7b97\u65b9\u5f0f\u90fd\u53ef\u4ee5\u5199\u6210\u5f20\u91cf\u6536\u7f29\u7684\u5f62\u5f0f\uff0c\u4e5f\u5c31\u662f\u77e9\u9635\u4e58\u6cd5\u7684\u6269\u5c55\uff0c\u5141\u8bb8\u5904\u7406\u66f4\u9ad8\u7ef4\u7684\u5f20\u91cf\uff0c\u5e76\u8fdb\u884c\u590d\u6742\u7684\u7ef4\u5ea6\u53d8\u6362\u548c\u6c42\u548c\u64cd\u4f5c\u3002\u4f7f\u7528\u8bf8\u5982 NumPy \u7684 einsum \u51fd\u6570(\u7231\u56e0\u65af\u5766\u6c42\u548c\u7ea6\u5b9a)\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u5b9e\u73b0\u8fd9\u79cd\u64cd\u4f5c\u3002
Y = contract(TN, SN, SP, TS \u2192 TP)(Q, K, V, L)<\/p>\n\n\n\n

\u5176\u4e2d\u8fd8\u53ef\u4ee5\u8fdb\u4e00\u6b65\u62c6\u89e3\u6210\u591a\u6b65\u6536\u7f29\uff0c\u53ef\u4ee5\u66f4\u9ad8\u6548\u5730\u5b9e\u73b0\u6ce8\u610f\u529b\u673a\u5236\uff0c\u63d0\u5347\u8ba1\u7b97\u6548\u7387\u3002
G= contract(TN, SN \u2192 TS)(Q,K)
M = contract(Ts,TS \u2192 TS)(G, L)
Y= contract(TS, SP \u2192 TP)(M, V)
(T,S)(T,S)(T,P)
\u4e5f\u5c31\u662f\u5148\u8ba1\u7b97\u76f8\u4f3c\u6027\u77e9\u9635 G=QK^T\uff0c\u5e94\u7528\u63a9\u7801\u77e9\u9635L\u540e\u5f97\u5230\u65b0\u7684\u76f8\u4f3c\u6027\u77e9\u9635 <\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u7136\u540e\u518d\u8ba1\u7b97\u6700\u7ec8\u7684\u8f93\u51fa Y=MV\uff0c\u540e\u9762\u5bf9\u5e94\u7684\u662f\u76f8\u5e94\u7684\u7ef4\u5ea6\u3002\u5f52\u7eb3\u6765\u8bf4\uff0c\u7528\u5f20\u91cf\u6536\u7f29\u6765\u5b9e\u73b0\uff0c\u4f7f\u5f97\u6ce8\u610f\u529b\u673a\u5236\u7684\u8ba1\u7b97\u8fc7\u7a0b\u66f4\u52a0\u6e05\u6670\u548c\u9ad8\u6548\u3002<\/p>\n\n\n\n

4.2 \u7ebf\u6027\u6ce8\u610f\u529b<\/h3>\n\n\n\n

\u7ebf\u6027\u6ce8\u610f\u529b\u53ca\u5176\u4ed6\u8bb8\u591a\u9ad8\u6548\u6ce8\u610f\u529b\u53d8\u79cd\uff0c\u901a\u5e38\u901a\u8fc7\u6539\u53d8\u77e9\u9635\u5173\u8054\u7684\u987a\u5e8f\u6765\u5b9e\u73b0\uff0c\u4f8b\u5982(OKT)V=Q(KTV).
\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u5c06\u6807\u51c6\u6ce8\u610f\u529b\u4e2d\u7684\u590d\u6742\u8ba1\u7b97\u7b80\u5316\u4e3a\u7d2f\u52a0\u548c\u64cd\u4f5c\uff0c\u4ece\u800c\u63d0\u9ad8\u4e86\u8ba1\u7b97\u6548\u7387\u3002
Y=Q\u00b7cumsum(KTV)
\u540c\u65f6\u53ef\u4ee5\u8bc1\u660e\u5b83\u4e00\u6837\u53ef\u4ee5\u7528\u5f20\u91cf\u6536\u7f29\u8868\u8fbe<\/p>\n\n\n\n

4.3 \u7ed3\u6784\u5316\u63a9\u7801\u6ce8\u610f\u529b<\/h3>\n\n\n\n

\u7ed3\u6784\u5316\u63a9\u7801\u6ce8\u610f\u529b\u662f\u7ed3\u5408\u4e86\u7ed3\u6784\u5316\u77e9\u9635\u548c\u63a9\u7801\u6ce8\u610f\u529b\uff0c\u66f4\u52a0\u9ad8\u6548\u7684\u8ba1\u7b97\u65b9\u5f0f\uff0c\u7528\u5f20\u91cf\u6536\u7f29\u6765\u5b9e\u73b0:
Z= contract(SP,SN \u2192 SPN)(V,K) (S,P,N)
H = contract(TS, SPN \u2192 TPN)(L,Z) (T,P,N)
Y = contract(TN, TPN \u2192 TP)(Q, H) (T,P)

