{"id":10053,"date":"2024-05-08T15:10:12","date_gmt":"2024-05-08T07:10:12","guid":{"rendered":"http:\/\/192.168.10.115\/?p=10053"},"modified":"2024-05-08T15:10:12","modified_gmt":"2024-05-08T07:10:12","slug":"2024-05-08-%e6%8c%91%e6%88%98transformer%ef%bc%9a%e5%85%a8%e6%96%b0%e6%9e%b6%e6%9e%84mamba%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"http:\/\/222.128.65.89:18086\/index.php\/2024\/05\/08\/10053\/","title":{"rendered":"2024-05-08 \u6311\u6218Transformer\uff1a\u5168\u65b0\u67b6\u6784Mamba\u8be6\u89e3"},"content":{"rendered":"\n

\u80cc\u666f<\/strong><\/p>\n\n\n\n

\u5c79\u7acb\u4e0d\u5012\u7684 Transformer \u8fce\u6765\u4e86\u4e00\u4e2a\u5f3a\u52b2\u7ade\u4e89\u8005\u3002<\/p>\n\n\n\n

\u81ea 2017 \u5e74\u88ab\u63d0\u51fa\u4ee5\u6765\uff0cTransformer \u5df2\u7ecf\u6210\u4e3a AI \u5927\u6a21\u578b\u7684\u4e3b\u6d41\u67b6\u6784\uff0c\u4f46\u968f\u7740\u6a21\u578b\u89c4\u6a21\u7684\u6269\u5c55\u548c\u9700\u8981\u5904\u7406\u7684\u5e8f\u5217\u4e0d\u65ad\u53d8\u957f\uff0cTransformer \u7684\u5c40\u9650\u6027\u4e5f\u9010\u6e10\u51f8\u663e\u3002\u4e00\u4e2a\u5f88\u660e\u663e\u7684\u7f3a\u9677\u662f\uff1aTransformer \u6a21\u578b\u4e2d\u81ea\u6ce8\u610f\u529b\u673a\u5236\u7684\u8ba1\u7b97\u91cf\u4f1a\u968f\u7740\u4e0a\u4e0b\u6587\u957f\u5ea6\u7684\u589e\u52a0\u5448\u5e73\u65b9\u7ea7\u589e\u957f\uff0c\u6bd4\u5982\u4e0a\u4e0b\u6587\u589e\u52a0 32 \u500d\u65f6\uff0c\u8ba1\u7b97\u91cf\u53ef\u80fd\u4f1a\u589e\u957f 1000 \u500d\uff0c\u8ba1\u7b97\u6548\u7387\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n

\u4e3a\u4e86\u514b\u670d\u8fd9\u4e9b\u7f3a\u9677\uff0c\u7814\u7a76\u8005\u4eec\u5f00\u53d1\u51fa\u4e86\u5f88\u591a\u6ce8\u610f\u529b\u673a\u5236\u7684\u9ad8\u6548\u53d8\u4f53\uff0c\u4f46\u8fd9\u5f80\u5f80\u4ee5\u727a\u7272\u5176\u6709\u6548\u6027\u7279\u4e3a\u4ee3\u4ef7\u3002\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u8fd9\u4e9b\u53d8\u4f53\u90fd\u8fd8\u6ca1\u6709\u88ab\u8bc1\u660e\u80fd\u5728\u4e0d\u540c\u9886\u57df\u53d1\u6325\u6709\u6548\u4f5c\u7528\u3002<\/p>\n\n\n\n

\u800c\u5c31\u5728\u6700\u8fd1\uff0c\u4e00\u540d\u4e3a Mamba \u7684\u67b6\u6784\u4f3c\u4e4e\u6253\u7834\u4e86\u8fd9\u4e00\u5c40\u9762\u3002<\/p>\n\n\n\n

\u4e0e\u7c7b\u4f3c\u89c4\u6a21\u7684 Transformer \u76f8\u6bd4\uff0cMamba \u5177\u6709 5 \u500d\u7684\u541e\u5410\u91cf\uff0c\u800c\u4e14 Mamba-3B \u7684\u6548\u679c\u4e0e\u4e24\u500d\u4e8e\u5176\u89c4\u6a21\u7684 Transformer \u76f8\u5f53<\/strong>\u3002\u6027\u80fd\u9ad8\u3001\u6548\u679c\u597d\uff0cMamba \u6210\u4e3a\u65b0\u7684\u7814\u7a76\u70ed\u70b9\u3002<\/p>\n\n\n\n

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

\u56fe1 Mamba \u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\u7684\u541e\u5410\u91cf\u5bf9\u6bd4<\/p>\n\n\n\n

\u672c\u6587\u5c06\u8be6\u7ec6\u7684\u89e3\u8bfb Mamba \u67b6\u6784\uff0c\u7531\u4e8e Mamba \u662f\u57fa\u4e8e SSM->HiPPO->S4->Mamba \u6f14\u5316\u8fc7\u6765\u7684\uff0c\u800c HiPPO\u3001S4\u3001Mamba \u7684\u4e00\u4f5c\u8005\u90fd\u662f\u5361\u5185\u57fa\u6885\u9686\u5927\u5b66\u673a\u5668\u5b66\u4e60\u7cfb\u52a9\u7406\u6559\u6388 Albert Gu<\/strong>\u3002\u56e0\u6b64\uff0c\u672c\u6587\u5c06\u4ece\u6807\u51c6 SSM \u5f00\u59cb\uff0c\u9010\u6b65\u4ecb\u7ecd HiPPO\u3001S4\u3001Mamba\u3002<\/p>\n\n\n\n

\u56fe2\u603b\u7ed3\u4e86SSM\u3001HiPPO\u3001S4\u3001Mamba\u7684\u4e3b\u8981\u533a\u522b\uff0c\u4ee5\u53ca\u5404\u4e2a\u6a21\u578b\u7684\u4e3b\u8981\u5185\u5bb9\u3002\u672c\u6587\u5185\u5bb9\u4e5f\u5c06\u6309\u56fe\u4e2d\u5185\u5bb9\u5c55\u5f00\u3002<\/p>\n\n\n\n

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

\u56fe2-2\uff1aHiPPO\u3001S4\u3001Mamba<\/p>\n\n\n\n

\u4e00\u3001\u73b0\u6709\u67b6\u6784\u95ee\u9898<\/strong><\/p>\n\n\n\n

\u5e8f\u5217\u5efa\u6a21\u7684\u6838\u5fc3\u95ee\u9898\u662f\uff1a\u540c\u65f6\u89e3\u51b3\u6709\u6548<\/strong>\u548c\u9ad8\u6548<\/strong>\u3002\u6709\u6548\u662f\u6307\u80fd\u591f\u9009\u62e9\u6027\u8bb0\u5fc6\u5386\u53f2\u4fe1\u606f\uff0c\u89e3\u51b3\u957f\u8ddd\u79bb\u4f9d\u8d56<\/strong>\uff08Long-Range Dependencies\uff0cLRDs\uff09\u95ee\u9898\uff1b\u9ad8\u6548\u662f\u6307\u8ba1\u7b97\u9ad8\u6548\u3002<\/p>\n\n\n\n

\u5c3d\u7ba1\u4f20\u7edf\u7684\u6a21\u578b\u5982\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08RNNs\uff09\u3001\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08CNNs\uff09\u548c Transformers \u5728\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\u65b9\u9762\u6709\u4e13\u95e8\u7684\u53d8\u4f53\uff0c\u4f46\u5b83\u4eec\u5728\u5904\u7406\u8d85\u8fc7 10000 \u6b65\u7684\u6781\u957f\u5e8f\u5217\u65f6\u4ecd\u7136\u9762\u4e34\u6311\u6218\u3002<\/strong><\/p>\n\n\n\n

1.1 Transformer \u95ee\u9898<\/strong><\/p>\n\n\n\n

Transformer \u7684\u4e00\u4e2a\u4e3b\u8981\u4f18\u70b9\u662f\uff0c\u65e0\u8bba\u5b83\u63a5\u6536\u5230\u591a\u957f\u7684\u8f93\u5165\uff0c\u5b83\u90fd\u4f7f\u7528\u5e8f\u5217\u4e2d\u7684\u6240\u6709 token \u4fe1\u606f\uff08\u65e0\u8bba\u5e8f\u5217\u6709\u591a\u957f\uff09\u6765\u5bf9\u8f93\u5165\u6570\u636e\u8fdb\u884c\u5904\u7406\u3002<\/p>\n\n\n\n

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

\u56fe1-1\uff1aTransformer\u4f1a\u67e5\u770b\u8fc7\u53bb\u6240\u6709 token<\/p>\n\n\n\n

\u4f46\u662f\u4e3a\u4e86\u83b7\u5f97\u5168\u5c40\u4fe1\u606f\uff0c\u6ce8\u610f\u529b\u673a\u5236\u5728\u957f\u5e8f\u5217\u4e0a\u975e\u5e38\u8017\u8d39\u663e\u5b58\u3002\u6ce8\u610f\u529b\u521b\u5efa\u4e00\u4e2a\u77e9\u9635\uff0c\u5c06\u6bcf\u4e2a token \u4e0e\u4e4b\u524d\u7684\u6bcf\u4e2a token \u8fdb\u884c\u6bd4\u8f83\u3002\u77e9\u9635\u4e2d\u7684\u6743\u91cd\u7531 token \u5bf9\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u51b3\u5b9a\u3002<\/p>\n\n\n\n

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

\u56fe1-2\uff1aTransformer \u4f1a\u8ba1\u7b97\u6bcf\u4e2a token \u4e4b\u95f4\u7684 Attention<\/p>\n\n\n\n

\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0cAttention \u8ba1\u7b97\u53ef\u4ee5\u5e76\u884c\u5316\uff0c\u6240\u4ee5\u53ef\u4ee5\u6781\u5927\u5730\u52a0\u5feb\u8bad\u7ec3\u901f\u5ea6\u3002\u4f46\u662f\u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\uff0c\u5f53\u751f\u6210\u4e0b\u4e00\u4e2a token \u65f6\uff0c\u6211\u4eec\u9700\u8981\u91cd\u65b0\u8ba1\u7b97\u6574\u4e2a\u5e8f\u5217\u7684\u6ce8\u610f\u529b\u3002<\/p>\n\n\n\n

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

\u56fe1-3\uff1a\u751f\u6210\u65b0 token \u65f6\u9700\u8981\u91cd\u65b0\u8ba1\u7b97\u6574\u4e2a\u5e8f\u5217\u7684\u6ce8\u610f\u529b<\/p>\n\n\n\n

\u957f\u5ea6\u4e3a L \u7684\u5e8f\u5217\u751f\u6210 token \u5927\u7ea6\u9700\u8981 L\u00b2 \u7684\u8ba1\u7b97\u91cf\uff0c\u5982\u679c\u5e8f\u5217\u957f\u5ea6\u589e\u52a0\uff0c\u8ba1\u7b97\u91cf\u4f1a\u5e73\u65b9\u7ea7\u589e\u957f\u3002\u56e0\u6b64\uff0c\u9700\u8981\u91cd\u65b0\u8ba1\u7b97\u6574\u4e2a\u5e8f\u5217\u662f Transformer \u4f53\u7cfb\u7ed3\u6784\u7684\u4e3b\u8981\u74f6\u9888\u3002<\/strong><\/p>\n\n\n\n

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

\u56fe1-4\uff1aTransformer \u8bad\u7ec3\u5feb\u3001\u63a8\u7406\u6162<\/p>\n\n\n\n

1.2 RNN \u7684\u95ee\u9898<\/strong><\/p>\n\n\n\n

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

\u56fe1-5\uff1a\u5faa\u73af\u795e\u7ecf\u7f51\u7edc RNN<\/p>\n\n\n\n

\u5728\u751f\u6210\u8f93\u51fa\u65f6\uff0cRNN \u53ea\u9700\u8981\u8003\u8651\u4e4b\u524d\u7684\u9690\u85cf\u72b6\u6001\u548c\u5f53\u524d\u7684\u8f93\u5165\u3002\u8fd9\u6837\u4e0d\u4f1a\u91cd\u65b0\u8ba1\u7b97\u4ee5\u524d\u7684\u9690\u85cf\u72b6\u6001\uff0c\u8fd9\u6b63Transformer \u4e0d\u5177\u5907\u7684\u3002<\/p>\n\n\n\n

\u8fd9\u79cd\u7ed3\u6784\u53ef\u4ee5\u8ba9 RNN \u8fdb\u884c\u5feb\u901f\u63a8\u7406<\/strong>\uff0c\u5e76\u4e14\u7406\u8bba\u4e0a\u53ef\u4ee5\u65e0\u9650\u6269\u5c55\u4e0a\u4e0b\u6587\u957f\u5ea6\uff0c\u56e0\u4e3a\u6bcf\u6b21\u63a8\u7406\u53ea\u53d6\u4e00\u4e2a\u9690\u85cf\u72b6\u6001\u548c\u5f53\u524d\u8f93\u5165\uff0c\u5185\u5b58\u5360\u7528\u975e\u5e38\u7a33\u5b9a\u3002<\/p>\n\n\n\n