\u7b2c\u4e00\u6b65\u4e3a\u6269\u5c55\u64cd\u4f5cV\u548cK\u8fd0\u7b97\uff0c\u7136\u540e\u662f\u7ebf\u6027\u90e8\u5206\u8ba1\u7b97(L,Z)\uff0c\u7136\u540e\u662f\u6536\u7f29\u64cd\u4f5c\u3002
\u5982\u4e0b\u56fe\u6240\u793a\u4e0d\u540c\u7684\u63a9\u7801\u77e9\u9635(\u5982\u56e0\u679c\u63a9\u7801\u3001\u8870\u51cf\u63a9\u7801\u3001Toeplitz \u77e9\u9635\u7b49)L\u5b9a\u4e49\u4e86\u4e0d\u540c\u7684\u5e8f\u5217\u53d8\u6362\u77e9\u9635 M\uff0c\u4ece\u800c\u5b9e\u73b0\u4e0d\u540c\u5f62\u5f0f\u7684\u7ed3\u6784\u5316\u6ce8\u610f\u529b\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5982\u540c\u524d\u9762\u7c7b\u6bd4 SSM \u4e3a\u7537\u4eba\uff0cSSS\u4e3a\u7cbe\u5b50\uff0c\u8fd9\u91cc\u4e0d\u540c\u7684\u6ce8\u610f\u529b\u673a\u5236\u5c31\u50cf\u662f\u5973\u4eba\uff0c\u800cstructuredmasked attention\uff0cSMA \u5c31\u50cf\u662f\u5375\u5b50
\u5bf9\u6bd4\u516c\u5f0f 15 \u548c\u516c\u5f0f8\uff0c\u9661\u7136\u4e4b\u95f4\u53d1\u73b0\u4ed6\u4eec\u4e00\u6837\uff0c\u8bf4\u660e\u65e0\u8bba\u662f\u4ece\u72b6\u6001\u7a7a\u95f4\u6a21\u578b(SSM)\u4fa7\uff0c\u8fd8\u662f\u4ece\u6ce8\u610f\u529b\u673a\u5236\u4fa7\u6765\u770b\uff0c\u90fd\u53ef\u4ee5\u7edf\u4e00\u5230\u5f20\u91cf\u6536\u7f29\u7684\u89c6\u89d2\u4e0b\u8fdb\u884c\u64cd\u4f5c\u3002\u8fd8\u662f\u501f\u7528\u4eba\u7c7b\u7684\u6bd4\u65b9\u7c7b\u6bd4\uff0c\u5f20\u867d\u6536\u7f29\u5c31\u5982\u540c\u751f\u6b96\u8fc7\u7a0b\uff0c\u6216\u8005\u8bf4\u9057\u4f20\u751f\u7269\u5b66\uff0c\u5bf9\u7537\u4eba\u5973\u4eba\u90fd\u662f\u7c7b\u4f3c\u7684\uff0c\u90fd\u9075\u5faa\u7740\u540c\u6837\u7684DNA \u9057\u4f20\u4fe1\u606f\u4f20\u9012\u3002<\/p>\n\n\n\n

\u4e94\u3001\u72b6\u6001\u7a7a\u95f4\u7684\u5bf9\u5076\u6027(SEX)<\/h2>\n\n\n\n

\u539f\u6587\u7b2c 5\u90e8\u5206\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86\u72b6\u6001\u7a7a\u95f4\u7684\u5bf9\u5076\u6027\u3002\u9996\u5148\uff0c\u4ece SSM \u4fa7\u6765\u770b\uff0c\u5047\u8bbeAj\u662f\u4e2a\u6807\u91cf\uff0c\u90a3\u4e48SSM\u7684\u77e9\u9635M\u4e3a:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u800c\u8fd9\u6b63\u662f\u4e8c\u6b21\u63a9\u7801\u6838\u6ce8\u610f\u529b\u5b9a\u4e49\u7684\u539f\u59cb\u5b9a\u4e49\u3002\u6362\u53e5\u8bdd\u8bf4\u6807\u91cf\u7ed3\u6784\u4e0b\u7684SSM\uff0c\u901a\u8fc7\u660e\u786e\u5199\u51faM\u7684\u77e9\u9635\u5f62\u5f0f\uff0c\u7136\u540e\u6267\u884c\u4e8c\u6b21\u77e9\u9635-\u5411\u867d\u4e58\u6cd5\u6765\u8ba1\u7b97\u8f93\u51fa\uff0c\u672c\u8d28\u4e0a\u662f\u5728\u6267\u884c\u4e0e\u4e8c\u6b21\u63a9\u7801\u6838\u6ce8\u610f\u529b\u76f8\u540c\u7684\u8ba1\u7b97\u6b65\u9aa4\u3002\u8fd9\u610f\u5473\u7740\u4ece\u8ba1\u7b97\u89d2\u5ea6\u6765\u770b\uff0c\u4e8c\u8005\u662f\u7b49\u4ef7\u7684\uff0c\u53ef\u4ee5\u76f8\u4e92\u8f6c\u6362\u3002\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0cSSM \u7684\u8ba1\u7b97\u65b9\u5f0f\u53ef\u4ee5\u89c6\u4e3a\u4e00\u79cd\u6ce8\u610f\u529b\u673a\u5236\uff0c\u7279\u522b\u662f\u5f53\u6211\u4eec\u4f7f\u7528\u6807\u661f\u7ed3\u6784\u548c\u534a\u53ef\u5206\u77e9\u9635\u65f6\u3002
\u53cd\u4e4b\uff0c\u4ece\u6ce8\u610f\u529b\u673a\u5236\u4fa7\u770b\uff0c\u5f53\u63a9\u7801\u77e9\u9635 LLL \u5177\u6709\u7279\u5b9a\u7684\u7ed3\u6784\u65f6(\u5982\u56e0\u679c\u63a9\u7801\u62161-\u534a\u53ef\u5206\u77e9\u9635)\uff0c\u6ce8\u610f\u529b\u673a\u5236\u7684\u8ba1\u7b97\u53ef\u4ee5\u89c6\u4e3a SSM \u7684\u8ba1\u7b97\u3002<\/p>\n\n\n\n

\u8fd9\u79cd\u5173\u7cfb\u4ece\u56fe4\u770b\u7684\u66f4\u52a0\u6e05\u695a\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u6838\u5fc3\u601d\u60f3:SSM \u548c SMA\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\u662f\u7b49\u4ef7\u7684\uff0c\u53ef\u4ee5\u901a\u8fc7\u76f8\u540c\u7684\u6570\u5b66\u64cd\u4f5c\u5b9e\u73b0\u3002\u8fd9\u79cd\u7b49\u4ef7\u6027\u4e3a\u7406\u89e3\u548c\u5b9e\u73b0\u8fd9\u4e9b\u6a21\u578b\u63d0\u4f9b\u4e86\u7edf\u4e00\u7684\u89c6\u89d2\u548c\u65b9\u6cd5\u3002\u65e0\u8bba\u662f\u5728\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u8fd8\u662f\u6ce8\u610f\u529b\u673a\u5236\u7684\u5e94\u7528\u4e2d\uff0c\u90fd\u53ef\u4ee5\u5229\u7528\u8fd9\u79cd\u7edf\u4e00\u89c6\u89d2\u6765\u9009\u62e9\u6700\u5408\u9002\u7684\u8ba1\u7b97\u65b9\u6cd5\uff0c\u4ece\u800c\u63d0\u9ad8\u6a21\u578b\u7684\u6548\u7387\u548c\u6548\u679c\u3002\u56fe\u4e2d\u663e\u793a\u4e86\u4e00\u5927\u7c7b\u7684\u72b6\u6001\u7a7a\u95f4\u53cc\u91cd\u6a21\u578b(SSD)\uff0c\u8fd9\u4e9b\u6a21\u578b\u6355\u6349\u4e86\u8bb8\u591a\u5e8f\u5217\u6a21\u578b\u7684\u7279\u6027\u3002\u7279\u522b\u7684\uff0c1-\u534a\u53ef\u5206 SMA \u548c\u6807\u91cf\u6052\u7b49 SSM \u5728\u8fd9\u4e00\u4ea4\u96c6\u4e2d\u3002\u4ea4\u96c6\u90e8\u5206\u786e\u5b9e\u53ef\u4ee5\u770b\u4f5c\u662f\u4e0d\u540c\u6a21\u578b(SSM \u548cSMA)\u7ed3\u5408\u540e\u7684\u7edf\u4e00\u4f53\uff0c\u5c31\u50cf\u7ed3\u5a5a\u540e\u7684\u4e00\u5bb6\u4eba\uff0c\u4e0d\u518d\u5206\u4f60\u6211\u3002<\/p>\n\n\n\n