RNN \u7684\u6bcf\u4e2a\u9690\u85cf\u72b6\u6001\u90fd\u662f\u4e4b\u524d\u6240\u6709\u9690\u85cf\u72b6\u6001\u7684\u805a\u5408\u3002\u4f46\u662f\u8fd9\u91cc\u4f1a\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u5728\u751f\u6210 token “Liang” \u65f6\uff0c\u6700\u540e\u4e00\u4e2a\u9690\u85cf\u72b6\u6001\u4e0d\u518d\u5305\u542b\u5173\u4e8e token “Hello” \u7684\u4fe1\u606f\u3002\u8fd9\u4f1a\u5bfc\u81f4\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\uff0cRNN \u4f1a\u5fd8\u8bb0\u66f4\u4e45\u7684\u4fe1\u606f\uff0c\u56e0\u4e3a\u5b83\u53ea\u8003\u8651\u524d\u4e00\u4e2a\u72b6\u6001\u3002<\/p>\n\n\n\n

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

\u56fe1-6\uff1a\u53ea\u8003\u8651\u524d\u4e00\u4e2a hidden state<\/p>\n\n\n\n

\u5e76\u4e14 RNN \u7684\u8fd9\u79cd\u987a\u5e8f\u6027\u4ea7\u751f\u4e86\u53e6\u4e00\u4e2a\u95ee\u9898\u3002\u8bad\u7ec3\u4e0d\u80fd\u5e76\u884c\u8fdb\u884c<\/strong>\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u6309\u987a\u5e8f\u5b8c\u6210\u6bcf\u4e00\u6b65\u3002<\/p>\n\n\n\n

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

\u56fe1-7\uff1aRNN \u8bad\u7ec3\u4e0d\u80fd\u5e76\u884c<\/p>\n\n\n\n

RNN\u7684\u7edf\u4e00\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n

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

\u53ef\u4ee5\u770b\u5230\uff0c\u5f53\u524d\u68af\u5ea6\u4f9d\u8d56\u4e0a\u4e2a token \u7684\u68af\u5ea6\u3002<\/p>\n\n\n\n

\u4e0e Transformer \u76f8\u6bd4\uff0cRNN \u7684\u95ee\u9898\u5b8c\u5168\u76f8\u53cd\uff01\u5b83\u7684\u63a8\u7406\u901f\u5ea6\u975e\u5e38\u5feb\uff0c\u4f46\u4e0d\u80fd\u5e76\u884c\u5316\u5bfc\u81f4\u8bad\u7ec3\u5f88\u6162\u3002<\/strong><\/p>\n\n\n\n

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

\u56fe1-8\uff1aRNN \u548c Transformer\u5bf9\u6bd4<\/p>\n\n\n\n

\u4eba\u4eec\u4e00\u76f4\u5728\u5bfb\u627e\u4e00\u79cd\u65e2\u80fd\u50cf Transformer \u90a3\u6837\u5e76\u884c\u5316\u8bad\u7ec3\uff0c\u80fd\u591f\u8bb0\u4f4f\u5148\u524d\u7684\u4fe1\u606f\uff0c\u53c8\u80fd\u5728\u63a8\u7406\u65f6\u65f6\u95f4\u662f\u968f\u5e8f\u5217\u957f\u5ea6\u7ebf\u6027\u589e\u957f\u7684\u6a21\u578b\uff0cMamba \u5c31\u662f\u8fd9\u6837\u5e94\u8fd0\u800c\u751f\u7684<\/strong>\u3002\u89e3\u4e0b\u6765\u6211\u4eec\u4ece SSM \u5f00\u59cb\uff0c\u9010\u6b65\u4ecb\u7ecd Mamaba\u3002<\/p>\n\n\n\n

\u4e8c\u3001\u72b6\u6001\u7a7a\u95f4\u6a21\u578b SSM<\/strong><\/p>\n\n\n\n

2.1 \u4ec0\u4e48\u662f SSM<\/strong><\/p>\n\n\n\n

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

2.2 SSM \u67b6\u6784<\/strong><\/p>\n\n\n\n

\u4e0b\u56fe\u662f SSM \u7684\u67b6\u6784\uff0c\u4e3b\u8981\u5305\u542b\u4e24\u4e2a\u90e8\u5206\uff1a\u72b6\u6001\u66f4\u65b0\u65b9\u7a0b\u548c\u8f93\u51fa\u65b9\u7a0b\u3002<\/p>\n\n\n\n

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

\u56fe2-1\uff1aSSM\u7ed3\u6784<\/p>\n\n\n\n

SSM \u53ef\u4ee5\u7b80\u5316\u4e3a\u4ee5\u4e0b\u7ed3\u6784\uff1a<\/p>\n\n\n\n

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

\u56fe2-2\uff1a\u7b80\u5316\u7684SSM\u7ed3\u6784<\/p>\n\n\n\n

\u4e0b\u9762\u6211\u4eec\u770b\u4e00\u4e0b\u66f4\u8be6\u7ec6\u7684\u7ed3\u6784\uff0c\u9996\u5148\u662f\u72b6\u6001\u66f4\u65b0\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n\n

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

\u56fe2-3\uff1a\u72b6\u6001\u66f4\u65b0\u8be6\u7ec6\u7ed3\u6784<\/p>\n\n\n\n

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

\u7136\u540e\u662f\u8f93\u51fa\u65b9\u7a0b\uff0c\u8be6\u7ec6\u673a\u6784\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n\n

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

\u56fe2-4\uff1a\u8f93\u51fa\u65b9\u7a0b\u8be6\u7ec6\u7ed3\u6784<\/p>\n\n\n\n

2.3 SSM \u4f8b\u5b50\uff1a\u5f39\u7c27\u632f\u5b50<\/strong><\/p>\n\n\n\n

\u4e0b\u9762\u4e3e\u4e00\u4e2a\u63cf\u8ff0\u5f39\u7c27\u632f\u5b50\u7cfb\u7edf\u7684 SSM \u4f8b\u5b50\u3002<\/p>\n\n\n\n

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

\u56fe2-5\uff1a\u5f39\u7c27\u632f\u5b50<\/p>\n\n\n\n

\u8003\u8651\u4e00\u4e2a\u8d28\u91cf\u4e3am\u7684\u7269\u4f53\uff0c\u5b83\u8fde\u63a5\u5728\u4e00\u4e2a\u52b2\u5ea6\u7cfb\u6570\u4e3ak\u7684\u5f39\u7c27\u4e0a\uff0c\u5e76\u4e14\u53d7\u5230\u963b\u5c3c\u7cfb\u6570\u4e3ac\u7684\u963b\u5c3c\u529b\u4f5c\u7528\u3002\u5f53\u7269\u4f53\u4ece\u5e73\u8861\u4f4d\u7f6e\u504f\u79bb\u65f6\uff0c\u5b83\u4f1a\u5728\u5f39\u7c27\u529b\u7684\u4f5c\u7528\u4e0b\u8fdb\u884c\u632f\u52a8\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u6765\u63cf\u8ff0\u8fd9\u4e2a\u7cfb\u7edf\u7684\u52a8\u6001\u3002<\/p>\n\n\n\n

\u72b6\u6001\u53d8\u91cf\u53ef\u4ee5\u9009\u62e9\u4e3a\u7269\u4f53\u7684\u4f4d\u79fbs(t)\u548c\u901f\u5ea6v(t)\u3002\u8f93\u5165u(t)\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\u53ef\u4ee5\u4e3a\u96f6\uff0c\u56e0\u4e3a\u6211\u4eec\u6ca1\u6709\u5916\u90e8\u529b\u4f5c\u7528\u5728\u7269\u4f53\u4e0a\u3002\u8f93\u51fay(t)\u53ef\u4ee5\u662f\u6211\u4eec\u611f\u5174\u8da3\u7684\u4f4d\u79fbs(t)\u3002<\/p>\n\n\n\n

\u72b6\u6001\u5411\u91cf\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n

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

\u8f93\u5165\u5411\u91cf\u4e3a\uff1a<\/p>\n\n\n\n

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

\u8f93\u51fa\u4f4d\u79fbs(t)\u3002\u5f39\u7c27\u632f\u5b50\u7684\u72b6\u6001\u7a7a\u95f4\u65b9\u7a0b\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n

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

\u5728\u4e86\u89e3 SSM \u57fa\u672c\u6982\u5ff5\u4e4b\u540e\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u4ecb\u7ecd\u57fa\u4e8e SSM \u7684 HiPPO \u67b6\u6784\u3002<\/p>\n\n\n\n

\u4e09\u3001HiPPO\uff08High-order Polynomial Projection Operators\uff09<\/strong><\/p>\n\n\n\n

HiPPO \u662f Albert Gu \u4e8e2020\u5e74\u5728\u8bba\u6587 HiPPO: Recurrent Memory with Optimal Polynomial Projections \u4e2d\u63d0\u51fa\u7684\u65b0\u67b6\u6784\u3002HiPPO \u4e3b\u8981\u4e3a\u4e86\u89e3\u51b3\u5982\u4f55\u5728\u6709\u9650\u7684\u5b58\u50a8\u7a7a\u95f4\u4e2d\u6709\u6548\u5730\u89e3\u51b3\u5e8f\u5217\u5efa\u6a21\u7684\u957f\u8ddd\u79bb\u4f9d\u8d56\u95ee\u9898\u3002<\/strong><\/p>\n\n\n\n

HiPPO \u901a\u8fc7\u51fd\u6570\u903c\u8fd1\u4ea7\u751f\u72b6\u6001\u77e9\u9635 A \u7684\u6700\u4f18\u89e3\uff0c\u6709\u6548\u7684\u89e3\u51b3\u4e86\u957f\u8ddd\u79bb\u4f9d\u8d56\u95ee\u9898\u3002<\/p>\n\n\n\n

\u95ee\u9898\u80cc\u666f<\/strong>\uff1a\u5728\u5904\u7406\u5e8f\u5217\u6570\u636e\u65f6\uff0c\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\u662f\u5982\u4f55\u5728\u589e\u91cf\u65b9\u5f0f\u4e0b\u8868\u793a\u7d2f\u79ef\u7684\u5386\u53f2\u4fe1\u606f\u3002\u8fd9\u6d89\u53ca\u5230\u5982\u4f55\u5728\u6709\u9650\u7684\u5b58\u50a8\u7a7a\u95f4\u4e2d\u6709\u6548\u5730\u66f4\u65b0\u548c\u7ef4\u62a4\u5386\u53f2\u6570\u636e\u7684\u8868\u793a\u3002<\/p>\n\n\n\n

HiPPO\u6846\u67b6<\/strong>\uff1a\u4f5c\u8005\u4ecb\u7ecd\u4e86\u4e00\u4e2a\u540d\u4e3a HiPPO\uff08High-order Polynomial Projection Operators\uff09\u7684\u901a\u7528\u6846\u67b6\uff0c\u5b83\u901a\u8fc7\u5c06\u8fde\u7eed\u4fe1\u53f7\u548c\u79bb\u6563\u65f6\u95f4\u5e8f\u5217\u6295\u5f71\u5230\u591a\u9879\u5f0f\u57fa\u4e0a\uff0c\u5b9e\u73b0\u4e86\u5728\u7ebf\u6570\u636e\u538b\u7f29\u3002<\/p>\n\n\n\n

\u91cd\u8981\u6027\u5ea6\u91cf<\/strong>\uff1aHiPPO \u6846\u67b6\u8003\u8651\u4e86\u4e00\u4e2a\u5ea6\u91cf\uff0c\u7528\u4e8e\u6307\u5b9a\u8fc7\u53bb\u6bcf\u4e2a\u65f6\u95f4\u6b65\u7684\u91cd\u8981\u6027\u3002\u8fd9\u4e2a\u5ea6\u91cf\u5e2e\u52a9HiPPO\u4ea7\u751f\u5728\u7ebf\u51fd\u6570\u903c\u8fd1\u95ee\u9898\u7684\u6700\u4f18\u89e3\u3002<\/p>\n\n\n\n

\u7406\u8bba\u8d21\u732e<\/strong>\uff1aHiPPO \u6846\u67b6\u4e0d\u4ec5\u63d0\u4f9b\u4e86\u5bf9\u73b0\u6709\u8bb0\u5fc6\u5355\u5143\u7684\u7b80\u77ed\u63a8\u5bfc\uff0c\u8fd8\u63a8\u5e7f\u4e86\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08\u5982GRUs\uff09\u4e2d\u666e\u904d\u5b58\u5728\u7684\u95e8\u63a7\u673a\u5236\u3002<\/p>\n\n\n\n

\u65b0\u7684\u8bb0\u5fc6\u66f4\u65b0\u673a\u5236<\/strong>\uff1a\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u7684\u8bb0\u5fc6\u66f4\u65b0\u673a\u5236\uff08HiPPO-LegS\uff09\uff0c\u5b83\u80fd\u591f\u968f\u65f6\u95f4\u6269\u5c55\u4ee5\u8bb0\u4f4f\u6240\u6709\u5386\u53f2\u4fe1\u606f\uff0c\u907f\u514d\u4e86\u5bf9\u65f6\u95f4\u5c3a\u5ea6\u7684\u5148\u9a8c\u5047\u8bbe\u3002<\/p>\n\n\n\n

\u7406\u8bba\u4f18\u52bf<\/strong>\uff1aHiPPO-LegS \u5177\u6709\u65f6\u95f4\u5c3a\u5ea6\u9c81\u68d2\u6027\u3001\u5feb\u901f\u66f4\u65b0\u548c\u6709\u754c\u68af\u5ea6\u7684\u7406\u8bba\u4f18\u52bf\u3002<\/p>\n\n\n\n