\u516d\u3001\u7b97\u6cd5\u793a\u4f8b(\u9020\u4eba)<\/h2>\n\n\n\n

6.1 \u7b97\u6cd5\u539f\u7406<\/h3>\n\n\n\n

\u65e2\u7136 SSM \u548c\u6ce8\u610f\u529b\u673a\u5236\u4e24\u79cd\u5bf9\u5076\u7b49\u4ef7\uff0c\u7ed3\u5408\u8d77\u6765\u8fdb\u884c\u8ba1\u7b97\u6548\u7387\u663e\u7136\u66f4\u9ad8\uff0c\u5982\u540c\u7537\u5973\u642d\u914d\u5e72\u6d3b\u4e0d\u7d2f\uff0c\u4f60\u4e2d\u6709\u6211\uff0c\u6211\u4e2d\u6709\u4f60\u3002\u6574\u4f53\u4e0a\u662fSSM\uff0c\u4f46\u662f\u901a\u8fc7\u5757\u5206\u89e3\u628a\u5927\u77e9\u9635\u62c6\u89e3\u6210\u5c0f\u7684\u5b50\u77e9\u9635\u6bcf\u4e2a\u5c0f\u95ee\u9898\u7279\u522b\u662f\u4f4e\u79e9\u5757\uff0c\u518d\u7528\u6ce8\u610f\u529b\u673a\u5236\u8ba1\u7b97\uff0c\u5229\u7528\u77e9\u9635\u4e58\u6cd5\u4e0a\u7684\u9ad8\u6548\u6027\u548c\u5e76\u884c\u8ba1\u7b97\u80fd\u529b\u4f7f\u5f97\u8ba1\u7b97\u8fc7\u7a0b\u66f4\u52a0\u9ad8\u6548\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u4e00\u4e2a\u5927\u7684M\u77e9\u9635\uff0c\u5206\u89e3\u62109\u5757\uff0c\u5176\u4e2d\u84dd\u8272\u5757\u7528\u77e9\u9635\u4e58\u6cd5\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u6574\u4e2a\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4e0b\u56fe\u6240\u793a\u3002\u534a\u53ef\u5206\u77e9\u9635 MMM \u88ab\u5206\u89e3\u6210\u591a\u4e2a\u5b50\u77e9\u9635\u5757\uff0c\u5305\u62ec\u5bf9\u89d2\u5757(Diagonal Block)\u548c\u4f4e\u79e9\u5757(Low-Rank Block)\u3002\u524d\u8005\u8868\u793a\u8f93\u5165\u5230\u8f93\u51fa\u7684\u8ba1\u7b97\uff0c\u540e\u8005\u88ab\u8fdb\u6b65\u5206\u6210\u4e09\u7c7b:\u4ece\u8f93\u5165\u5230\u72b6\u6001(Input-State)\uff0c\u4ece\u72b6\u6001\u5230\u72b6\u6001(State- State)\u4ece\u72b6\u6001\u5230\u8f93\u51fa(State – Output)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u56fe\u7684\u4e0b\u534a\u90e8\u5206\u5c55\u793a\u4e86\u901a\u8fc7\u8fd9\u79cd\u5757\u5206\u89e3\u65b9\u6cd5\u8fdb\u884c\u8ba1\u7b97\u7684\u6d41\u7a0b\u3002\u8f93\u5165\u5e8f\u5217 X \u88ab\u5206\u89e3\u6210\u591a\u4e2a\u5757\uff0c\u6bcf\u4e2a\u5757\u5bf9\u5e94\u56fe\u4e2d\u7684\u4e00\u4e2a\u9ed1\u8272\u865a\u7ebf\u6846\u3002\u8f93\u5165\u5757\u901a\u8fc7\u4f4e\u79e9\u5757(\u7eff\u8272\u7bad\u5934)\u548c\u5bf9\u89d2\u5757(\u8272\u7bad\u5934)\u8fdb\u884c\u8ba1\u7b97\uff0c\u5f97\u5230\u4e2d\u95f4\u7684\u72b6\u6001\u5757 H\u3002\u72b6\u6001\u5757\u4e4b\u95f4\u901a\u8fc7\u4f4e\u79e9\u5757(\u9ec4\u8272\u7bad\u5934)\u8fdb\u884c\u8ba1\u7b97\uff0c\u8868\u793a\u72b6\u6001\u95f4\u7684\u4f20\u9012\u3002\u6700\u7ec8\uff0c\u72b6\u6001\u5757\u901a\u8fc7\u5bf9\u89d2\u5757(\u84dd\u8272\u7bad\u5934)\u8ba1\u7b97\u5f97\u5230\u8f93\u51fa\u5757Y\u3002<\/p>\n\n\n\n

\u901a\u8fc7\u8fd9\u79cd\u5757\u5206\u89e3\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5c06\u4e00\u4e2a\u5927\u89c4\u6a21\u77e9\u9635\u8fd0\u7b97\u95ee\u9898\u5206\u89e3\u6210\u591a\u4e2a\u5c0f\u89c4\u6a21\u7684\u5757\u7ea7\u522b\u8fd0\u7b97\u95ee\u9898\uff0c\u6bcf\u4e2a\u5757\u53ef\u4ee5\u72ec\u7acb\u8fdb\u884c\u8ba1\u7b97\u3002\u8fd9\u79cd\u65b9\u6cd5\u5229\u7528\u4e86\u534a\u53ef\u5206\u77ed\u9635\u7684\u4f4e\u79e9\u7279\u6027\uff0c\u51cf\u5c11\u4e86\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u540c\u65f6\u63d0\u9ad8\u4e86\u5e76\u884c\u8ba1\u7b97\u80fd\u529b\uff0c\u4f7f\u5f97\u8ba1\u7b97\u8fc7\u7a0b\u66f4\u52a0\u786c\u4ef6\u53cb\u597d\u3002<\/p>\n\n\n\n