\u5b9e\u9a8c\u7ed3\u679c<\/strong>\uff1a\u5728\u57fa\u51c6\u6d4b\u8bd5\u4e2d\uff0cHiPPO-LegS \u5728\u6253\u4e71\u7684 MNIST \u6570\u636e\u96c6\u4e0a\u8fbe\u5230\u4e8698.3%\u7684\u65b0\u6700\u4f73\u51c6\u786e\u7387\u3002\u5728\u4e00\u4e2a\u65b0\u7684\u8f68\u8ff9\u5206\u7c7b\u4efb\u52a1\u4e2d\uff0cHiPPO-LegS \u5728\u5904\u7406\u5206\u5e03\u5916\u65f6\u95f4\u5c3a\u5ea6\u548c\u7f3a\u5931\u6570\u636e\u65b9\u9762\uff0c\u6bd4\u5176\u4ed6 RNN \u548c\u795e\u7ecf ODE\uff08\u4e00\u9636\u5e38\u5fae\u5206\u65b9\u7a0b\uff09\u57fa\u7ebf\u6a21\u578b\u7684\u6027\u80fd\u63d0\u9ad8\u4e8625-40%\u7684\u51c6\u786e\u7387\u3002<\/p>\n\n\n\n

\u4e0b\u9762\u4ecb\u7ecd HiPPO \u5b9e\u73b0\u7684\u5177\u4f53\u7ec6\u8282\u3002<\/p>\n\n\n\n

3.1 HiPPO \u67b6\u6784\uff1a\u9ad8\u9636\u591a\u9879\u5f0f\u6295\u5f71<\/strong><\/p>\n\n\n\n

3.1.1 HiPPO\u95ee\u9898\u8bbe\u7f6e<\/strong><\/p>\n\n\n\n

\u95ee\u9898\u5b9a\u4e49<\/strong><\/p>\n\n\n\n

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

\u7531\u4e8e\u51fd\u6570\u7a7a\u95f4\u7684\u5e9e\u5927\uff0c\u65e0\u6cd5\u5b8c\u7f8e\u8bb0\u4f4f\u6574\u4e2a\u5386\u53f2\uff0c\u56e0\u6b64\u9700\u8981\u5c06\u5176\u8fdb\u884c\u538b\u7f29\uff0cHiPPO \u63d0\u51fa\u4e86\u5c06\u5386\u53f2\u6295\u5f71\u5230\u6709\u754c\u7ef4\u6570\u7684\u5b50\u7a7a\u95f4\u7684\u4e00\u534a\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u51fd\u6570\u903c\u8fd1\u4e0e\u5ea6\u91cf<\/strong><\/p>\n\n\n\n

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

\u591a\u9879\u5f0f\u57fa\u5c55\u5f00<\/strong><\/p>\n\n\n\n

\u4efb\u4f55 N \u7ef4\u7684\u51fd\u6570\u5b50\u7a7a\u95f4 G \u90fd\u662f\u903c\u8fd1\u7684\u5408\u9002\u5019\u9009\u3002\u53c2\u6570 N \u5bf9\u5e94\u4e8e\u903c\u8fd1\u7684\u9636\u6570\uff0c\u6216\u8005\u8bf4\u538b\u7f29\u7684\u5927\u5c0f\uff1b\u6295\u5f71\u7684\u5386\u53f2\u53ef\u4ee5\u901a\u8fc7G\u7684\u4efb\u4f55\u57fa\u7684N\u4e2a\u7cfb\u6570\u6765\u8868\u793a\u3002<\/p>\n\n\n\n

\u8bba\u6587\u4e2d\u4f7f\u7528\u591a\u9879\u5f0f\u4f5c\u4e3a\u81ea\u7136\u57fa\uff0c\u56e0\u6b64G\u662f\u5c0f\u4e8eN\u9636\u7684\u591a\u9879\u5f0f\u7684\u96c6\u5408\u3002<\/p>\n\n\n\n

\u5728\u7ebf\u903c\u8fd1<\/strong><\/p>\n\n\n\n

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

\u6311\u6218<\/strong><\/p>\n\n\n\n

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

3.1.2 HiPPO \u901a\u7528\u67b6\u6784<\/strong><\/p>\n\n\n\n

\u901a\u8fc7\u8fde\u7eed\u52a8\u6001\u7cfb\u7edf\u8ba1\u7b97\u6295\u5f71<\/strong><\/p>\n\n\n\n

\u8fd9\u90e8\u5206\u662f HiPPO \u7684\u5173\u952e\u6b65\u9aa4\uff0c\u5b83\u6d89\u53ca\u5230\u5c06\u8f93\u5165\u51fd\u6570u(t)\u5728\u65f6\u95f4 t \u6295\u5f71\u5230\u4e00\u4e2a\u591a\u9879\u5f0f\u7a7a\u95f4\u4e0a\uff0c\u4ee5\u4fbf\u5728\u7ebf\u66f4\u65b0\u8bb0\u5fc6\u8868\u793a\u3002<\/p>\n\n\n\n

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

\u5728\u7ebf\u66f4\u65b0<\/strong>\uff1a\u901a\u8fc7\u8fd9\u4e2a\u8fde\u7eed\u52a8\u6001\u7cfb\u7edf\uff0cHiPPO \u6846\u67b6\u80fd\u591f\u5728\u7ebf\u66f4\u65b0\u8bb0\u5fc6\u8868\u793a\uff0c\u5373\u968f\u7740\u65b0\u6570\u636e\u7684\u5230\u6765\uff0c\u7cfb\u7edf\u80fd\u5b9e\u65f6\u5730\u8c03\u6574\u7cfb\u6570x(t)\u3002<\/p>\n\n\n\n

\u5728\u7ebf\u51fd\u6570\u903c\u8fd1<\/strong><\/p>\n\n\n\n

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

\u56fe3-1\uff1aHiPPO\u6846\u67b6<\/p>\n\n\n\n

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

3.1.3 \u9ad8\u9636\u6295\u5f71\uff1a\u5ea6\u91cf\u65b9\u6cd5\u4ee5\u53ca HiPPO \u52a8\u6001\u7cfb\u7edf<\/strong><\/p>\n\n\n\n

\u4f5c\u8005\u5b9a\u4e49\u4e86\u4e24\u79cd\u5ea6\u91cf\u65b9\u6cd5\uff0c\u5206\u522b\u662f LegT \u548c LagT\u3002LegT \u5ea6\u91cf\u4e3a\u6700\u8fd1\u7684\u5386\u53f2\u4fe1\u606f\u5206\u914d\u5747\u5300\u7684\u6743\u91cd\uff0c\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

LagT \u5ea6\u91cf\u4f7f\u7528\u6307\u6570\u8870\u51cf\u7684\u65b9\u5f0f\u6765\u8861\u91cf\u5386\u53f2\u4fe1\u606f\u7684\u91cd\u8981\u6027\uff0c\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u5bf9\u4e8e LegT \u548c LagT\uff0c\u7cfb\u6570x(t)\u53ef\u4ee5\u4f7f\u7528 ODE\uff08\u4e00\u9636\u5e38\u5fae\u5206\u65b9\u7a0b\uff09\u6765\u8868\u793a\uff1a<\/p>\n\n\n\n

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

\u5907\u6ce8\uff1a\u516c\u5f0f\uff089\uff09\u662f HiPPO \u6846\u67b6\u7684\u5173\u952e\u90e8\u5206\uff0c\u5177\u4f53\u63a8\u5bfc\u53ef\u4ee5\u53c2\u770b\u8bba\u6587\u4e2d\u7684\u9644\u5f55 D\u3002<\/strong><\/p>\n\n\n\n

\u5bf9\u4e8e LegT \u5ea6\u91cf\uff0c\u77e9\u9635 A \u548c \u77e9\u9635 B \u53ef\u4ee5\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u5bf9\u4e8e LagT \u5ea6\u91cf\uff0c\u53ef\u4ee5\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

3.1.4 HiPPO \u6846\u67b6\u4e2d\u7684\u8fde\u7eed\u65f6\u95f4\u52a8\u6001\u8f6c\u6362\u4e3a\u79bb\u6563\u65f6\u95f4\u9012\u5f52\u5173\u7cfb<\/strong><\/p>\n\n\n\n

\u7531\u4e8e\u6211\u4eec\u5904\u7406\u7684\u8f93\u5165\u5f80\u5f80\u662f\u79bb\u6563\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5c06\u516c\u5f0f\uff089\uff09\u7684 ODE \u79bb\u6563\u5316\u3002ODE \u79bb\u6563\u5316\u662f\u4e00\u79cd\u5e38\u7528\u7684\u6570\u636e\u6280\u672f\uff0c\u5b83\u5c06\u8fde\u7eed\u65f6\u95f4\u7684\u5e38\u5fae\u5206\u65b9\u7a0b\u8f6c\u6362\u4e3a\u79bb\u6563\u65f6\u95f4\u7684\u5dee\u5206\u65b9\u7a0b<\/strong>\u3002\u8fd9\u901a\u5e38\u6d89\u53ca\u5230\u9009\u62e9\u4e00\u4e2a\u5408\u9002\u7684\u65f6\u95f4\u6b65\u957f\uff08\u6216\u6b65\u957f\u0394t\uff09\uff0c\u5e76\u4f7f\u7528\u6570\u503c\u65b9\u6cd5\uff08\u5982\u6b27\u62c9\u65b9\u6cd5\u3001\u53cc\u7ebf\u6027\uff09\u6765\u8fd1\u4f3c\u8fde\u7eed\u5fae\u5206\u3002<\/p>\n\n\n\n

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

\u56fe3-2\uff1a\u8fde\u7eed\u4fe1\u53f7\u79bb\u6563\u5316<\/p>\n\n\n\n

\u4f7f\u7528\u53cc\u7ebf\u6027\u79bb\u6563\u5316\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n\n

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

\u7ed3\u5408\u516c\u5f0f\uff089\uff09\u548c\u516c\u5f0f\uff0811\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u79bb\u6563\u5316\u7684\u72b6\u6001\u66f4\u65b0\u516c\u5f0f\uff0c\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u79bb\u6563\u5316\u4e4b\u540e\u7684 SSM \u7ed3\u6784\u53ef\u4ee5\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u56fe3-3\uff1a\u79bb\u6563\u5316 SSM<\/p>\n\n\n\n

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

\u56fe3-4\uff1a\u6bcf\u4e2a\u65f6\u95f4\u6b65\u7684\u8ba1\u7b97<\/p>\n\n\n\n

\u8fd9\u79cd\u8868\u793a\u770b\u8d77\u6765\u662f\u4e0d\u662f\u6709\u70b9\u719f\u6089\uff1f\u5176\u5b9e\u4ed6\u7684\u5904\u7406\u65b9\u6cd5\u548cRNN\u4e00\u6837\u3002<\/p>\n\n\n\n

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

\u56fe3-5\uff1a\u79bb\u6563\u5316\u540e\u548cRNN\u7c7b\u4f3c<\/p>\n\n\n\n

3.2 HiPPO-LegS<\/strong><\/p>\n\n\n\n

HiPPO-LegS \u662f\u4f5c\u8005\u57fa\u4e8e\u65b0\u7684\u5ea6\u91cf\u63d0\u51fa\u7684\u5168\u65b0\u67b6\u6784\uff0c\u5177\u6709\u65f6\u95f4\u9c81\u68d2\u6027\u3001\u6709\u754c\u68af\u5ea6\u3001\u6709\u754c\u8fd1\u4f3c\u8bef\u5dee\u3001\u957f\u65f6\u95f4\u8bb0\u5fc6\u7b49\u6548\u679c\u3002<\/p>\n\n\n\n

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

\u5177\u4f53\u63a8\u5bfc\u5728\u8bba\u6587\u7684\u9644\u5f55 D.3 \u90e8\u5206\u3002<\/strong><\/p>\n\n\n\n

\u66f4\u597d\u7684\u5b66\u4e60\u957f\u671f\u4f9d\u8d56<\/strong><\/p>\n\n\n\n

HiPPO-LegS \u662f\u4e13\u95e8\u4e3a\u8bb0\u5fc6\u800c\u8bbe\u8ba1\u7684<\/strong>\uff0c\u5b83\u901a\u8fc7\u5176\u72ec\u7279\u7684\u7ed3\u6784\u548c\u66f4\u65b0\u673a\u5236\u6765\u907f\u514d\u68af\u5ea6\u6d88\u5931\u95ee\u9898\u3002LegS \u901a\u8fc7\u4f7f\u7528Legendre \u591a\u9879\u5f0f\u4f5c\u4e3a\u57fa\u51fd\u6570\uff0c\u5e76\u7ed3\u5408\u65f6\u95f4\u5c3a\u5ea6\u4e0d\u53d8\u7684\u5ea6\u91cf\uff0c\u6765\u4fdd\u6301\u68af\u5ea6\u7684\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n\n

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

\u8fd9\u4e2a\u6027\u8d28\u4f7f\u5f97 HiPPO-LegS \u80fd\u591f\u6709\u6548\u5730\u7f13\u89e3 RNN \u4e2d\u7684\u68af\u5ea6\u6d88\u5931\u95ee\u9898\u3002\u5373\u4f7f\u5728\u957f\u5e8f\u5217\u4e2d\uff0c\u68af\u5ea6\u4e5f\u4e0d\u4f1a\u8fc5\u901f\u8870\u51cf\u52300\uff0c\u8fd9\u6709\u52a9\u4e8e\u7f51\u7edc\u5728\u8bad\u7ec3\u4e2d\u66f4\u597d\u5730\u5b66\u4e60\u957f\u671f\u4f9d\u8d56\u3002<\/p>\n\n\n\n

\u8fd1\u4f3c\u6709\u754c\u8bef\u5dee<\/strong><\/p>\n\n\n\n

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

3.3 \u5b9e\u9a8c<\/strong><\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u6a21\u578b\u7ed3\u6784\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u4e0b\u9762\u662fpMINIST \u6570\u636e\u96c6\u4e0a\u7684\u7ed3\u679c\uff0c\u53ef\u4ee5\u770b\u5230 LegS \u7684\u6548\u679c\u8981\u597d\u4e8e LagT \u548c LegT\uff0c\u540c\u65f6 HiPPO \u7684\u6548\u679c\u597d\u4e8e\u4e4b\u524d\u7684\u5176\u5b83\u6a21\u578b\u3002<\/p>\n\n\n\n

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

\u5907\u6ce8\uff1apMNIST\uff08permuted MNIST\uff09\u662f\u4e00\u4e2a\u7ecf\u8fc7\u4fee\u6539\u7684MNIST\u6570\u636e\u96c6<\/strong>\uff0c\u5b83\u7528\u4e8e\u6d4b\u8bd5\u548c\u8bc4\u4f30\u673a\u5668\u5b66\u4e60\u6a21\u578b\u5728\u5904\u7406\u5e8f\u5217\u6570\u636e\u548c\u5b66\u4e60\u957f\u671f\u4f9d\u8d56\u5173\u7cfb\u65b9\u9762\u7684\u80fd\u529b\u3002\u5728 pMNIST \u4e2d\uff0c\u539f\u59cb MNIST \u56fe\u50cf\u7684\u50cf\u7d20\u88ab\u91cd\u65b0\u6392\u5217\u3002\u8fd9\u610f\u5473\u7740\u56fe\u50cf\u7684\u50cf\u7d20\u4e0d\u518d\u662f\u6309\u7167\u81ea\u7136\u987a\u5e8f\uff08\u4ece\u5de6\u5230\u53f3\uff0c\u4ece\u4e0a\u5230\u4e0b\uff09\u5448\u73b0\uff0c\u800c\u662f\u6309\u7167\u4e00\u4e2a\u56fa\u5b9a\u7684\u3001\u968f\u673a\u7684\u6392\u5217\u987a\u5e8f\u3002\u8fd9\u79cd\u6392\u5217\u65b9\u5f0f\u4f7f\u5f97\u6a21\u578b\u5fc5\u987b\u5b66\u4e60\u50cf\u7d20\u4e4b\u95f4\u7684\u957f\u671f\u4f9d\u8d56\u5173\u7cfb\uff0c\u800c\u4e0d\u80fd\u7b80\u5355\u5730\u4f9d\u8d56\u4e8e\u5c40\u90e8\u7a7a\u95f4\u7ed3\u6784\u3002<\/p>\n\n\n\n

\u56db\u3001S4 (Structured State Space Model)<\/strong><\/p>\n\n\n\n

S4 \u662f HiPPO \u7684\u540e\u7eed\u5de5\u4f5c\uff0c\u8bba\u6587\u540d\u79f0\u4e3a\uff1aEfficiently Modeling Long Sequences with Structured State Spaces\u3002<\/p>\n\n\n\n

S4 \u7684\u4e3b\u8981\u5de5\u4f5c\u662f\u5c06 HiPPO \u4e2d\u7684\u77e9\u9635 A\uff08\u79f0\u4e3a HiPPO \u77e9\u9635<\/strong>\uff09\u8f6c\u6362\u4e3a\u6b63\u89c4\u77e9\u9635\uff08\u6b63\u89c4\u77e9\u9635\u53ef\u4ee5\u5206\u89e3\u4e3a\u5bf9\u89d2\u77e9\u9635\uff09\u548c\u4f4e\u79e9\u77e9\u9635\u7684\u548c\uff0c\u4ee5\u6b64\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n\n\n\n

S4 \u901a\u8fc7\u8fd9\u79cd\u5206\u89e3\uff0c\u5c06\u8ba1\u7b97\u590d\u6742\u5ea6\u964d\u4f4e\u5230\u4e860(N+L)\uff0c\u5176\u4e2d N \u662f HiPPO \u77e9\u9635\u7684\u7ef4\u5ea6\uff0cL \u662f\u5e8f\u5217\u957f\u5ea6\u3002<\/p>\n\n\n\n

\u5728\u5904\u7406\u957f\u5ea6\u4e3a 16000 \u7684\u5e8f\u5217\u7684\u8bed\u97f3\u5206\u7c7b\u4efb\u52a1\u4e2d\uff0cS4 \u6a21\u578b\u5c06\u4e13\u95e8\u8bbe\u8ba1\u7684\u8bed\u97f3\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08Speech CNNs\uff09\u7684\u6d4b\u8bd5\u9519\u8bef\u7387\u964d\u4f4e\u4e86\u4e00\u534a\uff0c\u8fbe\u5230\u4e861.7%\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6240\u6709\u7684\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08RNN\uff09\u548c Transformer \u57fa\u7ebf\u6a21\u578b\u90fd\u65e0\u6cd5\u5b66\u4e60\uff0c\u9519\u8bef\u7387\u5747\u572870%\u4ee5\u4e0a\u3002<\/p>\n\n\n\n

\u4e0b\u9762\u6211\u4eec\u5c31\u6765\u4ecb\u7ecd\u4e00\u4e0b\u8fd9\u7bc7\u5de5\u4f5c\u3002<\/p>\n\n\n\n

4.1 HiPPO \u89e3\u51b3\u4e86\u957f\u671f\u4f9d\u8d56<\/strong><\/p>\n\n\n\n

\u4f5c\u8005\u8ba8\u8bba\u4e86\u5982\u4f55\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\uff08Long-Range Dependencies\uff0cLRDs\uff09\u7684\u95ee\u9898\uff0cLRDs \u662f\u5e8f\u5217\u5efa\u6a21\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u6311\u6218\uff0c\u56e0\u4e3a\u5b83\u4eec\u6d89\u53ca\u5230\u5728\u5e8f\u5217\u4e2d\u8de8\u8d8a\u5927\u91cf\u65f6\u95f4\u6b65\u7684\u4f9d\u8d56\u5173\u7cfb\u3002<\/p>\n\n\n\n

\u4f5c\u8005\u6307\u51fa\uff0c\u57fa\u672c\u7684 SSM \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u8868\u73b0\u4e0d\u4f73\uff0c\u7279\u522b\u662f\u5728\u5904\u7406 LRDs \u65f6\u3002\u8fd9\u662f\u56e0\u4e3a\u7ebf\u6027\u4e00\u9636\u5e38\u5fae\u5206\u65b9\u7a0b\uff08ODEs\uff09\u7684\u89e3\u901a\u5e38\u662f\u6307\u6570\u51fd\u6570\uff0c\u8fd9\u53ef\u80fd\u5bfc\u81f4\u68af\u5ea6\u5728\u5e8f\u5217\u957f\u5ea6\u4e0a\u5448\u6307\u6570\u7ea7\u589e\u957f\uff0c\u4ece\u800c\u5f15\u53d1\u68af\u5ea6\u6d88\u5931\u6216\u7206\u70b8\u7684\u95ee\u9898\u3002<\/strong><\/p>\n\n\n\n

\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4f5c\u8005\u5229\u7528\u4e86 HiPPO \u7406\u8bba\u3002HiPPO \u7406\u8bba\u6307\u5b9a\u4e86\u4e00\u7c7b\u7279\u6b8a\u7684\u77e9\u9635 A\uff0c\u5f53\u8fd9\u4e9b\u77e9\u9635\u88ab\u7eb3\u5165 SSM \u7684\u65b9\u7a0b\u4e2d\u65f6\uff0c\u53ef\u4ee5\u4f7f\u72b6\u6001 x(t) \u80fd\u591f\u8bb0\u4f4f\u8f93\u5165 u(t) \u7684\u5386\u53f2\u4fe1\u606f\u3002\u8fd9\u4e9b\u7279\u6b8a\u77e9\u9635\u88ab\u79f0\u4e3a HiPPO \u77e9\u9635\uff0c\u5b83\u4eec\u5177\u6709\u7279\u5b9a\u7684\u6570\u5b66\u5f62\u5f0f\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u6355\u6349\u957f\u671f\u4f9d\u8d56\u5173\u7cfb\u3002<\/strong><\/p>\n\n\n\n

HiPPO \u77e9\u9635\u7684\u4e00\u4e2a\u5173\u952e\u7279\u6027\u662f\u5b83\u4eec\u5141\u8bb8 SSM \u5728\u6570\u5b66\u548c\u5b9e\u8bc1\u4e0a\u6355\u6349 LRDs<\/strong>\u3002\u4f8b\u5982\uff0c\u901a\u8fc7\u5c06\u968f\u673a\u77e9\u9635 A \u66ff\u6362\u4e3a HiPPO \u77e9\u9635\uff0c\u53ef\u4ee5\u5728\u5e8f\u5217 MNIST \u57fa\u51c6\u6d4b\u8bd5\u4e0a\u663e\u8457\u63d0\u9ad8 SSM \u7684\u6027\u80fd\u3002<\/p>\n\n\n\n

HiPPO \u77e9\u9635\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

4.2 \u5728\u7ebf\u63a8\u7406\uff1a\u4f7f\u7528\u9012\u5f52\u5f62\u5f0f<\/strong><\/p>\n\n\n\n

S4 \u5728\u63a8\u7406\u65f6\uff0c\u4f7f\u7528\u516c\u5f0f\uff0812\uff09\u7684\u9012\u5f52\u5f62\u5f0f\uff0c\u6bcf\u6b21\u53ea\u9700\u8981\u548c\u4e0a\u4e00\u4e2a\u72b6\u6001\u8fdb\u884c\u8ba1\u7b97\uff0c\u5177\u6709\u548c RNN \u76f8\u4f3c\u7684\u63a8\u7406\u6548\u7387\u3002<\/p>\n\n\n\n

4.3 \u8bad\u7ec3 S4\uff1a\u5377\u79ef\u8868\u793a<\/strong><\/p>\n\n\n\n

\u7531\u4e8e\u79bb\u6563\u65f6\u95f4 SSM \u7684\u9012\u5f52\u6027\u8d28\uff0c\u5b83\u5728\u786c\u4ef6\u4e0a\u8fdb\u884c\u8bad\u7ec3\u65f6\u5b58\u5728\u6548\u7387\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u4f5c\u8005\u5c06\u79bb\u6563\u65f6\u95f4 SSM \u7684\u9012\u5f52\u65b9\u7a0b\u8f6c\u6362\u4e3a\u79bb\u6563\u5377\u79ef\u7684\u5f62\u5f0f<\/strong>\u3002\u901a\u8fc7\u5c55\u5f00\u9012\u5f52\u65b9\u7a0b\uff0c\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u5377\u79ef\u6838\uff0c\u8fd9\u4e2a\u5377\u79ef\u6838\u53ef\u4ee5\u7528\u6765\u5728\u5e8f\u5217\u6570\u636e\u4e0a\u5e94\u7528\u5377\u79ef\u64cd\u4f5c\u3002\u8fd9\u79cd\u8f6c\u6362\u5141\u8bb8 SSM \u5229\u7528\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\uff08FFT\uff09\u7b49\u9ad8\u6548\u7684\u5377\u79ef\u8ba1\u7b97\u65b9\u6cd5\uff0c\u4ece\u800c\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n\n\n\n

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

\u4e0a\u9762\u5f0f\u5b50\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5377\u79ef\u7684\u5f62\u5f0f\uff1a<\/p>\n\n\n\n

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

\u4f5c\u8005\u5728\u8fd9\u4e00\u8282\u4e2d\u8fd8\u8ba8\u8bba\u4e86\u5982\u4f55\u8ba1\u7b97 SSMn\u5377\u79ef\u6838\uff0c\u8fd9\u662f\u4ed6\u4eec\u6280\u672f\u8d21\u732e\u7684\u5173\u952e\u90e8\u5206\u3002\u901a\u8fc7\u8fd9\u79cd\u5377\u79ef\u8868\u793a\uff0cSSM \u53ef\u4ee5\u88ab\u6709\u6548\u5730\u8bad\u7ec3\uff0c\u540c\u65f6\u4fdd\u6301\u5176\u5728\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\uff08LRDs\uff09\u65b9\u9762\u7684\u80fd\u529b\u3002\u8fd9\u79cd\u8868\u793a\u5f62\u5f0f\u4e3a SSM \u5728\u5404\u79cd\u5e8f\u5217\u5efa\u6a21\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\u63d0\u4f9b\u4e86\u7075\u6d3b\u6027\uff0c\u5305\u62ec\u56fe\u50cf\u5904\u7406\u3001\u8bed\u97f3\u8bc6\u522b\u548c\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u7b49\u3002<\/p>\n\n\n\n