6.2\u4ee3\u7801\u5b9e\u73b0<\/h3>\n\n\n\n
\"\"
https:\/\/github.com\/state-spaces\/mamba <\/figcaption><\/figure>\n\n\n\n

segsum(x): \u662f\u4e00\u4e2a\u8f85\u52a9\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97\u5206\u6bb5\u7d2f\u52a0\u548c\u3002ssd(X\uff0cA\uff0cB,C\uff0cblock len=64,initial states=None): \u8fd9\u662f\u4e3b\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97 SSD \u6a21\u578bA\uff0cB\uff0cC:\u5206\u522b\u8868\u793a\u72b6\u6001\u77ed\u9635\u3001\u6269\u5c55\u77ed\u9635\u548c\u6536\u7f29\u77e9\u9635\u5148\u5bf9\u8f93\u5165\u5f20\u91cf X\u3001A\u3001B \u548c C \u8fdb\u884c\u91cd\u6392\uff0c\u5c06\u5b83\u4eec\u91cd\u6392\u6210\u5757\u7684\u5f62\u5f0f\u3002
1.\u5bf9\u6bcf\u4e2a\u5757\u5185\u7684\u5bf9\u89d2\u5757(Diagonal Block)\u8fdb\u884c\u8ba1\u7b97\uff0c\u4f7f\u7528 torch.einsum \u8ba1\u7b97\u5757\u5185\u7684\u77e9\u9635\u6765\u6cd5\u3002
2.\u8ba1\u7b97\u6bcf\u4e2a\u5757\u5185\u7684\u4f4e\u79e9\u5757(Low-Rank Block)\uff0c\u7528\u4e8e\u751f\u6210\u4e0b\u4e00\u4e2a\u5757\u7684\u8f93\u5165\u72b6\u6001\u3002
3.\u751f\u6210\u5757\u95f4\u7684\u72b6\u6001\u8f6c\u79fb\uff0c\u786e\u4fdd\u5728\u5757\u8fb9\u754c\u5904\u7684\u72b6\u6001\u6b63\u786e\u3002
4.\u5bf9\u5757\u5185\u7684\u4f4e\u79e9\u5757\u8fdb\u884c\u8ba1\u7b97\uff0c\u5c06\u72b6\u6001\u8f6c\u6362\u4e3a\u8f93\u51fa\u3002\u6700\u540e\u5c06\u5757\u5185\u548c\u5757\u95f4\u7684\u8f93\u51fa\u6c47\u603b\uff0c\u5f97\u5230\u6700\u7ec8\u8f93\u51faY\u548c\u6700\u7ec8\u72b6\u6001final state\u3002\u8be5\u4ee3\u7801\u7684\u4e3b\u8981\u76ee\u7684\u662f\u901a\u8fc7\u5757\u5206\u89e3\u7684\u65b9\u6cd5\uff0c\u5c06\u4e00\u4e2a\u5927\u89c4\u6a21\u7684\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u95ee\u9898\u5206\u89e3\u6210\u591a\u4e2a\u5c0f\u89c4\u6a21\u7684\u5757\u7ea7\u522b\u8fd0\u7b97\u95ee\u9898\u3002\u8fd9\u79cd\u65b9\u6cd5\u5229\u7528\u4e86\u534a\u53ef\u5206\u77e9\u9635\u7684\u7279\u6027\uff0c\u80fd\u591f\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u548c\u5e76\u884c\u6027\uff0c\u9002\u5408\u786c\u4ef6\u52a0\u901f\u3002<\/p>\n\n\n\n

\u4e03\u3001Mamba2 \u7f51\u7edc\u67b6\u6784(KIDS)<\/h2>\n\n\n\n

7.1 \u591a\u79cd\u8bbe\u8ba1<\/h3>\n\n\n\n

<\/p>\n\n\n\n

Mamba-1\u57fa\u4e8eSSM(\u72b6\u6001\u7a7a\u95f4\u6a21\u578b)\u8bbe\u8ba1\uff0c\u7ebf\u6027\u6295\u5f71\u4e4b\u540e\u751f\u6210SSM\u53c2\u6570 A,B,C\u3002Mamba-2\u7684\u4e24\u79cd\u5757\u8bbe\u8ba1:\u987a\u5e8f Mamba\u5757\u548c\u5e76\u884c Mamba\u5757\u3002SSM \u5c42\u4ece A,X,B,C\u76f4\u63a5\u6620\u5c04\u5230\u8f93\u51faY\uff0c\u524d\u8005\u5728\u5e8f\u5217\u53d8\u6362\u4e2d\u5e76\u884c\u751f\u6210\u53c2\u6570 A,B.C\uff0c\u540e\u8005\u5728\u5757\u5f00\u59cb\u65f6\u5e76\u884c\u751f\u6210\uff0c\u9002\u5408\u66f4\u5927\u89c4\u6a21\u7684\u5e76\u884c\u5904\u7406\u3002\u8fd9\u79cd\u65b9\u6cd5\u7c7b\u4f3c\u4e8e\u6807\u51c6\u6ce8\u610f\u529b\u67b6\u6784\u4e2d\u7684\u5e76\u884c\u751f\u6210 Q.K,V\u3002\u8fd9\u79cd\u8bbe\u8ba1\u51cf\u5c11\u53c2\u6570\u6570\u91cf\uff0c\u9002\u5408\u66f4\u5927\u6a21\u578b\u7684\u5f20\u91cf\u5e76\u884c\u8ba1\u7b97\u3002\u6bcf\u4e2a Mamba \u5757\u4e2d\u589e\u52a0\u989d\u5916\u5f52\u4e00\u5316\u5c42\uff0c\u6539\u5584\u6a21\u578b\u7a33\u5b9a\u6027\uff0c\u5c24\u5176\u662f\u5927\u6a21\u578b\u3002\u603b\u4f53\u6765\u8bf4\uff0cMamba-2\u6a21\u578b\u901a\u8fc7\u5e76\u884c\u5316\u548c\u589e\u52a0\u5f52\u4e00\u5316\u5c42\u6765\u4f18\u5316\u539f\u59cb Mamba \u6a21\u578b\u7684\u8ba1\u7b97\u6548\u7387\u548c\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

7.2 \u5e76\u884c\u5316\u5904\u7406\u65b9\u6cd5<\/h3>\n\n\n\n

\u4e3b\u8981\u5206\u4e3a\u4e24\u79cd\u7c7b\u578b:\u5f20\u91cf\u5e76\u884c(TensorParallelism)\u548c\u5e8f\u5217\/\u4e0a\u4e0b\u6587\u5e76\u884c(Sequence\/ContextParallelism)\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5de6\u8fb9\u8f93\u5165\u548c\u8f93\u51fa\u6295\u5f71\u77e9\u9635\u5206\u5272\uff0c\u5e76\u5728\u5355\u4e2a\u8bbe\u5907\u4e0a\u5904\u7406\u3002\u6bcf\u4e2aSSM\u5934(\u5373 A\u3001B\u3001C\u3001X)\u5230Y \u7684\u6620\u5c04\u90fd\u5728\u5355\u4e2a\u8bbe\u5907\u4e0a\u8fdb\u884c\u3002\u6700\u7ec8\u5f52\u4e00\u5316\u5c42\u9009\u62e9 GroupNorm\uff0c\u4ee5\u907f\u514d\u989d\u5916\u7684\u901a\u4fe1\u3002\u53f3\u56fe\u5c06\u5e8f\u5217\u7ef4\u5ea6\u4e0a\u7684\u8ba1\u7b97\u5206\u914d\u5230\u591a\u4e2a\u8bbe\u5907\u4e0a\uff0c\u6bcf\u4e2a\u8bbe\u5907\u8d1f\u8d23\u4e00\u90e8\u5206\u5e8f\u5217\u7684\u8ba1\u7b97\uff0c\u7136\u540e\u5c06\u7ed3\u679c\u4f20\u9012\u7ed9\u4e0b\u4e00\u4e2a\u8bbe\u5907\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u516b\u3001\u5b9e\u9a8c\u9a8c\u8bc1<\/h2>\n\n\n\n

8.1\u5408\u6210\u8bb0\u5fc6\u4efb\u52a1<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u4e0a\u56fe\u5c55\u793a\u4e86\u4e0d\u540c\u6a21\u578b\u5728\u591a\u67e5\u8be2\u5173\u8054\u8bb0\u5fc6(MQAR)\u4efb\u52a1\u4e2d\u7684\u8868\u73b0\u3002\u4e09\u5f20\u5b50\u56fe\u5bf9\u5e94\u4e0d\u540c\u7684\u5e8f\u5217\u957f\u5ea6(256\u3001512\u30011024)\u3002\u6a2a\u8f74\u4ee3\u8868\u6a21\u578b\u7684\u7ef4\u5ea6(32\u300164\u3001128\u3001256)\u7eb5\u8f74\u4ee3\u8868\u51c6\u786e\u7387(\u4ece0\u5230 1)Mamba-2 \u7cfb\u5217\u6a21\u578b\u5728\u8f83\u5927\u7684\u6a21\u578b\u7ef4\u5ea6\u4e0b\u8868\u73b0\u4f18\u5f02\uff0c\u7279\u522b\u662f\u5f53\u7ef4\u5ea6\u8fbe\u5230 128 \u548c 256 \u65f6\uff0c\u5176\u51c6\u786e\u7387\u63a5\u8fd1 1.0\u3002Mamba-2 \u6a21\u578b\u660e\u663e\u4f18\u4e8e Mamba-1 \u548c\u666e\u901a\u6ce8\u610f\u529b\u6a21\u578b\uff0c\u5c24\u5176\u5728\u66f4\u5927\u7684\u72b6\u6001\u89c4\u6a21(N=256)\u4e0b\u8868\u73b0\u5c24\u4e3a\u663e\u8457\u3002<\/p>\n\n\n\n

8.2\u8bed\u8a00\u6a21\u578b\u9884\u8bad\u7ec3\u4e0e\u8bc4\u4f30<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