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

\u56fe4-1\uff1aSSM \u5377\u79ef\u6838\u5f62\u5f0f<\/p>\n\n\n\n

\u4e0b\u9762\u662f\u4e00\u4e2a\u5177\u4f53\u7684\u4f8b\u5b50\uff0c\u5982\u4f55\u4f7f\u7528\u5377\u79ef\u6838\u751f\u6210\u8f93\u51fa\u3002<\/p>\n\n\n\n

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

\u56fe4-2\uff1a\u4f7f\u7528\u5377\u79ef\u6838\u751f\u6210\u8f93\u51fa<\/p>\n\n\n\n

\u5377\u79ef\u7684\u4e00\u4e2a\u4e3b\u8981\u597d\u5904\u662f\u5b83\u53ef\u4ee5\u5e76\u884c\u8bad\u7ec3\u3002\u4f46\u662f\u7531\u4e8e\u6838\u5927\u5c0f\u662f\u56fa\u5b9a\uff0c\u5b83\u4eec\u7684\u63a8\u7406\u4e0d\u5982 RNN \u5feb\u901f\u5e76\u4e14\u5bf9\u5e8f\u5217\u957f\u5ea6\u6709\u9650\u5236\u3002<\/p>\n\n\n\n

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

\u56fe4-3\uff1a\u9012\u5f52 SSM \u548c \u5377\u79ef SSM \u7684\u5bf9\u6bd4<\/p>\n\n\n\n

\u8fd9\u91cc\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u6280\u5de7\uff0c\u5373\u6839\u636e\u4efb\u52a1\u9009\u62e9\u8868\u793a\u3002\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u53ef\u4ee5\u5e76\u884c\u5316\u7684\u5377\u79ef\u8868\u793a\uff0c\u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u9ad8\u6548\u7684\u5faa\u73af\u8868\u793a\u3002<\/p>\n\n\n\n

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

\u56fe4-4\uff1a\u9012\u5f52\u63a8\u7406\u3001\u5377\u79ef\u8bad\u7ec3<\/p>\n\n\n\n

4.4 \u4e3a\u4ec0\u4e48\u5bf9\u89d2\u5316\u53ef\u4ee5\u51cf\u5c11 SSM \u8ba1\u7b97\u590d\u6742\u5ea6<\/strong><\/p>\n\n\n\n

\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63d0\u5347\u8ba1\u7b97\u6548\u7387\uff0c\u4f5c\u8005\u8ba8\u8bba\u4e86\u5bf9\u89d2\u5316\u5728\u8ba1\u7b97\u79bb\u6563\u65f6\u95f4\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff08SSM\uff09\u4e2d\u7684\u5e94\u7528\uff0c\u4ee5\u53ca\u4e3a\u4ec0\u4e48\u76f4\u63a5\u5e94\u7528\u5bf9\u89d2\u5316\u65b9\u6cd5\u5728\u5b9e\u8df5\u4e2d\u5e76\u4e0d\u53ef\u884c\u3002<\/p>\n\n\n\n

\u5bf9\u89d2\u5316\u662f\u4e00\u79cd\u7ebf\u6027\u4ee3\u6570\u6280\u672f\uff0c\u5b83\u53ef\u4ee5\u5c06\u4e00\u4e2a\u77e9\u9635\u8f6c\u6362\u4e3a\u5bf9\u89d2\u5f62\u5f0f\uff0c\u4ece\u800c\u7b80\u5316\u77e9\u9635\u7684\u4e58\u6cd5\u548c\u5176\u4ed6\u8fd0\u7b97\u3002\u5728 SSM \u7684\u4e0a\u4e0b\u6587\u4e2d\uff0c\u5bf9\u89d2\u5316\u53ef\u4ee5\u663e\u8457\u51cf\u5c11\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u56e0\u4e3a\u5bf9\u89d2\u77e9\u9635\u7684\u5e42\u8fd0\u7b97\uff08\u5982\u5728\u9012\u5f52\u65b9\u7a0b\u4e2d\u51fa\u73b0\u7684\uff09\u53ef\u4ee5\u901a\u8fc7\u7b80\u5355\u7684\u5143\u7d20\u6307\u6570\u8fd0\u7b97\u6765\u5b8c\u6210\u3002<\/p>\n\n\n\n

\u4e0b\u9762\u6211\u4eec\u89e3\u91ca\u4e0b\uff0c\u4e3a\u4ec0\u4e48\u5bf9\u89d2\u5316\u53ef\u4ee5\u51cf\u5c11 SSM \u8ba1\u7b97\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n

\u9996\u5148\uff0c\u6211\u4eec\u5f15\u5165\u8bba\u6587\u4e2d\u7684\u5b9a\u7406 3.1<\/p>\n\n\n\n

\uff08Lemma 3.1\uff09\uff1a\u5171\u8f6d\u662f SSM \u4e2d\u7684\u7b49\u4ef7\u5173\u7cfb\uff0c\u5373\uff1a<\/strong><\/p>\n\n\n\n

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

\u7b2c\u4e00\u4e2a SSM\uff1a<\/p>\n\n\n\n

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

\u7b2c\u4e8c\u4e2a SSM\uff1a<\/p>\n\n\n\n

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

\u901a\u8fc7V\u5c06\u7b2c\u4e8c SSM \u4e58\u4ee5V\u540e\uff0c\u53d8\u6210\u5982\u4e0b\u5f62\u5f0f\uff1a<\/p>\n\n\n\n

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

4.5 \u76f4\u63a5\u5bf9\u89d2\u5316 HiPPO \u77e9\u9635\u5bfc\u81f4\u6570\u503c\u6ea2\u51fa<\/strong><\/p>\n\n\n\n

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

\u4e0b\u9762\u8bc1\u660e\u4e0b\u8fd9\u4e2a\u7ed3\u8bba\u3002<\/p>\n\n\n\n

\u9996\u5148\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u77e9\u9635A\u7684\u4e00\u4e2a\u76f8\u4f3c\u77e9\u9635\uff0c\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u5176\u4e2d\uff1a<\/p>\n\n\n\n

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

\u90a3\u4e48\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u53ef\u9006\u77e9\u9635\uff1a<\/p>\n\n\n\n

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

\u5373\u7136\u65e0\u6cd5\u76f4\u63a5\u5bf9A\u77e9\u9635\u8fdb\u884c\u5bf9\u89d2\u5316\uff0c\u90a3\u4e48\u662f\u5426\u53ef\u4ee5\u5c06\u5176\u8f6c\u5316\u4e3a\u4f4e\u79e9\u77e9\u9635\u6216\u8005\u5176\u5b83\u53ef\u4ee5\u5bf9\u89d2\u5316\u7684\u77e9\u9635\uff1f\u89e3\u4e0b\u6765\u6211\u4eec\u4ecb\u7ecd\u4e0b\u5982\u4f55\u5c06\u5176\u8f6c\u6362\u4e3a\u6b63\u89c4\u77e9\u9635+\u4f4e\u79e9\u77e9\u9635\u3002<\/p>\n\n\n\n

4.6 S4 \u53c2\u6570\u5316\uff1a\u6b63\u89c4\u77e9\u9635+\u4f4e\u79e9\u77e9\u9635<\/strong><\/p>\n\n\n\n

\u867d\u7136\u77e9\u9635A\u4e0d\u80fd\u76f4\u63a5\u5bf9\u89d2\u5316\uff0c\u4f46\u662f\u53ef\u4ee5\u8868\u793a\u4e3a\u6b63\u89c4\u77e9\u9635+\u4f4e\u79e9\u77e9\u9635\u3002<\/p>\n\n\n\n

Theorem 1\uff1aHiPPO \u77e9\u9635A\u53ef\u4ee5\u8868\u793a\u4e3a\u6b63\u89c4\u77e9\u9635+\u4f4e\u79e9\u77e9\u9635\u7684\u5f62\u5f0f\uff0c\u5373\uff1a<\/p>\n\n\n\n

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

\u4e0b\u9762\u7b80\u5355\u8bc1\u660e\u4e0b\u8fd9\u4e2a\u5b9a\u7406\u3002<\/p>\n\n\n\n

\u5df2\u77e5 HiPPO \u77e9\u9635A\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n

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

\u8fd9\u6837\u6211\u4eec\u5c31\u5c06\u77e9\u9635A\u8f6c\u6362\u4e3a\u4e86\u6b63\u89c4\u77e9\u9635+\u4f4e\u79e9\u77e9\u9635\u7684\u5f62\u5f0f\u3002\u4e0b\u9762\u6211\u4eec\u770b\u4e00\u4e0b\u8f6c\u6362\u4e4b\u540e\u7684\u9012\u5f52\u8ba1\u7b97\u548c\u5377\u79ef\u8ba1\u7b97\u7684\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n

4.7 S4 \u7684\u8ba1\u7b97\u590d\u6742\u5ea6<\/strong><\/p>\n\n\n\n

\u7ecf\u8fc7\u6b63\u89c4\u77e9\u9635+\u4f4e\u79e9\u77e9\u9635\u5206\u89e3\u540e\uff0c\u6211\u4eec\u518d\u6765\u8003\u8651 S4 \u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u6709\u4ec0\u4e48\u53d8\u5316\u3002\u6211\u4eec\u540c\u65f6\u8003\u8651\u63a8\u7406\u65f6\u9012\u5f52\u8ba1\u7b97\u7684\u590d\u6742\u5ea6\u4ee5\u53ca\u8bad\u7ec3\u65f6\u5377\u79ef\u8ba1\u7b97\u7684\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n

\u5148\u7ed9\u51fa\u7ed3\u8bba\uff1a<\/p>\n\n\n\n

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

\u8fd9\u91cc\u7684 Cauchy \u77e9\u9635-\u5411\u91cf\u4e58\u6cd5\u590d\u6742\u5ea6\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n\n

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

\u5982\u679cCauchy \u77e9\u9635-\u5411\u91cf\u4e58\u6cd5\u6309\u7167\u7cbe\u786e\u8ba1\u7b97\uff0c\u90a3\u4e48 S4 \u7684\u5377\u79ef\u590d\u6742\u5ea6\u4e3a<\/p>\n\n\n\n

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

\u89e3\u4e0b\u6765\u6211\u4eec\u8be6\u7ec6\u4ecb\u7ecd S4 \u8ba1\u7b97\u590d\u6742\u5ea6\u7684\u5206\u6790\u8fc7\u7a0b\uff0c\u9996\u5148\u4ecb\u7ecd\u9012\u5f52\u8ba1\u7b97\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n

\u9012\u5f52\u8ba1\u7b97\u590d\u6742\u5ea6<\/strong><\/p>\n\n\n\n

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

\u7531\u4e8e\uff1a<\/p>\n\n\n\n

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

\u73b0\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u516c\u5f0f\uff0830\uff09\u91cd\u65b0\u8868\u793a\u4e3a\u4e0b\u9762\u7684\u5f62\u5f0f\uff1a<\/p>\n\n\n\n

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

\u516c\u5f0f\uff0812\uff09\u7684 SSM \u53ef\u4ee5\u91cd\u65b0\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n

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

\u5377\u79ef\u8ba1\u7b97\u590d\u6742\u5ea6<\/strong><\/p>\n\n\n\n

\u8fd9\u4e00\u5757\u5c31\u4e0d\u518d\u5177\u4f53\u4ecb\u7ecd\u4e86\uff0c\u611f\u5174\u8da3\u7684\u53ef\u4ee5\u76f4\u63a5\u53bb\u770b\u539f\u8bba\u6587\uff0c\u5728\u8bba\u6587\u7684\u9644\u5f55 C.3 \u6709\u8be6\u7ec6\u7684\u5206\u6790\u8fc7\u7a0b\u3002<\/p>\n\n\n\n

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

\u6700\u540e\u4f5c\u8005\u5bf9\u6bd4\u4e86 S4 \u548c\u539f\u59cb\u5377\u79ef\u3001\u9012\u5f52\u3001Attention \u4e4b\u95f4\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u53ef\u4ee5\u770b\u5230 S4 \u662f\u6700\u4f4e\u7684\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n

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

\u56fe4-5\uff1a\u8ba1\u7b97\u590d\u6742\u5ea6\u5bf9\u6bd4<\/p>\n\n\n\n

\u56fe\u4e2d L \u8868\u793a\u5e8f\u5217\u957f\u5ea6\uff0cB \u8868\u793a batch size\uff0cH \u8868\u793a\u9690\u85cf\u7ef4\u5ea6\u3002<\/p>\n\n\n\n

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

4.8 \u5b9e\u9a8c\u7ed3\u679c<\/strong><\/p>\n\n\n\n

\u63a8\u7406\u6548\u7387<\/strong><\/p>\n\n\n\n

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

\u5e8f\u5217\u957f\u5ea6\u4e3a 1024 \u65f6\uff0cS4 \u7684\u63a8\u7406\u901f\u5ea6\u662f Transformer \u7684 1.58 \u500d\uff1b\u5e8f\u5217\u957f\u5ea6\u4e3a 4096 \u65f6\uff0c\u662f Transformer \u63a8\u7406\u901f\u5ea6\u7684 5.19 \u500d\uff0c\u7531\u4e8e\u4e0d\u9700\u8981 KV cache\uff0c\u56e0\u6b64\u5185\u5b58\u5360\u7528\u975e\u5e38\u5c0f\u3002<\/p>\n\n\n\n

S4 \u4f5c\u4e3a\u751f\u6210\u6a21\u578b\u7684\u6548\u679c<\/strong><\/p>\n\n\n\n

\u5c06 S4 \u5e94\u7528\u5728\u751f\u6210\u6a21\u578b\u4e2d\uff0c\u5b9e\u9a8c\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\u3002<\/p>\n\n\n\n

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

\u56fe4-7\uff1aS4 \u4f5c\u4e3a\u751f\u6210\u6a21\u578b\u7684\u6548\u679c<\/p>\n\n\n\n

HiPPO \u5f71\u54cd<\/strong><\/p>\n\n\n\n

\u8fd9\u90e8\u5206\u4f5c\u8005\u8fdb\u884c\u4e86\u4e00\u7cfb\u5217\u7684\u6d88\u878d\u5b9e\u9a8c\uff08Ablations\uff09\uff0c\u4ee5\u8bc4\u4f30 HiPPO \u77e9\u9635\u5728\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff08SSM\uff09\u4e2d\u7684\u91cd\u8981\u6027\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u65e8\u5728\u63a2\u7a76 HiPPO \u77e9\u9635\u5728 S4 \u6a21\u578b\u4e2d\u7684\u4f5c\u7528\uff0c\u4ee5\u53ca\u5b83\u5bf9\u4e8e\u6a21\u578b\u6027\u80fd\u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n

HiPPO \u77e9\u9635\u662f S4 \u6a21\u578b\u4e2d\u7528\u4e8e\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\uff08LRDs\uff09\u7684\u5173\u952e\u7ec4\u4ef6\u3002\u5728\u8fd9\u4e00\u8282\u4e2d\uff0c\u4f5c\u8005\u901a\u8fc7\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u9762\u7684\u5b9e\u9a8c\u6765\u9a8c\u8bc1 HiPPO \u77e9\u9635\u7684\u91cd\u8981\u6027\uff1a<\/p>\n\n\n\n

    \n
  1. HiPPO \u521d\u59cb\u5316\uff1a\u4f5c\u8005\u9996\u5148\u7814\u7a76\u4e86\u4e0d\u540c\u521d\u59cb\u5316\u65b9\u6cd5\u5bf9 SSM \u6027\u80fd\u7684\u5f71\u54cd\uff0c\u5305\u62ec\u968f\u673a\u9ad8\u65af\u521d\u59cb\u5316\u3001HiPPO \u521d\u59cb\u5316\u4ee5\u53ca\u968f\u673a\u5bf9\u89d2\u9ad8\u65af\u77e9\u9635\u521d\u59cb\u5316\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0cHiPPO \u521d\u59cb\u5316\u5728\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u65b9\u9762\u8d77\u5230\u4e86\u5173\u952e\u4f5c\u7528\u3002<\/li>\n\n\n\n
  2. HiPPO \u77e9\u9635\u662f\u5426\u53ef\u8bad\u7ec3\uff1a\u4f5c\u8005\u8fd8\u63a2\u8ba8\u4e86 HiPPO \u77e9\u9635\u56fa\u5b9a\u4ee5\u53ca\u53ef\u8bad\u7ec3\u7684\u6548\u679c\u3002\u4ed6\u4eec\u53d1\u73b0\uff0c\u56fa\u5b9a HiPPO \u548c\u53ef\u8bad\u7ec3\u7684\u5dee\u5f02\u4e0d\u5927\u3002<\/li>\n\n\n\n
  3. NPLR SSMs\uff1a\u4f5c\u8005\u8fdb\u4e00\u6b65\u7814\u7a76\u4e86\u5728\u6ca1\u6709 HiPPO \u77e9\u9635\u7684\u60c5\u51b5\u4e0b\uff0c\u968f\u673a NPLR\uff08Normal Plus Low-Rank\uff0c\u6b63\u89c4+\u4f4e\u79e9\u77e9\u9635\uff09\u7684\u8868\u73b0\u3002\u7ed3\u679c\u8868\u660e\uff0c\u5373\u4f7f\u5728 NPLR \u5f62\u5f0f\u4e0b\uff0c\u8fd9\u4e9b\u968f\u673a\u77e9\u9635\u7684\u6027\u80fd\u4ecd\u7136\u4e0d\u4f73\uff0c\u8fd9\u9a8c\u8bc1\u4e86 HiPPO \u77e9\u9635\u5728 S4 \u6a21\u578b\u4e2d\u7684\u6838\u5fc3\u4f5c\u7528\u3002<\/li>\n<\/ol>\n\n\n\n

    \u901a\u8fc7\u8fd9\u4e9b\u6d88\u878d\u5b9e\u9a8c\uff0c\u4f5c\u8005\u5f3a\u8c03\u4e86 HiPPO \u77e9\u9635\u5728 S4 \u6a21\u578b\u4e2d\u7684\u91cd\u8981\u6027\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u7ed3\u679c\u4e0d\u4ec5\u8bc1\u5b9e\u4e86 HiPPO \u77e9\u9635\u5728\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\u65b9\u9762\u7684\u6709\u6548\u6027\uff0c\u800c\u4e14\u4e5f\u8868\u660e\u4e86\u5b83\u5728\u63d0\u5347\u6a21\u578b\u6574\u4f53\u6027\u80fd\u65b9\u9762\u7684\u5173\u952e\u4f5c\u7528\u3002\u8fd9\u4e9b\u53d1\u73b0\u5bf9\u4e8e\u7406\u89e3 S4 \u6a21\u578b\u7684\u8bbe\u8ba1\u548c\u4f18\u5316\u81f3\u5173\u91cd\u8981\u3002<\/p>\n\n\n\n

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

    \u56fe4-8\uff1aHiPPO \u77e9\u9635\u521d\u59cb\u5316\u6548\u679c\u8fdc\u8fdc\u9ad8\u4e8e\u5176\u5b83\u77e9\u9635\u521d\u59cb\u5316<\/p>\n\n\n\n

    \u867d\u7136 S4 \u5728\u4fdd\u8bc1\u4e86\u8ba1\u7b97\u6548\u7387\u7684\u540c\u65f6\uff0c\u4f18\u5316\u4e86\u957f\u8ddd\u79bb\u4f9d\u8d56\u95ee\u9898\u3002\u4f46\u662f\u7531\u4e8e\u77e9\u9635ABC\u662f\u56fa\u5b9a\u4e0d\u53d8\u7684\uff0c\u548c\u8f93\u5165 token \u65e0\u5173\uff0c\u8fd9\u5c31\u5bfc\u81f4\u4e86 S4 \u5728\u4e00\u4e9b\u5408\u6210\u4efb\u52a1\u4e0a\u6548\u679c\u4e0d\u4f73\uff0c\u6bd4\u5982\u9009\u62e9\u6027\u590d\u5236\u4efb\u52a1\u3002<\/p>\n\n\n\n

    \u800c\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86 Mamba \u67b6\u6784\uff0c\u901a\u8fc7\u9009\u62e9\u6027\u673a\u5236\u6539\u8fdb S4\uff0c\u6709\u6548\u89e3\u51b3\u4e86\u8fd9\u7c7b\u95ee\u9898\u3002\u4e0b\u9762\u6211\u4eec\u5c31\u6765\u4ecb\u7ecd\u4e0b\u6700\u8fd1\u5f88\u706b\u7684 Mamba \u7ed3\u6784\u3002<\/p>\n\n\n\n

    \u4e94\u3001Mamba<\/strong><\/p>\n\n\n\n

    \u6211\u4eec\u7ec8\u4e8e\u4ecb\u7ecd\u5b8c\u4e86\u7406\u89e3 Mamba \u6240\u9700\u8981\u7684\u57fa\u7840\u77e5\u8bc6\u3002\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u53ef\u7528\u4e8e\u5efa\u6a21\u6587\u672c\u5e8f\u5217\uff0c\u4f46\u4ecd\u6709\u4e00\u7cfb\u5217\u6211\u4eec\u60f3\u8981\u907f\u514d\u7684\u7f3a\u70b9\u3002<\/p>\n\n\n\n

    \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4ecb\u7ecd Mamba \u7684\u4e24\u5927\u4e3b\u8981\u8d21\u732e\uff1a<\/p>\n\n\n\n

      \n
    1. \u4e00\u79cd\u9009\u62e9\u6027\u626b\u63cf\u7b97\u6cd5\uff0c\u8be5\u7b97\u6cd5\u5141\u8bb8\u6a21\u578b\u8fc7\u6ee4\uff08\u4e0d\uff09\u76f8\u5173\u4fe1\u606f\uff1b<\/li>\n\n\n\n
    2. \u4e00\u79cd\u786c\u4ef6\u611f\u77e5\u7b97\u6cd5\uff0c\u8be5\u7b97\u6cd5\u5141\u8bb8\u901a\u8fc7\u5e76\u884c\u626b\u63cf\u3001\u5185\u6838\u878d\u5408\u548c\u91cd\u65b0\u8ba1\u7b97\u6765\u9ad8\u6548\u5b58\u50a8\uff08\u4e2d\u95f4\uff09\u7ed3\u679c\u3002<\/li>\n<\/ol>\n\n\n\n

      \u5b83\u4eec\u5171\u540c\u521b\u5efa\u4e86\u9009\u62e9\u6027 SSM \u6216 S6 \u6a21\u578b\uff0c\u8fd9\u4e9b\u6a21\u578b\u53ef\u4ee5\u50cf\u81ea\u6ce8\u610f\u529b\u4e00\u6837\u7528\u4e8e\u521b\u5efa Mamba \u5757\u3002<\/p>\n\n\n\n

      \u5728\u63a2\u8ba8\u8fd9\u4e24\u5927\u4e3b\u8981\u8d21\u732e\u4e4b\u524d\uff0c\u8ba9\u6211\u4eec\u9996\u5148\u63a2\u8ba8\u4e00\u4e0b\u4e3a\u4ec0\u4e48\u5b83\u4eec\u662f\u5fc5\u8981\u7684\u3002<\/p>\n\n\n\n

      \u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff0c\u751a\u81f3\u662fS4\uff08\u7ed3\u6784\u5316\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff09\uff0c\u5728\u67d0\u4e9b\u5bf9\u8bed\u8a00\u5efa\u6a21\u548c\u751f\u6210\u81f3\u5173\u91cd\u8981\u7684\u4efb\u52a1\u4e0a\u8868\u73b0\u4e0d\u4f73\uff0c\u5373\u5173\u6ce8\u6216\u5ffd\u7565\u7279\u5b9a\u8f93\u5165\u7684\u80fd\u529b\u3002<\/p>\n\n\n\n

      \u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e24\u4e2a\u5408\u6210\u4efb\u52a1\u6765\u8bf4\u660e\u8fd9\u4e00\u70b9\uff0c\u5373\u9009\u62e9\u6027\u590d\u5236\u548c\u5f52\u7eb3\u5934\u3002<\/p>\n\n\n\n

      \u5728\u9009\u62e9\u6027\u590d\u5236\u4efb\u52a1\u4e2d\uff0cSSM \u7684\u76ee\u6807\u662f\u590d\u5236\u8f93\u5165\u7684\u90e8\u5206\u5185\u5bb9\u5e76\u6309\u987a\u5e8f\u8f93\u51fa\u5b83\u4eec\uff1a<\/p>\n\n\n\n

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

      \u56fe5-1\uff1a\u9009\u62e9\u6027\u590d\u5236\u4efb\u52a1<\/p>\n\n\n\n

      \u7136\u800c\uff0c\u7531\u4e8e\uff08\u5faa\u73af\/\u5377\u79ef\uff09SSM \u662f\u7ebf\u6027\u65f6\u95f4\u4e0d\u53d8\u7684\uff0c\u56e0\u6b64\u5728\u8fd9\u9879\u4efb\u52a1\u4e2d\u8868\u73b0\u4e0d\u4f73\u3002\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5bf9\u4e8e SSM\u751f\u6210\u7684\u6bcf\u4e2a token\uff0c\u77e9\u9635 A\u3001B \u548c C \u90fd\u662f\u76f8\u540c\u7684\u3002<\/p>\n\n\n\n

      \u56e0\u6b64\uff0c\u7531\u4e8e\u56fa\u5b9a\u7684 A\u3001B \u548c C \u77e9\u9635\uff0cSSM \u65e0\u6cd5\u6267\u884c\u5185\u5bb9\u611f\u77e5\u63a8\u7406\uff0c\u56e0\u4e3a\u5b83\u5bf9\u6bcf\u4e2a token \u90fd\u4e00\u89c6\u540c\u4ec1\u3002\u8fd9\u662f\u4e00\u4e2a\u95ee\u9898\uff0c\u56e0\u4e3a\u6211\u4eec\u5e0c\u671b SSM \u80fd\u5bf9\u8f93\u5165\uff08\u63d0\u793a\uff09\u8fdb\u884c\u63a8\u7406\u3002<\/p>\n\n\n\n

      SSM \u8868\u73b0\u4e0d\u4f73\u7684\u7b2c\u4e8c\u9879\u4efb\u52a1\u662f\u5f52\u7eb3\u5934\uff0c\u5176\u76ee\u6807\u662f\u91cd\u73b0\u8f93\u5165\u4e2d\u53d1\u73b0\u7684\u6a21\u5f0f\uff1a<\/p>\n\n\n\n

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

      \u56fe5-2\uff1a\u91cd\u73b0\u8f93\u5165\u4e2d\u53d1\u73b0\u7684\u6a21\u5f0f<\/p>\n\n\n\n