(\u7f29\u653e\u5b9a\u5f8b)\u5728 The Pile \u4e0a\u8fdb\u884c\u8bad\u7ec3\u7684\u6a21\u578b\uff0cMamba-2\u7684\u6027\u80fd\u5339\u914d\u6216\u8d85\u8fc7\u4e86 Mamba \u548c\u5f3a\u5927\u7684\u201cTransformer++”\u65b9\u6848\u3002\u4e0e\u6211\u4eec\u7684 Transformer\u57fa\u7ebf\u76f8\u6bd4\uff0cMamba-2 \u5728\u6027\u80fd(\u56f0\u60d1\u5ea6)\u3001\u7406\u8bba FLOPs \u548c\u5b9e\u9645\u58c1\u949f\u65f6\u95f4\u4e0a\u90fd\u662f\u5e15\u7d2f\u6258\u5360\u4f18\u7684\u3002
\u96f6\u6837\u672c\u8bc4\u4f30<\/strong>:\u5728\u6bcf\u79cd\u6a21\u578b\u89c4\u6a21\u4e2d\uff0cMamba-2 \u6a21\u578b\u7684\u8868\u73b0\u666e\u904d\u4f18\u4e8e\u5176\u4ed6\u6a21\u578b\u3002\u7279\u522b\u662fMamba-2 \u5728\u8f83\u5927\u7684\u6a21\u578b\u89c4\u6a21\u4e0b(2.78 \u53c2\u6570)\u8868\u73b0\u5c24\u4e3a\u7a81\u51fa\uff0c\u8bc1\u660e\u5176\u5728\u4e0d\u540c\u4efb\u52a1\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\u66f4\u5f3a\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u4e0d\u540c\u6570\u91cf\u7684\u6ce8\u610f\u529b\u5c42\u4e0b\u7684\u56f0\u60d1\u5ea6\u3002\u5927\u7ea610%\u7684\u6ce8\u610f\u529b\u5c42\u6bd4\u4f8b\u8868\u73b0\u6700\u4f73\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u9002\u91cf\u7684\u6ce8\u610f\u529b\u5c42\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\uff0c\u8d85\u8fc7\u4e86\u5b8c\u5168\u4e0d\u4f7f\u7528\u6ce8\u610f\u529b\u5c42\u6216\u5b8c\u5168\u4f7f\u7528\u6ce8\u610f\u529b\u5c42\u7684\u60c5\u51b5\u3002<\/p>\n\n\n\n

(\u96f6\u6837\u672c\u8bc4\u4f30)\u6bd4\u8f83\u4e86 SSD\u3001MLP \u548c\u6ce8\u610f\u529b\u5c42\u7684\u4e0d\u540c\u7ec4\u5408\u65b9\u5f0f\uff0c\u57282.78\u89c4\u6a21\u4e0a\u8fdb\u884c\u8bc4\u4f30\u56f0\u60d1\u5ea6(ppl)\u548c\u51c6\u786e\u7387(acc)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Mamba-2\u4e0e\u6ce8\u610f\u529b\u5c42\u7684\u7ed3\u5408(\u540e4\u4e2a)\u5728\u591a\u4e2a\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\u4f18\u4e8e\u5176\u4ed6\u6a21\u578b\u7ec4\u5408\uff0c\u663e\u793a\u51fa\u66f4\u5f3a\u7684\u6cdb\u5316\u80fd\u529b\u548c\u4efb\u52a1\u9002\u5e94\u6027\u3002<\/p>\n\n\n\n

8.3 \u901f\u5ea6\u6027\u80fd<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u5de6\u56fe\u4e0d\u540c\u65b9\u6cd5\u5728\u5904\u7406\u5e8f\u5217\u957f\u5ea6(\u4ece512\u5230512k)\u65f6\u6240\u9700\u7684\u65f6\u95f4(\u4ee5\u6beb\u79d2\u4e3a\u5355\u4f4d)\u3002\u53f3\u56fe\u5c55\u793a\u4e86\u5728\u5904\u7406\u56fa\u5b9a\u5e8f\u5217\u957f\u5ea6(4K)\u65f6\uff0c\u4e0d\u540c\u72b6\u6001\u7ef4\u5ea6(\u4ece16\u5230256)\u4e0b\u6240\u9700\u7684\u65f6\u95f4(\u4ee5\u6beb\u79d2\u4e3a\u5355\u4f4d)\u3002SSD \u65b9\u6cd5\u5728\u5904\u7406\u5927\u72b6\u6001\u6269\u5c55\u65f6\u8868\u73b0\u4f18\u5f02\uff0c\u6bd4Mamba\u7684\u878d\u5408\u626b\u63cf\u5feb2\u52308\u500d(\u6bd4\u598264k\u65f6\u7d2b\u8272\u7ebf1\u6beb\u79d2\uff0cMamba\u4e3a 10\u6beb\u79d2)\uff0c\u5e76\u4e14\u5728\u5e8f\u5217\u957f\u5ea6\u8d85\u8fc72k\u65f6\u4e5f\u6bd4FlashAttention-2\u66f4\u5feb\u3002<\/p>\n\n\n\n