      \u5728\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u672c\u8d28\u4e0a\u662f\u5728\u6267\u884c\u4e00\u6b21\u63d0\u793a\uff0c\u6211\u4eec\u8bd5\u56fe\u201c\u6559\u201d\u6a21\u578b\u5728\u6bcf\u4e2a\u201cQ:\u201d\u4e4b\u540e\u63d0\u4f9b\u4e00\u4e2a\u201cA:\u201d\u7684\u56de\u5e94\u3002\u7136\u800c\uff0c\u7531\u4e8e SSM \u662f\u65f6\u95f4\u4e0d\u53d8\u7684\uff0c\u5b83\u65e0\u6cd5\u9009\u62e9\u4ece\u5386\u53f2\u4e2d\u56de\u5fc6\u54ea\u4e9b\u4e4b\u524d\u7684 token\u3002<\/p>\n\n\n\n

      \u8ba9\u6211\u4eec\u901a\u8fc7\u5173\u6ce8\u77e9\u9635 B \u6765\u8bf4\u660e\u8fd9\u4e00\u70b9\u3002\u65e0\u8bba\u8f93\u5165 u \u662f\u4ec0\u4e48\uff0c\u77e9\u9635 B \u90fd\u4fdd\u6301\u4e0d\u53d8\uff0c\u56e0\u6b64\u4e0e u \u65e0\u5173\uff1a<\/p>\n\n\n\n

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

      \u56fe5-3\uff1a\u77e9\u9635 B \u4e0e\u8f93\u5165 u \u65e0\u5173<\/p>\n\n\n\n

      \u540c\u7406\uff0c\u65e0\u8bba\u8f93\u5165\u662f\u4ec0\u4e48\uff0cA \u548c C \u4e5f\u4e0d\u53d8\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u4e0a\u9762\u8bf4\u7684\u9759\u6001\u3002<\/p>\n\n\n\n

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

      \u56fe5-4\uff1aA \u548c C \u77e9\u9635\u4e5f\u548c\u8f93\u5165 u \u65e0\u5173<\/p>\n\n\n\n

      \u76f8\u6bd4\u4e4b\u4e0b\uff0c\u8fd9\u4e9b\u4efb\u52a1\u5bf9\u4e8e Transformer \u6765\u8bf4\u76f8\u5bf9\u5bb9\u6613\uff0c\u56e0\u4e3a\u5b83\u4eec\u4f1a\u6839\u636e\u8f93\u5165\u5e8f\u5217\u52a8\u6001\u5730\u6539\u53d8\u81ea\u5df1\u7684\u6ce8\u610f\u529b\u3002\u5b83\u4eec\u53ef\u4ee5\u9009\u62e9\u6027\u5730\u201c\u67e5\u770b\u201d\u6216\u201c\u5173\u6ce8\u201d\u5e8f\u5217\u7684\u4e0d\u540c\u90e8\u5206\u3002<\/p>\n\n\n\n

      SSM \u5728\u8fd9\u4e9b\u4efb\u52a1\u4e0a\u7684\u7cdf\u7cd5\u8868\u73b0\u8bf4\u660e\u4e86\u65f6\u95f4\u4e0d\u53d8 SSM \u7684\u6f5c\u5728\u95ee\u9898\uff0c\u5373\u77e9\u9635 A\u3001B \u548c C \u7684\u9759\u6001\u6027\u8d28\u5bfc\u81f4\u5185\u5bb9\u611f\u77e5\u65b9\u9762\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n

      5.1 \u901a\u8fc7\u9009\u62e9\u673a\u5236\u6539\u8fdb SSM<\/strong><\/p>\n\n\n\n

      \u4e3a\u4e86\u89e3\u51b3\u4e0a\u9762\u7684\u95ee\u9898\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u9009\u62e9\u6027 SSM\uff08Selective State Space Models\uff0c\u7b80\u79f0 S6 \u6216 Mamba\uff09\u3002\u8fd9\u79cd\u6a21\u578b\u901a\u8fc7\u8ba9 SSM \u7684\u77e9\u9635 A\u3001B\u3001C \u4f9d\u8d56\u4e8e\u8f93\u5165\u6570\u636e<\/strong>\uff0c\u4ece\u800c\u5b9e\u73b0\u4e86\u9009\u62e9\u6027\u3002\u8fd9\u610f\u5473\u7740\u6a21\u578b\u53ef\u4ee5\u6839\u636e\u5f53\u524d\u7684\u8f93\u5165\u52a8\u6001\u5730\u8c03\u6574\u5176\u72b6\u6001\uff0c\u9009\u62e9\u6027\u5730\u4f20\u64ad\u6216\u5ffd\u7565\u4fe1\u606f\u3002<\/p>\n\n\n\n

      Mamba \u96c6\u6210\u4e86 S4 \u548c Transformer \u7684\u7cbe\u534e\uff0c\u4e00\u4e2a\u66f4\u52a0\u9ad8\u6548\uff08S4\uff09\uff0c\u4e00\u4e2a\u66f4\u52a0\u5f3a\u5927\uff08Transformer\uff09\u3002<\/p>\n\n\n\n

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

      \u56fe5-5\uff1aMamba \u96c6\u6210\u4e86 S4 \u548c Transformer \u5404\u81ea\u7684\u4f18\u70b9<\/p>\n\n\n\n

      \u6b63\u5982\u4e0a\u9762\u6240\u63d0\u5230\u7684\uff0c\u5b83\u662f\u901a\u8fc7\u6709\u9009\u62e9\u5730\u5c06\u6570\u636e\u538b\u7f29\u5230\u72b6\u6001\u4e2d\u6765\u5b9e\u73b0\u7684\u3002\u5f53\u4f60\u6709\u4e00\u4e2a\u8f93\u5165\u53e5\u5b50\u65f6\uff0c\u901a\u5e38\u4f1a\u6709\u4e00\u4e9b\u4fe1\u606f\uff0c\u6bd4\u5982\u505c\u7528\u8bcd\uff0c\u6ca1\u6709\u592a\u591a\u610f\u4e49\u3002<\/p>\n\n\n\n

      \u4e3a\u4e86\u6709\u9009\u62e9\u5730\u538b\u7f29\u4fe1\u606f\uff0c\u6211\u4eec\u9700\u8981\u8ba9\u53c2\u6570\u4f9d\u8d56\u4e8e\u8f93\u5165\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9996\u5148\u6765\u63a2\u8ba8\u4e00\u4e0b SSM \u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u8f93\u5165\u548c\u8f93\u51fa\u7684\u7ef4\u5ea6\u3002<\/p>\n\n\n\n

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

      \u56fe5-6\uff1aSSM \u8f93\u5165\uff08u\uff09\u8f93\u51fa\uff08y\uff09\u7ef4\u5ea6<\/p>\n\n\n\n

      \u5907\u6ce8<\/strong>\uff1a\u5728\u524d\u9762\u7684 HiPPO \u548c S4 \u4e2d\uff0c\u6211\u4eec\u5047\u8bbe\u7684\u8f93\u5165\u4fe1\u53f7u(t)\u662f 1 \u7ef4\u7684\uff0c\u800c\u5b9e\u9645\u5e94\u7528\u4e2d\u5927\u591a\u6570\u90fd\u662f\u591a\u7ef4\u7684\uff0c\u540e\u9762\u6211\u4eec\u9ed8\u8ba4\u662f\u591a\u7ef4\u8f93\u5165\uff08\u9ed8\u8ba4\u7ef4\u5ea6\u4e3a D\uff09\u3002\u800c\u4e14\u9700\u8981\u5f3a\u8c03\u7684\u662f S4 \u7528\u7684\u662f Single-input-single-output (SISO)\uff0c\u5373\u5bf9\u5e94\u4e8e\u6bcf\u4e00\u4e2a\u8f93\u5165\u7684\u7ef4\u5ea6\uff0c\u90fd\u6709\u4e00\u5957\u72ec\u7acb\u7684 SSM \u53c2\u6570 \uff08\u4f20\u7edf\u7684 RNN \u662f MIMO\uff0cmultiple-input-multiple-output, \u5f88\u5bb9\u6613\u6df7\u6dc6\uff09\u3002<\/strong><\/p>\n\n\n\n

      \u5728 S4 \u4e2d\uff0c\u77e9\u9635 A\u3001B \u548c C \u4e0e\u8f93\u5165\u65e0\u5173\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u7ef4\u5ea6 N \u548c D \u662f\u9759\u6001\u7684\uff0c\u4e0d\u4f1a\u6539\u53d8\u3002<\/p>\n\n\n\n

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

      \u56fe5-7\uff1aS4 \u4e2d\u7684\u77e9\u9635A\u3001B\u3001C<\/p>\n\n\n\n

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

      \u76f8\u53cd\uff0cMamba \u901a\u8fc7\u5c06\u8f93\u5165\u5e8f\u5217\u7684\u957f\u5ea6\u548c\u6279\u6b21\u5927\u5c0f\u7ed3\u5408\u8d77\u6765\uff0c\u4f7f\u77e9\u9635 B \u548c C\uff0c\u751a\u81f3\u6b65\u957f \u2206 \u90fd\u4f9d\u8d56\u4e8e\u8f93\u5165\uff1a<\/p>\n\n\n\n

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

      \u56fe5-8\uff1aMamba \u4e2d\u7684\u77e9\u9635B\u3001C\u548c\u8f93\u5165\u6709\u5173\uff08L\u662f\u5e8f\u5217\u957f\u5ea6\uff09<\/p>\n\n\n\n

      \u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u6bcf\u4e2a\u8f93\u5165 token\uff0c\u6211\u4eec\u73b0\u5728\u6709\u4e0d\u540c\u7684 B \u548c C \u77e9\u9635\u3002<\/p>\n\n\n\n

      \u5907\u6ce8<\/strong>\uff1a\u8fd9\u91cc\u77e9\u9635 A \u4fdd\u6301\u4e0d\u53d8\uff0c\u56e0\u4e3a\u6211\u4eec\u5e0c\u671b\u72b6\u6001\u672c\u8eab\u4fdd\u6301\u9759\u6001\uff0c\u4f46\u5f71\u54cd\u5b83\u7684\u65b9\u5f0f (\u901a\u8fc7 B \u548c C) \u662f\u52a8\u6001\u7684\u3002<\/p>\n\n\n\n

      \u5b83\u4eec\u4e00\u8d77\u9009\u62e9\u6027\u5730\u51b3\u5b9a\u5728\u9690\u85cf\u72b6\u6001\u4e2d\u4fdd\u7559\u4ec0\u4e48\u548c\u5ffd\u7565\u4ec0\u4e48\uff0c\u56e0\u4e3a\u5b83\u4eec\u73b0\u5728\u4f9d\u8d56\u4e8e\u8f93\u5165\u3002<\/p>\n\n\n\n

      \u5728 SSM \u4e2d\uff0c\u901a\u8fc7\u8c03\u6574 \u2206\uff0c\u6a21\u578b\u53ef\u4ee5\u63a7\u5236\u5bf9\u5f53\u524d\u8f93\u5165\u7684\u5173\u6ce8\u5ea6\uff0c\u4ece\u800c\u5b9e\u73b0\u7c7b\u4f3c\u4e8e RNN \u95e8\u63a7\u7684\u6548\u679c\u3002\u4f8b\u5982\uff0c\u5f53 \u2206 \u8f83\u5927\u65f6\uff0c\u6a21\u578b\u503e\u5411\u4e8e\u5173\u6ce8\u5f53\u524d\u8f93\u5165\u5e76\u5ffd\u7565\u4e4b\u524d\u7684\u4fe1\u606f<\/strong>\uff1b\u800c\u5f53\u2206\u8f83\u5c0f\u65f6\uff0c\u6a21\u578b\u5219\u503e\u5411\u4e8e\u4fdd\u7559\u66f4\u591a\u7684\u5386\u53f2\u4fe1\u606f\uff1a<\/p>\n\n\n\n

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

      \u56fe5-9\uff1a\u6b65\u957f \u2206 \u6548\u679c\u76f8\u5f53\u4e8e\u95e8\u63a7<\/p>\n\n\n\n

      \u4e0b\u9762\u6211\u4eec\u770b\u4e00\u4e0b\u9009\u62e9\u6027 SSM \u7684\u5b8c\u6574\u8fc7\u7a0b\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n\n

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

      \u7b97\u6cd5 2 \u5c55\u793a\u4e86\u4f5c\u8005\u6240\u4f7f\u7528\u7684\u4e3b\u8981\u9009\u62e9\u673a\u5236\u3002\u8fd9\u4e00\u5957\u7684\u601d\u8def\u7531\u6765\u5df2\u4e45\uff0cTransformers \u91cc\u9762\u7684 QKV\u3001LSTM\u91cc\u9762\u7684\u3001Gating \u90fd\u662f\u7c7b\u4f3c\u7684\u601d\u60f3\u3002<\/p>\n\n\n\n

      S4 \u548c \u9009\u62e9\u6027 SSM \u7684\u6838\u5fc3\u533a\u522b\u5728\u4e8e\uff0c\u5b83\u4eec\u5c06\u51e0\u4e2a\u5173\u952e\u53c2\u6570\uff08\u2206, B, C\uff09\u8bbe\u5b9a\u4e3a\u8f93\u5165\u7684\u51fd\u6570\uff0c\u5e76\u4e14\u4f34\u968f\u7740\u6574\u4e2a tensor \u5f62\u72b6\u7684\u76f8\u5173\u53d8\u5316\u3002\u7279\u522b\u662f\uff0c\u8fd9\u4e9b\u53c2\u6570\u73b0\u5728\u5177\u6709\u4e00\u4e2a\u957f\u5ea6\u7ef4\u5ea6 L\uff0c\u8fd9\u610f\u5473\u7740\u6a21\u578b\u5df2\u7ecf\u4ece\u65f6\u95f4\u4e0d\u53d8\uff08time-invariant\uff09\u8f6c\u53d8\u4e3a\u65f6\u95f4\u53d8\u5316\uff08time-varying\uff09\u3002<\/p>\n\n\n\n

      \u5176\u4e2d :<\/p>\n\n\n\n

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

      5.2 \u9009\u62e9\u6027 SSM \u548c\u95e8\u63a7\u4e4b\u95f4\u7684\u5173\u7cfb<\/strong><\/p>\n\n\n\n

      \u65f6\u95f4\u6b65\u2206<\/strong><\/p>\n\n\n\n

      \u65f6\u95f4\u6b65\u2206\u548c RNN \u7684\u95e8\u63a7\u6709\u5f88\u5f3a\u7684\u5173\u8054\uff0c\u4f9d\u8d56\u8f93\u5165\u7684\u2206\u8ddf RNN \u7684\u9057\u5fd8\u95e8\u7684\u529f\u80fd\u7c7b\u4f3c\u3002<\/strong><\/p>\n\n\n\n

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

      \u53ef\u4ee5\u770b\u5230\u8fd9\u5c31\u662f\u4e00\u4e2a\u5e26\u95e8\u63a7\u7684 RNN\u3002<\/p>\n\n\n\n

      \u77e9\u9635 B \u548c C<\/strong><\/p>\n\n\n\n

      \u5728 SSM \u4e2d\uff0c\u4fee\u6539 B \u548c C \u4ee5\u4f7f\u5176\u5177\u6709\u9009\u62e9\u6027\uff0c\u5141\u8bb8\u6a21\u578b\u66f4\u7cbe\u7ec6\u5730\u63a7\u5236\u662f\u5426\u8ba9\u8f93\u5165\u8fdb\u5165\u72b6\u6001 h \u6216\u72b6\u6001\u8fdb\u5165\u8f93\u51fa y\uff0c\u6240\u4ee5 B \u548c C \u7c7b\u4f3c\u4e8e RNN \u4e2d\u7684\u8f93\u5165\u95e8\u548c\u8f93\u51fa\u95e8\u3002<\/p>\n\n\n\n

      \u77e9\u9635 A<\/strong><\/p>\n\n\n\n

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

      5.3 Mamba \u9ad8\u6548\u5b9e\u73b0<\/strong><\/p>\n\n\n\n

      \u56e0\u4e3a\u73b0\u5728\u7684\u53c2\u6570ABC\u90fd\u662f\u8f93\u5165\u76f8\u5173\u4e86\uff0c\u6240\u4ee5\u4e0d\u518d\u662f\u7ebf\u6027\u65f6\u95f4\u4e0d\u53d8\u7cfb\u7edf\uff0c\u4e5f\u5c31\u5931\u53bb\u4e86\u5377\u79ef\u7684\u6027\u8d28\uff0c\u4e0d\u80fd\u7528 FFT\u6765\u8fdb\u884c\u9ad8\u6548\u8bad\u7ec3\u4e86\u3002<\/p>\n\n\n\n

      Mamba \u4f5c\u8005\u91c7\u7528\u4e86\u4e00\u79cd\u79f0\u4e3a\u786c\u4ef6\u611f\u77e5\u7684\u7b97\u6cd5\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u7528\u4e09\u79cd\u7ecf\u5178\u6280\u672f\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff1a\u5185\u6838\u878d\u5408\uff08kernel fusion\uff09\u3001\u5e76\u884c\u626b\u63cf\uff08parallel scan\uff09\u548c\u91cd\u8ba1\u7b97\uff08recomputation\uff09<\/strong><\/p>\n\n\n\n

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

      \u800c Mambda \u4f5c\u8005\u7684\u65b9\u6cd5\u662f\uff1a<\/p>\n\n\n\n

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

      \u56fe5-10\uff1aMamba \u7684 scan \u548c\u5176\u5b83\u65b9\u6cd5\u5bf9\u6bd4<\/p>\n\n\n\n

      Mamba \u7684\u5b9e\u73b0\u6bd4\u5176\u5b83\u65b9\u6cd5\u5b9e\u73b0\u5feb\u5f88\u591a\u500d\uff0cscan \u5728\u8f93\u5165\u957f\u5ea6 2k \u7684\u65f6\u5019\u5c31\u5f00\u59cb\u6bd4 FlashAttention \u5feb\u4e86\uff0c\u4e4b\u540e\u8d8a\u957f\u8d8a\u5feb\u3002\u540c\u65f6 scan \u4e5f\u6bd4 Convolution \u5feb\u3002<\/p>\n\n\n\n

      5.4 Mamba \u67b6\u6784<\/strong><\/p>\n\n\n\n

      \u4e0b\u56fe\u662f Mamba \u7684\u6a21\u578b\u7ed3\u6784\uff1a<\/p>\n\n\n\n

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

      \u56fe5-11\uff1aMamba \u6a21\u578b\u7ed3\u6784<\/p>\n\n\n\n

      \u4e4b\u524d\u7684 SSM \u6a21\u578b\u8981 work\uff0c\u90fd\u4f1a\u52a0\u4e0a output gating\uff0c\u4e4b\u540e\u518d\u8fc7\u4e2a\u7ebf\u6027\u5c42 channel mixing\uff0c\u5982\u4e0a\u56fe\u7684\u6700\u5de6\u8fb9\u6240\u793a\u3002\u8fd9\u4e24\u4e2a\u90e8\u5206\u8ddf Gated MLP\uff08\u4e0a\u56fe\u4e2d\u95f4\uff09\u53f3\u8fb9\u7684\u652f\u8def\u548c\u6700\u4e0a\u9762\u7684 channel mixing \u662f\u4e00\u6837\u7684\u3002\u6240\u4ee5 SSM \u5c42\u5982\u679c\u8ddfGated MLP \u5408\u5e76\u7684\u8bdd\uff0c\u96be\u514d\u4f1a\u611f\u89c9\u6709\u70b9\u5197\u4f59\uff0c\u6240\u4ee5\u4f5c\u8005\u5e72\u8106\u628a\u4e24\u4e2a\u5408\u4e8c\u4e3a\u4e00\uff0c\u628a token mixing \u5c42\u548c channel mixing\u3002<\/p>\n\n\n\n

      \u56fe 5-11 \u7684 Mamba \u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u5757\u6765\u5b9e\u73b0\uff0c\u5c31\u50cf\u6211\u4eec\u53ef\u4ee5\u5728\u89e3\u7801\u5668\u5757\u4e2d\u8868\u793a\u81ea\u6ce8\u610f\u529b\u4e00\u6837\u3002<\/p>\n\n\n\n

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

      \u56fe5-12\uff1aMamba \u5757<\/p>\n\n\n\n

      \u4e0e\u89e3\u7801\u5668\u4e00\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u5806\u53e0\u591a\u4e2a Mamba \u5757\uff0c\u5e76\u4f7f\u7528\u5b83\u4eec\u7684\u8f93\u51fa\u4f5c\u4e3a\u4e0b\u4e00\u4e2a Mamba \u5757\u7684\u8f93\u5165\uff1a<\/p>\n\n\n\n

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

      \u56fe5-13\uff1a\u591a\u4e2aMamba\u5757\u7ec4\u5408\u4f7f\u7528<\/p>\n\n\n\n

      \u5b83\u9996\u5148\u8fdb\u884c\u7ebf\u6027\u6295\u5f71\u4ee5\u6269\u5c55\u8f93\u5165 embedding\u3002\u7136\u540e\uff0c\u5728\u5e94\u7528\u9009\u62e9\u6027 SSM \u4e4b\u524d\u8fdb\u884c\u5377\u79ef\u3002\u9009\u62e9\u6027 SSM \u5177\u6709\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/p>\n\n\n\n

        \n
      • \u901a\u8fc7\u79bb\u6563\u5316\u521b\u5efa\u9012\u5f52 SSM\uff1b<\/li>\n\n\n\n
      • \u5bf9\u77e9\u9635 A \u8fdb\u884c HiPPO \u521d\u59cb\u5316\uff0c\u4ee5\u6355\u83b7\u8fdc\u7a0b\u4f9d\u8d56\u5173\u7cfb\uff1b<\/li>\n\n\n\n
      • \u9009\u62e9\u6027\u626b\u63cf\u7b97\u6cd5\uff0c\u6709\u9009\u62e9\u5730\u538b\u7f29\u4fe1\u606f\uff1b<\/li>\n\n\n\n
      • \u786c\u4ef6\u611f\u77e5\u7b97\u6cd5\uff0c\u52a0\u901f\u8ba1\u7b97\uff1b<\/li>\n<\/ul>\n\n\n\n

        \u4e0b\u9762\u662f\u4e00\u4e2a\u7aef\u5230\u7aef\uff08\u8f93\u5165\u5230\u8f93\u51fa\uff09\u7684\u4f8b\u5b50\uff1a<\/p>\n\n\n\n

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

        \u56fe5-14\uff1aMamba \u67b6\u6784\u7aef\u5230\u7aef\u8f93\u51fa\u4f8b\u5b50<\/p>\n\n\n\n

        \u4e0b\u9762\u6211\u4eec\u770b\u4e00\u4e0b Mamba \u548c Transformer \u4ee5\u53ca RNN \u7684\u5bf9\u6bd4\uff1a<\/p>\n\n\n\n

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

        \u56fe5-15\uff1aMamaba\u548cTransformer\u4ee5\u53caRNN\u5bf9\u6bd4<\/p>\n\n\n\n

        5.5 \u5b9e\u9a8c<\/strong><\/p>\n\n\n\n

        \u4e4b\u524d\u63d0\u5230\u2206\u7684\u4f5c\u7528\u7c7b\u4f3c\u9057\u5fd8\u95e8\uff0c\u800c\u9057\u5fd8\u95e8\u6beb\u65e0\u7591\u95ee\u662f LSTM \u91cc\u9762\u6700\u91cd\u8981\u7684\u95e8\uff0c\u4e0b\u9762\u8fd9\u4e2a\u6d88\u878d\u5b9e\u9a8c\u7ed3\u679c\u5c31\u8bba\u8bc1\u4e86\u2206data dependent \u5f71\u54cd\u6700\u5927\u3002<\/p>\n\n\n\n

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

        \u56fe5-16\uff1a\u5bf9\u4e0d\u540c\u53c2\u6570data dependent\u7684\u654f\u611f\u6027<\/p>\n\n\n\n

        \u6700\u540e\u518d\u770b\u4e00\u4e0b\u6a21\u578b\u6548\u679c\uff1a<\/p>\n\n\n\n

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

        \u56fe5-17\uff1aMamba\u548cTransformer\u5bf9\u6bd4<\/p>\n\n\n\n

        \u603b\u7ed3\u8d77\u6765\u5c31\u662f\uff0c\u6548\u679c\u6700\u597d\uff0c\u901f\u5ea6\u6700\u5feb\uff01<\/p>\n\n\n\n

        \u603b\u7ed3<\/strong><\/p>\n\n\n\n

        \u878d\u5408 SSM \u548c LSTM\uff0c\u5c06 LSTM \u9009\u62e9\u6027\u7684\u601d\u60f3\u878d\u5165 SSM \u4e2d\uff0c\u5168\u65b9\u4f4d\u7684\u5b9e\u73b0\u4f18\u5316\uff0c\u4f7f\u5f97 Mamaba \u5373\u5177\u5907\u50cf Transformer \u9ad8\u6548\u8bad\u7ec3\u7684\u7279\u70b9\uff0c\u53c8\u5177\u5907 S4 \u4e2d\u652f\u6301\u957f\u6587\u672c\u7684\u4f18\u70b9\uff0c\u540c\u65f6\u5177\u5907 LSTM \u4e00\u6837\u9009\u62e9\u6027\u8bb0\u5fc6\u7684\u7279\u70b9\u3002<\/p>\n\n\n\n

        \u5b9e\u9a8c\u8bc1\u660e\u4e86 Mamba \u7684\u4f18\u79c0\uff0c\u4f46\u662f\u8fd8\u9700\u8981\u66f4\u957f\u7684\u65f6\u95f4\u68c0\u9a8c\uff0c\u76ee\u524d\u8fd8\u6ca1\u6709 10B \u4ee5\u4e0a\u7684 Mamba \u6a21\u578b\uff0c\u5c31\u8ba9\u65f6\u95f4\u6765\u68c0\u9a8c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u80cc\u666f \u5c79\u7acb\u4e0d\u5012\u7684 Transformer \u8fce\u6765 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,1],"tags":[],"class_list":["post-10053","post","type-post","status-publish","format-standard","hentry","category-technology-frontier","category-home"],"views":0,"_links":{"self":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts\/10053"}],"collection":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/comments?post=10053"}],"version-history":[{"count":1,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts\/10053\/revisions"}],"predecessor-version":[{"id":10195,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts\/10053\/revisions\/10195"}],"wp:attachment":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/media?parent=10053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/categories?post=10053"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/tags?post=10053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}