\u603b\u4f53\u7ed3\u8bba:
Mamba-2 \u6a21\u5757\u5728\u7ed3\u5408\u5e76\u884c\u5904\u7406\u548c\u989d\u5916\u5f52\u4e00\u5316\u540e\uff0c\u663e\u8457\u63d0\u5347\u4e86\u6a21\u578b\u6027\u80fd\uff0c\u8868\u73b0\u4f18\u4e8e\u4f20\u7edf\u7684Mamba-1 \u6a21\u5757\u3002<\/p>\n\n\n\n

\u591a\u5934\u7ed3\u6784\u4e2d\uff0c\u590d\u6742\u7684\u5934\u7ec4\u5408\u548c\u72b6\u6001\u6269\u5c55\u901a\u5e38\u53ef\u4ee5\u63d0\u9ad8\u6027\u80fd\uff0c\u7279\u522b\u662f\u5f53\u578b\u89c4\u6a21\u589e\u5927\u65f6\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e\u6838\u8fd1\u4f3c\uff0cSwish\u548cLayerNorm \u65b9\u6cd5\u901a\u5e38\u6548\u679c\u8f83\u597d\uff0c\u4e14\u9002\u7528\u4e8e\u4e0d\u540c\u89c4\u6a21\u7684\u6a21\u578b\u00b7\u589e\u52a0\u590d\u6742\u5ea6\u548c\u5934\u7684\u6570\u867d\u4e00\u822c\u6709\u52a9\u4e8e\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\uff0c\u4f46\u9700\u8981\u6743\u8861\u53c2\u6570\u6570\u5448\u7684\u589e\u52a0\u3002<\/p>\n\n\n\n

\u4e5d\u3001\u5c0f\u7ed3<\/h2>\n\n\n\n

1.\u7edf\u4e00\u7684\u7406\u8bba\u6846\u67b6:\u5c06 SSM \u548c\u6ce8\u610f\u529b\u673a\u5236\u5728\u5f20\u91cf\u6536\u7f29\u89c6\u89d2\u4e0b\u5b9e\u73b0\u7edf\u4e00\uff0c\u5e76\u5efa\u7acb\u5bf9\u5076\u6027\u5173\u8054\u65e0\u7591\u662f\u672c\u6587\u6700\u5927\u7684\u8d21\u732e\u3002\u8fd9\u610f\u5473\u7740\u6ce8\u610f\u529b\u673a\u5236\u4e0e RNN\u4e24\u79cd\u7f51\u7edc\u5728\u5e95\u5c42\u903b\u8f91\u4e0a\u88ab\u5173\u8054\u8d77\u6765\u4e86\u6253\u7834\u4e86\u7537\u4eba\u548c\u5973\u4eba\u7684\u754c\u9650\uff0c\u5b9e\u73b0\u4e86\u7075\u6d3b\u7684\u6027\u522b\u8f6c\u6362\u3002
\u65b0\u578b\u6ce8\u610f\u529b\u673a\u5236:\u501f\u52a9 SSM \u65f6\u7a7a\u5efa\u6a21\uff0c\u5b9e\u73b0\u521b\u65b0\u3002\u4ece\u7537\u4eba\u7684\u89c6\u89d2\u7814\u7a76\u5973\u4eba\uff0c\u800c\u7ebf\u6027\u4ee3\u6570\u8981\u5728\u6ce8\u610f\u529b\u673a\u5236\u521b\u65b0\u4e2d\u8d77\u5230\u8d8a\u6765\u8d8a\u91cd\u8981\u7684\u5173\u952e\u6027\u4f5c\u7528\u3002
3.\u6df7\u5408\u6a21\u578b\u6210\u4e3a\u65b0\u7684\u8d8b\u52bf\u3002\u6574\u4f53 SSM\uff0c\u5c40\u90e8\u6ce8\u610f\u529b\u673a\u5236\uff0c\u5b9e\u73b0\u7075\u6d3b\u7ec4\u5408\uff0c\u63d0\u5347\u6574\u4f53\u6027\u80fd\u3002
\u5982\u679c\u4eca\u5929\u7684\u5206\u4eab\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9\uff0c\u6b22\u8fce\u4e09\u8fde\u652f\u6301\u3002\u6211\u662f\u76f4\u54e5\u3002\u5b66\u597dAI\u4e0d\u8ff7\u8def\u3002\u53ea\u8bf4\u4eba\u8bdd\uff0c\u4e13\u6cbb\u597d\u5947\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

Github\uff1ahttps:\/\/github.com\/state-spaces\/mamba \u8bba\u6587\uff1ahttps:\/ … \u7ee7\u7eed\u9605\u8bfbMamba-2 \u6a21\u578b\u89e3\u8bfb<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[21,4],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/15715"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=15715"}],"version-history":[{"count":119,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/15715\/revisions"}],"predecessor-version":[{"id":16101,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/15715\/revisions\/16101"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=15715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=15715"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=15715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}